[cig-commits] r19356 - in seismo/2D/SPECFEM2D/trunk: EXAMPLES/attenuation doc/USER_MANUAL src/specfem2D
dkomati1 at geodynamics.org
dkomati1 at geodynamics.org
Fri Jan 13 09:53:31 PST 2012
Author: dkomati1
Date: 2012-01-13 09:53:28 -0800 (Fri, 13 Jan 2012)
New Revision: 19356
Added:
seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution_viscoelastic.dat
seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution_viscoelastic.dat
seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_causality_problem_fixed_by_Xie_Zhinan.f
seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_ori_with_causality_problem.f
Removed:
seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution.dat
seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution.dat
Modified:
seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/plot_compare_to_analytical_solution.gnu
seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/bibliography.bib
seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.pdf
seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_energy.f90
seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_poro_fluid.f90
seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_poro_solid.f90
seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_viscoelastic.f90
seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_pressure.f90
seismo/2D/SPECFEM2D/trunk/src/specfem2D/specfem2D.F90
Log:
Xie Zhinan fixed the non-causal attenuation problem of the paper of Carcione et al. (1993).
Also updated the BibTeX manual.
Deleted: seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution.dat
===================================================================
--- seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution.dat 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution.dat 2012-01-13 17:53:28 UTC (rev 19356)
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Copied: seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution_viscoelastic.dat (from rev 19352, seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution.dat)
===================================================================
--- seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution_viscoelastic.dat (rev 0)
+++ seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution_viscoelastic.dat 2012-01-13 17:53:28 UTC (rev 19356)
@@ -0,0 +1,5290 @@
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Deleted: seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution.dat
===================================================================
--- seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution.dat 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution.dat 2012-01-13 17:53:28 UTC (rev 19356)
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Copied: seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution_viscoelastic.dat (from rev 19352, seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution.dat)
===================================================================
--- seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution_viscoelastic.dat (rev 0)
+++ seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution_viscoelastic.dat 2012-01-13 17:53:28 UTC (rev 19356)
@@ -0,0 +1,5290 @@
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+ 1.980990 9.253594 8.5904083E-04
+ 1.981380 9.247683 9.4656879E-04
+ 1.981771 9.241615 8.6107571E-04
+ 1.982161 9.235798 8.7255769E-04
+ 1.982552 9.228909 7.9663208E-04
+ 1.982943 9.223191 1.0337859E-03
+ 1.983333 9.216692 8.7692781E-04
+ 1.983724 9.210669 8.3765853E-04
+ 1.984115 9.204822 9.5689128E-04
+ 1.984505 9.198301 1.0692819E-03
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+ 1.986458 9.167337 8.2530361E-04
+ 1.986849 9.161644 7.4912829E-04
+ 1.987240 9.155951 1.0261324E-03
+ 1.987630 9.149439 8.5507584E-04
+ 1.988021 9.143480 7.7166595E-04
+ 1.988411 9.137188 9.4302953E-04
+ 1.988802 9.131702 8.1342214E-04
+ 1.989193 9.125019 9.8869507E-04
+ 1.989583 9.119307 8.6609251E-04
+ 1.989974 9.113072 7.8979379E-04
+ 1.990365 9.107043 8.7074668E-04
+ 1.990755 9.100910 8.6765754E-04
+ 1.991146 9.095106 7.8629417E-04
+ 1.991536 9.088943 8.4804132E-04
+ 1.991927 9.082683 8.7586790E-04
+ 1.992318 9.077036 8.9147629E-04
+ 1.992708 9.071012 8.0271496E-04
+ 1.993099 9.064978 7.8263879E-04
+ 1.993490 9.058522 8.2937593E-04
+ 1.993880 9.052624 8.1509101E-04
+ 1.994271 9.046752 7.7662326E-04
+ 1.994661 9.040997 9.0486091E-04
+ 1.995052 9.034273 8.7572983E-04
+ 1.995443 9.028849 8.2307094E-04
+ 1.995833 9.022727 8.3067804E-04
+ 1.996224 9.016701 8.3537603E-04
+ 1.996615 9.010897 8.6528301E-04
+ 1.997005 9.004853 8.4337476E-04
+ 1.997396 8.998837 8.1472599E-04
+ 1.997786 8.992805 8.2517706E-04
+ 1.998177 8.987185 8.5583987E-04
+ 1.998568 8.980694 8.5821818E-04
+ 1.998958 8.974730 8.4983814E-04
+ 1.999349 8.968607 7.5410784E-04
+ 1.999740 8.963206 8.2345406E-04
Added: seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_causality_problem_fixed_by_Xie_Zhinan.f
===================================================================
--- seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_causality_problem_fixed_by_Xie_Zhinan.f (rev 0)
+++ seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_causality_problem_fixed_by_Xie_Zhinan.f 2012-01-13 17:53:28 UTC (rev 19356)
@@ -0,0 +1,7677 @@
+
+ program analytical_sol
+
+ implicit none
+
+ integer iratio
+ parameter(iratio = 32)
+
+ integer nfreq,nt
+! DK DK parameter (nfreq = 4096)
+ parameter (nfreq = 8*65536)
+ parameter (nt = iratio * nfreq)
+
+ double precision freqmax
+ parameter (freqmax = 80.d0)
+
+ double precision freqseuil
+! DK DK parameter (freqseuil = 0.25d0)
+ parameter (freqseuil = 0.05d0)
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! for the solution in time domain
+ integer it
+ real wsave(4*nt+15)
+ complex c(nt)
+
+! properties of the medium
+ double precision rho
+ parameter(rho = 2000.d0)
+
+! definition position recepteur Carcione
+ double precision x1,x2
+
+! Definition source Dimitri
+ double precision f0,t0,eta
+ parameter(f0 = 18.d0)
+ parameter(t0 = 1.2d0 / f0)
+ parameter(eta = 0.5d0)
+
+! Definition source Carcione
+! double precision f0,t0,eta,epsil
+! parameter(f0 = 50.d0)
+! parameter(t0 = 0.075d0)
+! parameter(epsil = 1.d0)
+! parameter(eta = 0.5d0)
+
+! attenuation constants from Carcione 1988 GJI vol 95 p 604
+! two mechanisms for the moment
+ double precision tau_epsilon_nu1_mech1,
+ . tau_sigma_nu1_mech1,
+ . tau_epsilon_nu2_mech1, tau_sigma_nu2_mech1,
+ . tau_epsilon_nu1_mech2,
+ . tau_sigma_nu1_mech2, tau_epsilon_nu2_mech2,
+ . tau_sigma_nu2_mech2
+
+ parameter(tau_epsilon_nu1_mech1 = 0.0325305d0)
+ parameter(tau_sigma_nu1_mech1 = 0.0311465d0)
+ parameter(tau_epsilon_nu2_mech1 = 0.0332577d0)
+ parameter(tau_sigma_nu2_mech1 = 0.0304655d0)
+ parameter(tau_epsilon_nu1_mech2 = 0.0032530d0)
+ parameter(tau_sigma_nu1_mech2 = 0.0031146d0)
+ parameter(tau_epsilon_nu2_mech2 = 0.0033257d0)
+ parameter(tau_sigma_nu2_mech2 = 0.0030465d0)
+
+ integer Lnu
+
+ double precision M1,M2
+ parameter(M1 = 20.d9)
+ parameter(M2 = 16.d9)
+
+ integer ifreq,ifreq2
+ double precision deltafreq,freq,omega,omega0,deltat,time
+ double complex comparg
+
+! fourier transform of the Ricker wavelet source
+ double complex fomega(0:nfreq)
+
+! real and imaginary parts
+ double precision ra(0:nfreq),rb(0:nfreq)
+
+! spectral amplitude
+ double precision ampli(0:nfreq)
+
+! analytical solution for both components
+ double complex phi1(-nfreq:nfreq)
+ double complex phi2(-nfreq:nfreq)
+
+! external functions
+ double complex u1,u2
+ external u1,u2
+
+! modules elastiques
+ double complex M1C, M2C, E, V1, V2
+
+ logical correction_f0
+
+! ********** fin declarations ************
+
+! lecture des parametres de la simu
+ open(unit=10,file='params_carcione.dat',status='old')
+ read(10,*) x1
+ read(10,*) x2
+ read(10,*) correction_f0
+ close(10)
+
+ print *,'Recepteur en x1,x2 : ',x1,x2
+ print *,'Correction Hankel en f=0 :',correction_f0
+
+! step in frequency
+ deltafreq = freqmax / dble(nfreq)
+
+! define the spectrum of the source
+ do ifreq=0,nfreq
+ freq = deltafreq * dble(ifreq)
+ omega = 2.d0 * pi * freq
+ omega0 = 2.d0 * pi * f0
+ comparg = dcmplx(0.d0,omega*t0)
+
+! definir le spectre du ricker de carcione avec cos()
+! d'apres Carcione GJI vol 93 p 401 (1988)
+! fomega(ifreq) = pi * dsqrt(pi/eta) * (1.d0/omega0)
+! . * cdexp(comparg) *
+! . ( dexp(- (pi*pi/eta) * (epsil/2 - omega/omega0)**2)
+! . + dexp(- (pi*pi/eta) * (epsil/2 + omega/omega0)**2) )
+
+! definir le spectre du ricker de carcione avec cos()
+! d'apres Carcione GJI vol 93 p 401 (1988)
+ fomega(ifreq) = - omega**2 * 2.d0 * (dsqrt(pi)/omega0)
+! DK DK . * cdexp(comparg) * dexp(- (omega/omega0)**2)
+ . * cdexp(-comparg) * dexp(- (omega/omega0)**2)
+
+ ra(ifreq) = dreal(fomega(ifreq))
+ rb(ifreq) = dimag(fomega(ifreq))
+! prendre le module de l'amplitude spectrale
+ ampli(ifreq) = dsqrt(ra(ifreq)**2 + rb(ifreq)**2)
+ enddo
+
+! sauvegarde du spectre d'amplitude de la source en Hz au format Gnuplot
+ open(unit=10,file='spectre.gnu',status='unknown')
+ do ifreq = 0,nfreq
+ freq = deltafreq * dble(ifreq)
+ write(10,*) sngl(freq),sngl(ampli(ifreq))
+ enddo
+ close(10)
+
+! ************** calcul solution analytique ****************
+
+! d'apres Carcione GJI vol 95 p 611 (1988)
+ do ifreq=0,nfreq
+ freq = deltafreq * dble(ifreq)
+ omega = 2.d0 * pi * freq
+
+! critere ad-hoc pour eviter singularite en zero
+ if(freq .lt. freqseuil) omega = 2.d0 * pi * freqseuil
+
+! modules elastiques complexes
+ Lnu = 2
+ M1C = M1 /(1.d0 - Lnu+tau_epsilon_nu1_mech1/tau_sigma_nu1_mech1+
+ . tau_epsilon_nu1_mech2/tau_sigma_nu1_mech2)
+ . * (1.d0 - Lnu + dcmplx(1.d0,omega*tau_epsilon_nu1_mech1)
+ . / dcmplx(1.d0,omega*tau_sigma_nu1_mech1)
+ . + dcmplx(1.d0,omega*tau_epsilon_nu1_mech2)
+ . / dcmplx(1.d0,omega*tau_sigma_nu1_mech2) )
+ M2C = M2 /(1.d0 - Lnu+tau_epsilon_nu2_mech1/tau_sigma_nu2_mech1+
+ .tau_epsilon_nu2_mech2/tau_sigma_nu2_mech2)
+ .* (1.d0 - Lnu + dcmplx(1.d0,omega*tau_epsilon_nu2_mech1)
+ . / dcmplx(1.d0,omega*tau_sigma_nu2_mech1)
+ . + dcmplx(1.d0,omega*tau_epsilon_nu2_mech2)
+ . / dcmplx(1.d0,omega*tau_sigma_nu2_mech2) )
+ E = (M1C + M2C) / 2
+ V1 = cdsqrt(E / rho)
+ V2 = cdsqrt(M2C / (2.d0 * rho))
+
+! calcul de la solution analytique en frequence
+ phi1(ifreq) = u1(omega,V1,V2,x1,x2,rho) * fomega(ifreq)
+ phi2(ifreq) = u2(omega,V1,V2,x1,x2,rho) * fomega(ifreq)
+
+! a nouveau critere ad-hoc pour eviter singularite en zero
+ if(freq .lt. freqseuil) then
+ phi1(ifreq) = dcmplx(0.d0,0.d0)
+ phi2(ifreq) = dcmplx(0.d0,0.d0)
+ endif
+
+ enddo
+
+! pour eviter singularite en zero, prendre premiere valeur non nulle
+ if(correction_f0) then
+ do ifreq=0,nfreq
+ if(cdabs(phi1(ifreq)) .gt. 0.d0) goto 180
+ do ifreq2=ifreq,nfreq
+ if(cdabs(phi1(ifreq2)) .gt. 0.d0) goto 181
+ enddo
+ 181 continue
+ phi1(ifreq) = phi1(ifreq2)
+ phi2(ifreq) = phi2(ifreq2)
+ enddo
+ 180 continue
+ endif
+
+! take the conjugate value for negative frequencies
+ do ifreq=-nfreq,-1
+ phi1(ifreq) = dconjg(phi1(-ifreq))
+ phi2(ifreq) = dconjg(phi2(-ifreq))
+ enddo
+
+! save the result in the frequency domain
+ open(unit=11,file='cmplx_phi',status='unknown')
+ do ifreq=-nfreq,nfreq
+ freq = deltafreq * dble(ifreq)
+ write(11,*) sngl(freq),
+ . sngl(dreal(phi1(ifreq))),sngl(dimag(phi1(ifreq))),
+ . sngl(dreal(phi2(ifreq))),sngl(dimag(phi2(ifreq)))
+ enddo
+ close(11)
+
+! Calculation of the time domain solution using Netlib
+
+! initialize FFT arrays
+ call cffti(nt,wsave)
+
+! clear array of Fourier coefficients
+ do it=1,nt
+ c(it) = cmplx(0.,0.)
+ enddo
+
+! enter the fourier values for Ux
+ c(1) = cmplx(phi1(0))
+ do ifreq=1,nfreq-2
+ c(ifreq+1) = cmplx(phi1(ifreq))
+ c(nt+1-ifreq) = conjg(cmplx(phi1(ifreq)))
+ enddo
+
+! perform the inverse FFT for Ux
+ call cfftb(nt,c,wsave)
+
+! valeur d'un pas de temps
+ deltat = 1.d0 / (freqmax*dble(iratio))
+
+! save time result inverse FFT for Ux
+ open(unit=11,file='Ux_time_analytical_solution_viscoelastic.dat',
+ . status='unknown')
+ do it=1,nt
+!c DK DK Dec 2011: subtract t0 to be consistent with the SPECFEM2D code
+ time = dble(it)*deltat - t0
+ if(time.le.2.d0)
+ . write(11,*) sngl(time),real(c(it)),imag(c(it))
+ enddo
+ close(11)
+
+! clear array of Fourier coefficients
+ do it=1,nt
+ c(it) = cmplx(0.,0.)
+ enddo
+
+! enter the fourier values for Uz
+ c(1) = cmplx(phi2(0))
+ do ifreq=1,nfreq-2
+ c(ifreq+1) = cmplx(phi2(ifreq))
+ c(nt+1-ifreq) = conjg(cmplx(phi2(ifreq)))
+ enddo
+
+! perform the inverse FFT for Uz
+ call cfftb(nt,c,wsave)
+
+! save time result inverse FFT for Uz
+ open(unit=11,file='Uz_time_analytical_solution_viscoelastic.dat',
+ . status='unknown')
+ do it=1,nt
+!c DK DK Dec 2011: subtract t0 to be consistent with the SPECFEM2D code
+ time = dble(it)*deltat - t0
+ if(time.le.2.d0)
+ . write(11,*) sngl(time),real(c(it)),imag(c(it))
+ enddo
+ close(11)
+
+ end
+
+! -----------
+
+ double complex function u1(omega,v1,v2,x1,x2,rho)
+
+ implicit none
+
+ double precision omega
+ double complex v1,v2
+
+ double complex G1,G2
+ external G1,G2
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! amplitude de la force
+ double precision F
+ parameter(F = 1.d10)
+
+ double precision x1,x2,r,rho
+
+! source-receiver distance
+ r = dsqrt(x1**2 + x2**2)
+
+ u1 = F * x1 * x2 * (G1(r,omega,v1,v2) + G2(r,omega,v1,v2))
+ . / (2.d0 * pi * rho * r**2 )
+
+ return
+ end
+
+! -----------
+
+ double complex function u2(omega,v1,v2,x1,x2,rho)
+
+ implicit none
+
+ double precision omega
+ double complex v1,v2
+
+ double complex G1,G2
+ external G1,G2
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! amplitude de la force
+ double precision F
+ parameter(F = 1.d10)
+
+ double precision x1,x2,r,rho
+
+! source-receiver distance
+ r = dsqrt(x1**2 + x2**2)
+
+ u2 = F * (x2*x2*G1(r,omega,v1,v2) - x1*x1*G2(r,omega,v1,v2))
+ . / (2.d0 * pi * rho * r**2 )
+
+ return
+ end
+
+! -----------
+
+ double complex function G1(r,omega,v1,v2)
+
+ implicit none
+
+ double precision r,omega
+ double complex v1,v2
+
+ double complex hankel0,hankel1
+ external hankel0,hankel1
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! bug Carcione corrige : omega/(r*v) -> omega*r/v
+
+ G1 = ( hankel0(omega*r/v1)/(v1**2) +
+ . hankel1(omega*r/v2)/(omega*r*v2) -
+ . hankel1(omega*r/v1)/(omega*r*v1) ) *
+ . dcmplx(0.d0,- pi / 2.d0)
+
+ return
+ end
+
+! -----------
+
+ double complex function G2(r,omega,v1,v2)
+
+ implicit none
+
+ double precision r,omega
+ double complex v1,v2
+
+ double complex hankel0,hankel1
+ external hankel0,hankel1
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! bug Carcione corrige : omega/(r*v) -> omega*r/v
+
+ G2 = ( hankel0(omega*r/v2)/(v2**2) -
+ . hankel1(omega*r/v2)/(omega*r*v2) +
+ . hankel1(omega*r/v1)/(omega*r*v1) ) *
+ . dcmplx(0.d0,+ pi / 2.d0)
+
+ return
+ end
+
+! -----------
+
+ double complex function hankel0(z)
+
+ implicit none
+
+ double complex z
+
+! on utilise la routine NAG appelee S17DLE (simple precision)
+
+ integer ifail,nz
+ complex result
+
+ ifail = -1
+ call S17DLE(2,0.0,cmplx(z),1,'U',result,nz,ifail)
+ if(ifail .ne. 0) stop 'S17DLE failed in hankel0'
+ if(nz .gt. 0) print *,nz,' termes mis a zero par underflow'
+
+ hankel0 = dcmplx(result)
+
+ return
+ end
+
+! -----------
+
+ double complex function hankel1(z)
+
+ implicit none
+
+ double complex z
+
+! on utilise la routine NAG appelee S17DLE (simple precision)
+
+ integer ifail,nz
+ complex result
+
+ ifail = -1
+ call S17DLE(2,1.0,cmplx(z),1,'U',result,nz,ifail)
+ if(ifail .ne. 0) stop 'S17DLE failed in hankel1'
+ if(nz .gt. 0) print *,nz,' termes mis a zero par underflow'
+
+ hankel1 = dcmplx(result)
+
+ return
+ end
+
+! ***************** routine de FFT pour signal en temps ****************
+
+! FFT routine taken from Netlib
+
+ SUBROUTINE CFFTB (N,C,WSAVE)
+ DIMENSION C(1) ,WSAVE(1)
+ IF (N .EQ. 1) RETURN
+ IW1 = N+N+1
+ IW2 = IW1+N+N
+ CALL CFFTB1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2))
+ RETURN
+ END
+ SUBROUTINE CFFTB1 (N,C,CH,WA,IFAC)
+ DIMENSION CH(1) ,C(1) ,WA(1) ,IFAC(1)
+ NF = IFAC(2)
+ NA = 0
+ L1 = 1
+ IW = 1
+ DO 116 K1=1,NF
+ IP = IFAC(K1+2)
+ L2 = IP*L1
+ IDO = N/L2
+ IDOT = IDO+IDO
+ IDL1 = IDOT*L1
+ IF (IP .NE. 4) GO TO 103
+ IX2 = IW+IDOT
+ IX3 = IX2+IDOT
+ IF (NA .NE. 0) GO TO 101
+ CALL PASSB4 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3))
+ GO TO 102
+ 101 CALL PASSB4 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3))
+ 102 NA = 1-NA
+ GO TO 115
+ 103 IF (IP .NE. 2) GO TO 106
+ IF (NA .NE. 0) GO TO 104
+ CALL PASSB2 (IDOT,L1,C,CH,WA(IW))
+ GO TO 105
+ 104 CALL PASSB2 (IDOT,L1,CH,C,WA(IW))
+ 105 NA = 1-NA
+ GO TO 115
+ 106 IF (IP .NE. 3) GO TO 109
+ IX2 = IW+IDOT
+ IF (NA .NE. 0) GO TO 107
+ CALL PASSB3 (IDOT,L1,C,CH,WA(IW),WA(IX2))
+ GO TO 108
+ 107 CALL PASSB3 (IDOT,L1,CH,C,WA(IW),WA(IX2))
+ 108 NA = 1-NA
+ GO TO 115
+ 109 IF (IP .NE. 5) GO TO 112
+ IX2 = IW+IDOT
+ IX3 = IX2+IDOT
+ IX4 = IX3+IDOT
+ IF (NA .NE. 0) GO TO 110
+ CALL PASSB5 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+ GO TO 111
+ 110 CALL PASSB5 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+ 111 NA = 1-NA
+ GO TO 115
+ 112 IF (NA .NE. 0) GO TO 113
+ CALL PASSB (NAC,IDOT,IP,L1,IDL1,C,C,C,CH,CH,WA(IW))
+ GO TO 114
+ 113 CALL PASSB (NAC,IDOT,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW))
+ 114 IF (NAC .NE. 0) NA = 1-NA
+ 115 L1 = L2
+ IW = IW+(IP-1)*IDOT
+ 116 CONTINUE
+ IF (NA .EQ. 0) RETURN
+ N2 = N+N
+ DO 117 I=1,N2
+ C(I) = CH(I)
+ 117 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB (NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA)
+ DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) ,
+ 1 C1(IDO,L1,IP) ,WA(1) ,C2(IDL1,IP),
+ 2 CH2(IDL1,IP)
+ IDOT = IDO/2
+ NT = IP*IDL1
+ IPP2 = IP+2
+ IPPH = (IP+1)/2
+ IDP = IP*IDO
+!
+ IF (IDO .LT. L1) GO TO 106
+ DO 103 J=2,IPPH
+ JC = IPP2-J
+ DO 102 K=1,L1
+ DO 101 I=1,IDO
+ CH(I,K,J) = CC(I,J,K)+CC(I,JC,K)
+ CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K)
+ 101 CONTINUE
+ 102 CONTINUE
+ 103 CONTINUE
+ DO 105 K=1,L1
+ DO 104 I=1,IDO
+ CH(I,K,1) = CC(I,1,K)
+ 104 CONTINUE
+ 105 CONTINUE
+ GO TO 112
+ 106 DO 109 J=2,IPPH
+ JC = IPP2-J
+ DO 108 I=1,IDO
+ DO 107 K=1,L1
+ CH(I,K,J) = CC(I,J,K)+CC(I,JC,K)
+ CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K)
+ 107 CONTINUE
+ 108 CONTINUE
+ 109 CONTINUE
+ DO 111 I=1,IDO
+ DO 110 K=1,L1
+ CH(I,K,1) = CC(I,1,K)
+ 110 CONTINUE
+ 111 CONTINUE
+ 112 IDL = 2-IDO
+ INC = 0
+ DO 116 L=2,IPPH
+ LC = IPP2-L
+ IDL = IDL+IDO
+ DO 113 IK=1,IDL1
+ C2(IK,L) = CH2(IK,1)+WA(IDL-1)*CH2(IK,2)
+ C2(IK,LC) = WA(IDL)*CH2(IK,IP)
+ 113 CONTINUE
+ IDLJ = IDL
+ INC = INC+IDO
+ DO 115 J=3,IPPH
+ JC = IPP2-J
+ IDLJ = IDLJ+INC
+ IF (IDLJ .GT. IDP) IDLJ = IDLJ-IDP
+ WAR = WA(IDLJ-1)
+ WAI = WA(IDLJ)
+ DO 114 IK=1,IDL1
+ C2(IK,L) = C2(IK,L)+WAR*CH2(IK,J)
+ C2(IK,LC) = C2(IK,LC)+WAI*CH2(IK,JC)
+ 114 CONTINUE
+ 115 CONTINUE
+ 116 CONTINUE
+ DO 118 J=2,IPPH
+ DO 117 IK=1,IDL1
+ CH2(IK,1) = CH2(IK,1)+CH2(IK,J)
+ 117 CONTINUE
+ 118 CONTINUE
+ DO 120 J=2,IPPH
+ JC = IPP2-J
+ DO 119 IK=2,IDL1,2
+ CH2(IK-1,J) = C2(IK-1,J)-C2(IK,JC)
+ CH2(IK-1,JC) = C2(IK-1,J)+C2(IK,JC)
+ CH2(IK,J) = C2(IK,J)+C2(IK-1,JC)
+ CH2(IK,JC) = C2(IK,J)-C2(IK-1,JC)
+ 119 CONTINUE
+ 120 CONTINUE
+ NAC = 1
+ IF (IDO .EQ. 2) RETURN
+ NAC = 0
+ DO 121 IK=1,IDL1
+ C2(IK,1) = CH2(IK,1)
+ 121 CONTINUE
+ DO 123 J=2,IP
+ DO 122 K=1,L1
+ C1(1,K,J) = CH(1,K,J)
+ C1(2,K,J) = CH(2,K,J)
+ 122 CONTINUE
+ 123 CONTINUE
+ IF (IDOT .GT. L1) GO TO 127
+ IDIJ = 0
+ DO 126 J=2,IP
+ IDIJ = IDIJ+2
+ DO 125 I=4,IDO,2
+ IDIJ = IDIJ+2
+ DO 124 K=1,L1
+ C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)-WA(IDIJ)*CH(I,K,J)
+ C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)+WA(IDIJ)*CH(I-1,K,J)
+ 124 CONTINUE
+ 125 CONTINUE
+ 126 CONTINUE
+ RETURN
+ 127 IDJ = 2-IDO
+ DO 130 J=2,IP
+ IDJ = IDJ+IDO
+ DO 129 K=1,L1
+ IDIJ = IDJ
+ DO 128 I=4,IDO,2
+ IDIJ = IDIJ+2
+ C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)-WA(IDIJ)*CH(I,K,J)
+ C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)+WA(IDIJ)*CH(I-1,K,J)
+ 128 CONTINUE
+ 129 CONTINUE
+ 130 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB2 (IDO,L1,CC,CH,WA1)
+ DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) ,
+ 1 WA1(1)
+ IF (IDO .GT. 2) GO TO 102
+ DO 101 K=1,L1
+ CH(1,K,1) = CC(1,1,K)+CC(1,2,K)
+ CH(1,K,2) = CC(1,1,K)-CC(1,2,K)
+ CH(2,K,1) = CC(2,1,K)+CC(2,2,K)
+ CH(2,K,2) = CC(2,1,K)-CC(2,2,K)
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ CH(I-1,K,1) = CC(I-1,1,K)+CC(I-1,2,K)
+ TR2 = CC(I-1,1,K)-CC(I-1,2,K)
+ CH(I,K,1) = CC(I,1,K)+CC(I,2,K)
+ TI2 = CC(I,1,K)-CC(I,2,K)
+ CH(I,K,2) = WA1(I-1)*TI2+WA1(I)*TR2
+ CH(I-1,K,2) = WA1(I-1)*TR2-WA1(I)*TI2
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB3 (IDO,L1,CC,CH,WA1,WA2)
+ DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) ,
+ 1 WA1(1) ,WA2(1)
+ DATA TAUR,TAUI /-.5,.866025403784439/
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TR2 = CC(1,2,K)+CC(1,3,K)
+ CR2 = CC(1,1,K)+TAUR*TR2
+ CH(1,K,1) = CC(1,1,K)+TR2
+ TI2 = CC(2,2,K)+CC(2,3,K)
+ CI2 = CC(2,1,K)+TAUR*TI2
+ CH(2,K,1) = CC(2,1,K)+TI2
+ CR3 = TAUI*(CC(1,2,K)-CC(1,3,K))
+ CI3 = TAUI*(CC(2,2,K)-CC(2,3,K))
+ CH(1,K,2) = CR2-CI3
+ CH(1,K,3) = CR2+CI3
+ CH(2,K,2) = CI2+CR3
+ CH(2,K,3) = CI2-CR3
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TR2 = CC(I-1,2,K)+CC(I-1,3,K)
+ CR2 = CC(I-1,1,K)+TAUR*TR2
+ CH(I-1,K,1) = CC(I-1,1,K)+TR2
+ TI2 = CC(I,2,K)+CC(I,3,K)
+ CI2 = CC(I,1,K)+TAUR*TI2
+ CH(I,K,1) = CC(I,1,K)+TI2
+ CR3 = TAUI*(CC(I-1,2,K)-CC(I-1,3,K))
+ CI3 = TAUI*(CC(I,2,K)-CC(I,3,K))
+ DR2 = CR2-CI3
+ DR3 = CR2+CI3
+ DI2 = CI2+CR3
+ DI3 = CI2-CR3
+ CH(I,K,2) = WA1(I-1)*DI2+WA1(I)*DR2
+ CH(I-1,K,2) = WA1(I-1)*DR2-WA1(I)*DI2
+ CH(I,K,3) = WA2(I-1)*DI3+WA2(I)*DR3
+ CH(I-1,K,3) = WA2(I-1)*DR3-WA2(I)*DI3
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB4 (IDO,L1,CC,CH,WA1,WA2,WA3)
+ DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) ,
+ 1 WA1(1) ,WA2(1) ,WA3(1)
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TI1 = CC(2,1,K)-CC(2,3,K)
+ TI2 = CC(2,1,K)+CC(2,3,K)
+ TR4 = CC(2,4,K)-CC(2,2,K)
+ TI3 = CC(2,2,K)+CC(2,4,K)
+ TR1 = CC(1,1,K)-CC(1,3,K)
+ TR2 = CC(1,1,K)+CC(1,3,K)
+ TI4 = CC(1,2,K)-CC(1,4,K)
+ TR3 = CC(1,2,K)+CC(1,4,K)
+ CH(1,K,1) = TR2+TR3
+ CH(1,K,3) = TR2-TR3
+ CH(2,K,1) = TI2+TI3
+ CH(2,K,3) = TI2-TI3
+ CH(1,K,2) = TR1+TR4
+ CH(1,K,4) = TR1-TR4
+ CH(2,K,2) = TI1+TI4
+ CH(2,K,4) = TI1-TI4
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TI1 = CC(I,1,K)-CC(I,3,K)
+ TI2 = CC(I,1,K)+CC(I,3,K)
+ TI3 = CC(I,2,K)+CC(I,4,K)
+ TR4 = CC(I,4,K)-CC(I,2,K)
+ TR1 = CC(I-1,1,K)-CC(I-1,3,K)
+ TR2 = CC(I-1,1,K)+CC(I-1,3,K)
+ TI4 = CC(I-1,2,K)-CC(I-1,4,K)
+ TR3 = CC(I-1,2,K)+CC(I-1,4,K)
+ CH(I-1,K,1) = TR2+TR3
+ CR3 = TR2-TR3
+ CH(I,K,1) = TI2+TI3
+ CI3 = TI2-TI3
+ CR2 = TR1+TR4
+ CR4 = TR1-TR4
+ CI2 = TI1+TI4
+ CI4 = TI1-TI4
+ CH(I-1,K,2) = WA1(I-1)*CR2-WA1(I)*CI2
+ CH(I,K,2) = WA1(I-1)*CI2+WA1(I)*CR2
+ CH(I-1,K,3) = WA2(I-1)*CR3-WA2(I)*CI3
+ CH(I,K,3) = WA2(I-1)*CI3+WA2(I)*CR3
+ CH(I-1,K,4) = WA3(I-1)*CR4-WA3(I)*CI4
+ CH(I,K,4) = WA3(I-1)*CI4+WA3(I)*CR4
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB5 (IDO,L1,CC,CH,WA1,WA2,WA3,WA4)
+ DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) ,
+ 1 WA1(1) ,WA2(1) ,WA3(1) ,WA4(1)
+ DATA TR11,TI11,TR12,TI12 /.309016994374947,.951056516295154,
+ 1-.809016994374947,.587785252292473/
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TI5 = CC(2,2,K)-CC(2,5,K)
+ TI2 = CC(2,2,K)+CC(2,5,K)
+ TI4 = CC(2,3,K)-CC(2,4,K)
+ TI3 = CC(2,3,K)+CC(2,4,K)
+ TR5 = CC(1,2,K)-CC(1,5,K)
+ TR2 = CC(1,2,K)+CC(1,5,K)
+ TR4 = CC(1,3,K)-CC(1,4,K)
+ TR3 = CC(1,3,K)+CC(1,4,K)
+ CH(1,K,1) = CC(1,1,K)+TR2+TR3
+ CH(2,K,1) = CC(2,1,K)+TI2+TI3
+ CR2 = CC(1,1,K)+TR11*TR2+TR12*TR3
+ CI2 = CC(2,1,K)+TR11*TI2+TR12*TI3
+ CR3 = CC(1,1,K)+TR12*TR2+TR11*TR3
+ CI3 = CC(2,1,K)+TR12*TI2+TR11*TI3
+ CR5 = TI11*TR5+TI12*TR4
+ CI5 = TI11*TI5+TI12*TI4
+ CR4 = TI12*TR5-TI11*TR4
+ CI4 = TI12*TI5-TI11*TI4
+ CH(1,K,2) = CR2-CI5
+ CH(1,K,5) = CR2+CI5
+ CH(2,K,2) = CI2+CR5
+ CH(2,K,3) = CI3+CR4
+ CH(1,K,3) = CR3-CI4
+ CH(1,K,4) = CR3+CI4
+ CH(2,K,4) = CI3-CR4
+ CH(2,K,5) = CI2-CR5
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TI5 = CC(I,2,K)-CC(I,5,K)
+ TI2 = CC(I,2,K)+CC(I,5,K)
+ TI4 = CC(I,3,K)-CC(I,4,K)
+ TI3 = CC(I,3,K)+CC(I,4,K)
+ TR5 = CC(I-1,2,K)-CC(I-1,5,K)
+ TR2 = CC(I-1,2,K)+CC(I-1,5,K)
+ TR4 = CC(I-1,3,K)-CC(I-1,4,K)
+ TR3 = CC(I-1,3,K)+CC(I-1,4,K)
+ CH(I-1,K,1) = CC(I-1,1,K)+TR2+TR3
+ CH(I,K,1) = CC(I,1,K)+TI2+TI3
+ CR2 = CC(I-1,1,K)+TR11*TR2+TR12*TR3
+ CI2 = CC(I,1,K)+TR11*TI2+TR12*TI3
+ CR3 = CC(I-1,1,K)+TR12*TR2+TR11*TR3
+ CI3 = CC(I,1,K)+TR12*TI2+TR11*TI3
+ CR5 = TI11*TR5+TI12*TR4
+ CI5 = TI11*TI5+TI12*TI4
+ CR4 = TI12*TR5-TI11*TR4
+ CI4 = TI12*TI5-TI11*TI4
+ DR3 = CR3-CI4
+ DR4 = CR3+CI4
+ DI3 = CI3+CR4
+ DI4 = CI3-CR4
+ DR5 = CR2+CI5
+ DR2 = CR2-CI5
+ DI5 = CI2-CR5
+ DI2 = CI2+CR5
+ CH(I-1,K,2) = WA1(I-1)*DR2-WA1(I)*DI2
+ CH(I,K,2) = WA1(I-1)*DI2+WA1(I)*DR2
+ CH(I-1,K,3) = WA2(I-1)*DR3-WA2(I)*DI3
+ CH(I,K,3) = WA2(I-1)*DI3+WA2(I)*DR3
+ CH(I-1,K,4) = WA3(I-1)*DR4-WA3(I)*DI4
+ CH(I,K,4) = WA3(I-1)*DI4+WA3(I)*DR4
+ CH(I-1,K,5) = WA4(I-1)*DR5-WA4(I)*DI5
+ CH(I,K,5) = WA4(I-1)*DI5+WA4(I)*DR5
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+
+
+
+ SUBROUTINE CFFTI (N,WSAVE)
+ DIMENSION WSAVE(1)
+ IF (N .EQ. 1) RETURN
+ IW1 = N+N+1
+ IW2 = IW1+N+N
+ CALL CFFTI1 (N,WSAVE(IW1),WSAVE(IW2))
+ RETURN
+ END
+ SUBROUTINE CFFTI1 (N,WA,IFAC)
+ DIMENSION WA(1) ,IFAC(1) ,NTRYH(4)
+ DATA NTRYH(1),NTRYH(2),NTRYH(3),NTRYH(4)/3,4,2,5/
+ NL = N
+ NF = 0
+ J = 0
+ 101 J = J+1
+ IF (J-4) 102,102,103
+ 102 NTRY = NTRYH(J)
+ GO TO 104
+ 103 NTRY = NTRY+2
+ 104 NQ = NL/NTRY
+ NR = NL-NTRY*NQ
+ IF (NR) 101,105,101
+ 105 NF = NF+1
+ IFAC(NF+2) = NTRY
+ NL = NQ
+ IF (NTRY .NE. 2) GO TO 107
+ IF (NF .EQ. 1) GO TO 107
+ DO 106 I=2,NF
+ IB = NF-I+2
+ IFAC(IB+2) = IFAC(IB+1)
+ 106 CONTINUE
+ IFAC(3) = 2
+ 107 IF (NL .NE. 1) GO TO 104
+ IFAC(1) = N
+ IFAC(2) = NF
+ TPI = 6.28318530717959
+ ARGH = TPI/FLOAT(N)
+ I = 2
+ L1 = 1
+ DO 110 K1=1,NF
+ IP = IFAC(K1+2)
+ LD = 0
+ L2 = L1*IP
+ IDO = N/L2
+ IDOT = IDO+IDO+2
+ IPM = IP-1
+ DO 109 J=1,IPM
+ I1 = I
+ WA(I-1) = 1.
+ WA(I) = 0.
+ LD = LD+L1
+ FI = 0.
+ ARGLD = FLOAT(LD)*ARGH
+ DO 108 II=4,IDOT,2
+ I = I+2
+ FI = FI+1.
+ ARG = FI*ARGLD
+ WA(I-1) = COS(ARG)
+ WA(I) = SIN(ARG)
+ 108 CONTINUE
+ IF (IP .LE. 5) GO TO 109
+ WA(I1-1) = WA(I-1)
+ WA(I1) = WA(I)
+ 109 CONTINUE
+ L1 = L2
+ 110 CONTINUE
+ RETURN
+ END
+
+
+
+
+
+ SUBROUTINE CFFTF (N,C,WSAVE)
+ DIMENSION C(1) ,WSAVE(1)
+ IF (N .EQ. 1) RETURN
+ IW1 = N+N+1
+ IW2 = IW1+N+N
+ CALL CFFTF1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2))
+ RETURN
+ END
+ SUBROUTINE CFFTF1 (N,C,CH,WA,IFAC)
+ DIMENSION CH(1) ,C(1) ,WA(1) ,IFAC(1)
+ NF = IFAC(2)
+ NA = 0
+ L1 = 1
+ IW = 1
+ DO 116 K1=1,NF
+ IP = IFAC(K1+2)
+ L2 = IP*L1
+ IDO = N/L2
+ IDOT = IDO+IDO
+ IDL1 = IDOT*L1
+ IF (IP .NE. 4) GO TO 103
+ IX2 = IW+IDOT
+ IX3 = IX2+IDOT
+ IF (NA .NE. 0) GO TO 101
+ CALL PASSF4 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3))
+ GO TO 102
+ 101 CALL PASSF4 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3))
+ 102 NA = 1-NA
+ GO TO 115
+ 103 IF (IP .NE. 2) GO TO 106
+ IF (NA .NE. 0) GO TO 104
+ CALL PASSF2 (IDOT,L1,C,CH,WA(IW))
+ GO TO 105
+ 104 CALL PASSF2 (IDOT,L1,CH,C,WA(IW))
+ 105 NA = 1-NA
+ GO TO 115
+ 106 IF (IP .NE. 3) GO TO 109
+ IX2 = IW+IDOT
+ IF (NA .NE. 0) GO TO 107
+ CALL PASSF3 (IDOT,L1,C,CH,WA(IW),WA(IX2))
+ GO TO 108
+ 107 CALL PASSF3 (IDOT,L1,CH,C,WA(IW),WA(IX2))
+ 108 NA = 1-NA
+ GO TO 115
+ 109 IF (IP .NE. 5) GO TO 112
+ IX2 = IW+IDOT
+ IX3 = IX2+IDOT
+ IX4 = IX3+IDOT
+ IF (NA .NE. 0) GO TO 110
+ CALL PASSF5 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+ GO TO 111
+ 110 CALL PASSF5 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+ 111 NA = 1-NA
+ GO TO 115
+ 112 IF (NA .NE. 0) GO TO 113
+ CALL PASSF (NAC,IDOT,IP,L1,IDL1,C,C,C,CH,CH,WA(IW))
+ GO TO 114
+ 113 CALL PASSF (NAC,IDOT,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW))
+ 114 IF (NAC .NE. 0) NA = 1-NA
+ 115 L1 = L2
+ IW = IW+(IP-1)*IDOT
+ 116 CONTINUE
+ IF (NA .EQ. 0) RETURN
+ N2 = N+N
+ DO 117 I=1,N2
+ C(I) = CH(I)
+ 117 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF (NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA)
+ DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) ,
+ 1 C1(IDO,L1,IP) ,WA(1) ,C2(IDL1,IP),
+ 2 CH2(IDL1,IP)
+ IDOT = IDO/2
+ NT = IP*IDL1
+ IPP2 = IP+2
+ IPPH = (IP+1)/2
+ IDP = IP*IDO
+!
+ IF (IDO .LT. L1) GO TO 106
+ DO 103 J=2,IPPH
+ JC = IPP2-J
+ DO 102 K=1,L1
+ DO 101 I=1,IDO
+ CH(I,K,J) = CC(I,J,K)+CC(I,JC,K)
+ CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K)
+ 101 CONTINUE
+ 102 CONTINUE
+ 103 CONTINUE
+ DO 105 K=1,L1
+ DO 104 I=1,IDO
+ CH(I,K,1) = CC(I,1,K)
+ 104 CONTINUE
+ 105 CONTINUE
+ GO TO 112
+ 106 DO 109 J=2,IPPH
+ JC = IPP2-J
+ DO 108 I=1,IDO
+ DO 107 K=1,L1
+ CH(I,K,J) = CC(I,J,K)+CC(I,JC,K)
+ CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K)
+ 107 CONTINUE
+ 108 CONTINUE
+ 109 CONTINUE
+ DO 111 I=1,IDO
+ DO 110 K=1,L1
+ CH(I,K,1) = CC(I,1,K)
+ 110 CONTINUE
+ 111 CONTINUE
+ 112 IDL = 2-IDO
+ INC = 0
+ DO 116 L=2,IPPH
+ LC = IPP2-L
+ IDL = IDL+IDO
+ DO 113 IK=1,IDL1
+ C2(IK,L) = CH2(IK,1)+WA(IDL-1)*CH2(IK,2)
+ C2(IK,LC) = -WA(IDL)*CH2(IK,IP)
+ 113 CONTINUE
+ IDLJ = IDL
+ INC = INC+IDO
+ DO 115 J=3,IPPH
+ JC = IPP2-J
+ IDLJ = IDLJ+INC
+ IF (IDLJ .GT. IDP) IDLJ = IDLJ-IDP
+ WAR = WA(IDLJ-1)
+ WAI = WA(IDLJ)
+ DO 114 IK=1,IDL1
+ C2(IK,L) = C2(IK,L)+WAR*CH2(IK,J)
+ C2(IK,LC) = C2(IK,LC)-WAI*CH2(IK,JC)
+ 114 CONTINUE
+ 115 CONTINUE
+ 116 CONTINUE
+ DO 118 J=2,IPPH
+ DO 117 IK=1,IDL1
+ CH2(IK,1) = CH2(IK,1)+CH2(IK,J)
+ 117 CONTINUE
+ 118 CONTINUE
+ DO 120 J=2,IPPH
+ JC = IPP2-J
+ DO 119 IK=2,IDL1,2
+ CH2(IK-1,J) = C2(IK-1,J)-C2(IK,JC)
+ CH2(IK-1,JC) = C2(IK-1,J)+C2(IK,JC)
+ CH2(IK,J) = C2(IK,J)+C2(IK-1,JC)
+ CH2(IK,JC) = C2(IK,J)-C2(IK-1,JC)
+ 119 CONTINUE
+ 120 CONTINUE
+ NAC = 1
+ IF (IDO .EQ. 2) RETURN
+ NAC = 0
+ DO 121 IK=1,IDL1
+ C2(IK,1) = CH2(IK,1)
+ 121 CONTINUE
+ DO 123 J=2,IP
+ DO 122 K=1,L1
+ C1(1,K,J) = CH(1,K,J)
+ C1(2,K,J) = CH(2,K,J)
+ 122 CONTINUE
+ 123 CONTINUE
+ IF (IDOT .GT. L1) GO TO 127
+ IDIJ = 0
+ DO 126 J=2,IP
+ IDIJ = IDIJ+2
+ DO 125 I=4,IDO,2
+ IDIJ = IDIJ+2
+ DO 124 K=1,L1
+ C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)+WA(IDIJ)*CH(I,K,J)
+ C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)-WA(IDIJ)*CH(I-1,K,J)
+ 124 CONTINUE
+ 125 CONTINUE
+ 126 CONTINUE
+ RETURN
+ 127 IDJ = 2-IDO
+ DO 130 J=2,IP
+ IDJ = IDJ+IDO
+ DO 129 K=1,L1
+ IDIJ = IDJ
+ DO 128 I=4,IDO,2
+ IDIJ = IDIJ+2
+ C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)+WA(IDIJ)*CH(I,K,J)
+ C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)-WA(IDIJ)*CH(I-1,K,J)
+ 128 CONTINUE
+ 129 CONTINUE
+ 130 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF2 (IDO,L1,CC,CH,WA1)
+ DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) ,
+ 1 WA1(1)
+ IF (IDO .GT. 2) GO TO 102
+ DO 101 K=1,L1
+ CH(1,K,1) = CC(1,1,K)+CC(1,2,K)
+ CH(1,K,2) = CC(1,1,K)-CC(1,2,K)
+ CH(2,K,1) = CC(2,1,K)+CC(2,2,K)
+ CH(2,K,2) = CC(2,1,K)-CC(2,2,K)
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ CH(I-1,K,1) = CC(I-1,1,K)+CC(I-1,2,K)
+ TR2 = CC(I-1,1,K)-CC(I-1,2,K)
+ CH(I,K,1) = CC(I,1,K)+CC(I,2,K)
+ TI2 = CC(I,1,K)-CC(I,2,K)
+ CH(I,K,2) = WA1(I-1)*TI2-WA1(I)*TR2
+ CH(I-1,K,2) = WA1(I-1)*TR2+WA1(I)*TI2
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF3 (IDO,L1,CC,CH,WA1,WA2)
+ DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) ,
+ 1 WA1(1) ,WA2(1)
+ DATA TAUR,TAUI /-.5,-.866025403784439/
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TR2 = CC(1,2,K)+CC(1,3,K)
+ CR2 = CC(1,1,K)+TAUR*TR2
+ CH(1,K,1) = CC(1,1,K)+TR2
+ TI2 = CC(2,2,K)+CC(2,3,K)
+ CI2 = CC(2,1,K)+TAUR*TI2
+ CH(2,K,1) = CC(2,1,K)+TI2
+ CR3 = TAUI*(CC(1,2,K)-CC(1,3,K))
+ CI3 = TAUI*(CC(2,2,K)-CC(2,3,K))
+ CH(1,K,2) = CR2-CI3
+ CH(1,K,3) = CR2+CI3
+ CH(2,K,2) = CI2+CR3
+ CH(2,K,3) = CI2-CR3
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TR2 = CC(I-1,2,K)+CC(I-1,3,K)
+ CR2 = CC(I-1,1,K)+TAUR*TR2
+ CH(I-1,K,1) = CC(I-1,1,K)+TR2
+ TI2 = CC(I,2,K)+CC(I,3,K)
+ CI2 = CC(I,1,K)+TAUR*TI2
+ CH(I,K,1) = CC(I,1,K)+TI2
+ CR3 = TAUI*(CC(I-1,2,K)-CC(I-1,3,K))
+ CI3 = TAUI*(CC(I,2,K)-CC(I,3,K))
+ DR2 = CR2-CI3
+ DR3 = CR2+CI3
+ DI2 = CI2+CR3
+ DI3 = CI2-CR3
+ CH(I,K,2) = WA1(I-1)*DI2-WA1(I)*DR2
+ CH(I-1,K,2) = WA1(I-1)*DR2+WA1(I)*DI2
+ CH(I,K,3) = WA2(I-1)*DI3-WA2(I)*DR3
+ CH(I-1,K,3) = WA2(I-1)*DR3+WA2(I)*DI3
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF4 (IDO,L1,CC,CH,WA1,WA2,WA3)
+ DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) ,
+ 1 WA1(1) ,WA2(1) ,WA3(1)
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TI1 = CC(2,1,K)-CC(2,3,K)
+ TI2 = CC(2,1,K)+CC(2,3,K)
+ TR4 = CC(2,2,K)-CC(2,4,K)
+ TI3 = CC(2,2,K)+CC(2,4,K)
+ TR1 = CC(1,1,K)-CC(1,3,K)
+ TR2 = CC(1,1,K)+CC(1,3,K)
+ TI4 = CC(1,4,K)-CC(1,2,K)
+ TR3 = CC(1,2,K)+CC(1,4,K)
+ CH(1,K,1) = TR2+TR3
+ CH(1,K,3) = TR2-TR3
+ CH(2,K,1) = TI2+TI3
+ CH(2,K,3) = TI2-TI3
+ CH(1,K,2) = TR1+TR4
+ CH(1,K,4) = TR1-TR4
+ CH(2,K,2) = TI1+TI4
+ CH(2,K,4) = TI1-TI4
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TI1 = CC(I,1,K)-CC(I,3,K)
+ TI2 = CC(I,1,K)+CC(I,3,K)
+ TI3 = CC(I,2,K)+CC(I,4,K)
+ TR4 = CC(I,2,K)-CC(I,4,K)
+ TR1 = CC(I-1,1,K)-CC(I-1,3,K)
+ TR2 = CC(I-1,1,K)+CC(I-1,3,K)
+ TI4 = CC(I-1,4,K)-CC(I-1,2,K)
+ TR3 = CC(I-1,2,K)+CC(I-1,4,K)
+ CH(I-1,K,1) = TR2+TR3
+ CR3 = TR2-TR3
+ CH(I,K,1) = TI2+TI3
+ CI3 = TI2-TI3
+ CR2 = TR1+TR4
+ CR4 = TR1-TR4
+ CI2 = TI1+TI4
+ CI4 = TI1-TI4
+ CH(I-1,K,2) = WA1(I-1)*CR2+WA1(I)*CI2
+ CH(I,K,2) = WA1(I-1)*CI2-WA1(I)*CR2
+ CH(I-1,K,3) = WA2(I-1)*CR3+WA2(I)*CI3
+ CH(I,K,3) = WA2(I-1)*CI3-WA2(I)*CR3
+ CH(I-1,K,4) = WA3(I-1)*CR4+WA3(I)*CI4
+ CH(I,K,4) = WA3(I-1)*CI4-WA3(I)*CR4
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF5 (IDO,L1,CC,CH,WA1,WA2,WA3,WA4)
+ DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) ,
+ 1 WA1(1) ,WA2(1) ,WA3(1) ,WA4(1)
+ DATA TR11,TI11,TR12,TI12 /.309016994374947,-.951056516295154,
+ 1-.809016994374947,-.587785252292473/
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TI5 = CC(2,2,K)-CC(2,5,K)
+ TI2 = CC(2,2,K)+CC(2,5,K)
+ TI4 = CC(2,3,K)-CC(2,4,K)
+ TI3 = CC(2,3,K)+CC(2,4,K)
+ TR5 = CC(1,2,K)-CC(1,5,K)
+ TR2 = CC(1,2,K)+CC(1,5,K)
+ TR4 = CC(1,3,K)-CC(1,4,K)
+ TR3 = CC(1,3,K)+CC(1,4,K)
+ CH(1,K,1) = CC(1,1,K)+TR2+TR3
+ CH(2,K,1) = CC(2,1,K)+TI2+TI3
+ CR2 = CC(1,1,K)+TR11*TR2+TR12*TR3
+ CI2 = CC(2,1,K)+TR11*TI2+TR12*TI3
+ CR3 = CC(1,1,K)+TR12*TR2+TR11*TR3
+ CI3 = CC(2,1,K)+TR12*TI2+TR11*TI3
+ CR5 = TI11*TR5+TI12*TR4
+ CI5 = TI11*TI5+TI12*TI4
+ CR4 = TI12*TR5-TI11*TR4
+ CI4 = TI12*TI5-TI11*TI4
+ CH(1,K,2) = CR2-CI5
+ CH(1,K,5) = CR2+CI5
+ CH(2,K,2) = CI2+CR5
+ CH(2,K,3) = CI3+CR4
+ CH(1,K,3) = CR3-CI4
+ CH(1,K,4) = CR3+CI4
+ CH(2,K,4) = CI3-CR4
+ CH(2,K,5) = CI2-CR5
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TI5 = CC(I,2,K)-CC(I,5,K)
+ TI2 = CC(I,2,K)+CC(I,5,K)
+ TI4 = CC(I,3,K)-CC(I,4,K)
+ TI3 = CC(I,3,K)+CC(I,4,K)
+ TR5 = CC(I-1,2,K)-CC(I-1,5,K)
+ TR2 = CC(I-1,2,K)+CC(I-1,5,K)
+ TR4 = CC(I-1,3,K)-CC(I-1,4,K)
+ TR3 = CC(I-1,3,K)+CC(I-1,4,K)
+ CH(I-1,K,1) = CC(I-1,1,K)+TR2+TR3
+ CH(I,K,1) = CC(I,1,K)+TI2+TI3
+ CR2 = CC(I-1,1,K)+TR11*TR2+TR12*TR3
+ CI2 = CC(I,1,K)+TR11*TI2+TR12*TI3
+ CR3 = CC(I-1,1,K)+TR12*TR2+TR11*TR3
+ CI3 = CC(I,1,K)+TR12*TI2+TR11*TI3
+ CR5 = TI11*TR5+TI12*TR4
+ CI5 = TI11*TI5+TI12*TI4
+ CR4 = TI12*TR5-TI11*TR4
+ CI4 = TI12*TI5-TI11*TI4
+ DR3 = CR3-CI4
+ DR4 = CR3+CI4
+ DI3 = CI3+CR4
+ DI4 = CI3-CR4
+ DR5 = CR2+CI5
+ DR2 = CR2-CI5
+ DI5 = CI2-CR5
+ DI2 = CI2+CR5
+ CH(I-1,K,2) = WA1(I-1)*DR2+WA1(I)*DI2
+ CH(I,K,2) = WA1(I-1)*DI2-WA1(I)*DR2
+ CH(I-1,K,3) = WA2(I-1)*DR3+WA2(I)*DI3
+ CH(I,K,3) = WA2(I-1)*DI3-WA2(I)*DR3
+ CH(I-1,K,4) = WA3(I-1)*DR4+WA3(I)*DI4
+ CH(I,K,4) = WA3(I-1)*DI4-WA3(I)*DR4
+ CH(I-1,K,5) = WA4(I-1)*DR5+WA4(I)*DI5
+ CH(I,K,5) = WA4(I-1)*DI5-WA4(I)*DR5
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+
+! !!!!!!!! DK DK NAG routines included below
+
+! DK DK march99 : routines recuperees sur le Cray (simple precision)
+
+ SUBROUTINE ABZP01
+! MARK 11.5(F77) RELEASE. NAG COPYRIGHT 1986.
+!
+! Terminates execution when a hard failure occurs.
+!
+! ******************** IMPLEMENTATION NOTE ********************
+! The following STOP statement may be replaced by a call to an
+! implementation-dependent routine to display a message and/or
+! to abort the program.
+! *************************************************************
+! .. Executable Statements ..
+ STOP
+ END
+
+ SUBROUTINE DCYS18(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-785 (DEC 1989).
+!
+! Original name: CUNK2
+!
+! DCYS18 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
+! RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
+! UNIFORM ASYMPTOTIC EXPANSIONS FOR H(KIND,FNU,ZN) AND J(FNU,ZN)
+! WHERE ZN IS IN THE RIGHT HALF PLANE, KIND=(3-MR)/2, MR=+1 OR
+! -1. HERE ZN=ZR*I OR -ZR*I WHERE ZR=Z IF Z IS IN THE RIGHT
+! HALF PLANE OR ZR=-Z IF Z IS IN THE LEFT HALF PLANE. MR INDIC-
+! ATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
+! NZ=-1 MEANS AN OVERFLOW WILL OCCUR
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX AI, ARGD, ASUMD, BSUMD, C1, C2, CFN, CI, CK,
+ * CONE, CR1, CR2, CRSC, CS, CSCL, CSGN, CSPN,
+ * CZERO, DAI, PHID, RZ, S1, S2, ZB, ZETA1D,
+ * ZETA2D, ZN, ZR
+ REAL AARG, AIC, ANG, APHI, ASC, ASCLE, C2I, C2M, C2R,
+ * CAR, CPN, FMR, FN, FNF, HPI, PI, RS1, SAR, SGN,
+ * SPN, X, YY
+ INTEGER I, IB, IC, IDUM, IFLAG, IFN, IL, IN, INU, IPARD,
+ * IUF, J, K, KDFLG, KFLAG, KK, NAI, NDAI, NW
+! .. Local Arrays ..
+ COMPLEX ARG(2), ASUM(2), BSUM(2), CIP(4), CSR(3),
+ * CSS(3), CY(2), PHI(2), ZETA1(2), ZETA2(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEUS17, S17DGE, DGSS17, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, CONJG, COS, EXP, INT, LOG,
+ * MAX, MOD, REAL, SIGN, SIN
+! .. Data statements ..
+ DATA CZERO, CONE, CI, CR1, CR2/(0.0E0,0.0E0),
+ * (1.0E0,0.0E0), (0.0E0,1.0E0),
+ * (1.0E0,1.73205080756887729E0),
+ * (-0.5E0,-8.66025403784438647E-01)/
+ DATA HPI, PI, AIC/1.57079632679489662E+00,
+ * 3.14159265358979324E+00,
+ * 1.26551212348464539E+00/
+ DATA CIP(1), CIP(2), CIP(3), CIP(4)/(1.0E0,0.0E0),
+ * (0.0E0,-1.0E0), (-1.0E0,0.0E0), (0.0E0,1.0E0)/
+! .. Executable Statements ..
+!
+ KDFLG = 1
+ NZ = 0
+! ------------------------------------------------------------------
+! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
+! THE UNDERFLOW LIMIT
+! ------------------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ X = REAL(Z)
+ ZR = Z
+ IF (X.LT.0.0E0) ZR = -Z
+ YY = AIMAG(ZR)
+ ZN = -ZR*CI
+ ZB = ZR
+ INU = INT(FNU)
+ FNF = FNU - INU
+ ANG = -HPI*FNF
+ CAR = COS(ANG)
+ SAR = SIN(ANG)
+ CPN = -HPI*CAR
+ SPN = -HPI*SAR
+ C2 = CMPLX(-SPN,CPN)
+ KK = MOD(INU,4) + 1
+ CS = CR1*C2*CIP(KK)
+ IF (YY.LE.0.0E0) THEN
+ ZN = CONJG(-ZN)
+ ZB = CONJG(ZB)
+ END IF
+! ------------------------------------------------------------------
+! K(FNU,Z) IS COMPUTED FROM H(2,FNU,-I*Z) WHERE Z IS IN THE FIRST
+! QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY
+! CONJUGATION SINCE THE K FUNCTION IS REAL ON THE POSITIVE REAL AXIS
+! ------------------------------------------------------------------
+ J = 2
+ DO 40 I = 1, N
+! ---------------------------------------------------------------
+! J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
+! ---------------------------------------------------------------
+ J = 3 - J
+ FN = FNU + I - 1
+ CALL DEUS17(ZN,FN,0,TOL,PHI(J),ARG(J),ZETA1(J),ZETA2(J),ASUM(J)
+ * ,BSUM(J),ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = ZETA1(J) - ZETA2(J)
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = ZETA1(J) - CFN*(CFN/(ZB+ZETA2(J)))
+ END IF
+! ---------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ---------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (KDFLG.EQ.1) KFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ---------------------------------------------------------
+! REFINE TEST AND SCALE
+! ---------------------------------------------------------
+ APHI = ABS(PHI(J))
+ AARG = ABS(ARG(J))
+ RS1 = RS1 + LOG(APHI) - 0.25E0*LOG(AARG) - AIC
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 20
+ ELSE
+ IF (KDFLG.EQ.1) KFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (KDFLG.EQ.1) KFLAG = 3
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------
+! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
+! EXPONENT EXTREMES
+! ------------------------------------------------------------
+ C2 = ARG(J)*CR2
+ IDUM = 1
+! S17DGE assumed not to fail, therefore IDUM set to one.
+ CALL S17DGE('F',C2,'S',AI,NAI,IDUM)
+ IDUM = 1
+ CALL S17DGE('D',C2,'S',DAI,NDAI,IDUM)
+ S2 = CS*PHI(J)*(AI*ASUM(J)+CR2*DAI*BSUM(J))
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(KFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (KFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) GO TO 20
+ END IF
+ IF (YY.LE.0.0E0) S2 = CONJG(S2)
+ CY(KDFLG) = S2
+ Y(I) = S2*CSR(KFLAG)
+ CS = -CI*CS
+ IF (KDFLG.EQ.2) THEN
+ GO TO 60
+ ELSE
+ KDFLG = 2
+ GO TO 40
+ END IF
+ END IF
+ 20 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+! ------------------------------------------------------------
+! FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+! ------------------------------------------------------------
+ ELSE IF (X.LT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ KDFLG = 1
+ Y(I) = CZERO
+ CS = -CI*CS
+ NZ = NZ + 1
+ IF (I.NE.1) THEN
+ IF (Y(I-1).NE.CZERO) THEN
+ Y(I-1) = CZERO
+ NZ = NZ + 1
+ END IF
+ END IF
+ END IF
+ 40 CONTINUE
+ I = N
+ 60 RZ = CMPLX(2.0E0,0.0E0)/ZR
+ CK = CMPLX(FN,0.0E0)*RZ
+ IB = I + 1
+ IF (N.GE.IB) THEN
+! ---------------------------------------------------------------
+! TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW, SET SEQUENCE TO
+! ZERO ON UNDERFLOW
+! ---------------------------------------------------------------
+ FN = FNU + N - 1
+ IPARD = 1
+ IF (MR.NE.0) IPARD = 0
+ CALL DEUS17(ZN,FN,IPARD,TOL,PHID,ARGD,ZETA1D,ZETA2D,ASUMD,
+ * BSUMD,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = ZETA1D - ZETA2D
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = ZETA1D - CFN*(CFN/(ZB+ZETA2D))
+ END IF
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (ABS(RS1).GE.ALIM) THEN
+! ---------------------------------------------------------
+! REFINE ESTIMATE AND TEST
+! ---------------------------------------------------------
+ APHI = ABS(PHID)
+ AARG = ABS(ARGD)
+ RS1 = RS1 + LOG(APHI) - 0.25E0*LOG(AARG) - AIC
+ IF (ABS(RS1).GE.ELIM) GO TO 100
+ END IF
+! ------------------------------------------------------------
+! SCALED FORWARD RECURRENCE FOR REMAINDER OF THE SEQUENCE
+! ------------------------------------------------------------
+ S1 = CY(1)
+ S2 = CY(2)
+ C1 = CSR(KFLAG)
+ ASCLE = BRY(KFLAG)
+ DO 80 I = IB, N
+ C2 = S2
+ S2 = CK*S2 + S1
+ S1 = C2
+ CK = CK + RZ
+ C2 = S2*C1
+ Y(I) = C2
+ IF (KFLAG.LT.3) THEN
+ C2R = REAL(C2)
+ C2I = AIMAG(C2)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ KFLAG = KFLAG + 1
+ ASCLE = BRY(KFLAG)
+ S1 = S1*C1
+ S2 = C2
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ C1 = CSR(KFLAG)
+ END IF
+ END IF
+ 80 CONTINUE
+ GO TO 140
+ END IF
+ 100 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+! ------------------------------------------------------------
+! FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+! ------------------------------------------------------------
+ ELSE IF (X.LT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ NZ = N
+ DO 120 I = 1, N
+ Y(I) = CZERO
+ 120 CONTINUE
+ RETURN
+ END IF
+ END IF
+ 140 IF (MR.EQ.0) THEN
+ RETURN
+ ELSE
+! ---------------------------------------------------------------
+! ANALYTIC CONTINUATION FOR RE(Z).LT.0.0E0
+! ---------------------------------------------------------------
+ NZ = 0
+ FMR = MR
+ SGN = -SIGN(PI,FMR)
+! ---------------------------------------------------------------
+! CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP.
+! ---------------------------------------------------------------
+ CSGN = CMPLX(0.0E0,SGN)
+ IF (YY.LE.0.0E0) CSGN = CONJG(CSGN)
+ IFN = INU + N - 1
+ ANG = FNF*SGN
+ CPN = COS(ANG)
+ SPN = SIN(ANG)
+ CSPN = CMPLX(CPN,SPN)
+ IF (MOD(IFN,2).EQ.1) CSPN = -CSPN
+! ---------------------------------------------------------------
+! CS=COEFF OF THE J FUNCTION TO GET THE I FUNCTION. I(FNU,Z) IS
+! COMPUTED FROM EXP(I*FNU*HPI)*J(FNU,-I*Z) WHERE Z IS IN THE
+! FIRST QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE
+! COMPUTED BY CONJUGATION SINCE THE I FUNCTION IS REAL ON THE
+! POSITIVE REAL AXIS
+! ---------------------------------------------------------------
+ CS = CMPLX(CAR,-SAR)*CSGN
+ IN = MOD(IFN,4) + 1
+ C2 = CIP(IN)
+ CS = CS*CONJG(C2)
+ ASC = BRY(1)
+ KK = N
+ KDFLG = 1
+ IB = IB - 1
+ IC = IB - 1
+ IUF = 0
+ DO 220 K = 1, N
+! ------------------------------------------------------------
+! LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
+! FUNCTION ABOVE
+! ------------------------------------------------------------
+ FN = FNU + KK - 1
+ IF (N.GT.2) THEN
+ IF ((KK.EQ.N) .AND. (IB.LT.N)) THEN
+ GO TO 160
+ ELSE IF ((KK.NE.IB) .AND. (KK.NE.IC)) THEN
+ CALL DEUS17(ZN,FN,0,TOL,PHID,ARGD,ZETA1D,ZETA2D,ASUMD,
+ * BSUMD,ELIM)
+ GO TO 160
+ END IF
+ END IF
+ PHID = PHI(J)
+ ARGD = ARG(J)
+ ZETA1D = ZETA1(J)
+ ZETA2D = ZETA2(J)
+ ASUMD = ASUM(J)
+ BSUMD = BSUM(J)
+ J = 3 - J
+ 160 IF (KODE.EQ.1) THEN
+ S1 = -ZETA1D + ZETA2D
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = -ZETA1D + CFN*(CFN/(ZB+ZETA2D))
+ END IF
+! ------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (KDFLG.EQ.1) IFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ------------------------------------------------------
+! REFINE TEST AND SCALE
+! ------------------------------------------------------
+ APHI = ABS(PHID)
+ AARG = ABS(ARGD)
+ RS1 = RS1 + LOG(APHI) - 0.25E0*LOG(AARG) - AIC
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 180
+ ELSE
+ IF (KDFLG.EQ.1) IFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (KDFLG.EQ.1) IFLAG = 3
+ END IF
+ END IF
+ END IF
+ IDUM = 1
+! S17DGE assumed not to fail, therefore IDUM set to one.
+ CALL S17DGE('F',ARGD,'S',AI,NAI,IDUM)
+ IDUM = 1
+ CALL S17DGE('D',ARGD,'S',DAI,NDAI,IDUM)
+ S2 = CS*PHID*(AI*ASUMD+DAI*BSUMD)
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(IFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (IFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) S2 = CMPLX(0.0E0,0.0E0)
+ END IF
+ GO TO 200
+ END IF
+ 180 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ S2 = CZERO
+ END IF
+ 200 IF (YY.LE.0.0E0) S2 = CONJG(S2)
+ CY(KDFLG) = S2
+ C2 = S2
+ S2 = S2*CSR(IFLAG)
+! ------------------------------------------------------------
+! ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
+! ------------------------------------------------------------
+ S1 = Y(KK)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZR,S1,S2,NW,ASC,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(KK) = S1*CSPN + S2
+ KK = KK - 1
+ CSPN = -CSPN
+ CS = -CS*CI
+ IF (C2.EQ.CZERO) THEN
+ KDFLG = 1
+ ELSE IF (KDFLG.EQ.2) THEN
+ GO TO 240
+ ELSE
+ KDFLG = 2
+ END IF
+ 220 CONTINUE
+ K = N
+ 240 IL = N - K
+ IF (IL.NE.0) THEN
+! ------------------------------------------------------------
+! RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
+! K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO
+! KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT
+! EXTREMES.
+! ------------------------------------------------------------
+ S1 = CY(1)
+ S2 = CY(2)
+ CS = CSR(IFLAG)
+ ASCLE = BRY(IFLAG)
+ FN = INU + IL
+ DO 260 I = 1, IL
+ C2 = S2
+ S2 = S1 + CMPLX(FN+FNF,0.0E0)*RZ*S2
+ S1 = C2
+ FN = FN - 1.0E0
+ C2 = S2*CS
+ CK = C2
+ C1 = Y(KK)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZR,C1,C2,NW,ASC,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(KK) = C1*CSPN + C2
+ KK = KK - 1
+ CSPN = -CSPN
+ IF (IFLAG.LT.3) THEN
+ C2R = REAL(CK)
+ C2I = AIMAG(CK)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*CS
+ S2 = CK
+ S1 = S1*CSS(IFLAG)
+ S2 = S2*CSS(IFLAG)
+ CS = CSR(IFLAG)
+ END IF
+ END IF
+ 260 CONTINUE
+ END IF
+ RETURN
+ END IF
+ 280 NZ = -1
+ RETURN
+ END
+ SUBROUTINE DCZS18(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-786 (DEC 1989).
+!
+! Original name: CUNK1
+!
+! DCZS18 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
+! RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
+! UNIFORM ASYMPTOTIC EXPANSION.
+! MR INDICATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
+! NZ=-1 MEANS AN OVERFLOW WILL OCCUR
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CFN, CK, CONE, CRSC, CS, CSCL, CSGN,
+ * CSPN, CZERO, PHID, RZ, S1, S2, SUMD, ZETA1D,
+ * ZETA2D, ZR
+ REAL ANG, APHI, ASC, ASCLE, C2I, C2M, C2R, CPN, FMR,
+ * FN, FNF, PI, RS1, SGN, SPN, X
+ INTEGER I, IB, IC, IFLAG, IFN, IL, INITD, INU, IPARD,
+ * IUF, J, K, KDFLG, KFLAG, KK, M, NW
+! .. Local Arrays ..
+ COMPLEX CSR(3), CSS(3), CWRK(16,3), CY(2), PHI(2),
+ * SUM(2), ZETA1(2), ZETA2(2)
+ REAL BRY(3)
+ INTEGER INIT(2)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEWS17, DGSS17, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, INT, LOG, MAX, MOD,
+ * REAL, SIGN, SIN
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+ DATA PI/3.14159265358979324E0/
+! .. Executable Statements ..
+!
+ KDFLG = 1
+ NZ = 0
+! ------------------------------------------------------------------
+! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
+! THE UNDERFLOW LIMIT
+! ------------------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ X = REAL(Z)
+ ZR = Z
+ IF (X.LT.0.0E0) ZR = -Z
+ J = 2
+ DO 40 I = 1, N
+! ---------------------------------------------------------------
+! J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
+! ---------------------------------------------------------------
+ J = 3 - J
+ FN = FNU + I - 1
+ INIT(J) = 0
+ CALL DEWS17(ZR,FN,2,0,TOL,INIT(J),PHI(J),ZETA1(J),ZETA2(J),
+ * SUM(J),CWRK(1,J),ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = ZETA1(J) - ZETA2(J)
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = ZETA1(J) - CFN*(CFN/(ZR+ZETA2(J)))
+ END IF
+! ---------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ---------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (KDFLG.EQ.1) KFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ---------------------------------------------------------
+! REFINE TEST AND SCALE
+! ---------------------------------------------------------
+ APHI = ABS(PHI(J))
+ RS1 = RS1 + LOG(APHI)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 20
+ ELSE
+ IF (KDFLG.EQ.1) KFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (KDFLG.EQ.1) KFLAG = 3
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------
+! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
+! EXPONENT EXTREMES
+! ------------------------------------------------------------
+ S2 = PHI(J)*SUM(J)
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(KFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (KFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) GO TO 20
+ END IF
+ CY(KDFLG) = S2
+ Y(I) = S2*CSR(KFLAG)
+ IF (KDFLG.EQ.2) THEN
+ GO TO 60
+ ELSE
+ KDFLG = 2
+ GO TO 40
+ END IF
+ END IF
+ 20 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+! ------------------------------------------------------------
+! FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+! ------------------------------------------------------------
+ ELSE IF (X.LT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ KDFLG = 1
+ Y(I) = CZERO
+ NZ = NZ + 1
+ IF (I.NE.1) THEN
+ IF (Y(I-1).NE.CZERO) THEN
+ Y(I-1) = CZERO
+ NZ = NZ + 1
+ END IF
+ END IF
+ END IF
+ 40 CONTINUE
+ I = N
+ 60 RZ = CMPLX(2.0E0,0.0E0)/ZR
+ CK = CMPLX(FN,0.0E0)*RZ
+ IB = I + 1
+ IF (N.GE.IB) THEN
+! ---------------------------------------------------------------
+! TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW, SET SEQUENCE TO
+! ZERO ON UNDERFLOW
+! ---------------------------------------------------------------
+ FN = FNU + N - 1
+ IPARD = 1
+ IF (MR.NE.0) IPARD = 0
+ INITD = 0
+ CALL DEWS17(ZR,FN,2,IPARD,TOL,INITD,PHID,ZETA1D,ZETA2D,SUMD,
+ * CWRK(1,3),ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = ZETA1D - ZETA2D
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = ZETA1D - CFN*(CFN/(ZR+ZETA2D))
+ END IF
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (ABS(RS1).GE.ALIM) THEN
+! ---------------------------------------------------------
+! REFINE ESTIMATE AND TEST
+! ---------------------------------------------------------
+ APHI = ABS(PHID)
+ RS1 = RS1 + LOG(APHI)
+ IF (ABS(RS1).GE.ELIM) GO TO 100
+ END IF
+! ------------------------------------------------------------
+! RECUR FORWARD FOR REMAINDER OF THE SEQUENCE
+! ------------------------------------------------------------
+ S1 = CY(1)
+ S2 = CY(2)
+ C1 = CSR(KFLAG)
+ ASCLE = BRY(KFLAG)
+ DO 80 I = IB, N
+ C2 = S2
+ S2 = CK*S2 + S1
+ S1 = C2
+ CK = CK + RZ
+ C2 = S2*C1
+ Y(I) = C2
+ IF (KFLAG.LT.3) THEN
+ C2R = REAL(C2)
+ C2I = AIMAG(C2)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ KFLAG = KFLAG + 1
+ ASCLE = BRY(KFLAG)
+ S1 = S1*C1
+ S2 = C2
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ C1 = CSR(KFLAG)
+ END IF
+ END IF
+ 80 CONTINUE
+ GO TO 140
+ END IF
+ 100 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+! ------------------------------------------------------------
+! FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+! ------------------------------------------------------------
+ ELSE IF (X.LT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ NZ = N
+ DO 120 I = 1, N
+ Y(I) = CZERO
+ 120 CONTINUE
+ RETURN
+ END IF
+ END IF
+ 140 IF (MR.EQ.0) THEN
+ RETURN
+ ELSE
+! ---------------------------------------------------------------
+! ANALYTIC CONTINUATION FOR RE(Z).LT.0.0E0
+! ---------------------------------------------------------------
+ NZ = 0
+ FMR = MR
+ SGN = -SIGN(PI,FMR)
+! ---------------------------------------------------------------
+! CSPN AND CSGN ARE COEFF OF K AND I FUNCIONS RESP.
+! ---------------------------------------------------------------
+ CSGN = CMPLX(0.0E0,SGN)
+ INU = INT(FNU)
+ FNF = FNU - INU
+ IFN = INU + N - 1
+ ANG = FNF*SGN
+ CPN = COS(ANG)
+ SPN = SIN(ANG)
+ CSPN = CMPLX(CPN,SPN)
+ IF (MOD(IFN,2).EQ.1) CSPN = -CSPN
+ ASC = BRY(1)
+ KK = N
+ IUF = 0
+ KDFLG = 1
+ IB = IB - 1
+ IC = IB - 1
+ DO 220 K = 1, N
+ FN = FNU + KK - 1
+! ------------------------------------------------------------
+! LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
+! FUNCTION ABOVE
+! ------------------------------------------------------------
+ M = 3
+ IF (N.GT.2) THEN
+ IF ((KK.EQ.N) .AND. (IB.LT.N)) THEN
+ GO TO 160
+ ELSE IF ((KK.NE.IB) .AND. (KK.NE.IC)) THEN
+ INITD = 0
+ GO TO 160
+ END IF
+ END IF
+ INITD = INIT(J)
+ PHID = PHI(J)
+ ZETA1D = ZETA1(J)
+ ZETA2D = ZETA2(J)
+ SUMD = SUM(J)
+ M = J
+ J = 3 - J
+ 160 CALL DEWS17(ZR,FN,1,0,TOL,INITD,PHID,ZETA1D,ZETA2D,SUMD,
+ * CWRK(1,M),ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1D + ZETA2D
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = -ZETA1D + CFN*(CFN/(ZR+ZETA2D))
+ END IF
+! ------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (KDFLG.EQ.1) IFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ------------------------------------------------------
+! REFINE TEST AND SCALE
+! ------------------------------------------------------
+ APHI = ABS(PHID)
+ RS1 = RS1 + LOG(APHI)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 180
+ ELSE
+ IF (KDFLG.EQ.1) IFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (KDFLG.EQ.1) IFLAG = 3
+ END IF
+ END IF
+ END IF
+ S2 = CSGN*PHID*SUMD
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(IFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (IFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) S2 = CMPLX(0.0E0,0.0E0)
+ END IF
+ GO TO 200
+ END IF
+ 180 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ S2 = CZERO
+ END IF
+ 200 CY(KDFLG) = S2
+ C2 = S2
+ S2 = S2*CSR(IFLAG)
+! ------------------------------------------------------------
+! ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
+! ------------------------------------------------------------
+ S1 = Y(KK)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZR,S1,S2,NW,ASC,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(KK) = S1*CSPN + S2
+ KK = KK - 1
+ CSPN = -CSPN
+ IF (C2.EQ.CZERO) THEN
+ KDFLG = 1
+ ELSE IF (KDFLG.EQ.2) THEN
+ GO TO 240
+ ELSE
+ KDFLG = 2
+ END IF
+ 220 CONTINUE
+ K = N
+ 240 IL = N - K
+ IF (IL.NE.0) THEN
+! ------------------------------------------------------------
+! RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
+! K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO
+! KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT
+! EXTREMES.
+! ------------------------------------------------------------
+ S1 = CY(1)
+ S2 = CY(2)
+ CS = CSR(IFLAG)
+ ASCLE = BRY(IFLAG)
+ FN = INU + IL
+ DO 260 I = 1, IL
+ C2 = S2
+ S2 = S1 + CMPLX(FN+FNF,0.0E0)*RZ*S2
+ S1 = C2
+ FN = FN - 1.0E0
+ C2 = S2*CS
+ CK = C2
+ C1 = Y(KK)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZR,C1,C2,NW,ASC,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(KK) = C1*CSPN + C2
+ KK = KK - 1
+ CSPN = -CSPN
+ IF (IFLAG.LT.3) THEN
+ C2R = REAL(CK)
+ C2I = AIMAG(CK)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*CS
+ S2 = CK
+ S1 = S1*CSS(IFLAG)
+ S2 = S2*CSS(IFLAG)
+ CS = CSR(IFLAG)
+ END IF
+ END IF
+ 260 CONTINUE
+ END IF
+ RETURN
+ END IF
+ 280 NZ = -1
+ RETURN
+ END
+ SUBROUTINE DERS17(Z,FNU,N,CY,TOL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-761 (DEC 1989).
+!
+! Original name: CRATI
+!
+! DERS17 COMPUTES RATIOS OF I BESSEL FUNCTIONS BY BACKWARD
+! RECURRENCE. THE STARTING INDEX IS DETERMINED BY FORWARD
+! RECURRENCE AS DESCRIBED IN J. RES. OF NAT. BUR. OF STANDARDS-B,
+! MATHEMATICAL SCIENCES, VOL 77B, P111-114, SEPTEMBER, 1973,
+! BESSEL FUNCTIONS I AND J OF COMPLEX ARGUMENT AND INTEGER ORDER,
+! BY D. J. SOOKNE.
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL FNU, TOL
+ INTEGER N
+! .. Array Arguments ..
+ COMPLEX CY(N)
+! .. Local Scalars ..
+ COMPLEX CDFNU, CONE, CZERO, P1, P2, PT, RZ, T1
+ REAL AK, AMAGZ, AP1, AP2, ARG, AZ, DFNU, FDNU, FLAM,
+ * FNUP, RAP1, RHO, TEST, TEST1
+ INTEGER I, ID, IDNU, INU, ITIME, K, KK, MAGZ
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, INT, MAX, MIN, REAL, SQRT
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ AZ = ABS(Z)
+ INU = INT(FNU)
+ IDNU = INU + N - 1
+ FDNU = IDNU
+ MAGZ = INT(AZ)
+ AMAGZ = MAGZ + 1
+ FNUP = MAX(AMAGZ,FDNU)
+ ID = IDNU - MAGZ - 1
+ ITIME = 1
+ K = 1
+ RZ = (CONE+CONE)/Z
+ T1 = CMPLX(FNUP,0.0E0)*RZ
+ P2 = -T1
+ P1 = CONE
+ T1 = T1 + RZ
+ IF (ID.GT.0) ID = 0
+ AP2 = ABS(P2)
+ AP1 = ABS(P1)
+! ------------------------------------------------------------------
+! THE OVERFLOW TEST ON K(FNU+I-1,Z) BEFORE THE CALL TO CBKNX
+! GUARANTEES THAT P2 IS ON SCALE. SCALE TEST1 AND ALL SUBSEQUENT
+! P2 VALUES BY AP1 TO ENSURE THAT AN OVERFLOW DOES NOT OCCUR
+! PREMATURELY.
+! ------------------------------------------------------------------
+ ARG = (AP2+AP2)/(AP1*TOL)
+ TEST1 = SQRT(ARG)
+ TEST = TEST1
+ RAP1 = 1.0E0/AP1
+ P1 = P1*CMPLX(RAP1,0.0E0)
+ P2 = P2*CMPLX(RAP1,0.0E0)
+ AP2 = AP2*RAP1
+ 20 CONTINUE
+ K = K + 1
+ AP1 = AP2
+ PT = P2
+ P2 = P1 - T1*P2
+ P1 = PT
+ T1 = T1 + RZ
+ AP2 = ABS(P2)
+ IF (AP1.LE.TEST) THEN
+ GO TO 20
+ ELSE IF (ITIME.NE.2) THEN
+ AK = ABS(T1)*0.5E0
+ FLAM = AK + SQRT(AK*AK-1.0E0)
+ RHO = MIN(AP2/AP1,FLAM)
+ TEST = TEST1*SQRT(RHO/(RHO*RHO-1.0E0))
+ ITIME = 2
+ GO TO 20
+ END IF
+ KK = K + 1 - ID
+ AK = KK
+ DFNU = FNU + N - 1
+ CDFNU = CMPLX(DFNU,0.0E0)
+ T1 = CMPLX(AK,0.0E0)
+ P1 = CMPLX(1.0E0/AP2,0.0E0)
+ P2 = CZERO
+ DO 40 I = 1, KK
+ PT = P1
+ P1 = RZ*(CDFNU+T1)*P1 + P2
+ P2 = PT
+ T1 = T1 - CONE
+ 40 CONTINUE
+ IF (REAL(P1).EQ.0.0E0 .AND. AIMAG(P1).EQ.0.0E0) P1 = CMPLX(TOL,
+ * TOL)
+ CY(N) = P2/P1
+ IF (N.NE.1) THEN
+ K = N - 1
+ AK = K
+ T1 = CMPLX(AK,0.0E0)
+ CDFNU = CMPLX(FNU,0.0E0)*RZ
+ DO 60 I = 2, N
+ PT = CDFNU + T1*RZ + CY(K+1)
+ IF (REAL(PT).EQ.0.0E0 .AND. AIMAG(PT).EQ.0.0E0)
+ * PT = CMPLX(TOL,TOL)
+ CY(K) = CONE/PT
+ T1 = T1 - CONE
+ K = K - 1
+ 60 CONTINUE
+ END IF
+ RETURN
+ END
+ SUBROUTINE DESS17(ZR,FNU,KODE,N,Y,NZ,CW,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-762 (DEC 1989).
+!
+! Original name: CWRSK
+!
+! DESS17 COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY
+! NORMALIZING THE I FUNCTION RATIOS FROM DERS17 BY THE WRONSKIAN
+!
+! .. Scalar Arguments ..
+ COMPLEX ZR
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX CW(2), Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CINU, CSCL, CT, RCT, ST
+ REAL ACT, ACW, ASCLE, S1, S2, YY
+ INTEGER I, NW
+! .. External Functions ..
+ REAL X02AME
+ EXTERNAL X02AME
+! .. External Subroutines ..
+ EXTERNAL DERS17, DGXS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, CONJG, COS, SIN
+! .. Executable Statements ..
+! ------------------------------------------------------------------
+! I(FNU+I-1,Z) BY BACKWARD RECURRENCE FOR RATIOS
+! Y(I)=I(FNU+I,Z)/I(FNU+I-1,Z) FROM DERS17 NORMALIZED BY THE
+! WRONSKIAN WITH K(FNU,Z) AND K(FNU+1,Z) FROM DGXS17.
+! ------------------------------------------------------------------
+ NZ = 0
+ CALL DGXS17(ZR,FNU,KODE,2,CW,NW,TOL,ELIM,ALIM)
+ IF (NW.NE.0) THEN
+ NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ IF (NW.EQ.(-3)) NZ = -3
+ ELSE
+ CALL DERS17(ZR,FNU,N,Y,TOL)
+! ---------------------------------------------------------------
+! RECUR FORWARD ON I(FNU+1,Z) = R(FNU,Z)*I(FNU,Z),
+! R(FNU+J-1,Z)=Y(J), J=1,...,N
+! ---------------------------------------------------------------
+ CINU = CMPLX(1.0E0,0.0E0)
+ IF (KODE.NE.1) THEN
+ YY = AIMAG(ZR)
+ S1 = COS(YY)
+ S2 = SIN(YY)
+ CINU = CMPLX(S1,S2)
+ END IF
+! ---------------------------------------------------------------
+! ON LOW EXPONENT MACHINES THE K FUNCTIONS CAN BE CLOSE TO BOTH
+! THE UNDER AND OVERFLOW LIMITS AND THE NORMALIZATION MUST BE
+! SCALED TO PREVENT OVER OR UNDERFLOW. DEVS17 HAS DETERMINED THAT
+! THE RESULT IS ON SCALE.
+! ---------------------------------------------------------------
+ ACW = ABS(CW(2))
+ ASCLE = (1.0E+3*X02AME())/TOL
+ CSCL = CMPLX(1.0E0,0.0E0)
+ IF (ACW.GT.ASCLE) THEN
+ ASCLE = 1.0E0/ASCLE
+ IF (ACW.GE.ASCLE) CSCL = CMPLX(TOL,0.0E0)
+ ELSE
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ END IF
+ C1 = CW(1)*CSCL
+ C2 = CW(2)*CSCL
+ ST = Y(1)
+! ---------------------------------------------------------------
+! CINU=CINU*(CONJG(CT)/CABS(CT))*(1.0E0/CABS(CT) PREVENTS
+! UNDER- OR OVERFLOW PREMATURELY BY SQUARING CABS(CT)
+! ---------------------------------------------------------------
+ CT = ZR*(C2+ST*C1)
+ ACT = ABS(CT)
+ RCT = CMPLX(1.0E0/ACT,0.0E0)
+ CT = CONJG(CT)*RCT
+ CINU = CINU*RCT*CT
+ Y(1) = CINU*CSCL
+ IF (N.NE.1) THEN
+ DO 20 I = 2, N
+ CINU = ST*CINU
+ ST = Y(I)
+ Y(I) = CINU*CSCL
+ 20 CONTINUE
+ END IF
+ END IF
+ RETURN
+ END
+ SUBROUTINE DETS17(Z,FNU,KODE,N,Y,NZ,NLAST,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-763 (DEC 1989).
+!
+! Original name: CUNI2
+!
+! DETS17 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF
+! UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I
+! OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO.
+!
+! FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
+! EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
+! NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
+! FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
+! Y(I)=CZERO FOR I=NLAST+1,N
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, TOL
+ INTEGER KODE, N, NLAST, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX AI, ARG, ASUM, BSUM, C1, C2, CFN, CI, CID, CONE,
+ * CRSC, CSCL, CZERO, DAI, PHI, RZ, S1, S2, ZB,
+ * ZETA1, ZETA2, ZN
+ REAL AARG, AIC, ANG, APHI, ASCLE, AY, C2I, C2M, C2R,
+ * CAR, FN, HPI, RS1, SAR, YY
+ INTEGER I, IDUM, IFLAG, IN, INU, J, K, NAI, ND, NDAI,
+ * NN, NUF, NW
+! .. Local Arrays ..
+ COMPLEX CIP(4), CSR(3), CSS(3), CY(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEUS17, DEVS17, S17DGE, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, CONJG, COS, EXP, INT, LOG,
+ * MAX, MIN, MOD, REAL, SIN
+! .. Data statements ..
+ DATA CZERO, CONE, CI/(0.0E0,0.0E0), (1.0E0,0.0E0),
+ * (0.0E0,1.0E0)/
+ DATA CIP(1), CIP(2), CIP(3), CIP(4)/(1.0E0,0.0E0),
+ * (0.0E0,1.0E0), (-1.0E0,0.0E0), (0.0E0,-1.0E0)/
+ DATA HPI, AIC/1.57079632679489662E+00,
+ * 1.265512123484645396E+00/
+! .. Executable Statements ..
+!
+ NZ = 0
+ ND = N
+ NLAST = 0
+! ------------------------------------------------------------------
+! COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
+! NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
+! EXP(ALIM)=EXP(ELIM)*TOL
+! ------------------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ YY = AIMAG(Z)
+! ------------------------------------------------------------------
+! ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI
+! ------------------------------------------------------------------
+ ZN = -Z*CI
+ ZB = Z
+ CID = -CI
+ INU = INT(FNU)
+ ANG = HPI*(FNU-INU)
+ CAR = COS(ANG)
+ SAR = SIN(ANG)
+ C2 = CMPLX(CAR,SAR)
+ IN = INU + N - 1
+ IN = MOD(IN,4)
+ C2 = C2*CIP(IN+1)
+ IF (YY.LE.0.0E0) THEN
+ ZN = CONJG(-ZN)
+ ZB = CONJG(ZB)
+ CID = -CID
+ C2 = CONJG(C2)
+ END IF
+! ------------------------------------------------------------------
+! CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
+! ------------------------------------------------------------------
+ FN = MAX(FNU,1.0E0)
+ CALL DEUS17(ZN,FN,1,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,BSUM,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1 + ZETA2
+ ELSE
+ CFN = CMPLX(FNU,0.0E0)
+ S1 = -ZETA1 + CFN*(CFN/(ZB+ZETA2))
+ END IF
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ 20 CONTINUE
+ NN = MIN(2,ND)
+ DO 40 I = 1, NN
+ FN = FNU + ND - I
+ CALL DEUS17(ZN,FN,0,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,BSUM,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1 + ZETA2
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ AY = ABS(YY)
+ S1 = -ZETA1 + CFN*(CFN/(ZB+ZETA2)) + CMPLX(0.0E0,AY)
+ END IF
+! ------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 60
+ ELSE
+ IF (I.EQ.1) IFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ------------------------------------------------------
+! REFINE TEST AND SCALE
+! ------------------------------------------------------
+! ------------------------------------------------------
+ APHI = ABS(PHI)
+ AARG = ABS(ARG)
+ RS1 = RS1 + LOG(APHI) - 0.25E0*LOG(AARG) - AIC
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 60
+ ELSE
+ IF (I.EQ.1) IFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (I.EQ.1) IFLAG = 3
+ END IF
+ END IF
+ END IF
+! ---------------------------------------------------------
+! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
+! EXPONENT EXTREMES
+! ---------------------------------------------------------
+ IDUM = 1
+! S17DGE assumed not to fail, therefore IDUM set to one.
+ CALL S17DGE('F',ARG,'S',AI,NAI,IDUM)
+ IDUM = 1
+ CALL S17DGE('D',ARG,'S',DAI,NDAI,IDUM)
+ S2 = PHI*(AI*ASUM+DAI*BSUM)
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(IFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (IFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) GO TO 60
+ END IF
+ IF (YY.LE.0.0E0) S2 = CONJG(S2)
+ J = ND - I + 1
+ S2 = S2*C2
+ CY(I) = S2
+ Y(J) = S2*CSR(IFLAG)
+ C2 = C2*CID
+ END IF
+ 40 CONTINUE
+ GO TO 80
+ 60 IF (RS1.GT.0.0E0) THEN
+ GO TO 160
+ ELSE
+! ------------------------------------------------------------
+! SET UNDERFLOW AND UPDATE PARAMETERS
+! ------------------------------------------------------------
+ Y(ND) = CZERO
+ NZ = NZ + 1
+ ND = ND - 1
+ IF (ND.EQ.0) THEN
+ RETURN
+ ELSE
+ CALL DEVS17(Z,FNU,KODE,1,ND,Y,NUF,TOL,ELIM,ALIM)
+ IF (NUF.LT.0) THEN
+ GO TO 160
+ ELSE
+ ND = ND - NUF
+ NZ = NZ + NUF
+ IF (ND.EQ.0) THEN
+ RETURN
+ ELSE
+ FN = FNU + ND - 1
+ IF (FN.LT.FNUL) THEN
+ GO TO 120
+ ELSE
+! FN = AIMAG(CID)
+! J = NUF + 1
+! K = MOD(J,4) + 1
+! S1 = CIP(K)
+! IF (FN.LT.0.0E0) S1 = CONJG(S1)
+! C2 = C2*S1
+! The above 6 lines were replaced by the 5 below
+! to fix a bug discovered during implementation
+! on a Multics machine, whereby some results
+! were returned wrongly scaled by sqrt(-1.0). MWP.
+ C2 = CMPLX(CAR,SAR)
+ IN = INU + ND - 1
+ IN = MOD(IN,4) + 1
+ C2 = C2*CIP(IN)
+ IF (YY.LE.0.0E0) C2 = CONJG(C2)
+ GO TO 20
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+ 80 IF (ND.GT.2) THEN
+ RZ = CMPLX(2.0E0,0.0E0)/Z
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ S1 = CY(1)
+ S2 = CY(2)
+ C1 = CSR(IFLAG)
+ ASCLE = BRY(IFLAG)
+ K = ND - 2
+ FN = K
+ DO 100 I = 3, ND
+ C2 = S2
+ S2 = S1 + CMPLX(FNU+FN,0.0E0)*RZ*S2
+ S1 = C2
+ C2 = S2*C1
+ Y(K) = C2
+ K = K - 1
+ FN = FN - 1.0E0
+ IF (IFLAG.LT.3) THEN
+ C2R = REAL(C2)
+ C2I = AIMAG(C2)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*C1
+ S2 = C2
+ S1 = S1*CSS(IFLAG)
+ S2 = S2*CSS(IFLAG)
+ C1 = CSR(IFLAG)
+ END IF
+ END IF
+ 100 CONTINUE
+ END IF
+ RETURN
+ 120 NLAST = ND
+ RETURN
+ ELSE IF (RS1.LE.0.0E0) THEN
+ NZ = N
+ DO 140 I = 1, N
+ Y(I) = CZERO
+ 140 CONTINUE
+ RETURN
+ END IF
+ 160 NZ = -1
+ RETURN
+ END
+ SUBROUTINE DEUS17(Z,FNU,IPMTR,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,BSUM,
+ * ELIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-764 (DEC 1989).
+!
+! Original name: CUNHJ
+!
+! REFERENCES
+! HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A.
+! STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9.
+!
+! ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC
+! PRESS, N.Y., 1974, PAGE 420
+!
+! ABSTRACT
+! DEUS17 COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) =
+! J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU
+! BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION
+!
+! C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) )
+!
+! FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS
+! AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE.
+!
+! (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2,
+!
+! ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING
+! PURPOSES IN AIRY FUNCTIONS FROM S17DGE OR S17DHE.
+!
+! MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND
+! MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR=
+! 1 COMPUTES ALL EXCEPT ASUM AND BSUM.
+!
+! .. Scalar Arguments ..
+ COMPLEX ARG, ASUM, BSUM, PHI, Z, ZETA1, ZETA2
+ REAL ELIM, FNU, TOL
+ INTEGER IPMTR
+! .. Local Scalars ..
+ COMPLEX CFNU, CONE, CZERO, PRZTH, PTFN, RFN13, RTZTA,
+ * RZTH, SUMA, SUMB, T2, TFN, W, W2, ZA, ZB, ZC,
+ * ZETA, ZTH
+ REAL ANG, ASUMI, ASUMR, ATOL, AW2, AZTH, BSUMI,
+ * BSUMR, BTOL, EX1, EX2, FN13, FN23, HPI, PI, PP,
+ * RFNU, RFNU2, TEST, THPI, TSTI, TSTR, WI, WR,
+ * ZCI, ZCR, ZETAI, ZETAR, ZTHI, ZTHR
+ INTEGER IAS, IBS, IS, J, JR, JU, K, KMAX, KP1, KS, L,
+ * L1, L2, LR, LRP1, M
+! .. Local Arrays ..
+ COMPLEX CR(14), DR(14), P(30), UP(14)
+ REAL ALFA(180), AP(30), AR(14), BETA(210), BR(14),
+ * C(105), GAMA(30)
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, ATAN, CMPLX, COS, EXP, LOG, REAL,
+ * SIN, SQRT
+! .. Data statements ..
+ DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7),
+ * AR(8), AR(9), AR(10), AR(11), AR(12), AR(13),
+ * AR(14)/1.00000000000000000E+00,
+ * 1.04166666666666667E-01,
+ * 8.35503472222222222E-02,
+ * 1.28226574556327160E-01,
+ * 2.91849026464140464E-01,
+ * 8.81627267443757652E-01,
+ * 3.32140828186276754E+00,
+ * 1.49957629868625547E+01,
+ * 7.89230130115865181E+01,
+ * 4.74451538868264323E+02,
+ * 3.20749009089066193E+03,
+ * 2.40865496408740049E+04,
+ * 1.98923119169509794E+05,
+ * 1.79190200777534383E+06/
+ DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7),
+ * BR(8), BR(9), BR(10), BR(11), BR(12), BR(13),
+ * BR(14)/1.00000000000000000E+00,
+ * -1.45833333333333333E-01,
+ * -9.87413194444444444E-02,
+ * -1.43312053915895062E-01,
+ * -3.17227202678413548E-01,
+ * -9.42429147957120249E-01,
+ * -3.51120304082635426E+00,
+ * -1.57272636203680451E+01,
+ * -8.22814390971859444E+01,
+ * -4.92355370523670524E+02,
+ * -3.31621856854797251E+03,
+ * -2.48276742452085896E+04,
+ * -2.04526587315129788E+05,
+ * -1.83844491706820990E+06/
+ DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8),
+ * C(9), C(10), C(11), C(12), C(13), C(14), C(15),
+ * C(16)/1.00000000000000000E+00,
+ * -2.08333333333333333E-01,
+ * 1.25000000000000000E-01,
+ * 3.34201388888888889E-01,
+ * -4.01041666666666667E-01,
+ * 7.03125000000000000E-02,
+ * -1.02581259645061728E+00,
+ * 1.84646267361111111E+00,
+ * -8.91210937500000000E-01,
+ * 7.32421875000000000E-02,
+ * 4.66958442342624743E+00,
+ * -1.12070026162229938E+01,
+ * 8.78912353515625000E+00,
+ * -2.36408691406250000E+00,
+ * 1.12152099609375000E-01,
+ * -2.82120725582002449E+01/
+ DATA C(17), C(18), C(19), C(20), C(21), C(22), C(23),
+ * C(24)/8.46362176746007346E+01,
+ * -9.18182415432400174E+01,
+ * 4.25349987453884549E+01,
+ * -7.36879435947963170E+00,
+ * 2.27108001708984375E-01,
+ * 2.12570130039217123E+02,
+ * -7.65252468141181642E+02,
+ * 1.05999045252799988E+03/
+ DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31),
+ * C(32), C(33), C(34), C(35), C(36), C(37), C(38),
+ * C(39), C(40)/-6.99579627376132541E+02,
+ * 2.18190511744211590E+02,
+ * -2.64914304869515555E+01,
+ * 5.72501420974731445E-01,
+ * -1.91945766231840700E+03,
+ * 8.06172218173730938E+03,
+ * -1.35865500064341374E+04,
+ * 1.16553933368645332E+04,
+ * -5.30564697861340311E+03,
+ * 1.20090291321635246E+03,
+ * -1.08090919788394656E+02,
+ * 1.72772750258445740E+00,
+ * 2.02042913309661486E+04,
+ * -9.69805983886375135E+04,
+ * 1.92547001232531532E+05,
+ * -2.03400177280415534E+05/
+ DATA C(41), C(42), C(43), C(44), C(45), C(46), C(47),
+ * C(48)/1.22200464983017460E+05,
+ * -4.11926549688975513E+04,
+ * 7.10951430248936372E+03,
+ * -4.93915304773088012E+02,
+ * 6.07404200127348304E+00,
+ * -2.42919187900551333E+05,
+ * 1.31176361466297720E+06,
+ * -2.99801591853810675E+06/
+ DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55),
+ * C(56), C(57), C(58), C(59), C(60), C(61), C(62),
+ * C(63), C(64)/3.76327129765640400E+06,
+ * -2.81356322658653411E+06,
+ * 1.26836527332162478E+06,
+ * -3.31645172484563578E+05,
+ * 4.52187689813627263E+04,
+ * -2.49983048181120962E+03,
+ * 2.43805296995560639E+01,
+ * 3.28446985307203782E+06,
+ * -1.97068191184322269E+07,
+ * 5.09526024926646422E+07,
+ * -7.41051482115326577E+07,
+ * 6.63445122747290267E+07,
+ * -3.75671766607633513E+07,
+ * 1.32887671664218183E+07,
+ * -2.78561812808645469E+06,
+ * 3.08186404612662398E+05/
+ DATA C(65), C(66), C(67), C(68), C(69), C(70), C(71),
+ * C(72)/-1.38860897537170405E+04,
+ * 1.10017140269246738E+02,
+ * -4.93292536645099620E+07,
+ * 3.25573074185765749E+08,
+ * -9.39462359681578403E+08,
+ * 1.55359689957058006E+09,
+ * -1.62108055210833708E+09,
+ * 1.10684281682301447E+09/
+ DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79),
+ * C(80), C(81), C(82), C(83), C(84), C(85), C(86),
+ * C(87), C(88)/-4.95889784275030309E+08,
+ * 1.42062907797533095E+08,
+ * -2.44740627257387285E+07,
+ * 2.24376817792244943E+06,
+ * -8.40054336030240853E+04,
+ * 5.51335896122020586E+02,
+ * 8.14789096118312115E+08,
+ * -5.86648149205184723E+09,
+ * 1.86882075092958249E+10,
+ * -3.46320433881587779E+10,
+ * 4.12801855797539740E+10,
+ * -3.30265997498007231E+10,
+ * 1.79542137311556001E+10,
+ * -6.56329379261928433E+09,
+ * 1.55927986487925751E+09,
+ * -2.25105661889415278E+08/
+ DATA C(89), C(90), C(91), C(92), C(93), C(94), C(95),
+ * C(96)/1.73951075539781645E+07,
+ * -5.49842327572288687E+05,
+ * 3.03809051092238427E+03,
+ * -1.46792612476956167E+10,
+ * 1.14498237732025810E+11,
+ * -3.99096175224466498E+11,
+ * 8.19218669548577329E+11,
+ * -1.09837515608122331E+12/
+ DATA C(97), C(98), C(99), C(100), C(101), C(102),
+ * C(103), C(104), C(105)/1.00815810686538209E+12,
+ * -6.45364869245376503E+11,
+ * 2.87900649906150589E+11,
+ * -8.78670721780232657E+10,
+ * 1.76347306068349694E+10,
+ * -2.16716498322379509E+09,
+ * 1.43157876718888981E+08,
+ * -3.87183344257261262E+06,
+ * 1.82577554742931747E+04/
+ DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5),
+ * ALFA(6), ALFA(7), ALFA(8), ALFA(9), ALFA(10),
+ * ALFA(11), ALFA(12), ALFA(13),
+ * ALFA(14)/-4.44444444444444444E-03,
+ * -9.22077922077922078E-04,
+ * -8.84892884892884893E-05,
+ * 1.65927687832449737E-04,
+ * 2.46691372741792910E-04,
+ * 2.65995589346254780E-04,
+ * 2.61824297061500945E-04,
+ * 2.48730437344655609E-04,
+ * 2.32721040083232098E-04,
+ * 2.16362485712365082E-04,
+ * 2.00738858762752355E-04,
+ * 1.86267636637545172E-04,
+ * 1.73060775917876493E-04,
+ * 1.61091705929015752E-04/
+ DATA ALFA(15), ALFA(16), ALFA(17), ALFA(18),
+ * ALFA(19), ALFA(20), ALFA(21),
+ * ALFA(22)/1.50274774160908134E-04,
+ * 1.40503497391269794E-04,
+ * 1.31668816545922806E-04,
+ * 1.23667445598253261E-04,
+ * 1.16405271474737902E-04,
+ * 1.09798298372713369E-04,
+ * 1.03772410422992823E-04,
+ * 9.82626078369363448E-05/
+ DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26),
+ * ALFA(27), ALFA(28), ALFA(29), ALFA(30),
+ * ALFA(31), ALFA(32), ALFA(33), ALFA(34),
+ * ALFA(35), ALFA(36)/9.32120517249503256E-05,
+ * 8.85710852478711718E-05,
+ * 8.42963105715700223E-05,
+ * 8.03497548407791151E-05,
+ * 7.66981345359207388E-05,
+ * 7.33122157481777809E-05,
+ * 7.01662625163141333E-05,
+ * 6.72375633790160292E-05,
+ * 6.93735541354588974E-04,
+ * 2.32241745182921654E-04,
+ * -1.41986273556691197E-05,
+ * -1.16444931672048640E-04,
+ * -1.50803558053048762E-04,
+ * -1.55121924918096223E-04/
+ DATA ALFA(37), ALFA(38), ALFA(39), ALFA(40),
+ * ALFA(41), ALFA(42), ALFA(43),
+ * ALFA(44)/-1.46809756646465549E-04,
+ * -1.33815503867491367E-04,
+ * -1.19744975684254051E-04,
+ * -1.06184319207974020E-04,
+ * -9.37699549891194492E-05,
+ * -8.26923045588193274E-05,
+ * -7.29374348155221211E-05,
+ * -6.44042357721016283E-05/
+ DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48),
+ * ALFA(49), ALFA(50), ALFA(51), ALFA(52),
+ * ALFA(53), ALFA(54), ALFA(55), ALFA(56),
+ * ALFA(57), ALFA(58)/-5.69611566009369048E-05,
+ * -5.04731044303561628E-05,
+ * -4.48134868008882786E-05,
+ * -3.98688727717598864E-05,
+ * -3.55400532972042498E-05,
+ * -3.17414256609022480E-05,
+ * -2.83996793904174811E-05,
+ * -2.54522720634870566E-05,
+ * -2.28459297164724555E-05,
+ * -2.05352753106480604E-05,
+ * -1.84816217627666085E-05,
+ * -1.66519330021393806E-05,
+ * -1.50179412980119482E-05,
+ * -1.35554031379040526E-05/
+ DATA ALFA(59), ALFA(60), ALFA(61), ALFA(62),
+ * ALFA(63), ALFA(64), ALFA(65),
+ * ALFA(66)/-1.22434746473858131E-05,
+ * -1.10641884811308169E-05,
+ * -3.54211971457743841E-04,
+ * -1.56161263945159416E-04,
+ * 3.04465503594936410E-05,
+ * 1.30198655773242693E-04,
+ * 1.67471106699712269E-04,
+ * 1.70222587683592569E-04/
+ DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70),
+ * ALFA(71), ALFA(72), ALFA(73), ALFA(74),
+ * ALFA(75), ALFA(76), ALFA(77), ALFA(78),
+ * ALFA(79), ALFA(80)/1.56501427608594704E-04,
+ * 1.36339170977445120E-04,
+ * 1.14886692029825128E-04,
+ * 9.45869093034688111E-05,
+ * 7.64498419250898258E-05,
+ * 6.07570334965197354E-05,
+ * 4.74394299290508799E-05,
+ * 3.62757512005344297E-05,
+ * 2.69939714979224901E-05,
+ * 1.93210938247939253E-05,
+ * 1.30056674793963203E-05,
+ * 7.82620866744496661E-06,
+ * 3.59257485819351583E-06,
+ * 1.44040049814251817E-07/
+ DATA ALFA(81), ALFA(82), ALFA(83), ALFA(84),
+ * ALFA(85), ALFA(86), ALFA(87),
+ * ALFA(88)/-2.65396769697939116E-06,
+ * -4.91346867098485910E-06,
+ * -6.72739296091248287E-06,
+ * -8.17269379678657923E-06,
+ * -9.31304715093561232E-06,
+ * -1.02011418798016441E-05,
+ * -1.08805962510592880E-05,
+ * -1.13875481509603555E-05/
+ DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92),
+ * ALFA(93), ALFA(94), ALFA(95), ALFA(96),
+ * ALFA(97), ALFA(98), ALFA(99), ALFA(100),
+ * ALFA(101), ALFA(102)/-1.17519675674556414E-05,
+ * -1.19987364870944141E-05,
+ * 3.78194199201772914E-04,
+ * 2.02471952761816167E-04,
+ * -6.37938506318862408E-05,
+ * -2.38598230603005903E-04,
+ * -3.10916256027361568E-04,
+ * -3.13680115247576316E-04,
+ * -2.78950273791323387E-04,
+ * -2.28564082619141374E-04,
+ * -1.75245280340846749E-04,
+ * -1.25544063060690348E-04,
+ * -8.22982872820208365E-05,
+ * -4.62860730588116458E-05/
+ DATA ALFA(103), ALFA(104), ALFA(105), ALFA(106),
+ * ALFA(107), ALFA(108), ALFA(109),
+ * ALFA(110)/-1.72334302366962267E-05,
+ * 5.60690482304602267E-06,
+ * 2.31395443148286800E-05,
+ * 3.62642745856793957E-05,
+ * 4.58006124490188752E-05,
+ * 5.24595294959114050E-05,
+ * 5.68396208545815266E-05,
+ * 5.94349820393104052E-05/
+ DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114),
+ * ALFA(115), ALFA(116), ALFA(117), ALFA(118),
+ * ALFA(119), ALFA(120), ALFA(121),
+ * ALFA(122)/6.06478527578421742E-05,
+ * 6.08023907788436497E-05,
+ * 6.01577894539460388E-05,
+ * 5.89199657344698500E-05,
+ * 5.72515823777593053E-05,
+ * 5.52804375585852577E-05,
+ * 5.31063773802880170E-05,
+ * 5.08069302012325706E-05,
+ * 4.84418647620094842E-05,
+ * 4.60568581607475370E-05,
+ * -6.91141397288294174E-04,
+ * -4.29976633058871912E-04/
+ DATA ALFA(123), ALFA(124), ALFA(125), ALFA(126),
+ * ALFA(127), ALFA(128), ALFA(129),
+ * ALFA(130)/1.83067735980039018E-04,
+ * 6.60088147542014144E-04,
+ * 8.75964969951185931E-04,
+ * 8.77335235958235514E-04,
+ * 7.49369585378990637E-04,
+ * 5.63832329756980918E-04,
+ * 3.68059319971443156E-04,
+ * 1.88464535514455599E-04/
+ DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134),
+ * ALFA(135), ALFA(136), ALFA(137), ALFA(138),
+ * ALFA(139), ALFA(140), ALFA(141),
+ * ALFA(142)/3.70663057664904149E-05,
+ * -8.28520220232137023E-05,
+ * -1.72751952869172998E-04,
+ * -2.36314873605872983E-04,
+ * -2.77966150694906658E-04,
+ * -3.02079514155456919E-04,
+ * -3.12594712643820127E-04,
+ * -3.12872558758067163E-04,
+ * -3.05678038466324377E-04,
+ * -2.93226470614557331E-04,
+ * -2.77255655582934777E-04,
+ * -2.59103928467031709E-04/
+ DATA ALFA(143), ALFA(144), ALFA(145), ALFA(146),
+ * ALFA(147), ALFA(148), ALFA(149),
+ * ALFA(150)/-2.39784014396480342E-04,
+ * -2.20048260045422848E-04,
+ * -2.00443911094971498E-04,
+ * -1.81358692210970687E-04,
+ * -1.63057674478657464E-04,
+ * -1.45712672175205844E-04,
+ * -1.29425421983924587E-04,
+ * -1.14245691942445952E-04/
+ DATA ALFA(151), ALFA(152), ALFA(153), ALFA(154),
+ * ALFA(155), ALFA(156), ALFA(157), ALFA(158),
+ * ALFA(159), ALFA(160), ALFA(161),
+ * ALFA(162)/1.92821964248775885E-03,
+ * 1.35592576302022234E-03,
+ * -7.17858090421302995E-04,
+ * -2.58084802575270346E-03,
+ * -3.49271130826168475E-03,
+ * -3.46986299340960628E-03,
+ * -2.82285233351310182E-03,
+ * -1.88103076404891354E-03,
+ * -8.89531718383947600E-04,
+ * 3.87912102631035228E-06,
+ * 7.28688540119691412E-04,
+ * 1.26566373053457758E-03/
+ DATA ALFA(163), ALFA(164), ALFA(165), ALFA(166),
+ * ALFA(167), ALFA(168), ALFA(169),
+ * ALFA(170)/1.62518158372674427E-03,
+ * 1.83203153216373172E-03,
+ * 1.91588388990527909E-03,
+ * 1.90588846755546138E-03,
+ * 1.82798982421825727E-03,
+ * 1.70389506421121530E-03,
+ * 1.55097127171097686E-03,
+ * 1.38261421852276159E-03/
+ DATA ALFA(171), ALFA(172), ALFA(173), ALFA(174),
+ * ALFA(175), ALFA(176), ALFA(177), ALFA(178),
+ * ALFA(179), ALFA(180)/1.20881424230064774E-03,
+ * 1.03676532638344962E-03,
+ * 8.71437918068619115E-04,
+ * 7.16080155297701002E-04,
+ * 5.72637002558129372E-04,
+ * 4.42089819465802277E-04,
+ * 3.24724948503090564E-04,
+ * 2.20342042730246599E-04,
+ * 1.28412898401353882E-04,
+ * 4.82005924552095464E-05/
+ DATA BETA(1), BETA(2), BETA(3), BETA(4), BETA(5),
+ * BETA(6), BETA(7), BETA(8), BETA(9), BETA(10),
+ * BETA(11), BETA(12), BETA(13),
+ * BETA(14)/1.79988721413553309E-02,
+ * 5.59964911064388073E-03,
+ * 2.88501402231132779E-03,
+ * 1.80096606761053941E-03,
+ * 1.24753110589199202E-03,
+ * 9.22878876572938311E-04,
+ * 7.14430421727287357E-04,
+ * 5.71787281789704872E-04,
+ * 4.69431007606481533E-04,
+ * 3.93232835462916638E-04,
+ * 3.34818889318297664E-04,
+ * 2.88952148495751517E-04,
+ * 2.52211615549573284E-04,
+ * 2.22280580798883327E-04/
+ DATA BETA(15), BETA(16), BETA(17), BETA(18),
+ * BETA(19), BETA(20), BETA(21),
+ * BETA(22)/1.97541838033062524E-04,
+ * 1.76836855019718004E-04,
+ * 1.59316899661821081E-04,
+ * 1.44347930197333986E-04,
+ * 1.31448068119965379E-04,
+ * 1.20245444949302884E-04,
+ * 1.10449144504599392E-04,
+ * 1.01828770740567258E-04/
+ DATA BETA(23), BETA(24), BETA(25), BETA(26),
+ * BETA(27), BETA(28), BETA(29), BETA(30),
+ * BETA(31), BETA(32), BETA(33), BETA(34),
+ * BETA(35), BETA(36)/9.41998224204237509E-05,
+ * 8.74130545753834437E-05,
+ * 8.13466262162801467E-05,
+ * 7.59002269646219339E-05,
+ * 7.09906300634153481E-05,
+ * 6.65482874842468183E-05,
+ * 6.25146958969275078E-05,
+ * 5.88403394426251749E-05,
+ * -1.49282953213429172E-03,
+ * -8.78204709546389328E-04,
+ * -5.02916549572034614E-04,
+ * -2.94822138512746025E-04,
+ * -1.75463996970782828E-04,
+ * -1.04008550460816434E-04/
+ DATA BETA(37), BETA(38), BETA(39), BETA(40),
+ * BETA(41), BETA(42), BETA(43),
+ * BETA(44)/-5.96141953046457895E-05,
+ * -3.12038929076098340E-05,
+ * -1.26089735980230047E-05,
+ * -2.42892608575730389E-07,
+ * 8.05996165414273571E-06,
+ * 1.36507009262147391E-05,
+ * 1.73964125472926261E-05,
+ * 1.98672978842133780E-05/
+ DATA BETA(45), BETA(46), BETA(47), BETA(48),
+ * BETA(49), BETA(50), BETA(51), BETA(52),
+ * BETA(53), BETA(54), BETA(55), BETA(56),
+ * BETA(57), BETA(58)/2.14463263790822639E-05,
+ * 2.23954659232456514E-05,
+ * 2.28967783814712629E-05,
+ * 2.30785389811177817E-05,
+ * 2.30321976080909144E-05,
+ * 2.28236073720348722E-05,
+ * 2.25005881105292418E-05,
+ * 2.20981015361991429E-05,
+ * 2.16418427448103905E-05,
+ * 2.11507649256220843E-05,
+ * 2.06388749782170737E-05,
+ * 2.01165241997081666E-05,
+ * 1.95913450141179244E-05,
+ * 1.90689367910436740E-05/
+ DATA BETA(59), BETA(60), BETA(61), BETA(62),
+ * BETA(63), BETA(64), BETA(65),
+ * BETA(66)/1.85533719641636667E-05,
+ * 1.80475722259674218E-05,
+ * 5.52213076721292790E-04,
+ * 4.47932581552384646E-04,
+ * 2.79520653992020589E-04,
+ * 1.52468156198446602E-04,
+ * 6.93271105657043598E-05,
+ * 1.76258683069991397E-05/
+ DATA BETA(67), BETA(68), BETA(69), BETA(70),
+ * BETA(71), BETA(72), BETA(73), BETA(74),
+ * BETA(75), BETA(76), BETA(77), BETA(78),
+ * BETA(79), BETA(80)/-1.35744996343269136E-05,
+ * -3.17972413350427135E-05,
+ * -4.18861861696693365E-05,
+ * -4.69004889379141029E-05,
+ * -4.87665447413787352E-05,
+ * -4.87010031186735069E-05,
+ * -4.74755620890086638E-05,
+ * -4.55813058138628452E-05,
+ * -4.33309644511266036E-05,
+ * -4.09230193157750364E-05,
+ * -3.84822638603221274E-05,
+ * -3.60857167535410501E-05,
+ * -3.37793306123367417E-05,
+ * -3.15888560772109621E-05/
+ DATA BETA(81), BETA(82), BETA(83), BETA(84),
+ * BETA(85), BETA(86), BETA(87),
+ * BETA(88)/-2.95269561750807315E-05,
+ * -2.75978914828335759E-05,
+ * -2.58006174666883713E-05,
+ * -2.41308356761280200E-05,
+ * -2.25823509518346033E-05,
+ * -2.11479656768912971E-05,
+ * -1.98200638885294927E-05,
+ * -1.85909870801065077E-05/
+ DATA BETA(89), BETA(90), BETA(91), BETA(92),
+ * BETA(93), BETA(94), BETA(95), BETA(96),
+ * BETA(97), BETA(98), BETA(99), BETA(100),
+ * BETA(101), BETA(102)/-1.74532699844210224E-05,
+ * -1.63997823854497997E-05,
+ * -4.74617796559959808E-04,
+ * -4.77864567147321487E-04,
+ * -3.20390228067037603E-04,
+ * -1.61105016119962282E-04,
+ * -4.25778101285435204E-05,
+ * 3.44571294294967503E-05,
+ * 7.97092684075674924E-05,
+ * 1.03138236708272200E-04,
+ * 1.12466775262204158E-04,
+ * 1.13103642108481389E-04,
+ * 1.08651634848774268E-04,
+ * 1.01437951597661973E-04/
+ DATA BETA(103), BETA(104), BETA(105), BETA(106),
+ * BETA(107), BETA(108), BETA(109),
+ * BETA(110)/9.29298396593363896E-05,
+ * 8.40293133016089978E-05,
+ * 7.52727991349134062E-05,
+ * 6.69632521975730872E-05,
+ * 5.92564547323194704E-05,
+ * 5.22169308826975567E-05,
+ * 4.58539485165360646E-05,
+ * 4.01445513891486808E-05/
+ DATA BETA(111), BETA(112), BETA(113), BETA(114),
+ * BETA(115), BETA(116), BETA(117), BETA(118),
+ * BETA(119), BETA(120), BETA(121),
+ * BETA(122)/3.50481730031328081E-05,
+ * 3.05157995034346659E-05,
+ * 2.64956119950516039E-05,
+ * 2.29363633690998152E-05,
+ * 1.97893056664021636E-05,
+ * 1.70091984636412623E-05,
+ * 1.45547428261524004E-05,
+ * 1.23886640995878413E-05,
+ * 1.04775876076583236E-05,
+ * 8.79179954978479373E-06,
+ * 7.36465810572578444E-04,
+ * 8.72790805146193976E-04/
+ DATA BETA(123), BETA(124), BETA(125), BETA(126),
+ * BETA(127), BETA(128), BETA(129),
+ * BETA(130)/6.22614862573135066E-04,
+ * 2.85998154194304147E-04,
+ * 3.84737672879366102E-06,
+ * -1.87906003636971558E-04,
+ * -2.97603646594554535E-04,
+ * -3.45998126832656348E-04,
+ * -3.53382470916037712E-04,
+ * -3.35715635775048757E-04/
+ DATA BETA(131), BETA(132), BETA(133), BETA(134),
+ * BETA(135), BETA(136), BETA(137), BETA(138),
+ * BETA(139), BETA(140), BETA(141),
+ * BETA(142)/-3.04321124789039809E-04,
+ * -2.66722723047612821E-04,
+ * -2.27654214122819527E-04,
+ * -1.89922611854562356E-04,
+ * -1.55058918599093870E-04,
+ * -1.23778240761873630E-04,
+ * -9.62926147717644187E-05,
+ * -7.25178327714425337E-05,
+ * -5.22070028895633801E-05,
+ * -3.50347750511900522E-05,
+ * -2.06489761035551757E-05,
+ * -8.70106096849767054E-06/
+ DATA BETA(143), BETA(144), BETA(145), BETA(146),
+ * BETA(147), BETA(148), BETA(149),
+ * BETA(150)/1.13698686675100290E-06,
+ * 9.16426474122778849E-06,
+ * 1.56477785428872620E-05,
+ * 2.08223629482466847E-05,
+ * 2.48923381004595156E-05,
+ * 2.80340509574146325E-05,
+ * 3.03987774629861915E-05,
+ * 3.21156731406700616E-05/
+ DATA BETA(151), BETA(152), BETA(153), BETA(154),
+ * BETA(155), BETA(156), BETA(157), BETA(158),
+ * BETA(159), BETA(160), BETA(161),
+ * BETA(162)/-1.80182191963885708E-03,
+ * -2.43402962938042533E-03,
+ * -1.83422663549856802E-03,
+ * -7.62204596354009765E-04,
+ * 2.39079475256927218E-04,
+ * 9.49266117176881141E-04,
+ * 1.34467449701540359E-03,
+ * 1.48457495259449178E-03,
+ * 1.44732339830617591E-03,
+ * 1.30268261285657186E-03,
+ * 1.10351597375642682E-03,
+ * 8.86047440419791759E-04/
+ DATA BETA(163), BETA(164), BETA(165), BETA(166),
+ * BETA(167), BETA(168), BETA(169),
+ * BETA(170)/6.73073208165665473E-04,
+ * 4.77603872856582378E-04,
+ * 3.05991926358789362E-04,
+ * 1.60315694594721630E-04,
+ * 4.00749555270613286E-05,
+ * -5.66607461635251611E-05,
+ * -1.32506186772982638E-04,
+ * -1.90296187989614057E-04/
+ DATA BETA(171), BETA(172), BETA(173), BETA(174),
+ * BETA(175), BETA(176), BETA(177), BETA(178),
+ * BETA(179), BETA(180), BETA(181),
+ * BETA(182)/-2.32811450376937408E-04,
+ * -2.62628811464668841E-04,
+ * -2.82050469867598672E-04,
+ * -2.93081563192861167E-04,
+ * -2.97435962176316616E-04,
+ * -2.96557334239348078E-04,
+ * -2.91647363312090861E-04,
+ * -2.83696203837734166E-04,
+ * -2.73512317095673346E-04,
+ * -2.61750155806768580E-04,
+ * 6.38585891212050914E-03,
+ * 9.62374215806377941E-03/
+ DATA BETA(183), BETA(184), BETA(185), BETA(186),
+ * BETA(187), BETA(188), BETA(189),
+ * BETA(190)/7.61878061207001043E-03,
+ * 2.83219055545628054E-03,
+ * -2.09841352012720090E-03,
+ * -5.73826764216626498E-03,
+ * -7.70804244495414620E-03,
+ * -8.21011692264844401E-03,
+ * -7.65824520346905413E-03,
+ * -6.47209729391045177E-03/
+ DATA BETA(191), BETA(192), BETA(193), BETA(194),
+ * BETA(195), BETA(196), BETA(197), BETA(198),
+ * BETA(199), BETA(200), BETA(201),
+ * BETA(202)/-4.99132412004966473E-03,
+ * -3.45612289713133280E-03,
+ * -2.01785580014170775E-03,
+ * -7.59430686781961401E-04,
+ * 2.84173631523859138E-04,
+ * 1.10891667586337403E-03,
+ * 1.72901493872728771E-03,
+ * 2.16812590802684701E-03,
+ * 2.45357710494539735E-03,
+ * 2.61281821058334862E-03,
+ * 2.67141039656276912E-03,
+ * 2.65203073395980430E-03/
+ DATA BETA(203), BETA(204), BETA(205), BETA(206),
+ * BETA(207), BETA(208), BETA(209),
+ * BETA(210)/2.57411652877287315E-03,
+ * 2.45389126236094427E-03,
+ * 2.30460058071795494E-03,
+ * 2.13684837686712662E-03,
+ * 1.95896528478870911E-03,
+ * 1.77737008679454412E-03,
+ * 1.59690280765839059E-03,
+ * 1.42111975664438546E-03/
+ DATA GAMA(1), GAMA(2), GAMA(3), GAMA(4), GAMA(5),
+ * GAMA(6), GAMA(7), GAMA(8), GAMA(9), GAMA(10),
+ * GAMA(11), GAMA(12), GAMA(13),
+ * GAMA(14)/6.29960524947436582E-01,
+ * 2.51984209978974633E-01,
+ * 1.54790300415655846E-01,
+ * 1.10713062416159013E-01,
+ * 8.57309395527394825E-02,
+ * 6.97161316958684292E-02,
+ * 5.86085671893713576E-02,
+ * 5.04698873536310685E-02,
+ * 4.42600580689154809E-02,
+ * 3.93720661543509966E-02,
+ * 3.54283195924455368E-02,
+ * 3.21818857502098231E-02,
+ * 2.94646240791157679E-02,
+ * 2.71581677112934479E-02/
+ DATA GAMA(15), GAMA(16), GAMA(17), GAMA(18),
+ * GAMA(19), GAMA(20), GAMA(21),
+ * GAMA(22)/2.51768272973861779E-02,
+ * 2.34570755306078891E-02,
+ * 2.19508390134907203E-02,
+ * 2.06210828235646240E-02,
+ * 1.94388240897880846E-02,
+ * 1.83810633800683158E-02,
+ * 1.74293213231963172E-02,
+ * 1.65685837786612353E-02/
+ DATA GAMA(23), GAMA(24), GAMA(25), GAMA(26),
+ * GAMA(27), GAMA(28), GAMA(29),
+ * GAMA(30)/1.57865285987918445E-02,
+ * 1.50729501494095594E-02,
+ * 1.44193250839954639E-02,
+ * 1.38184805735341786E-02,
+ * 1.32643378994276568E-02,
+ * 1.27517121970498651E-02,
+ * 1.22761545318762767E-02,
+ * 1.18338262398482403E-02/
+ DATA EX1, EX2, HPI, PI, THPI/3.33333333333333333E-01,
+ * 6.66666666666666667E-01,
+ * 1.57079632679489662E+00,
+ * 3.14159265358979324E+00,
+ * 4.71238898038468986E+00/
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ RFNU = 1.0E0/FNU
+ TSTR = REAL(Z)
+ TSTI = AIMAG(Z)
+ TEST = FNU*EXP(-ELIM)
+ IF (ABS(TSTR).LT.TEST) TSTR = 0.0E0
+ IF (ABS(TSTI).LT.TEST) TSTI = 0.0E0
+ IF (TSTR.EQ.0.0E0 .AND. TSTI.EQ.0.0E0) THEN
+ ZETA1 = CMPLX(ELIM+ELIM+FNU,0.0E0)
+ ZETA2 = CMPLX(FNU,0.0E0)
+ PHI = CONE
+ ARG = CONE
+ RETURN
+ END IF
+ ZB = CMPLX(TSTR,TSTI)*CMPLX(RFNU,0.0E0)
+ RFNU2 = RFNU*RFNU
+! ------------------------------------------------------------------
+! COMPUTE IN THE FOURTH QUADRANT
+! ------------------------------------------------------------------
+ FN13 = FNU**EX1
+ FN23 = FN13*FN13
+ RFN13 = CMPLX(1.0E0/FN13,0.0E0)
+ W2 = CONE - ZB*ZB
+ AW2 = ABS(W2)
+ IF (AW2.GT.0.25E0) THEN
+! ---------------------------------------------------------------
+! CABS(W2).GT.0.25E0
+! ---------------------------------------------------------------
+ W = SQRT(W2)
+ WR = REAL(W)
+ WI = AIMAG(W)
+ IF (WR.LT.0.0E0) WR = 0.0E0
+ IF (WI.LT.0.0E0) WI = 0.0E0
+ W = CMPLX(WR,WI)
+ ZA = (CONE+W)/ZB
+ ZC = LOG(ZA)
+ ZCR = REAL(ZC)
+ ZCI = AIMAG(ZC)
+ IF (ZCI.LT.0.0E0) ZCI = 0.0E0
+ IF (ZCI.GT.HPI) ZCI = HPI
+ IF (ZCR.LT.0.0E0) ZCR = 0.0E0
+ ZC = CMPLX(ZCR,ZCI)
+ ZTH = (ZC-W)*CMPLX(1.5E0,0.0E0)
+ CFNU = CMPLX(FNU,0.0E0)
+ ZETA1 = ZC*CFNU
+ ZETA2 = W*CFNU
+ AZTH = ABS(ZTH)
+ ZTHR = REAL(ZTH)
+ ZTHI = AIMAG(ZTH)
+ ANG = THPI
+ IF (ZTHR.LT.0.0E0 .OR. ZTHI.GE.0.0E0) THEN
+ ANG = HPI
+ IF (ZTHR.NE.0.0E0) THEN
+ ANG = ATAN(ZTHI/ZTHR)
+ IF (ZTHR.LT.0.0E0) ANG = ANG + PI
+ END IF
+ END IF
+ PP = AZTH**EX2
+ ANG = ANG*EX2
+ ZETAR = PP*COS(ANG)
+ ZETAI = PP*SIN(ANG)
+ IF (ZETAI.LT.0.0E0) ZETAI = 0.0E0
+ ZETA = CMPLX(ZETAR,ZETAI)
+ ARG = ZETA*CMPLX(FN23,0.0E0)
+ RTZTA = ZTH/ZETA
+ ZA = RTZTA/W
+ PHI = SQRT(ZA+ZA)*RFN13
+ IF (IPMTR.NE.1) THEN
+ TFN = CMPLX(RFNU,0.0E0)/W
+ RZTH = CMPLX(RFNU,0.0E0)/ZTH
+ ZC = RZTH*CMPLX(AR(2),0.0E0)
+ T2 = CONE/W2
+ UP(2) = (T2*CMPLX(C(2),0.0E0)+CMPLX(C(3),0.0E0))*TFN
+ BSUM = UP(2) + ZC
+ ASUM = CZERO
+ IF (RFNU.GE.TOL) THEN
+ PRZTH = RZTH
+ PTFN = TFN
+ UP(1) = CONE
+ PP = 1.0E0
+ BSUMR = REAL(BSUM)
+ BSUMI = AIMAG(BSUM)
+ BTOL = TOL*(ABS(BSUMR)+ABS(BSUMI))
+ KS = 0
+ KP1 = 2
+ L = 3
+ IAS = 0
+ IBS = 0
+ DO 100 LR = 2, 12, 2
+ LRP1 = LR + 1
+! ------------------------------------------------------
+! COMPUTE TWO ADDITIONAL CR, DR, AND UP FOR TWO MORE
+! TERMS IN NEXT SUMA AND SUMB
+! ------------------------------------------------------
+ DO 40 K = LR, LRP1
+ KS = KS + 1
+ KP1 = KP1 + 1
+ L = L + 1
+ ZA = CMPLX(C(L),0.0E0)
+ DO 20 J = 2, KP1
+ L = L + 1
+ ZA = ZA*T2 + CMPLX(C(L),0.0E0)
+ 20 CONTINUE
+ PTFN = PTFN*TFN
+ UP(KP1) = PTFN*ZA
+ CR(KS) = PRZTH*CMPLX(BR(KS+1),0.0E0)
+ PRZTH = PRZTH*RZTH
+ DR(KS) = PRZTH*CMPLX(AR(KS+2),0.0E0)
+ 40 CONTINUE
+ PP = PP*RFNU2
+ IF (IAS.NE.1) THEN
+ SUMA = UP(LRP1)
+ JU = LRP1
+ DO 60 JR = 1, LR
+ JU = JU - 1
+ SUMA = SUMA + CR(JR)*UP(JU)
+ 60 CONTINUE
+ ASUM = ASUM + SUMA
+ ASUMR = REAL(ASUM)
+ ASUMI = AIMAG(ASUM)
+ TEST = ABS(ASUMR) + ABS(ASUMI)
+ IF (PP.LT.TOL .AND. TEST.LT.TOL) IAS = 1
+ END IF
+ IF (IBS.NE.1) THEN
+ SUMB = UP(LR+2) + UP(LRP1)*ZC
+ JU = LRP1
+ DO 80 JR = 1, LR
+ JU = JU - 1
+ SUMB = SUMB + DR(JR)*UP(JU)
+ 80 CONTINUE
+ BSUM = BSUM + SUMB
+ BSUMR = REAL(BSUM)
+ BSUMI = AIMAG(BSUM)
+ TEST = ABS(BSUMR) + ABS(BSUMI)
+ IF (PP.LT.BTOL .AND. TEST.LT.TOL) IBS = 1
+ END IF
+ IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 120
+ 100 CONTINUE
+ END IF
+ 120 ASUM = ASUM + CONE
+ BSUM = -BSUM*RFN13/RTZTA
+ END IF
+ ELSE
+! ---------------------------------------------------------------
+! POWER SERIES FOR CABS(W2).LE.0.25E0
+! ---------------------------------------------------------------
+ K = 1
+ P(1) = CONE
+ SUMA = CMPLX(GAMA(1),0.0E0)
+ AP(1) = 1.0E0
+ IF (AW2.GE.TOL) THEN
+ DO 140 K = 2, 30
+ P(K) = P(K-1)*W2
+ SUMA = SUMA + P(K)*CMPLX(GAMA(K),0.0E0)
+ AP(K) = AP(K-1)*AW2
+ IF (AP(K).LT.TOL) GO TO 160
+ 140 CONTINUE
+ K = 30
+ END IF
+ 160 KMAX = K
+ ZETA = W2*SUMA
+ ARG = ZETA*CMPLX(FN23,0.0E0)
+ ZA = SQRT(SUMA)
+ ZETA2 = SQRT(W2)*CMPLX(FNU,0.0E0)
+ ZETA1 = ZETA2*(CONE+ZETA*ZA*CMPLX(EX2,0.0E0))
+ ZA = ZA + ZA
+ PHI = SQRT(ZA)*RFN13
+ IF (IPMTR.NE.1) THEN
+! ------------------------------------------------------------
+! SUM SERIES FOR ASUM AND BSUM
+! ------------------------------------------------------------
+ SUMB = CZERO
+ DO 180 K = 1, KMAX
+ SUMB = SUMB + P(K)*CMPLX(BETA(K),0.0E0)
+ 180 CONTINUE
+ ASUM = CZERO
+ BSUM = SUMB
+ L1 = 0
+ L2 = 30
+ BTOL = TOL*ABS(BSUM)
+ ATOL = TOL
+ PP = 1.0E0
+ IAS = 0
+ IBS = 0
+ IF (RFNU2.GE.TOL) THEN
+ DO 280 IS = 2, 7
+ ATOL = ATOL/RFNU2
+ PP = PP*RFNU2
+ IF (IAS.NE.1) THEN
+ SUMA = CZERO
+ DO 200 K = 1, KMAX
+ M = L1 + K
+ SUMA = SUMA + P(K)*CMPLX(ALFA(M),0.0E0)
+ IF (AP(K).LT.ATOL) GO TO 220
+ 200 CONTINUE
+ 220 ASUM = ASUM + SUMA*CMPLX(PP,0.0E0)
+ IF (PP.LT.TOL) IAS = 1
+ END IF
+ IF (IBS.NE.1) THEN
+ SUMB = CZERO
+ DO 240 K = 1, KMAX
+ M = L2 + K
+ SUMB = SUMB + P(K)*CMPLX(BETA(M),0.0E0)
+ IF (AP(K).LT.ATOL) GO TO 260
+ 240 CONTINUE
+ 260 BSUM = BSUM + SUMB*CMPLX(PP,0.0E0)
+ IF (PP.LT.BTOL) IBS = 1
+ END IF
+ IF (IAS.EQ.1 .AND. IBS.EQ.1) THEN
+ GO TO 300
+ ELSE
+ L1 = L1 + 30
+ L2 = L2 + 30
+ END IF
+ 280 CONTINUE
+ END IF
+ 300 ASUM = ASUM + CONE
+ PP = RFNU*REAL(RFN13)
+ BSUM = BSUM*CMPLX(PP,0.0E0)
+ END IF
+ END IF
+ RETURN
+ END
+ SUBROUTINE DEVS17(Z,FNU,KODE,IKFLG,N,Y,NUF,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-765 (DEC 1989).
+!
+! Original name: CUOIK
+!
+! DEVS17 COMPUTES THE LEADING TERMS OF THE UNIFORM ASYMPTOTIC
+! EXPANSIONS FOR THE I AND K FUNCTIONS AND COMPARES THEM
+! (IN LOGARITHMIC FORM) TO ALIM AND ELIM FOR OVER AND UNDERFLOW
+! WHERE ALIM.LT.ELIM. IF THE MAGNITUDE, BASED ON THE LEADING
+! EXPONENTIAL, IS LESS THAN ALIM OR GREATER THAN -ALIM, THEN
+! THE RESULT IS ON SCALE. IF NOT, THEN A REFINED TEST USING OTHER
+! MULTIPLIERS (IN LOGARITHMIC FORM) IS MADE BASED ON ELIM. HERE
+! EXP(-ELIM)=SMALLEST MACHINE NUMBER*1.0E+3 AND EXP(-ALIM)=
+! EXP(-ELIM)/TOL
+!
+! IKFLG=1 MEANS THE I SEQUENCE IS TESTED
+! =2 MEANS THE K SEQUENCE IS TESTED
+! NUF = 0 MEANS THE LAST MEMBER OF THE SEQUENCE IS ON SCALE
+! =-1 MEANS AN OVERFLOW WOULD OCCUR
+! IKFLG=1 AND NUF.GT.0 MEANS THE LAST NUF Y VALUES WERE SET TO ZERO
+! THE FIRST N-NUF VALUES MUST BE SET BY ANOTHER ROUTINE
+! IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO
+! IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY
+! ANOTHER ROUTINE
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER IKFLG, KODE, N, NUF
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX ARG, ASUM, BSUM, CZ, CZERO, PHI, SUM, ZB, ZETA1,
+ * ZETA2, ZN, ZR
+ REAL AARG, AIC, APHI, ASCLE, AX, AY, FNN, GNN, GNU,
+ * RCZ, X, YY
+ INTEGER I, IFORM, INIT, NN, NW
+! .. Local Arrays ..
+ COMPLEX CWRK(16)
+! .. External Functions ..
+ REAL X02AME
+ EXTERNAL X02AME
+! .. External Subroutines ..
+ EXTERNAL DEUS17, DEWS17, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, CONJG, COS, EXP, LOG, MAX,
+ * REAL, SIN
+! .. Data statements ..
+ DATA CZERO/(0.0E0,0.0E0)/
+ DATA AIC/1.265512123484645396E+00/
+! .. Executable Statements ..
+!
+ NUF = 0
+ NN = N
+ X = REAL(Z)
+ ZR = Z
+ IF (X.LT.0.0E0) ZR = -Z
+ ZB = ZR
+ YY = AIMAG(ZR)
+ AX = ABS(X)*1.7321E0
+ AY = ABS(YY)
+ IFORM = 1
+ IF (AY.GT.AX) IFORM = 2
+ GNU = MAX(FNU,1.0E0)
+ IF (IKFLG.NE.1) THEN
+ FNN = NN
+ GNN = FNU + FNN - 1.0E0
+ GNU = MAX(GNN,FNN)
+ END IF
+! ------------------------------------------------------------------
+! ONLY THE MAGNITUDE OF ARG AND PHI ARE NEEDED ALONG WITH THE
+! REAL PARTS OF ZETA1, ZETA2 AND ZB. NO ATTEMPT IS MADE TO GET
+! THE SIGN OF THE IMAGINARY PART CORRECT.
+! ------------------------------------------------------------------
+ IF (IFORM.EQ.2) THEN
+ ZN = -ZR*CMPLX(0.0E0,1.0E0)
+ IF (YY.LE.0.0E0) ZN = CONJG(-ZN)
+ CALL DEUS17(ZN,GNU,1,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,BSUM,ELIM)
+ CZ = -ZETA1 + ZETA2
+ AARG = ABS(ARG)
+ ELSE
+ INIT = 0
+ CALL DEWS17(ZR,GNU,IKFLG,1,TOL,INIT,PHI,ZETA1,ZETA2,SUM,CWRK,
+ * ELIM)
+ CZ = -ZETA1 + ZETA2
+ END IF
+ IF (KODE.EQ.2) CZ = CZ - ZB
+ IF (IKFLG.EQ.2) CZ = -CZ
+ APHI = ABS(PHI)
+ RCZ = REAL(CZ)
+! ------------------------------------------------------------------
+! OVERFLOW TEST
+! ------------------------------------------------------------------
+ IF (RCZ.LE.ELIM) THEN
+ IF (RCZ.LT.ALIM) THEN
+! ------------------------------------------------------------
+! UNDERFLOW TEST
+! ------------------------------------------------------------
+ IF (RCZ.GE.(-ELIM)) THEN
+ IF (RCZ.GT.(-ALIM)) THEN
+ GO TO 40
+ ELSE
+ RCZ = RCZ + LOG(APHI)
+ IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*LOG(AARG) - AIC
+ IF (RCZ.GT.(-ELIM)) THEN
+ ASCLE = (1.0E+3*X02AME())/TOL
+ CZ = CZ + LOG(PHI)
+ IF (IFORM.NE.1) CZ = CZ - CMPLX(0.25E0,0.0E0)
+ * *LOG(ARG) - CMPLX(AIC,0.0E0)
+ AX = EXP(RCZ)/TOL
+ AY = AIMAG(CZ)
+ CZ = CMPLX(AX,0.0E0)*CMPLX(COS(AY),SIN(AY))
+ CALL DGVS17(CZ,NW,ASCLE,TOL)
+ IF (NW.NE.1) GO TO 40
+ END IF
+ END IF
+ END IF
+ DO 20 I = 1, NN
+ Y(I) = CZERO
+ 20 CONTINUE
+ NUF = NN
+ RETURN
+ ELSE
+ RCZ = RCZ + LOG(APHI)
+ IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*LOG(AARG) - AIC
+ IF (RCZ.GT.ELIM) GO TO 80
+ END IF
+ 40 IF (IKFLG.NE.2) THEN
+ IF (N.NE.1) THEN
+ 60 CONTINUE
+! ---------------------------------------------------------
+! SET UNDERFLOWS ON I SEQUENCE
+! ---------------------------------------------------------
+ GNU = FNU + NN - 1
+ IF (IFORM.EQ.2) THEN
+ CALL DEUS17(ZN,GNU,1,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,
+ * BSUM,ELIM)
+ CZ = -ZETA1 + ZETA2
+ AARG = ABS(ARG)
+ ELSE
+ INIT = 0
+ CALL DEWS17(ZR,GNU,IKFLG,1,TOL,INIT,PHI,ZETA1,ZETA2,
+ * SUM,CWRK,ELIM)
+ CZ = -ZETA1 + ZETA2
+ END IF
+ IF (KODE.EQ.2) CZ = CZ - ZB
+ APHI = ABS(PHI)
+ RCZ = REAL(CZ)
+ IF (RCZ.GE.(-ELIM)) THEN
+ IF (RCZ.GT.(-ALIM)) THEN
+ RETURN
+ ELSE
+ RCZ = RCZ + LOG(APHI)
+ IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*LOG(AARG) - AIC
+ IF (RCZ.GT.(-ELIM)) THEN
+ ASCLE = (1.0E+3*X02AME())/TOL
+ CZ = CZ + LOG(PHI)
+ IF (IFORM.NE.1) CZ = CZ - CMPLX(0.25E0,0.0E0)
+ * *LOG(ARG) - CMPLX(AIC,
+ * 0.0E0)
+ AX = EXP(RCZ)/TOL
+ AY = AIMAG(CZ)
+ CZ = CMPLX(AX,0.0E0)*CMPLX(COS(AY),SIN(AY))
+ CALL DGVS17(CZ,NW,ASCLE,TOL)
+ IF (NW.NE.1) RETURN
+ END IF
+ END IF
+ END IF
+ Y(NN) = CZERO
+ NN = NN - 1
+ NUF = NUF + 1
+ IF (NN.NE.0) GO TO 60
+ END IF
+ END IF
+ RETURN
+ END IF
+ 80 NUF = -1
+ RETURN
+ END
+ SUBROUTINE DEWS17(ZR,FNU,IKFLG,IPMTR,TOL,INIT,PHI,ZETA1,ZETA2,SUM,
+ * CWRK,ELIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-766 (DEC 1989).
+!
+! Original name: CUNIK
+!
+! DEWS17 COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC
+! EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2
+! RESPECTIVELY BY
+!
+! W(FNU,ZR) = PHI*EXP(ZETA)*SUM
+!
+! WHERE ZETA=-ZETA1 + ZETA2 OR
+! ZETA1 - ZETA2
+!
+! THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE
+! SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG=
+! 1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK
+! ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI,
+! ZETA1,ZETA2.
+!
+! .. Scalar Arguments ..
+ COMPLEX PHI, SUM, ZETA1, ZETA2, ZR
+ REAL ELIM, FNU, TOL
+ INTEGER IKFLG, INIT, IPMTR
+! .. Array Arguments ..
+ COMPLEX CWRK(16)
+! .. Local Scalars ..
+ COMPLEX CFN, CONE, CRFN, CZERO, S, SR, T, T2, ZN
+ REAL AC, RFN, TEST, TSTI, TSTR
+ INTEGER I, J, K, L
+! .. Local Arrays ..
+ COMPLEX CON(2)
+ REAL C(120)
+!bc
+! .. external Functions ..
+ real x02ane
+ external x02ane
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, EXP, LOG, REAL, SQRT
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+ DATA CON(1), CON(2)/(3.98942280401432678E-01,0.0E0),
+ * (1.25331413731550025E+00,0.0E0)/
+ DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8),
+ * C(9), C(10), C(11), C(12), C(13), C(14), C(15),
+ * C(16)/1.00000000000000000E+00,
+ * -2.08333333333333333E-01,
+ * 1.25000000000000000E-01,
+ * 3.34201388888888889E-01,
+ * -4.01041666666666667E-01,
+ * 7.03125000000000000E-02,
+ * -1.02581259645061728E+00,
+ * 1.84646267361111111E+00,
+ * -8.91210937500000000E-01,
+ * 7.32421875000000000E-02,
+ * 4.66958442342624743E+00,
+ * -1.12070026162229938E+01,
+ * 8.78912353515625000E+00,
+ * -2.36408691406250000E+00,
+ * 1.12152099609375000E-01,
+ * -2.82120725582002449E+01/
+ DATA C(17), C(18), C(19), C(20), C(21), C(22), C(23),
+ * C(24)/8.46362176746007346E+01,
+ * -9.18182415432400174E+01,
+ * 4.25349987453884549E+01,
+ * -7.36879435947963170E+00,
+ * 2.27108001708984375E-01,
+ * 2.12570130039217123E+02,
+ * -7.65252468141181642E+02,
+ * 1.05999045252799988E+03/
+ DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31),
+ * C(32), C(33), C(34), C(35), C(36), C(37), C(38),
+ * C(39), C(40)/-6.99579627376132541E+02,
+ * 2.18190511744211590E+02,
+ * -2.64914304869515555E+01,
+ * 5.72501420974731445E-01,
+ * -1.91945766231840700E+03,
+ * 8.06172218173730938E+03,
+ * -1.35865500064341374E+04,
+ * 1.16553933368645332E+04,
+ * -5.30564697861340311E+03,
+ * 1.20090291321635246E+03,
+ * -1.08090919788394656E+02,
+ * 1.72772750258445740E+00,
+ * 2.02042913309661486E+04,
+ * -9.69805983886375135E+04,
+ * 1.92547001232531532E+05,
+ * -2.03400177280415534E+05/
+ DATA C(41), C(42), C(43), C(44), C(45), C(46), C(47),
+ * C(48)/1.22200464983017460E+05,
+ * -4.11926549688975513E+04,
+ * 7.10951430248936372E+03,
+ * -4.93915304773088012E+02,
+ * 6.07404200127348304E+00,
+ * -2.42919187900551333E+05,
+ * 1.31176361466297720E+06,
+ * -2.99801591853810675E+06/
+ DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55),
+ * C(56), C(57), C(58), C(59), C(60), C(61), C(62),
+ * C(63), C(64)/3.76327129765640400E+06,
+ * -2.81356322658653411E+06,
+ * 1.26836527332162478E+06,
+ * -3.31645172484563578E+05,
+ * 4.52187689813627263E+04,
+ * -2.49983048181120962E+03,
+ * 2.43805296995560639E+01,
+ * 3.28446985307203782E+06,
+ * -1.97068191184322269E+07,
+ * 5.09526024926646422E+07,
+ * -7.41051482115326577E+07,
+ * 6.63445122747290267E+07,
+ * -3.75671766607633513E+07,
+ * 1.32887671664218183E+07,
+ * -2.78561812808645469E+06,
+ * 3.08186404612662398E+05/
+ DATA C(65), C(66), C(67), C(68), C(69), C(70), C(71),
+ * C(72)/-1.38860897537170405E+04,
+ * 1.10017140269246738E+02,
+ * -4.93292536645099620E+07,
+ * 3.25573074185765749E+08,
+ * -9.39462359681578403E+08,
+ * 1.55359689957058006E+09,
+ * -1.62108055210833708E+09,
+ * 1.10684281682301447E+09/
+ DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79),
+ * C(80), C(81), C(82), C(83), C(84), C(85), C(86),
+ * C(87), C(88)/-4.95889784275030309E+08,
+ * 1.42062907797533095E+08,
+ * -2.44740627257387285E+07,
+ * 2.24376817792244943E+06,
+ * -8.40054336030240853E+04,
+ * 5.51335896122020586E+02,
+ * 8.14789096118312115E+08,
+ * -5.86648149205184723E+09,
+ * 1.86882075092958249E+10,
+ * -3.46320433881587779E+10,
+ * 4.12801855797539740E+10,
+ * -3.30265997498007231E+10,
+ * 1.79542137311556001E+10,
+ * -6.56329379261928433E+09,
+ * 1.55927986487925751E+09,
+ * -2.25105661889415278E+08/
+ DATA C(89), C(90), C(91), C(92), C(93), C(94), C(95),
+ * C(96)/1.73951075539781645E+07,
+ * -5.49842327572288687E+05,
+ * 3.03809051092238427E+03,
+ * -1.46792612476956167E+10,
+ * 1.14498237732025810E+11,
+ * -3.99096175224466498E+11,
+ * 8.19218669548577329E+11,
+ * -1.09837515608122331E+12/
+ DATA C(97), C(98), C(99), C(100), C(101), C(102),
+ * C(103), C(104), C(105), C(106), C(107), C(108),
+ * C(109), C(110)/1.00815810686538209E+12,
+ * -6.45364869245376503E+11,
+ * 2.87900649906150589E+11,
+ * -8.78670721780232657E+10,
+ * 1.76347306068349694E+10,
+ * -2.16716498322379509E+09,
+ * 1.43157876718888981E+08,
+ * -3.87183344257261262E+06,
+ * 1.82577554742931747E+04,
+ * 2.86464035717679043E+11,
+ * -2.40629790002850396E+12,
+ * 9.10934118523989896E+12,
+ * -2.05168994109344374E+13,
+ * 3.05651255199353206E+13/
+ DATA C(111), C(112), C(113), C(114), C(115), C(116),
+ * C(117), C(118), C(119),
+ * C(120)/-3.16670885847851584E+13,
+ * 2.33483640445818409E+13,
+ * -1.23204913055982872E+13,
+ * 4.61272578084913197E+12,
+ * -1.19655288019618160E+12,
+ * 2.05914503232410016E+11,
+ * -2.18229277575292237E+10,
+ * 1.24700929351271032E+09,
+ * -2.91883881222208134E+07,
+ * 1.18838426256783253E+05/
+! .. Executable Statements ..
+!
+ IF (INIT.EQ.0) THEN
+! ---------------------------------------------------------------
+! INITIALIZE ALL VARIABLES
+! ---------------------------------------------------------------
+ RFN = 1.0E0/FNU
+ CRFN = CMPLX(RFN,0.0E0)
+ TSTR = REAL(ZR)
+ TSTI = AIMAG(ZR)
+ TEST = FNU*EXP(-ELIM)
+ IF (ABS(TSTR).LT.TEST) TSTR = 0.0E0
+ IF (ABS(TSTI).LT.TEST) TSTI = 0.0E0
+!bc IF (TSTR.EQ.0.0E0 .AND. TSTI.EQ.0.0E0) THEN
+ IF (abs(tstr).le.x02ane().and.abs(tsti).le.x02ane()) then
+ ZETA1 = CMPLX(ELIM+ELIM+FNU,0.0E0)
+ ZETA2 = CMPLX(FNU,0.0E0)
+ PHI = CONE
+ RETURN
+ END IF
+ T = CMPLX(TSTR,TSTI)*CRFN
+ S = CONE + T*T
+ SR = SQRT(S)
+ CFN = CMPLX(FNU,0.0E0)
+ ZN = (CONE+SR)/T
+ ZETA1 = CFN*LOG(ZN)
+ ZETA2 = CFN*SR
+ T = CONE/SR
+ SR = T*CRFN
+ CWRK(16) = SQRT(SR)
+ PHI = CWRK(16)*CON(IKFLG)
+ IF (IPMTR.NE.0) THEN
+ RETURN
+ ELSE
+ T2 = CONE/S
+ CWRK(1) = CONE
+ CRFN = CONE
+ AC = 1.0E0
+ L = 1
+ DO 40 K = 2, 15
+ S = CZERO
+ DO 20 J = 1, K
+ L = L + 1
+ S = S*T2 + CMPLX(C(L),0.0E0)
+ 20 CONTINUE
+ CRFN = CRFN*SR
+ CWRK(K) = CRFN*S
+ AC = AC*RFN
+ TSTR = REAL(CWRK(K))
+ TSTI = AIMAG(CWRK(K))
+ TEST = ABS(TSTR) + ABS(TSTI)
+ IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 60
+ 40 CONTINUE
+ K = 15
+ 60 INIT = K
+ END IF
+ END IF
+ IF (IKFLG.EQ.2) THEN
+! ---------------------------------------------------------------
+! COMPUTE SUM FOR THE K FUNCTION
+! ---------------------------------------------------------------
+ S = CZERO
+ T = CONE
+ DO 80 I = 1, INIT
+ S = S + T*CWRK(I)
+ T = -T
+ 80 CONTINUE
+ SUM = S
+ PHI = CWRK(16)*CON(2)
+ ELSE
+! ---------------------------------------------------------------
+! COMPUTE SUM FOR THE I FUNCTION
+! ---------------------------------------------------------------
+ S = CZERO
+ DO 100 I = 1, INIT
+ S = S + CWRK(I)
+ 100 CONTINUE
+ SUM = S
+ PHI = CWRK(16)*CON(1)
+ END IF
+ RETURN
+ END
+ SUBROUTINE DEXS17(Z,FNU,KODE,N,Y,NZ,NLAST,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-767 (DEC 1989).
+!
+! Original name: CUNI1
+!
+! DEXS17 COMPUTES I(FNU,Z) BY MEANS OF THE UNIFORM ASYMPTOTIC
+! EXPANSION FOR I(FNU,Z) IN -PI/3.LE.ARG Z.LE.PI/3.
+!
+! FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
+! EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
+! NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
+! FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
+! Y(I)=CZERO FOR I=NLAST+1,N
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, TOL
+ INTEGER KODE, N, NLAST, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CFN, CONE, CRSC, CSCL, CZERO, PHI, RZ,
+ * S1, S2, SUM, ZETA1, ZETA2
+ REAL APHI, ASCLE, C2I, C2M, C2R, FN, RS1, YY
+ INTEGER I, IFLAG, INIT, K, M, ND, NN, NUF, NW
+! .. Local Arrays ..
+ COMPLEX CSR(3), CSS(3), CWRK(16), CY(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEVS17, DEWS17, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, LOG, MAX, MIN,
+ * REAL, SIN
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ ND = N
+ NLAST = 0
+! ------------------------------------------------------------------
+! COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
+! NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
+! EXP(ALIM)=EXP(ELIM)*TOL
+! ------------------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+! ------------------------------------------------------------------
+! CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
+! ------------------------------------------------------------------
+ FN = MAX(FNU,1.0E0)
+ INIT = 0
+ CALL DEWS17(Z,FN,1,1,TOL,INIT,PHI,ZETA1,ZETA2,SUM,CWRK,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1 + ZETA2
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = -ZETA1 + CFN*(CFN/(Z+ZETA2))
+ END IF
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ 20 CONTINUE
+ NN = MIN(2,ND)
+ DO 40 I = 1, NN
+ FN = FNU + ND - I
+ INIT = 0
+ CALL DEWS17(Z,FN,1,0,TOL,INIT,PHI,ZETA1,ZETA2,SUM,CWRK,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1 + ZETA2
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ YY = AIMAG(Z)
+ S1 = -ZETA1 + CFN*(CFN/(Z+ZETA2)) + CMPLX(0.0E0,YY)
+ END IF
+! ------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 60
+ ELSE
+ IF (I.EQ.1) IFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ------------------------------------------------------
+! REFINE TEST AND SCALE
+! ------------------------------------------------------
+ APHI = ABS(PHI)
+ RS1 = RS1 + LOG(APHI)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 60
+ ELSE
+ IF (I.EQ.1) IFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (I.EQ.1) IFLAG = 3
+ END IF
+ END IF
+ END IF
+! ---------------------------------------------------------
+! SCALE S1 IF CABS(S1).LT.ASCLE
+! ---------------------------------------------------------
+ S2 = PHI*SUM
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(IFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (IFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) GO TO 60
+ END IF
+ M = ND - I + 1
+ CY(I) = S2
+ Y(M) = S2*CSR(IFLAG)
+ END IF
+ 40 CONTINUE
+ GO TO 80
+! ---------------------------------------------------------------
+! SET UNDERFLOW AND UPDATE PARAMETERS
+! ---------------------------------------------------------------
+ 60 CONTINUE
+ IF (RS1.GT.0.0E0) THEN
+ GO TO 160
+ ELSE
+ Y(ND) = CZERO
+ NZ = NZ + 1
+ ND = ND - 1
+ IF (ND.EQ.0) THEN
+ RETURN
+ ELSE
+ CALL DEVS17(Z,FNU,KODE,1,ND,Y,NUF,TOL,ELIM,ALIM)
+ IF (NUF.LT.0) THEN
+ GO TO 160
+ ELSE
+ ND = ND - NUF
+ NZ = NZ + NUF
+ IF (ND.EQ.0) THEN
+ RETURN
+ ELSE
+ FN = FNU + ND - 1
+ IF (FN.GE.FNUL) THEN
+ GO TO 20
+ ELSE
+ GO TO 120
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+ 80 IF (ND.GT.2) THEN
+ RZ = CMPLX(2.0E0,0.0E0)/Z
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ S1 = CY(1)
+ S2 = CY(2)
+ C1 = CSR(IFLAG)
+ ASCLE = BRY(IFLAG)
+ K = ND - 2
+ FN = K
+ DO 100 I = 3, ND
+ C2 = S2
+ S2 = S1 + CMPLX(FNU+FN,0.0E0)*RZ*S2
+ S1 = C2
+ C2 = S2*C1
+ Y(K) = C2
+ K = K - 1
+ FN = FN - 1.0E0
+ IF (IFLAG.LT.3) THEN
+ C2R = REAL(C2)
+ C2I = AIMAG(C2)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*C1
+ S2 = C2
+ S1 = S1*CSS(IFLAG)
+ S2 = S2*CSS(IFLAG)
+ C1 = CSR(IFLAG)
+ END IF
+ END IF
+ 100 CONTINUE
+ END IF
+ RETURN
+ 120 NLAST = ND
+ RETURN
+ ELSE IF (RS1.LE.0.0E0) THEN
+ NZ = N
+ DO 140 I = 1, N
+ Y(I) = CZERO
+ 140 CONTINUE
+ RETURN
+ END IF
+ 160 NZ = -1
+ RETURN
+ END
+ SUBROUTINE DEYS17(Z,FNU,KODE,N,Y,NZ,NUI,NLAST,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-768 (DEC 1989).
+!
+! Original name: CBUNI
+!
+! DEYS17 COMPUTES THE I BESSEL FUNCTION FOR LARGE CABS(Z).GT.
+! FNUL AND FNU+N-1.LT.FNUL. THE ORDER IS INCREASED FROM
+! FNU+N-1 GREATER THAN FNUL BY ADDING NUI AND COMPUTING
+! ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR I(FNU,Z)
+! ON IFORM=1 AND THE EXPANSION FOR J(FNU,Z) ON IFORM=2
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, TOL
+ INTEGER KODE, N, NLAST, NUI, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX CSCL, CSCR, RZ, S1, S2, ST
+ REAL ASCLE, AX, AY, DFNU, FNUI, GNU, STI, STM, STR,
+ * XX, YY
+ INTEGER I, IFLAG, IFORM, K, NL, NW
+! .. Local Arrays ..
+ COMPLEX CY(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME
+ EXTERNAL X02AME
+! .. External Subroutines ..
+ EXTERNAL DETS17, DEXS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, MAX, REAL
+! .. Executable Statements ..
+!
+ NZ = 0
+ XX = REAL(Z)
+ YY = AIMAG(Z)
+ AX = ABS(XX)*1.7321E0
+ AY = ABS(YY)
+ IFORM = 1
+ IF (AY.GT.AX) IFORM = 2
+ IF (NUI.EQ.0) THEN
+ IF (IFORM.EQ.2) THEN
+! ------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
+! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
+! AND HPI=PI/2
+! ------------------------------------------------------------
+ CALL DETS17(Z,FNU,KODE,N,Y,NW,NLAST,FNUL,TOL,ELIM,ALIM)
+ ELSE
+! ------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
+! -PI/3.LE.ARG(Z).LE.PI/3
+! ------------------------------------------------------------
+ CALL DEXS17(Z,FNU,KODE,N,Y,NW,NLAST,FNUL,TOL,ELIM,ALIM)
+ END IF
+ IF (NW.GE.0) THEN
+ NZ = NW
+ RETURN
+ END IF
+ ELSE
+ FNUI = NUI
+ DFNU = FNU + N - 1
+ GNU = DFNU + FNUI
+ IF (IFORM.EQ.2) THEN
+! ------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
+! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
+! AND HPI=PI/2
+! ------------------------------------------------------------
+ CALL DETS17(Z,GNU,KODE,2,CY,NW,NLAST,FNUL,TOL,ELIM,ALIM)
+ ELSE
+! ------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
+! -PI/3.LE.ARG(Z).LE.PI/3
+! ------------------------------------------------------------
+ CALL DEXS17(Z,GNU,KODE,2,CY,NW,NLAST,FNUL,TOL,ELIM,ALIM)
+ END IF
+ IF (NW.GE.0) THEN
+ IF (NW.NE.0) THEN
+ NLAST = N
+ ELSE
+ AY = ABS(CY(1))
+! ---------------------------------------------------------
+! SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER
+! USED
+! ---------------------------------------------------------
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = BRY(2)
+ IFLAG = 2
+ ASCLE = BRY(2)
+ AX = 1.0E0
+ CSCL = CMPLX(AX,0.0E0)
+ IF (AY.LE.BRY(1)) THEN
+ IFLAG = 1
+ ASCLE = BRY(1)
+ AX = 1.0E0/TOL
+ CSCL = CMPLX(AX,0.0E0)
+ ELSE IF (AY.GE.BRY(2)) THEN
+ IFLAG = 3
+ ASCLE = BRY(3)
+ AX = TOL
+ CSCL = CMPLX(AX,0.0E0)
+ END IF
+ AY = 1.0E0/AX
+ CSCR = CMPLX(AY,0.0E0)
+ S1 = CY(2)*CSCL
+ S2 = CY(1)*CSCL
+ RZ = CMPLX(2.0E0,0.0E0)/Z
+ DO 20 I = 1, NUI
+ ST = S2
+ S2 = CMPLX(DFNU+FNUI,0.0E0)*RZ*S2 + S1
+ S1 = ST
+ FNUI = FNUI - 1.0E0
+ IF (IFLAG.LT.3) THEN
+ ST = S2*CSCR
+ STR = REAL(ST)
+ STI = AIMAG(ST)
+ STR = ABS(STR)
+ STI = ABS(STI)
+ STM = MAX(STR,STI)
+ IF (STM.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*CSCR
+ S2 = ST
+ AX = AX*TOL
+ AY = 1.0E0/AX
+ CSCL = CMPLX(AX,0.0E0)
+ CSCR = CMPLX(AY,0.0E0)
+ S1 = S1*CSCL
+ S2 = S2*CSCL
+ END IF
+ END IF
+ 20 CONTINUE
+ Y(N) = S2*CSCR
+ IF (N.NE.1) THEN
+ NL = N - 1
+ FNUI = NL
+ K = NL
+ DO 40 I = 1, NL
+ ST = S2
+ S2 = CMPLX(FNU+FNUI,0.0E0)*RZ*S2 + S1
+ S1 = ST
+ ST = S2*CSCR
+ Y(K) = ST
+ FNUI = FNUI - 1.0E0
+ K = K - 1
+ IF (IFLAG.LT.3) THEN
+ STR = REAL(ST)
+ STI = AIMAG(ST)
+ STR = ABS(STR)
+ STI = ABS(STI)
+ STM = MAX(STR,STI)
+ IF (STM.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*CSCR
+ S2 = ST
+ AX = AX*TOL
+ AY = 1.0E0/AX
+ CSCL = CMPLX(AX,0.0E0)
+ CSCR = CMPLX(AY,0.0E0)
+ S1 = S1*CSCL
+ S2 = S2*CSCL
+ END IF
+ END IF
+ 40 CONTINUE
+ END IF
+ END IF
+ RETURN
+ END IF
+ END IF
+ NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ RETURN
+ END
+ SUBROUTINE DEZS17(Z,FNU,KODE,N,CY,NZ,RL,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-769 (DEC 1989).
+!
+! Original name: CBINU
+!
+! DEZS17 COMPUTES THE I FUNCTION IN THE RIGHT HALF Z PLANE
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, RL, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX CY(N)
+! .. Local Scalars ..
+ COMPLEX CZERO
+ REAL AZ, DFNU
+ INTEGER I, INW, NLAST, NN, NUI, NW
+! .. Local Arrays ..
+ COMPLEX CW(2)
+! .. External Subroutines ..
+ EXTERNAL DESS17, DEVS17, DEYS17, DGRS17, DGTS17, DGYS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, INT, MAX
+! .. Data statements ..
+ DATA CZERO/(0.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ AZ = ABS(Z)
+ NN = N
+ DFNU = FNU + N - 1
+ IF (AZ.GT.2.0E0) THEN
+ IF (AZ*AZ*0.25E0.GT.DFNU+1.0E0) GO TO 20
+ END IF
+! ------------------------------------------------------------------
+! POWER SERIES
+! ------------------------------------------------------------------
+ CALL DGRS17(Z,FNU,KODE,NN,CY,NW,TOL,ELIM,ALIM)
+ INW = ABS(NW)
+ NZ = NZ + INW
+ NN = NN - INW
+ IF (NN.EQ.0) THEN
+ RETURN
+ ELSE IF (NW.GE.0) THEN
+ RETURN
+ ELSE
+ DFNU = FNU + NN - 1
+ END IF
+ 20 IF (AZ.GE.RL) THEN
+ IF (DFNU.GT.1.0E0) THEN
+ IF (AZ+AZ.LT.DFNU*DFNU) GO TO 40
+ END IF
+! ---------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR LARGE Z
+! ---------------------------------------------------------------
+ CALL DGYS17(Z,FNU,KODE,NN,CY,NW,RL,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 120
+ ELSE
+ RETURN
+ END IF
+ ELSE IF (DFNU.LE.1.0E0) THEN
+ GO TO 100
+ END IF
+! ------------------------------------------------------------------
+! OVERFLOW AND UNDERFLOW TEST ON I SEQUENCE FOR MILLER ALGORITHM
+! ------------------------------------------------------------------
+ 40 CALL DEVS17(Z,FNU,KODE,1,NN,CY,NW,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 120
+ ELSE
+ NZ = NZ + NW
+ NN = NN - NW
+ IF (NN.EQ.0) THEN
+ RETURN
+ ELSE
+ DFNU = FNU + NN - 1
+ IF (DFNU.LE.FNUL) THEN
+ IF (AZ.LE.FNUL) GO TO 60
+ END IF
+! ------------------------------------------------------------
+! INCREMENT FNU+NN-1 UP TO FNUL, COMPUTE AND RECUR BACKWARD
+! ------------------------------------------------------------
+ NUI = INT(FNUL-DFNU) + 1
+ NUI = MAX(NUI,0)
+ CALL DEYS17(Z,FNU,KODE,NN,CY,NW,NUI,NLAST,FNUL,TOL,ELIM,
+ * ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 120
+ ELSE
+ NZ = NZ + NW
+ IF (NLAST.EQ.0) THEN
+ RETURN
+ ELSE
+ NN = NLAST
+ END IF
+ END IF
+ 60 IF (AZ.GT.RL) THEN
+! ---------------------------------------------------------
+! MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN
+! ---------------------------------------------------------
+! ---------------------------------------------------------
+! OVERFLOW TEST ON K FUNCTIONS USED IN WRONSKIAN
+! ---------------------------------------------------------
+ CALL DEVS17(Z,FNU,KODE,2,2,CW,NW,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ NZ = NN
+ DO 80 I = 1, NN
+ CY(I) = CZERO
+ 80 CONTINUE
+ RETURN
+ ELSE IF (NW.GT.0) THEN
+ GO TO 120
+ ELSE
+ CALL DESS17(Z,FNU,KODE,NN,CY,NW,CW,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 120
+ ELSE
+ RETURN
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------------
+! MILLER ALGORITHM NORMALIZED BY THE SERIES
+! ------------------------------------------------------------------
+ 100 CALL DGTS17(Z,FNU,KODE,NN,CY,NW,TOL)
+ IF (NW.GE.0) RETURN
+ 120 NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ IF (NW.EQ.(-3)) NZ = -3
+ RETURN
+ END
+ SUBROUTINE DGRS17(Z,FNU,KODE,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-771 (DEC 1989).
+!
+! Original name: CSERI
+!
+! DGRS17 COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY
+! MEANS OF THE POWER SERIES FOR LARGE CABS(Z) IN THE
+! REGION CABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN.
+! NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO
+! DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE
+! CONDITION CABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE
+! COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ).
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX AK1, CK, COEF, CONE, CRSC, CZ, CZERO, HZ, RZ,
+ * S1, S2
+ REAL AA, ACZ, AK, ARM, ASCLE, ATOL, AZ, DFNU, FNUP,
+ * RAK1, RS, RTR1, S, SS, X
+ INTEGER I, IB, IDUM, IFLAG, IL, K, L, M, NN, NW
+! .. Local Arrays ..
+ COMPLEX W(2)
+! .. External Functions ..
+ REAL S14ABE, X02AME
+ EXTERNAL S14ABE, X02AME
+! .. External Subroutines ..
+ EXTERNAL DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, LOG, MIN, REAL,
+ * SIN, SQRT
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ AZ = ABS(Z)
+ IF (AZ.NE.0.0E0) THEN
+ X = REAL(Z)
+ ARM = 1.0E+3*X02AME()
+ RTR1 = SQRT(ARM)
+ CRSC = CMPLX(1.0E0,0.0E0)
+ IFLAG = 0
+ IF (AZ.LT.ARM) THEN
+ NZ = N
+ IF (FNU.EQ.0.0E0) NZ = NZ - 1
+ ELSE
+ HZ = Z*CMPLX(0.5E0,0.0E0)
+ CZ = CZERO
+ IF (AZ.GT.RTR1) CZ = HZ*HZ
+ ACZ = ABS(CZ)
+ NN = N
+ CK = LOG(HZ)
+ 20 CONTINUE
+ DFNU = FNU + NN - 1
+ FNUP = DFNU + 1.0E0
+! ------------------------------------------------------------
+! UNDERFLOW TEST
+! ------------------------------------------------------------
+ AK1 = CK*CMPLX(DFNU,0.0E0)
+ IDUM = 0
+! S14ABE assumed not to fail, therefore IDUM set to zero.
+ AK = S14ABE(FNUP,IDUM)
+ AK1 = AK1 - CMPLX(AK,0.0E0)
+ IF (KODE.EQ.2) AK1 = AK1 - CMPLX(X,0.0E0)
+ RAK1 = REAL(AK1)
+ IF (RAK1.GT.(-ELIM)) THEN
+ IF (RAK1.LE.(-ALIM)) THEN
+ IFLAG = 1
+ SS = 1.0E0/TOL
+ CRSC = CMPLX(TOL,0.0E0)
+ ASCLE = ARM*SS
+ END IF
+ AK = AIMAG(AK1)
+ AA = EXP(RAK1)
+ IF (IFLAG.EQ.1) AA = AA*SS
+ COEF = CMPLX(AA,0.0E0)*CMPLX(COS(AK),SIN(AK))
+ ATOL = TOL*ACZ/FNUP
+ IL = MIN(2,NN)
+ DO 60 I = 1, IL
+ DFNU = FNU + NN - I
+ FNUP = DFNU + 1.0E0
+ S1 = CONE
+ IF (ACZ.GE.TOL*FNUP) THEN
+ AK1 = CONE
+ AK = FNUP + 2.0E0
+ S = FNUP
+ AA = 2.0E0
+ 40 CONTINUE
+ RS = 1.0E0/S
+ AK1 = AK1*CZ*CMPLX(RS,0.0E0)
+ S1 = S1 + AK1
+ S = S + AK
+ AK = AK + 2.0E0
+ AA = AA*ACZ*RS
+ IF (AA.GT.ATOL) GO TO 40
+ END IF
+ M = NN - I + 1
+ S2 = S1*COEF
+ W(I) = S2
+ IF (IFLAG.NE.0) THEN
+ CALL DGVS17(S2,NW,ASCLE,TOL)
+ IF (NW.NE.0) GO TO 80
+ END IF
+ Y(M) = S2*CRSC
+ IF (I.NE.IL) COEF = COEF*CMPLX(DFNU,0.0E0)/HZ
+ 60 CONTINUE
+ GO TO 100
+ END IF
+ 80 NZ = NZ + 1
+ Y(NN) = CZERO
+ IF (ACZ.GT.DFNU) THEN
+ GO TO 180
+ ELSE
+ NN = NN - 1
+ IF (NN.EQ.0) THEN
+ RETURN
+ ELSE
+ GO TO 20
+ END IF
+ END IF
+ 100 IF (NN.GT.2) THEN
+ K = NN - 2
+ AK = K
+ RZ = (CONE+CONE)/Z
+ IF (IFLAG.EQ.1) THEN
+! ------------------------------------------------------
+! RECUR BACKWARD WITH SCALED VALUES
+! ------------------------------------------------------
+! ------------------------------------------------------
+! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE
+! THE UNDERFLOW LIMIT = ASCLE = X02AME()*CSCL*1.0E+3
+! ------------------------------------------------------
+ S1 = W(1)
+ S2 = W(2)
+ DO 120 L = 3, NN
+ CK = S2
+ S2 = S1 + CMPLX(AK+FNU,0.0E0)*RZ*S2
+ S1 = CK
+ CK = S2*CRSC
+ Y(K) = CK
+ AK = AK - 1.0E0
+ K = K - 1
+ IF (ABS(CK).GT.ASCLE) GO TO 140
+ 120 CONTINUE
+ RETURN
+ 140 IB = L + 1
+ IF (IB.GT.NN) RETURN
+ ELSE
+ IB = 3
+ END IF
+ DO 160 I = IB, NN
+ Y(K) = CMPLX(AK+FNU,0.0E0)*RZ*Y(K+1) + Y(K+2)
+ AK = AK - 1.0E0
+ K = K - 1
+ 160 CONTINUE
+ END IF
+ RETURN
+! ------------------------------------------------------------
+! RETURN WITH NZ.LT.0 IF CABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE
+! THE CALCULATION IN DEZS17 WITH N=N-IABS(NZ)
+! ------------------------------------------------------------
+ 180 CONTINUE
+ NZ = -NZ
+ RETURN
+ END IF
+ END IF
+ Y(1) = CZERO
+ IF (FNU.EQ.0.0E0) Y(1) = CONE
+ IF (N.NE.1) THEN
+ DO 200 I = 2, N
+ Y(I) = CZERO
+ 200 CONTINUE
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGSS17(ZR,S1,S2,NZ,ASCLE,ALIM,IUF)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-772 (DEC 1989).
+!
+! Original name: CS1S2
+!
+! DGSS17 TESTS FOR A POSSIBLE UNDERFLOW RESULTING FROM THE
+! ADDITION OF THE I AND K FUNCTIONS IN THE ANALYTIC CON-
+! TINUATION FORMULA WHERE S1=K FUNCTION AND S2=I FUNCTION.
+! ON KODE=1 THE I AND K FUNCTIONS ARE DIFFERENT ORDERS OF
+! MAGNITUDE, BUT FOR KODE=2 THEY CAN BE OF THE SAME ORDER
+! OF MAGNITUDE AND THE MAXIMUM MUST BE AT LEAST ONE
+! PRECISION ABOVE THE UNDERFLOW LIMIT.
+!
+! .. Scalar Arguments ..
+ COMPLEX S1, S2, ZR
+ REAL ALIM, ASCLE
+ INTEGER IUF, NZ
+! .. Local Scalars ..
+ COMPLEX C1, CZERO, S1D
+ REAL AA, ALN, AS1, AS2, XX
+ INTEGER IF1
+! .. External Functions ..
+ COMPLEX S01EAE
+ EXTERNAL S01EAE
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, LOG, MAX, REAL
+! .. Data statements ..
+ DATA CZERO/(0.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ AS1 = ABS(S1)
+ AS2 = ABS(S2)
+ AA = REAL(S1)
+ ALN = AIMAG(S1)
+ IF (AA.NE.0.0E0 .OR. ALN.NE.0.0E0) THEN
+ IF (AS1.NE.0.0E0) THEN
+ XX = REAL(ZR)
+ ALN = -XX - XX + LOG(AS1)
+ S1D = S1
+ S1 = CZERO
+ AS1 = 0.0E0
+ IF (ALN.GE.(-ALIM)) THEN
+ C1 = LOG(S1D) - ZR - ZR
+! S1 = EXP(C1)
+ IF1 = 1
+ S1 = S01EAE(C1,IF1)
+ AS1 = ABS(S1)
+ IUF = IUF + 1
+ END IF
+ END IF
+ END IF
+ AA = MAX(AS1,AS2)
+ IF (AA.LE.ASCLE) THEN
+ S1 = CZERO
+ S2 = CZERO
+ NZ = 1
+ IUF = 0
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGTS17(Z,FNU,KODE,N,Y,NZ,TOL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-773 (DEC 1989).
+! Mark 17 REVISED. IER-1703 (JUN 1995).
+!
+! Original name: CMLRI
+!
+! DGTS17 COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY THE
+! MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES.
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL FNU, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX CK, CNORM, CONE, CTWO, CZERO, P1, P2, PT, RZ,
+ * SUM
+ REAL ACK, AK, AP, AT, AZ, BK, FKAP, FKK, FLAM, FNF,
+ * RHO, RHO2, SCLE, TFNF, TST, X
+ INTEGER I, IAZ, IDUM, IFL, IFNU, INU, ITIME, K, KK, KM,
+ * M
+! .. External Functions ..
+ COMPLEX S01EAE
+ REAL S14ABE, X02ANE
+ EXTERNAL S14ABE, S01EAE, X02ANE
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, CMPLX, CONJG, EXP, INT, LOG, MAX, MIN,
+ * REAL, SQRT
+! .. Data statements ..
+ DATA CZERO, CONE, CTWO/(0.0E0,0.0E0), (1.0E0,0.0E0),
+ * (2.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ SCLE = (1.0E+3*X02ANE())/TOL
+ NZ = 0
+ AZ = ABS(Z)
+ X = REAL(Z)
+ IAZ = INT(AZ)
+ IFNU = INT(FNU)
+ INU = IFNU + N - 1
+ AT = IAZ + 1.0E0
+ CK = CMPLX(AT,0.0E0)/Z
+ RZ = CTWO/Z
+ P1 = CZERO
+ P2 = CONE
+ ACK = (AT+1.0E0)/AZ
+ RHO = ACK + SQRT(ACK*ACK-1.0E0)
+ RHO2 = RHO*RHO
+ TST = (RHO2+RHO2)/((RHO2-1.0E0)*(RHO-1.0E0))
+ TST = TST/TOL
+! ------------------------------------------------------------------
+! COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES
+! ------------------------------------------------------------------
+ AK = AT
+ DO 20 I = 1, 80
+ PT = P2
+ P2 = P1 - CK*P2
+ P1 = PT
+ CK = CK + RZ
+ AP = ABS(P2)
+ IF (AP.GT.TST*AK*AK) THEN
+ GO TO 40
+ ELSE
+ AK = AK + 1.0E0
+ END IF
+ 20 CONTINUE
+ GO TO 180
+ 40 I = I + 1
+ K = 0
+ IF (INU.GE.IAZ) THEN
+! ---------------------------------------------------------------
+! COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS
+! ---------------------------------------------------------------
+ P1 = CZERO
+ P2 = CONE
+ AT = INU + 1.0E0
+ CK = CMPLX(AT,0.0E0)/Z
+ ACK = AT/AZ
+ TST = SQRT(ACK/TOL)
+ ITIME = 1
+ DO 60 K = 1, 80
+ PT = P2
+ P2 = P1 - CK*P2
+ P1 = PT
+ CK = CK + RZ
+ AP = ABS(P2)
+ IF (AP.GE.TST) THEN
+ IF (ITIME.EQ.2) THEN
+ GO TO 80
+ ELSE
+ ACK = ABS(CK)
+ FLAM = ACK + SQRT(ACK*ACK-1.0E0)
+ FKAP = AP/ABS(P1)
+ RHO = MIN(FLAM,FKAP)
+ TST = TST*SQRT(RHO/(RHO*RHO-1.0E0))
+ ITIME = 2
+ END IF
+ END IF
+ 60 CONTINUE
+ GO TO 180
+ END IF
+! ------------------------------------------------------------------
+! BACKWARD RECURRENCE AND SUM NORMALIZING RELATION
+! ------------------------------------------------------------------
+ 80 K = K + 1
+ KK = MAX(I+IAZ,K+INU)
+ FKK = KK
+ P1 = CZERO
+! ------------------------------------------------------------------
+! SCALE P2 AND SUM BY SCLE
+! ------------------------------------------------------------------
+ P2 = CMPLX(SCLE,0.0E0)
+ FNF = FNU - IFNU
+ TFNF = FNF + FNF
+ IDUM = 0
+! S14ABE assumed not to fail, therefore IDUM set to zero.
+ BK = S14ABE(FKK+TFNF+1.0E0,IDUM) - S14ABE(FKK+1.0E0,IDUM) -
+ * S14ABE(TFNF+1.0E0,IDUM)
+ BK = EXP(BK)
+ SUM = CZERO
+ KM = KK - INU
+ DO 100 I = 1, KM
+ PT = P2
+ P2 = P1 + CMPLX(FKK+FNF,0.0E0)*RZ*P2
+ P1 = PT
+ AK = 1.0E0 - TFNF/(FKK+TFNF)
+ ACK = BK*AK
+ SUM = SUM + CMPLX(ACK+BK,0.0E0)*P1
+ BK = ACK
+ FKK = FKK - 1.0E0
+ 100 CONTINUE
+ Y(N) = P2
+ IF (N.NE.1) THEN
+ DO 120 I = 2, N
+ PT = P2
+ P2 = P1 + CMPLX(FKK+FNF,0.0E0)*RZ*P2
+ P1 = PT
+ AK = 1.0E0 - TFNF/(FKK+TFNF)
+ ACK = BK*AK
+ SUM = SUM + CMPLX(ACK+BK,0.0E0)*P1
+ BK = ACK
+ FKK = FKK - 1.0E0
+ M = N - I + 1
+ Y(M) = P2
+ 120 CONTINUE
+ END IF
+ IF (IFNU.GT.0) THEN
+ DO 140 I = 1, IFNU
+ PT = P2
+ P2 = P1 + CMPLX(FKK+FNF,0.0E0)*RZ*P2
+ P1 = PT
+ AK = 1.0E0 - TFNF/(FKK+TFNF)
+ ACK = BK*AK
+ SUM = SUM + CMPLX(ACK+BK,0.0E0)*P1
+ BK = ACK
+ FKK = FKK - 1.0E0
+ 140 CONTINUE
+ END IF
+ PT = Z
+ IF (KODE.EQ.2) PT = PT - CMPLX(X,0.0E0)
+ P1 = -CMPLX(FNF,0.0E0)*LOG(RZ) + PT
+ IDUM = 0
+! S14ABE assumed not to fail, therefore IDUM set to zero.
+ AP = S14ABE(1.0E0+FNF,IDUM)
+ PT = P1 - CMPLX(AP,0.0E0)
+! ------------------------------------------------------------------
+! THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW
+! IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES
+! ------------------------------------------------------------------
+ P2 = P2 + SUM
+ AP = ABS(P2)
+ P1 = CMPLX(1.0E0/AP,0.0E0)
+! CK = EXP(PT)*P1
+ IFL = 1
+ CK = S01EAE(PT,IFL)*P1
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 200
+ PT = CONJG(P2)*P1
+ CNORM = CK*PT
+ DO 160 I = 1, N
+ Y(I) = Y(I)*CNORM
+ 160 CONTINUE
+ RETURN
+ 180 NZ = -2
+ RETURN
+ 200 NZ = -3
+ RETURN
+ END
+ SUBROUTINE DGUS17(Z,CSH,CCH)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-774 (DEC 1989).
+!
+! Original name: CSHCH
+!
+! DGUS17 COMPUTES THE COMPLEX HYPERBOLIC FUNCTIONS CSH=SINH(X+I*Y)
+! AND CCH=COSH(X+I*Y), WHERE I**2=-1.
+!
+! .. Scalar Arguments ..
+ COMPLEX CCH, CSH, Z
+! .. Local Scalars ..
+ REAL CCHI, CCHR, CH, CN, CSHI, CSHR, SH, SN, X, Y
+! .. Intrinsic Functions ..
+ INTRINSIC AIMAG, CMPLX, COS, COSH, REAL, SIN, SINH
+! .. Executable Statements ..
+!
+ X = REAL(Z)
+ Y = AIMAG(Z)
+ SH = SINH(X)
+ CH = COSH(X)
+ SN = SIN(Y)
+ CN = COS(Y)
+ CSHR = SH*CN
+ CSHI = CH*SN
+ CSH = CMPLX(CSHR,CSHI)
+ CCHR = CH*CN
+ CCHI = SH*SN
+ CCH = CMPLX(CCHR,CCHI)
+ RETURN
+ END
+ SUBROUTINE DGVS17(Y,NZ,ASCLE,TOL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-775 (DEC 1989).
+!
+! Original name: CUCHK
+!
+! Y ENTERS AS A SCALED QUANTITY WHOSE MAGNITUDE IS GREATER THAN
+! EXP(-ALIM)=ASCLE=1.0E+3*X02AME()/TOL. THE TEST IS MADE TO SEE
+! IF THE MAGNITUDE OF THE REAL OR IMAGINARY PART WOULD UNDERFLOW
+! WHEN Y IS SCALED (BY TOL) TO ITS PROPER VALUE. Y IS ACCEPTED
+! IF THE UNDERFLOW IS AT LEAST ONE PRECISION BELOW THE MAGNITUDE
+! OF THE LARGEST COMPONENT; OTHERWISE THE PHASE ANGLE DOES NOT HAVE
+! ABSOLUTE ACCURACY AND AN UNDERFLOW IS ASSUMED.
+!
+! .. Scalar Arguments ..
+ COMPLEX Y
+ REAL ASCLE, TOL
+ INTEGER NZ
+! .. Local Scalars ..
+ REAL SS, ST, YI, YR
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, MAX, MIN, REAL
+! .. Executable Statements ..
+!
+ NZ = 0
+ YR = REAL(Y)
+ YI = AIMAG(Y)
+ YR = ABS(YR)
+ YI = ABS(YI)
+ ST = MIN(YR,YI)
+ IF (ST.LE.ASCLE) THEN
+ SS = MAX(YR,YI)
+ ST = ST/TOL
+ IF (SS.LT.ST) NZ = 1
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGWS17(ZR,FNU,N,Y,NZ,RZ,ASCLE,TOL,ELIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-776 (DEC 1989).
+!
+! Original name: CKSCL
+!
+! SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE
+! ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN
+! RETURN WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL.
+!
+! .. Scalar Arguments ..
+ COMPLEX RZ, ZR
+ REAL ASCLE, ELIM, FNU, TOL
+ INTEGER N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX CELM, CK, CS, CZERO, S1, S2, ZD
+ REAL AA, ACS, ALAS, AS, CSI, CSR, ELM, FN, HELIM, XX,
+ * ZRI
+ INTEGER I, IC, K, KK, NN, NW
+! .. Local Arrays ..
+ COMPLEX CY(2)
+! .. External Subroutines ..
+ EXTERNAL DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, LOG, MIN, REAL, SIN
+! .. Data statements ..
+ DATA CZERO/(0.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ IC = 0
+ XX = REAL(ZR)
+ NN = MIN(2,N)
+ DO 20 I = 1, NN
+ S1 = Y(I)
+ CY(I) = S1
+ AS = ABS(S1)
+ ACS = -XX + LOG(AS)
+ NZ = NZ + 1
+ Y(I) = CZERO
+ IF (ACS.GE.(-ELIM)) THEN
+ CS = -ZR + LOG(S1)
+ CSR = REAL(CS)
+ CSI = AIMAG(CS)
+ AA = EXP(CSR)/TOL
+ CS = CMPLX(AA,0.0E0)*CMPLX(COS(CSI),SIN(CSI))
+ CALL DGVS17(CS,NW,ASCLE,TOL)
+ IF (NW.EQ.0) THEN
+ Y(I) = CS
+ NZ = NZ - 1
+ IC = I
+ END IF
+ END IF
+ 20 CONTINUE
+ IF (N.NE.1) THEN
+ IF (IC.LE.1) THEN
+ Y(1) = CZERO
+ NZ = 2
+ END IF
+ IF (N.NE.2) THEN
+ IF (NZ.NE.0) THEN
+ FN = FNU + 1.0E0
+ CK = CMPLX(FN,0.0E0)*RZ
+ S1 = CY(1)
+ S2 = CY(2)
+ HELIM = 0.5E0*ELIM
+ ELM = EXP(-ELIM)
+ CELM = CMPLX(ELM,0.0E0)
+ ZRI = AIMAG(ZR)
+ ZD = ZR
+!
+! FIND TWO CONSECUTIVE Y VALUES ON SCALE. SCALE
+! RECURRENCE IF S2 GETS LARGER THAN EXP(ELIM/2)
+!
+ DO 40 I = 3, N
+ KK = I
+ CS = S2
+ S2 = CK*S2 + S1
+ S1 = CS
+ CK = CK + RZ
+ AS = ABS(S2)
+ ALAS = LOG(AS)
+ ACS = -XX + ALAS
+ NZ = NZ + 1
+ Y(I) = CZERO
+ IF (ACS.GE.(-ELIM)) THEN
+ CS = -ZD + LOG(S2)
+ CSR = REAL(CS)
+ CSI = AIMAG(CS)
+ AA = EXP(CSR)/TOL
+ CS = CMPLX(AA,0.0E0)*CMPLX(COS(CSI),SIN(CSI))
+ CALL DGVS17(CS,NW,ASCLE,TOL)
+ IF (NW.EQ.0) THEN
+ Y(I) = CS
+ NZ = NZ - 1
+ IF (IC.EQ.(KK-1)) THEN
+ GO TO 60
+ ELSE
+ IC = KK
+ GO TO 40
+ END IF
+ END IF
+ END IF
+ IF (ALAS.GE.HELIM) THEN
+ XX = XX - ELIM
+ S1 = S1*CELM
+ S2 = S2*CELM
+ ZD = CMPLX(XX,ZRI)
+ END IF
+ 40 CONTINUE
+ NZ = N
+ IF (IC.EQ.N) NZ = N - 1
+ GO TO 80
+ 60 NZ = KK - 2
+ 80 DO 100 K = 1, NZ
+ Y(K) = CZERO
+ 100 CONTINUE
+ END IF
+ END IF
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGXS17(Z,FNU,KODE,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-777 (DEC 1989).
+!
+! Original name: CBKNU
+!
+! DGXS17 COMPUTES THE K BESSEL FUNCTION IN THE RIGHT HALF Z PLANE
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX CCH, CELM, CK, COEF, CONE, CRSC, CS, CSCL, CSH,
+ * CTWO, CZ, CZERO, F, FMU, P, P1, P2, PT, Q, RZ,
+ * S1, S2, SMU, ST, ZD
+ REAL A1, A2, AA, AK, ALAS, AS, ASCLE, BB, BK, CAZ,
+ * DNU, DNU2, ELM, ETEST, FC, FHS, FK, FKS, FPI,
+ * G1, G2, HELIM, HPI, P2I, P2M, P2R, PI, R1, RK,
+ * RTHPI, S, SPI, T1, T2, TM, TTH, XD, XX, YD, YY
+ INTEGER I, IC, IDUM, IFL, IFLAG, INU, INUB, J, K, KFLAG,
+ * KK, KMAX, KODED, NW
+! .. Local Arrays ..
+ COMPLEX CSR(3), CSS(3), CY(2)
+ REAL BRY(3), CC(8)
+! .. External Functions ..
+ COMPLEX S01EAE
+ REAL S14ABE, X02AME, X02ALE
+ INTEGER X02BHE, X02BJE
+ EXTERNAL S14ABE, S01EAE, X02AME, X02ALE, X02BHE, X02BJE
+! .. External Subroutines ..
+ EXTERNAL DGUS17, DGVS17, DGWS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, ATAN, CMPLX, CONJG, COS, EXP, INT,
+ * LOG, LOG10, MAX, MIN, REAL, SIN, SQRT
+! .. Data statements ..
+!
+!
+!
+ DATA KMAX/30/
+ DATA R1/2.0E0/
+ DATA CZERO, CONE, CTWO/(0.0E0,0.0E0), (1.0E0,0.0E0),
+ * (2.0E0,0.0E0)/
+ DATA PI, RTHPI, SPI, HPI, FPI,
+ * TTH/3.14159265358979324E0,
+ * 1.25331413731550025E0, 1.90985931710274403E0,
+ * 1.57079632679489662E0, 1.89769999331517738E0,
+ * 6.66666666666666666E-01/
+ DATA CC(1), CC(2), CC(3), CC(4), CC(5), CC(6), CC(7),
+ * CC(8)/5.77215664901532861E-01,
+ * -4.20026350340952355E-02,
+ * -4.21977345555443367E-02,
+ * 7.21894324666309954E-03,
+ * -2.15241674114950973E-04,
+ * -2.01348547807882387E-05,
+ * 1.13302723198169588E-06,
+ * 6.11609510448141582E-09/
+! .. Executable Statements ..
+!
+ XX = REAL(Z)
+ YY = AIMAG(Z)
+ CAZ = ABS(Z)
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ NZ = 0
+ IFLAG = 0
+ KODED = KODE
+ RZ = CTWO/Z
+ INU = INT(FNU+0.5E0)
+ DNU = FNU - INU
+ IF (ABS(DNU).NE.0.5E0) THEN
+ DNU2 = 0.0E0
+ IF (ABS(DNU).GT.TOL) DNU2 = DNU*DNU
+ IF (CAZ.LE.R1) THEN
+! ------------------------------------------------------------
+! SERIES FOR CABS(Z).LE.R1
+! ------------------------------------------------------------
+ FC = 1.0E0
+ SMU = LOG(RZ)
+ FMU = SMU*CMPLX(DNU,0.0E0)
+ CALL DGUS17(FMU,CSH,CCH)
+ IF (DNU.NE.0.0E0) THEN
+ FC = DNU*PI
+ FC = FC/SIN(FC)
+ SMU = CSH*CMPLX(1.0E0/DNU,0.0E0)
+ END IF
+ A2 = 1.0E0 + DNU
+! ------------------------------------------------------------
+! GAM(1-Z)*GAM(1+Z)=PI*Z/SIN(PI*Z), T1=1/GAM(1-DNU),
+! T2=1/GAM(1+DNU)
+! ------------------------------------------------------------
+ IDUM = 0
+! S14ABE assumed not to fail, therefore IDUM set to zero.
+ T2 = EXP(-S14ABE(A2,IDUM))
+ T1 = 1.0E0/(T2*FC)
+ IF (ABS(DNU).GT.0.1E0) THEN
+ G1 = (T1-T2)/(DNU+DNU)
+ ELSE
+! ---------------------------------------------------------
+! SERIES FOR F0 TO RESOLVE INDETERMINACY FOR SMALL ABS(DNU)
+! ---------------------------------------------------------
+ AK = 1.0E0
+ S = CC(1)
+ DO 20 K = 2, 8
+ AK = AK*DNU2
+ TM = CC(K)*AK
+ S = S + TM
+ IF (ABS(TM).LT.TOL) GO TO 40
+ 20 CONTINUE
+ 40 G1 = -S
+ END IF
+ G2 = 0.5E0*(T1+T2)*FC
+ G1 = G1*FC
+ F = CMPLX(G1,0.0E0)*CCH + SMU*CMPLX(G2,0.0E0)
+ IFL = 1
+ PT = S01EAE(FMU,IFL)
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 320
+ P = CMPLX(0.5E0/T2,0.0E0)*PT
+ Q = CMPLX(0.5E0/T1,0.0E0)/PT
+ S1 = F
+ S2 = P
+ AK = 1.0E0
+ A1 = 1.0E0
+ CK = CONE
+ BK = 1.0E0 - DNU2
+ IF (INU.GT.0 .OR. N.GT.1) THEN
+! ---------------------------------------------------------
+! GENERATE K(DNU,Z) AND K(DNU+1,Z) FOR FORWARD RECURRENCE
+! ---------------------------------------------------------
+ IF (CAZ.GE.TOL) THEN
+ CZ = Z*Z*CMPLX(0.25E0,0.0E0)
+ T1 = 0.25E0*CAZ*CAZ
+ 60 CONTINUE
+ F = (F*CMPLX(AK,0.0E0)+P+Q)*CMPLX(1.0E0/BK,0.0E0)
+ P = P*CMPLX(1.0E0/(AK-DNU),0.0E0)
+ Q = Q*CMPLX(1.0E0/(AK+DNU),0.0E0)
+ RK = 1.0E0/AK
+ CK = CK*CZ*CMPLX(RK,0.0E0)
+ S1 = S1 + CK*F
+ S2 = S2 + CK*(P-F*CMPLX(AK,0.0E0))
+ A1 = A1*T1*RK
+ BK = BK + AK + AK + 1.0E0
+ AK = AK + 1.0E0
+ IF (A1.GT.TOL) GO TO 60
+ END IF
+ KFLAG = 2
+ BK = REAL(SMU)
+ A1 = FNU + 1.0E0
+ AK = A1*ABS(BK)
+ IF (AK.GT.ALIM) KFLAG = 3
+ P2 = S2*CSS(KFLAG)
+ S2 = P2*RZ
+ S1 = S1*CSS(KFLAG)
+ IF (KODED.NE.1) THEN
+! F = EXP(Z)
+ IFL = 1
+ F = S01EAE(Z,IFL)
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 320
+ S1 = S1*F
+ S2 = S2*F
+ END IF
+ GO TO 160
+ ELSE
+! ---------------------------------------------------------
+! GENERATE K(FNU,Z), 0.0D0 .LE. FNU .LT. 0.5D0 AND N=1
+! ---------------------------------------------------------
+ IF (CAZ.GE.TOL) THEN
+ CZ = Z*Z*CMPLX(0.25E0,0.0E0)
+ T1 = 0.25E0*CAZ*CAZ
+ 80 CONTINUE
+ F = (F*CMPLX(AK,0.0E0)+P+Q)*CMPLX(1.0E0/BK,0.0E0)
+ P = P*CMPLX(1.0E0/(AK-DNU),0.0E0)
+ Q = Q*CMPLX(1.0E0/(AK+DNU),0.0E0)
+ RK = 1.0E0/AK
+ CK = CK*CZ*CMPLX(RK,0.0E0)
+ S1 = S1 + CK*F
+ A1 = A1*T1*RK
+ BK = BK + AK + AK + 1.0E0
+ AK = AK + 1.0E0
+ IF (A1.GT.TOL) GO TO 80
+ END IF
+ Y(1) = S1
+! IF (KODED.NE.1) Y(1) = S1*EXP(Z)
+ IF (KODED.NE.1) THEN
+ IFL = 1
+ Y(1) = S01EAE(Z,IFL)
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 320
+ Y(1) = S1*Y(1)
+ END IF
+ RETURN
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------------
+! IFLAG=0 MEANS NO UNDERFLOW OCCURRED
+! IFLAG=1 MEANS AN UNDERFLOW OCCURRED- COMPUTATION PROCEEDS WITH
+! KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD
+! RECURSION
+! ------------------------------------------------------------------
+ COEF = CMPLX(RTHPI,0.0E0)/SQRT(Z)
+ KFLAG = 2
+ IF (KODED.NE.2) THEN
+ IF (XX.GT.ALIM) THEN
+! ------------------------------------------------------------
+! SCALE BY EXP(Z), IFLAG = 1 CASES
+! ------------------------------------------------------------
+ KODED = 2
+ IFLAG = 1
+ KFLAG = 2
+ ELSE
+! BLANK LINE
+! A1 = EXP(-XX)*REAL(CSS(KFLAG))
+! PT = CMPLX(A1,0.0E0)*CMPLX(COS(YY),-SIN(YY))
+ IFL = 1
+ PT = S01EAE(CMPLX(-XX,-YY),IFL)
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 320
+ PT = PT*REAL(CSS(KFLAG))
+ COEF = COEF*PT
+ END IF
+ END IF
+ IF (ABS(DNU).NE.0.5E0) THEN
+! ---------------------------------------------------------------
+! MILLER ALGORITHM FOR CABS(Z).GT.R1
+! ---------------------------------------------------------------
+ AK = COS(PI*DNU)
+ AK = ABS(AK)
+ IF (AK.NE.0.0E0) THEN
+ FHS = ABS(0.25E0-DNU2)
+ IF (FHS.NE.0.0E0) THEN
+! ---------------------------------------------------------
+! COMPUTE R2=F(E). IF CABS(Z).GE.R2, USE FORWARD RECURRENCE
+! TO DETERMINE THE BACKWARD INDEX K. R2=F(E) IS A STRAIGHT
+! LINE ON 12.LE.E.LE.60. E IS COMPUTED FROM
+! 2**(-E)=B**(1-X02BJE())=TOL WHERE B IS THE BASE OF THE
+! ARITHMETIC.
+! ---------------------------------------------------------
+ T1 = (X02BJE()-1)*LOG10(REAL(X02BHE()))*3.321928094E0
+ T1 = MAX(T1,12.0E0)
+ T1 = MIN(T1,60.0E0)
+ T2 = TTH*T1 - 6.0E0
+ IF (XX.NE.0.0E0) THEN
+ T1 = ATAN(YY/XX)
+ T1 = ABS(T1)
+ ELSE
+ T1 = HPI
+ END IF
+ IF (T2.GT.CAZ) THEN
+! ------------------------------------------------------
+! COMPUTE BACKWARD INDEX K FOR CABS(Z).LT.R2
+! ------------------------------------------------------
+ A2 = SQRT(CAZ)
+ AK = FPI*AK/(TOL*SQRT(A2))
+ AA = 3.0E0*T1/(1.0E0+CAZ)
+ BB = 14.7E0*T1/(28.0E0+CAZ)
+ AK = (LOG(AK)+CAZ*COS(AA)/(1.0E0+0.008E0*CAZ))/COS(BB)
+ FK = 0.12125E0*AK*AK/CAZ + 1.5E0
+ ELSE
+! ------------------------------------------------------
+! FORWARD RECURRENCE LOOP WHEN CABS(Z).GE.R2
+! ------------------------------------------------------
+ ETEST = AK/(PI*CAZ*TOL)
+ FK = 1.0E0
+ IF (ETEST.GE.1.0E0) THEN
+ FKS = 2.0E0
+ RK = CAZ + CAZ + 2.0E0
+ A1 = 0.0E0
+ A2 = 1.0E0
+ DO 100 I = 1, KMAX
+ AK = FHS/FKS
+ BK = RK/(FK+1.0E0)
+ TM = A2
+ A2 = BK*A2 - AK*A1
+ A1 = TM
+ RK = RK + 2.0E0
+ FKS = FKS + FK + FK + 2.0E0
+ FHS = FHS + FK + FK
+ FK = FK + 1.0E0
+ TM = ABS(A2)*FK
+ IF (ETEST.LT.TM) GO TO 120
+ 100 CONTINUE
+ NZ = -2
+ RETURN
+ 120 FK = FK + SPI*T1*SQRT(T2/CAZ)
+ FHS = ABS(0.25E0-DNU2)
+ END IF
+ END IF
+ K = INT(FK)
+! ---------------------------------------------------------
+! BACKWARD RECURRENCE LOOP FOR MILLER ALGORITHM
+! ---------------------------------------------------------
+ FK = K
+ FKS = FK*FK
+ P1 = CZERO
+ P2 = CMPLX(TOL,0.0E0)
+ CS = P2
+ DO 140 I = 1, K
+ A1 = FKS - FK
+ A2 = (FKS+FK)/(A1+FHS)
+ RK = 2.0E0/(FK+1.0E0)
+ T1 = (FK+XX)*RK
+ T2 = YY*RK
+ PT = P2
+ P2 = (P2*CMPLX(T1,T2)-P1)*CMPLX(A2,0.0E0)
+ P1 = PT
+ CS = CS + P2
+ FKS = A1 - FK + 1.0E0
+ FK = FK - 1.0E0
+ 140 CONTINUE
+! ---------------------------------------------------------
+! COMPUTE (P2/CS)=(P2/CABS(CS))*(CONJG(CS)/CABS(CS)) FOR
+! BETTER SCALING
+! ---------------------------------------------------------
+ TM = ABS(CS)
+ PT = CMPLX(1.0E0/TM,0.0E0)
+ S1 = PT*P2
+ CS = CONJG(CS)*PT
+ S1 = COEF*S1*CS
+ IF (INU.GT.0 .OR. N.GT.1) THEN
+! ------------------------------------------------------
+! COMPUTE P1/P2=(P1/CABS(P2)*CONJG(P2)/CABS(P2) FOR
+! SCALING
+! ------------------------------------------------------
+ TM = ABS(P2)
+ PT = CMPLX(1.0E0/TM,0.0E0)
+ P1 = PT*P1
+ P2 = CONJG(P2)*PT
+ PT = P1*P2
+ S2 = S1*(CONE+(CMPLX(DNU+0.5E0,0.0E0)-PT)/Z)
+ GO TO 160
+ ELSE
+ ZD = Z
+ IF (IFLAG.EQ.1) THEN
+ GO TO 240
+ ELSE
+ GO TO 260
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------------
+! FNU=HALF ODD INTEGER CASE, DNU=-0.5
+! ------------------------------------------------------------------
+ S1 = COEF
+ S2 = COEF
+! ------------------------------------------------------------------
+! FORWARD RECURSION ON THE THREE TERM RECURSION RELATION WITH
+! SCALING NEAR EXPONENT EXTREMES ON KFLAG=1 OR KFLAG=3
+! ------------------------------------------------------------------
+ 160 CONTINUE
+ CK = CMPLX(DNU+1.0E0,0.0E0)*RZ
+ IF (N.EQ.1) INU = INU - 1
+ IF (INU.GT.0) THEN
+ INUB = 1
+ IF (IFLAG.EQ.1) THEN
+! ------------------------------------------------------------
+! IFLAG=1 CASES, FORWARD RECURRENCE ON SCALED VALUES ON
+! UNDERFLOW
+! ------------------------------------------------------------
+ HELIM = 0.5E0*ELIM
+ ELM = EXP(-ELIM)
+ CELM = CMPLX(ELM,0.0E0)
+ ASCLE = BRY(1)
+ ZD = Z
+ XD = XX
+ YD = YY
+ IC = -1
+ J = 2
+ DO 180 I = 1, INU
+ ST = S2
+ S2 = CK*S2 + S1
+ S1 = ST
+ CK = CK + RZ
+ AS = ABS(S2)
+ ALAS = LOG(AS)
+ P2R = -XD + ALAS
+ IF (P2R.GE.(-ELIM)) THEN
+ P2 = -ZD + LOG(S2)
+ P2R = REAL(P2)
+ P2I = AIMAG(P2)
+ P2M = EXP(P2R)/TOL
+ P1 = CMPLX(P2M,0.0E0)*CMPLX(COS(P2I),SIN(P2I))
+ CALL DGVS17(P1,NW,ASCLE,TOL)
+ IF (NW.EQ.0) THEN
+ J = 3 - J
+ CY(J) = P1
+ IF (IC.EQ.(I-1)) THEN
+ GO TO 200
+ ELSE
+ IC = I
+ GO TO 180
+ END IF
+ END IF
+ END IF
+ IF (ALAS.GE.HELIM) THEN
+ XD = XD - ELIM
+ S1 = S1*CELM
+ S2 = S2*CELM
+ ZD = CMPLX(XD,YD)
+ END IF
+ 180 CONTINUE
+ IF (N.EQ.1) S1 = S2
+ GO TO 240
+ 200 KFLAG = 1
+ INUB = I + 1
+ S2 = CY(J)
+ J = 3 - J
+ S1 = CY(J)
+ IF (INUB.GT.INU) THEN
+ IF (N.EQ.1) S1 = S2
+ GO TO 260
+ END IF
+ END IF
+ P1 = CSR(KFLAG)
+ ASCLE = BRY(KFLAG)
+ DO 220 I = INUB, INU
+ ST = S2
+ S2 = CK*S2 + S1
+ S1 = ST
+ CK = CK + RZ
+ IF (KFLAG.LT.3) THEN
+ P2 = S2*P1
+ P2R = REAL(P2)
+ P2I = AIMAG(P2)
+ P2R = ABS(P2R)
+ P2I = ABS(P2I)
+ P2M = MAX(P2R,P2I)
+ IF (P2M.GT.ASCLE) THEN
+ KFLAG = KFLAG + 1
+ ASCLE = BRY(KFLAG)
+ S1 = S1*P1
+ S2 = P2
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ P1 = CSR(KFLAG)
+ END IF
+ END IF
+ 220 CONTINUE
+ IF (N.EQ.1) S1 = S2
+ GO TO 260
+ ELSE
+ IF (N.EQ.1) S1 = S2
+ ZD = Z
+ IF (IFLAG.NE.1) GO TO 260
+ END IF
+ 240 Y(1) = S1
+ IF (N.NE.1) Y(2) = S2
+ ASCLE = BRY(1)
+ CALL DGWS17(ZD,FNU,N,Y,NZ,RZ,ASCLE,TOL,ELIM)
+ INU = N - NZ
+ IF (INU.LE.0) THEN
+ RETURN
+ ELSE
+ KK = NZ + 1
+ S1 = Y(KK)
+ Y(KK) = S1*CSR(1)
+ IF (INU.EQ.1) THEN
+ RETURN
+ ELSE
+ KK = NZ + 2
+ S2 = Y(KK)
+ Y(KK) = S2*CSR(1)
+ IF (INU.EQ.2) THEN
+ RETURN
+ ELSE
+ T2 = FNU + KK - 1
+ CK = CMPLX(T2,0.0E0)*RZ
+ KFLAG = 1
+ GO TO 280
+ END IF
+ END IF
+ END IF
+ 260 Y(1) = S1*CSR(KFLAG)
+ IF (N.EQ.1) THEN
+ RETURN
+ ELSE
+ Y(2) = S2*CSR(KFLAG)
+ IF (N.EQ.2) THEN
+ RETURN
+ ELSE
+ KK = 2
+ END IF
+ END IF
+ 280 KK = KK + 1
+ IF (KK.LE.N) THEN
+ P1 = CSR(KFLAG)
+ ASCLE = BRY(KFLAG)
+ DO 300 I = KK, N
+ P2 = S2
+ S2 = CK*S2 + S1
+ S1 = P2
+ CK = CK + RZ
+ P2 = S2*P1
+ Y(I) = P2
+ IF (KFLAG.LT.3) THEN
+ P2R = REAL(P2)
+ P2I = AIMAG(P2)
+ P2R = ABS(P2R)
+ P2I = ABS(P2I)
+ P2M = MAX(P2R,P2I)
+ IF (P2M.GT.ASCLE) THEN
+ KFLAG = KFLAG + 1
+ ASCLE = BRY(KFLAG)
+ S1 = S1*P1
+ S2 = P2
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ P1 = CSR(KFLAG)
+ END IF
+ END IF
+ 300 CONTINUE
+ END IF
+ RETURN
+ 320 NZ = -3
+ RETURN
+ END
+ SUBROUTINE DGYS17(Z,FNU,KODE,N,Y,NZ,RL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-778 (DEC 1989).
+!
+! Original name: CASYI
+!
+! DGYS17 COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY
+! MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE
+! REGION CABS(Z).GT.MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL RETURN.
+! NZ.LT.0 INDICATES AN OVERFLOW ON KODE=1.
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, RL, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX AK1, CK, CONE, CS1, CS2, CZ, CZERO, DK, EZ, P1,
+ * RZ, S2
+ REAL AA, ACZ, AEZ, AK, ARG, ARM, ATOL, AZ, BB, BK,
+ * DFNU, DNU2, FDN, PI, RTPI, RTR1, S, SGN, SQK, X,
+ * YY
+ INTEGER I, IB, IERR1, IL, INU, J, JL, K, KODED, M, NN
+! .. External Functions ..
+ COMPLEX S01EAE
+ REAL X02AME
+ EXTERNAL S01EAE, X02AME
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, INT, MIN, MOD,
+ * REAL, SIN, SQRT
+! .. Data statements ..
+ DATA PI, RTPI/3.14159265358979324E0,
+ * 0.159154943091895336E0/
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ AZ = ABS(Z)
+ X = REAL(Z)
+ ARM = 1.0E+3*X02AME()
+ RTR1 = SQRT(ARM)
+ IL = MIN(2,N)
+ DFNU = FNU + N - IL
+! ------------------------------------------------------------------
+! OVERFLOW TEST
+! ------------------------------------------------------------------
+ AK1 = CMPLX(RTPI,0.0E0)/Z
+ AK1 = SQRT(AK1)
+ CZ = Z
+ IF (KODE.EQ.2) CZ = Z - CMPLX(X,0.0E0)
+ ACZ = REAL(CZ)
+ IF (ABS(ACZ).GT.ELIM) THEN
+ NZ = -1
+ ELSE
+ DNU2 = DFNU + DFNU
+ KODED = 1
+ IF ((ABS(ACZ).LE.ALIM) .OR. (N.LE.2)) THEN
+ KODED = 0
+ IERR1 = 1
+ AK1 = AK1*S01EAE(CZ,IERR1)
+! Allow reduced precision from S01EAE, but disallow other errors.
+ IF ((IERR1.GE.1 .AND. IERR1.LE.3) .OR. IERR1.EQ.5) GO TO 140
+ END IF
+ FDN = 0.0E0
+ IF (DNU2.GT.RTR1) FDN = DNU2*DNU2
+ EZ = Z*CMPLX(8.0E0,0.0E0)
+! ---------------------------------------------------------------
+! WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO
+! THE FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF
+! THE EXPANSION FOR THE IMAGINARY PART.
+! ---------------------------------------------------------------
+ AEZ = 8.0E0*AZ
+ S = TOL/AEZ
+ JL = INT(RL+RL) + 2
+ YY = AIMAG(Z)
+ P1 = CZERO
+ IF (YY.NE.0.0E0) THEN
+! ------------------------------------------------------------
+! CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF
+! SIGNIFICANCE WHEN FNU OR N IS LARGE
+! ------------------------------------------------------------
+ INU = INT(FNU)
+ ARG = (FNU-INU)*PI
+ INU = INU + N - IL
+ AK = -SIN(ARG)
+ BK = COS(ARG)
+ IF (YY.LT.0.0E0) BK = -BK
+ P1 = CMPLX(AK,BK)
+ IF (MOD(INU,2).EQ.1) P1 = -P1
+ END IF
+ DO 60 K = 1, IL
+ SQK = FDN - 1.0E0
+ ATOL = S*ABS(SQK)
+ SGN = 1.0E0
+ CS1 = CONE
+ CS2 = CONE
+ CK = CONE
+ AK = 0.0E0
+ AA = 1.0E0
+ BB = AEZ
+ DK = EZ
+ DO 20 J = 1, JL
+ CK = CK*CMPLX(SQK,0.0E0)/DK
+ CS2 = CS2 + CK
+ SGN = -SGN
+ CS1 = CS1 + CK*CMPLX(SGN,0.0E0)
+ DK = DK + EZ
+ AA = AA*ABS(SQK)/BB
+ BB = BB + AEZ
+ AK = AK + 8.0E0
+ SQK = SQK - AK
+ IF (AA.LE.ATOL) GO TO 40
+ 20 CONTINUE
+ GO TO 120
+ 40 S2 = CS1
+ IF (X+X.LT.ELIM) THEN
+ IERR1 = 1
+ S2 = S2 + P1*CS2*S01EAE(-Z-Z,IERR1)
+ IF ((IERR1.GE.1 .AND. IERR1.LE.3) .OR. IERR1.EQ.5)
+ * GO TO 140
+ END IF
+ FDN = FDN + 8.0E0*DFNU + 4.0E0
+ P1 = -P1
+ M = N - IL + K
+ Y(M) = S2*AK1
+ 60 CONTINUE
+ IF (N.GT.2) THEN
+ NN = N
+ K = NN - 2
+ AK = K
+ RZ = (CONE+CONE)/Z
+ IB = 3
+ DO 80 I = IB, NN
+ Y(K) = CMPLX(AK+FNU,0.0E0)*RZ*Y(K+1) + Y(K+2)
+ AK = AK - 1.0E0
+ K = K - 1
+ 80 CONTINUE
+ IF (KODED.NE.0) THEN
+ IERR1 = 1
+ CK = S01EAE(CZ,IERR1)
+ IF ((IERR1.GE.1 .AND. IERR1.LE.3) .OR. IERR1.EQ.5)
+ * GO TO 140
+ DO 100 I = 1, NN
+ Y(I) = Y(I)*CK
+ 100 CONTINUE
+ END IF
+ END IF
+ RETURN
+ 120 NZ = -2
+ RETURN
+ 140 NZ = -3
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGZS17(Z,FNU,KODE,MR,N,Y,NZ,RL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-779 (DEC 1989).
+!
+! Original name: CACAI
+!
+! DGZS17 APPLIES THE ANALYTIC CONTINUATION FORMULA
+!
+! K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
+! MP=PI*MR*CMPLX(0.0,1.0)
+!
+! TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
+! HALF Z PLANE FOR USE WITH S17DGE WHERE FNU=1/3 OR 2/3 AND N=1.
+! DGZS17 IS THE SAME AS DLZS17 WITH THE PARTS FOR LARGER ORDERS AND
+! RECURRENCE REMOVED. A RECURSIVE CALL TO DLZS17 CAN RESULT IF S17DL
+! IS CALLED FROM S17DGE.
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, RL, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CSGN, CSPN, ZN
+ REAL ARG, ASCLE, AZ, CPN, DFNU, FMR, PI, SGN, SPN, YY
+ INTEGER INU, IUF, NN, NW
+! .. Local Arrays ..
+ COMPLEX CY(2)
+! .. External Functions ..
+ REAL X02AME
+ EXTERNAL X02AME
+! .. External Subroutines ..
+ EXTERNAL DGRS17, DGSS17, DGTS17, DGXS17, DGYS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, INT, MOD, SIGN, SIN
+! .. Data statements ..
+ DATA PI/3.14159265358979324E0/
+! .. Executable Statements ..
+!
+ NZ = 0
+ ZN = -Z
+ AZ = ABS(Z)
+ NN = N
+ DFNU = FNU + N - 1
+ IF (AZ.GT.2.0E0) THEN
+ IF (AZ*AZ*0.25E0.GT.DFNU+1.0E0) THEN
+ IF (AZ.LT.RL) THEN
+! ---------------------------------------------------------
+! MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I
+! FUNCTION
+! ---------------------------------------------------------
+ CALL DGTS17(ZN,FNU,KODE,NN,Y,NW,TOL)
+ IF (NW.LT.0) THEN
+ GO TO 40
+ ELSE
+ GO TO 20
+ END IF
+ ELSE
+! ---------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION
+! ---------------------------------------------------------
+ CALL DGYS17(ZN,FNU,KODE,NN,Y,NW,RL,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 40
+ ELSE
+ GO TO 20
+ END IF
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------------
+! POWER SERIES FOR THE I FUNCTION
+! ------------------------------------------------------------------
+ CALL DGRS17(ZN,FNU,KODE,NN,Y,NW,TOL,ELIM,ALIM)
+! ------------------------------------------------------------------
+! ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
+! ------------------------------------------------------------------
+ 20 CALL DGXS17(ZN,FNU,KODE,1,CY,NW,TOL,ELIM,ALIM)
+ IF (NW.EQ.0) THEN
+ FMR = MR
+ SGN = -SIGN(PI,FMR)
+ CSGN = CMPLX(0.0E0,SGN)
+ IF (KODE.NE.1) THEN
+ YY = -AIMAG(ZN)
+ CPN = COS(YY)
+ SPN = SIN(YY)
+ CSGN = CSGN*CMPLX(CPN,SPN)
+ END IF
+! ---------------------------------------------------------------
+! CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+! WHEN FNU IS LARGE
+! ---------------------------------------------------------------
+ INU = INT(FNU)
+ ARG = (FNU-INU)*SGN
+ CPN = COS(ARG)
+ SPN = SIN(ARG)
+ CSPN = CMPLX(CPN,SPN)
+ IF (MOD(INU,2).EQ.1) CSPN = -CSPN
+ C1 = CY(1)
+ C2 = Y(1)
+ IF (KODE.NE.1) THEN
+ IUF = 0
+ ASCLE = (1.0E+3*X02AME())/TOL
+ CALL DGSS17(ZN,C1,C2,NW,ASCLE,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(1) = CSPN*C1 + CSGN*C2
+ RETURN
+ END IF
+ 40 NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ IF (NW.EQ.(-3)) NZ = -3
+ RETURN
+ END
+ SUBROUTINE DLYS17(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-782 (DEC 1989).
+!
+! Original name: CBUNK
+!
+! DLYS17 COMPUTES THE K BESSEL FUNCTION FOR FNU.GT.FNUL.
+! ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR K(FNU,Z)
+! IN DCZS18 AND THE EXPANSION FOR H(2,FNU,Z) IN DCYS18
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ REAL AX, AY, XX, YY
+! .. External Subroutines ..
+ EXTERNAL DCYS18, DCZS18
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, REAL
+! .. Executable Statements ..
+!
+ NZ = 0
+ XX = REAL(Z)
+ YY = AIMAG(Z)
+ AX = ABS(XX)*1.7321E0
+ AY = ABS(YY)
+ IF (AY.GT.AX) THEN
+! ---------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR H(2,FNU,Z*EXP(M*HPI)) FOR LARGE FNU
+! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
+! AND HPI=PI/2
+! ---------------------------------------------------------------
+ CALL DCYS18(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+ ELSE
+! ---------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR K(FNU,Z) FOR LARGE FNU APPLIED IN
+! -PI/3.LE.ARG(Z).LE.PI/3
+! ---------------------------------------------------------------
+ CALL DCZS18(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+ END IF
+ RETURN
+ END
+ SUBROUTINE DLZS17(Z,FNU,KODE,MR,N,Y,NZ,RL,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-783 (DEC 1989).
+!
+! Original name: CACON
+!
+! DLZS17 APPLIES THE ANALYTIC CONTINUATION FORMULA
+!
+! K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
+! MP=PI*MR*CMPLX(0.0,1.0)
+!
+! TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
+! HALF Z PLANE
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, RL, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CK, CONE, CS, CSCL, CSCR, CSGN, CSPN,
+ * RZ, S1, S2, SC1, SC2, ST, ZN
+ REAL ARG, AS2, ASCLE, BSCLE, C1I, C1M, C1R, CPN, FMR,
+ * PI, SGN, SPN, YY
+ INTEGER I, INU, IUF, KFLAG, NN, NW
+! .. Local Arrays ..
+ COMPLEX CSR(3), CSS(3), CY(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEZS17, DGSS17, DGXS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, INT, MAX, MIN, MOD,
+ * REAL, SIGN, SIN
+! .. Data statements ..
+ DATA PI/3.14159265358979324E0/
+ DATA CONE/(1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ ZN = -Z
+ NN = N
+ CALL DEZS17(ZN,FNU,KODE,NN,Y,NW,RL,FNUL,TOL,ELIM,ALIM)
+ IF (NW.GE.0) THEN
+! ---------------------------------------------------------------
+! ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
+! ---------------------------------------------------------------
+ NN = MIN(2,N)
+ CALL DGXS17(ZN,FNU,KODE,NN,CY,NW,TOL,ELIM,ALIM)
+ IF (NW.EQ.0) THEN
+ S1 = CY(1)
+ FMR = MR
+ SGN = -SIGN(PI,FMR)
+ CSGN = CMPLX(0.0E0,SGN)
+ IF (KODE.NE.1) THEN
+ YY = -AIMAG(ZN)
+ CPN = COS(YY)
+ SPN = SIN(YY)
+ CSGN = CSGN*CMPLX(CPN,SPN)
+ END IF
+! ------------------------------------------------------------
+! CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF
+! SIGNIFICANCE WHEN FNU IS LARGE
+! ------------------------------------------------------------
+ INU = INT(FNU)
+ ARG = (FNU-INU)*SGN
+ CPN = COS(ARG)
+ SPN = SIN(ARG)
+ CSPN = CMPLX(CPN,SPN)
+ IF (MOD(INU,2).EQ.1) CSPN = -CSPN
+ IUF = 0
+ C1 = S1
+ C2 = Y(1)
+ ASCLE = (1.0E+3*X02AME())/TOL
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZN,C1,C2,NW,ASCLE,ALIM,IUF)
+ NZ = NZ + NW
+ SC1 = C1
+ END IF
+ Y(1) = CSPN*C1 + CSGN*C2
+ IF (N.NE.1) THEN
+ CSPN = -CSPN
+ S2 = CY(2)
+ C1 = S2
+ C2 = Y(2)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZN,C1,C2,NW,ASCLE,ALIM,IUF)
+ NZ = NZ + NW
+ SC2 = C1
+ END IF
+ Y(2) = CSPN*C1 + CSGN*C2
+ IF (N.NE.2) THEN
+ CSPN = -CSPN
+ RZ = CMPLX(2.0E0,0.0E0)/ZN
+ CK = CMPLX(FNU+1.0E0,0.0E0)*RZ
+! ------------------------------------------------------
+! SCALE NEAR EXPONENT EXTREMES DURING RECURRENCE ON
+! K FUNCTIONS
+! ------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CSCR = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CSCR
+ CSR(1) = CSCR
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = ASCLE
+ BRY(2) = 1.0E0/ASCLE
+ BRY(3) = X02ALE()
+ AS2 = ABS(S2)
+ KFLAG = 2
+ IF (AS2.LE.BRY(1)) THEN
+ KFLAG = 1
+ ELSE IF (AS2.GE.BRY(2)) THEN
+ KFLAG = 3
+ END IF
+ BSCLE = BRY(KFLAG)
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ CS = CSR(KFLAG)
+ DO 20 I = 3, N
+ ST = S2
+ S2 = CK*S2 + S1
+ S1 = ST
+ C1 = S2*CS
+ ST = C1
+ C2 = Y(I)
+ IF (KODE.NE.1) THEN
+ IF (IUF.GE.0) THEN
+ CALL DGSS17(ZN,C1,C2,NW,ASCLE,ALIM,IUF)
+ NZ = NZ + NW
+ SC1 = SC2
+ SC2 = C1
+ IF (IUF.EQ.3) THEN
+ IUF = -4
+ S1 = SC1*CSS(KFLAG)
+ S2 = SC2*CSS(KFLAG)
+ ST = SC2
+ END IF
+ END IF
+ END IF
+ Y(I) = CSPN*C1 + CSGN*C2
+ CK = CK + RZ
+ CSPN = -CSPN
+ IF (KFLAG.LT.3) THEN
+ C1R = REAL(C1)
+ C1I = AIMAG(C1)
+ C1R = ABS(C1R)
+ C1I = ABS(C1I)
+ C1M = MAX(C1R,C1I)
+ IF (C1M.GT.BSCLE) THEN
+ KFLAG = KFLAG + 1
+ BSCLE = BRY(KFLAG)
+ S1 = S1*CS
+ S2 = ST
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ CS = CSR(KFLAG)
+ END IF
+ END IF
+ 20 CONTINUE
+ END IF
+ END IF
+ RETURN
+ END IF
+ END IF
+ NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ IF (NW.EQ.(-3)) NZ = -3
+ RETURN
+ END
+ INTEGER FUNCTION P01ABE(IFAIL,IERROR,SRNAME,NREC,REC)
+! MARK 11.5(F77) RELEASE. NAG COPYRIGHT 1986.
+! MARK 13 REVISED. IER-621 (APR 1988).
+! MARK 13B REVISED. IER-668 (AUG 1988).
+!
+! P01ABE is the error-handling routine for the NAG Library.
+!
+! P01ABE either returns the value of IERROR through the routine
+! name (soft failure), or terminates execution of the program
+! (hard failure). Diagnostic messages may be output.
+!
+! If IERROR = 0 (successful exit from the calling routine),
+! the value 0 is returned through the routine name, and no
+! message is output
+!
+! If IERROR is non-zero (abnormal exit from the calling routine),
+! the action taken depends on the value of IFAIL.
+!
+! IFAIL = 1: soft failure, silent exit (i.e. no messages are
+! output)
+! IFAIL = -1: soft failure, noisy exit (i.e. messages are output)
+! IFAIL =-13: soft failure, noisy exit but standard messages from
+! P01ABE are suppressed
+! IFAIL = 0: hard failure, noisy exit
+!
+! For compatibility with certain routines included before Mark 12
+! P01ABE also allows an alternative specification of IFAIL in which
+! it is regarded as a decimal integer with least significant digits
+! cba. Then
+!
+! a = 0: hard failure a = 1: soft failure
+! b = 0: silent exit b = 1: noisy exit
+!
+! except that hard failure now always implies a noisy exit.
+!
+! S.Hammarling, M.P.Hooper and J.J.du Croz, NAG Central Office.
+!
+! .. Scalar Arguments ..
+ INTEGER IERROR, IFAIL, NREC
+ CHARACTER*(*) SRNAME
+! .. Array Arguments ..
+ CHARACTER*(*) REC(*)
+! .. Local Scalars ..
+ INTEGER I, NERR
+ CHARACTER*72 MESS
+! .. External Subroutines ..
+ EXTERNAL ABZP01, X04AAE, X04BAE
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, MOD
+! .. Executable Statements ..
+ IF (IERROR.NE.0) THEN
+! Abnormal exit from calling routine
+ IF (IFAIL.EQ.-1 .OR. IFAIL.EQ.0 .OR. IFAIL.EQ.-13 .OR.
+ * (IFAIL.GT.0 .AND. MOD(IFAIL/10,10).NE.0)) THEN
+! Noisy exit
+ CALL X04AAE(0,NERR)
+ DO 20 I = 1, NREC
+ CALL X04BAE(NERR,REC(I))
+ 20 CONTINUE
+ IF (IFAIL.NE.-13) THEN
+ WRITE (MESS,FMT=99999) SRNAME, IERROR
+ CALL X04BAE(NERR,MESS)
+ IF (ABS(MOD(IFAIL,10)).NE.1) THEN
+! Hard failure
+ CALL X04BAE(NERR,
+ * ' ** NAG hard failure - execution terminated'
+ * )
+ CALL ABZP01
+ ELSE
+! Soft failure
+ CALL X04BAE(NERR,
+ * ' ** NAG soft failure - control returned')
+ END IF
+ END IF
+ END IF
+ END IF
+ P01ABE = IERROR
+ RETURN
+!
+99999 FORMAT (' ** ABNORMAL EXIT from NAG Library routine ',A,': IFAIL',
+ * ' =',I6)
+ END
+ COMPLEX FUNCTION S01EAE(Z,IFAIL)
+! MARK 14 RELEASE. NAG COPYRIGHT 1989.
+! Returns exp(Z) for complex Z.
+! .. Parameters ..
+ REAL ONE, ZERO
+ PARAMETER (ONE=1.0E0,ZERO=0.0E0)
+ CHARACTER*6 SRNAME
+ PARAMETER (SRNAME='S01EAE')
+! .. Scalar Arguments ..
+ COMPLEX Z
+ INTEGER IFAIL
+! .. Local Scalars ..
+ REAL COSY, EXPX, LNSAFE, RECEPS, RESI, RESR,
+ * RTSAFS, SAFE, SAFSIN, SINY, X, XPLNCY,
+ * XPLNSY, Y
+ INTEGER IER, NREC
+ LOGICAL FIRST
+! .. Local Arrays ..
+ CHARACTER*80 REC(2)
+! .. External Functions ..
+ REAL X02AHE, X02AJE, X02AME
+ INTEGER P01ABE
+ EXTERNAL X02AHE, X02AJE, X02AME, P01ABE
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, LOG, MIN,
+ * REAL, SIGN, SIN, SQRT
+! .. Save statement ..
+ SAVE SAFE, LNSAFE, SAFSIN, RTSAFS, FIRST
+! .. Data statements ..
+ DATA FIRST/.TRUE./
+! .. Executable Statements ..
+ IF (FIRST) THEN
+ FIRST = .FALSE.
+ SAFE = ONE/X02AME()
+ LNSAFE = LOG(SAFE)
+ RECEPS = ONE/X02AJE()
+ SAFSIN = MIN(X02AHE(ONE),RECEPS)
+ IF (SAFSIN.LT.RECEPS**0.75E0) THEN
+! Assume that SAFSIN is approximately sqrt(RECEPS), in which
+! case IFAIL=4 cannot occur.
+ RTSAFS = SAFSIN
+ ELSE
+! Set RTSAFS to the argument above which SINE and COSINE will
+! return results of less than half precision, assuming that
+! SAFSIN is approximately equal to RECEPS.
+ RTSAFS = SQRT(SAFSIN)
+ END IF
+ END IF
+ NREC = 0
+ IER = 0
+ X = REAL(Z)
+ Y = AIMAG(Z)
+ IF (ABS(Y).GT.SAFSIN) THEN
+ IER = 5
+ NREC = 2
+ WRITE (REC,FMT=99995) Z
+ S01EAE = ZERO
+ ELSE
+ COSY = COS(Y)
+ SINY = SIN(Y)
+ IF (X.GT.LNSAFE) THEN
+ IF (COSY.EQ.ZERO) THEN
+ RESR = ZERO
+ ELSE
+ XPLNCY = X + LOG(ABS(COSY))
+ IF (XPLNCY.GT.LNSAFE) THEN
+ IER = 1
+ RESR = SIGN(SAFE,COSY)
+ ELSE
+ RESR = SIGN(EXP(XPLNCY),COSY)
+ END IF
+ END IF
+ IF (SINY.EQ.ZERO) THEN
+ RESI = ZERO
+ ELSE
+ XPLNSY = X + LOG(ABS(SINY))
+ IF (XPLNSY.GT.LNSAFE) THEN
+ IER = IER + 2
+ RESI = SIGN(SAFE,SINY)
+ ELSE
+ RESI = SIGN(EXP(XPLNSY),SINY)
+ END IF
+ END IF
+ ELSE
+ EXPX = EXP(X)
+ RESR = EXPX*COSY
+ RESI = EXPX*SINY
+ END IF
+ S01EAE = CMPLX(RESR,RESI)
+ IF (IER.EQ.3) THEN
+ NREC = 2
+ WRITE (REC,FMT=99997) Z
+ ELSE IF (ABS(Y).GT.RTSAFS) THEN
+ IER = 4
+ NREC = 2
+ WRITE (REC,FMT=99996) Z
+ ELSE IF (IER.EQ.1) THEN
+ NREC = 2
+ WRITE (REC,FMT=99999) Z
+ ELSE IF (IER.EQ.2) THEN
+ NREC = 2
+ WRITE (REC,FMT=99998) Z
+ END IF
+ END IF
+ IFAIL = P01ABE(IFAIL,IER,SRNAME,NREC,REC)
+ RETURN
+!
+99999 FORMAT (1X,'** Argument Z causes overflow in real part of result:'
+ * ,/4X,'Z = (',1P,E13.5,',',E13.5,')')
+99998 FORMAT (1X,'** Argument Z causes overflow in imaginary part of r',
+ * 'esult:',/4X,'Z = (',1P,E13.5,',',E13.5,')')
+99997 FORMAT (1X,'** Argument Z causes overflow in both real and imagi',
+ * 'nary parts of result:',/4X,'Z = (',1P,E13.5,',',E13.5,')')
+99996 FORMAT (1X,'** The imaginary part of argument Z is so large that',
+ * ' the result is',/4X,'accurate to less than half precisio',
+ * 'n: Z = (',1P,E13.5,',',E13.5,')')
+99995 FORMAT (1X,'** The imaginary part of argument Z is so large that',
+ * ' the result has no',/4X,'precision: Z = (',1P,E13.5,',',
+ * E13.5,')')
+ END
+ REAL FUNCTION S14ABE(X,IFAIL)
+! MARK 8 RELEASE. NAG COPYRIGHT 1979.
+! MARK 11.5(F77) REVISED. (SEPT 1985.)
+! LNGAMMA(X) FUNCTION
+! ABRAMOWITZ AND STEGUN CH.6
+!
+! **************************************************************
+!
+! TO EXTRACT THE CORRECT CODE FOR A PARTICULAR MACHINE-RANGE,
+! ACTIVATE THE STATEMENTS CONTAINED IN COMMENTS BEGINNING CDD ,
+! WHERE DD IS THE APPROXIMATE NUMBER OF SIGNIFICANT DECIMAL
+! DIGITS REPRESENTED BY THE MACHINE
+! DELETE THE ILLEGAL DUMMY STATEMENTS OF THE FORM
+! * EXPANSION (NNNN) *
+!
+! ALSO INSERT APPROPRIATE DATA STATEMENTS TO DEFINE CONSTANTS
+! WHICH DEPEND ON THE RANGE OF NUMBERS REPRESENTED BY THE
+! MACHINE, RATHER THAN THE PRECISION (SUITABLE STATEMENTS FOR
+! SOME MACHINES ARE CONTAINED IN COMMENTS BEGINNING CRD WHERE
+! D IS A DIGIT WHICH SIMPLY DISTINGUISHES A GROUP OF MACHINES).
+! DELETE THE ILLEGAL DUMMY DATA STATEMENTS WITH VALUES WRITTEN
+! *VALUE*
+!
+! **************************************************************
+!
+! IMPLEMENTATION DEPENDENT CONSTANTS
+!
+! IF(X.LT.XSMALL)GAMMA(X)=1/X
+! I.E. XSMALL*EULGAM.LE.XRELPR
+! LNGAM(XVBIG)=GBIG.LE.XOVFLO
+! LNR2PI=LN(SQRT(2*PI))
+! IF(X.GT.XBIG)LNGAM(X)=(X-0.5)LN(X)-X+LNR2PI
+!
+! .. Parameters ..
+ CHARACTER*6 SRNAME
+ PARAMETER (SRNAME='S14ABE')
+! .. Scalar Arguments ..
+ REAL X
+ INTEGER IFAIL
+! .. Local Scalars ..
+ REAL G, GBIG, LNR2PI, T, XBIG, XSMALL, XVBIG, Y
+ INTEGER I, M
+! .. Local Arrays ..
+ CHARACTER*1 P01REC(1)
+! .. External Functions ..
+ INTEGER P01ABE
+ EXTERNAL P01ABE
+! .. Intrinsic Functions ..
+ INTRINSIC LOG, REAL
+! .. Data statements ..
+!08 DATA XSMALL,XBIG,LNR2PI/
+!08 *1.0E-8,1.2E+3,9.18938533E-1/
+!09 DATA XSMALL,XBIG,LNR2PI/
+!09 *1.0E-9,4.8E+3,9.189385332E-1/
+!12 DATA XSMALL,XBIG,LNR2PI/
+!12 *1.0E-12,3.7E+5,9.189385332047E-1/
+ DATA XSMALL,XBIG,LNR2PI/
+ *1.0E-15,6.8E+6,9.189385332046727E-1/
+!17 DATA XSMALL,XBIG,LNR2PI/
+!17 *1.0E-17,7.7E+7,9.18938533204672742E-1/
+!19 DATA XSMALL,XBIG,LNR2PI/
+!19 *1.0E-19,3.1E+8,9.189385332046727418E-1/
+!
+! RANGE DEPENDENT CONSTANTS
+! DK DK DATA XVBIG,GBIG/4.81E+2461,2.72E+2465/
+ DATA XVBIG,GBIG/4.08E+36,3.40E+38/
+! FOR IEEE SINGLE PRECISION
+!R0 DATA XVBIG,GBIG/4.08E+36,3.40E+38/
+! FOR IBM 360/370 AND SIMILAR MACHINES
+!R1 DATA XVBIG,GBIG/4.29E+73,7.231E+75/
+! FOR DEC10, HONEYWELL, UNIVAC 1100 (S.P.)
+!R2 DATA XVBIG,GBIG/2.05E36,1.69E38/
+! FOR ICL 1900
+!R3 DATA XVBIG,GBIG/3.39E+74,5.784E+76/
+! FOR CDC 7600/CYBER
+!R4 DATA XVBIG,GBIG/1.72E+319,1.26E+322/
+! FOR UNIVAC 1100 (D.P.)
+!R5 DATA XVBIG,GBIG/1.28E305,8.98E+307/
+! FOR IEEE DOUBLE PRECISION
+!R7 DATA XVBIG,GBIG/2.54D+305,1.79D+308/
+! .. Executable Statements ..
+ IF (X.GT.XSMALL) GO TO 20
+! VERY SMALL RANGE
+ IF (X.LE.0.0) GO TO 160
+ IFAIL = 0
+ S14ABE = -LOG(X)
+ GO TO 200
+!
+ 20 IF (X.GT.15.0) GO TO 120
+! MAIN SMALL X RANGE
+ M = X
+ T = X - FLOAT(M)
+ M = M - 1
+ G = 1.0
+ IF (M) 40, 100, 60
+ 40 G = G/X
+ GO TO 100
+ 60 DO 80 I = 1, M
+ G = (X-FLOAT(I))*G
+ 80 CONTINUE
+ 100 T = 2.0*T - 1.0
+!
+! * EXPANSION (0026) *
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 08E.09
+!08 Y = (((((((((((+1.88278283E-6*T-5.48272091E-6)*T+1.03144033E-5)
+!08 * *T-3.13088821E-5)*T+1.01593694E-4)*T-2.98340924E-4)
+!08 * *T+9.15547391E-4)*T-2.42216251E-3)*T+9.04037536E-3)
+!08 * *T-1.34119055E-2)*T+1.03703361E-1)*T+1.61692007E-2)*T +
+!08 * 8.86226925E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 09E.10
+!09 Y = ((((((((((((-6.463247484E-7*T+1.882782826E-6)
+!09 * *T-3.382165478E-6)*T+1.031440334E-5)*T-3.393457634E-5)
+!09 * *T+1.015936944E-4)*T-2.967655076E-4)*T+9.155473906E-4)
+!09 * *T-2.422622002E-3)*T+9.040375355E-3)*T-1.341184808E-2)
+!09 * *T+1.037033609E-1)*T+1.616919866E-2)*T + 8.862269255E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 12E.13
+!12 Y = ((((((((((((((((-8.965837291520E-9*T+2.612707393536E-8)
+!12 * *T-3.802866827264E-8)*T+1.173294768947E-7)
+!12 * *T-4.275076254106E-7)*T+1.276176602829E-6)
+!12 * *T-3.748495971011E-6)*T+1.123829871408E-5)
+!12 * *T-3.364018663166E-5)*T+1.009331480887E-4)
+!12 * *T-2.968895120407E-4)*T+9.157850115110E-4)
+!12 * *T-2.422595461409E-3)*T+9.040335037321E-3)
+!12 * *T-1.341185056618E-2)*T+1.037033634184E-1)
+!12 * *T+1.616919872437E-2)*T + 8.862269254528E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 15E.16
+ Y = (((((((((((((((-1.243191705600000E-10*T+
+ * 3.622882508800000E-10)*T-4.030909644800000E-10)
+ * *T+1.265236705280000E-9)*T-5.419466096640000E-9)
+ * *T+1.613133578240000E-8)*T-4.620920340480000E-8)
+ * *T+1.387603440435200E-7)*T-4.179652784537600E-7)
+ * *T+1.253148247777280E-6)*T-3.754930502328320E-6)
+ * *T+1.125234962812416E-5)*T-3.363759801664768E-5)
+ * *T+1.009281733953869E-4)*T-2.968901194293069E-4)
+ * *T+9.157859942174304E-4)*T-2.422595384546340E-3
+ Y = ((((Y*T+9.040334940477911E-3)*T-1.341185057058971E-2)
+ * *T+1.037033634220705E-1)*T+1.616919872444243E-2)*T +
+ * 8.862269254527580E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 17E.18
+!17 Y = (((((((((((((((-1.46381209600000000E-11*T+
+!17 * 4.26560716800000000E-11)*T-4.01499750400000000E-11)
+!17 * *T+1.27679856640000000E-10)*T-6.13513953280000000E-10)
+!17 * *T+1.82243164160000000E-9)*T-5.11961333760000000E-9)
+!17 * *T+1.53835215257600000E-8)*T-4.64774927155200000E-8)
+!17 * *T+1.39383522590720000E-7)*T-4.17808776355840000E-7)
+!17 * *T+1.25281466396672000E-6)*T-3.75499034136576000E-6)
+!17 * *T+1.12524642975590400E-5)*T-3.36375833240268800E-5)
+!17 * *T+1.00928148823365120E-4)*T-2.96890121633200000E-4
+!17 Y = ((((((Y*T+9.15785997288933120E-4)*T-2.42259538436268176E-3)
+!17 * *T+9.04033494028101968E-3)*T-1.34118505705967765E-2)
+!17 * *T+1.03703363422075456E-1)*T+1.61691987244425092E-2)*T +
+!17 * 8.86226925452758013E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 19E.19
+!19 Y = (((((((((((((((+6.710886400000000000E-13*T-
+!19 * 1.677721600000000000E-12)*T+6.710886400000000000E-13)
+!19 * *T-4.152360960000000000E-12)*T+2.499805184000000000E-11)
+!19 * *T-6.898581504000000000E-11)*T+1.859597107200000000E-10)
+!19 * *T-5.676387532800000000E-10)*T+1.725556326400000000E-9)
+!19 * *T-5.166307737600000000E-9)*T+1.548131827712000000E-8)
+!19 * *T-4.644574052352000000E-8)*T+1.393195837030400000E-7)
+!19 * *T-4.178233990758400000E-7)*T+1.252842254950400000E-6)
+!19 * *T-3.754985815285760000E-6)*T+1.125245651030528000E-5
+!19 Y = (((((((((Y*T-3.363758423922688000E-5)
+!19 * *T+1.009281502108083200E-4)
+!19 * *T-2.968901215188000000E-4)*T+9.157859971435078400E-4)
+!19 * *T-2.422595384370689760E-3)*T+9.040334940288877920E-3)
+!19 * *T-1.341185057059651648E-2)*T+1.037033634220752902E-1)
+!19 * *T+1.616919872444250674E-2)*T + 8.862269254527580137E-1
+!
+ S14ABE = LOG(Y*G)
+ IFAIL = 0
+ GO TO 200
+!
+ 120 IF (X.GT.XBIG) GO TO 140
+! MAIN LARGE X RANGE
+ T = 450.0/(X*X) - 1.0
+!
+! * EXPANSION (0059) *
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 08E.09
+!08 Y = (+3.89980902E-9*T-6.16502533E-6)*T + 8.33271644E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 09E.10
+!09 Y = (+3.899809019E-9*T-6.165025333E-6)*T + 8.332716441E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 12E.13
+!12 Y = ((-6.451144077930E-12*T+3.899809018958E-9)
+!12 * *T-6.165020494506E-6)*T + 8.332716440658E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 15E.16
+ Y = (((+2.002019273379824E-14*T-6.451144077929628E-12)
+ * *T+3.899788998764847E-9)*T-6.165020494506090E-6)*T +
+ * 8.332716440657866E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 17E.18
+!17 Y = ((((-9.94561064728159347E-17*T+2.00201927337982364E-14)
+!17 * *T-6.45101975779653651E-12)*T+3.89978899876484712E-9)
+!17 * *T-6.16502049453716986E-6)*T + 8.33271644065786580E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 19E.19
+!19 Y = (((((+7.196406678180202240E-19*T-9.945610647281593472E-17)
+!19 * *T+2.001911327279650935E-14)*T-6.451019757796536510E-12)
+!19 * *T+3.899788999169644998E-9)*T-6.165020494537169862E-6)*T +
+!19 * 8.332716440657865795E-2
+!
+ S14ABE = (X-0.5)*LOG(X) - X + LNR2PI + Y/X
+ IFAIL = 0
+ GO TO 200
+!
+ 140 IF (X.GT.XVBIG) GO TO 180
+! ASYMPTOTIC LARGE X RANGE
+ S14ABE = (X-0.5)*LOG(X) - X + LNR2PI
+ IFAIL = 0
+ GO TO 200
+!
+! FAILURE EXITS
+ 160 IFAIL = P01ABE(IFAIL,1,SRNAME,0,P01REC)
+ S14ABE = 0.0
+ GO TO 200
+ 180 IFAIL = P01ABE(IFAIL,2,SRNAME,0,P01REC)
+ S14ABE = GBIG
+!
+ 200 RETURN
+!
+ END
+ SUBROUTINE S17DGE(DERIV,Z,SCALE,AI,NZ,IFAIL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-770 (DEC 1989).
+!
+! Original name: CAIRY
+!
+! PURPOSE TO COMPUTE AIRY FUNCTIONS AI(Z) AND DAI(Z) FOR COMPLEX Z
+!
+! DESCRIPTION
+! ===========
+!
+! ON SCALE='U', S17DGE COMPUTES THE COMPLEX AIRY FUNCTION AI(Z)
+! OR ITS DERIVATIVE DAI(Z)/DZ ON DERIV='F' OR DERIV='D'
+! RESPECTIVELY. ON SCALE='S', A SCALING OPTION
+! CEXP(ZTA)*AI(Z) OR CEXP(ZTA)*DAI(Z)/DZ IS PROVIDED TO REMOVE
+! THE EXPONENTIAL DECAY IN -PI/3.LT.ARG(Z).LT.PI/3 AND THE
+! EXPONENTIAL GROWTH IN PI/3.LT.ABS(ARG(Z)).LT.PI WHERE
+! ZTA=(2/3)*Z*CSQRT(Z)
+!
+! WHILE THE AIRY FUNCTIONS AI(Z) AND DAI(Z)/DZ ARE ANALYTIC IN
+! THE WHOLE Z PLANE, THE CORRESPONDING SCALED FUNCTIONS DEFINED
+! FOR SCALE='S' HAVE A CUT ALONG THE NEGATIVE REAL AXIS.
+! DEFINITIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF
+! MATHEMATICAL FUNCTIONS (REF. 1).
+!
+! INPUT
+! Z - Z=CMPLX(X,Y)
+! DERIV - RETURN FUNCTION (DERIV='F') OR DERIVATIVE
+! (DERIV='D')
+! SCALE - A PARAMETER TO INDICATE THE SCALING OPTION
+! SCALE = 'U' OR 'u' RETURNS
+! AI=AI(Z) ON DERIV='F' OR
+! AI=DAI(Z)/DZ ON DERIV='D'
+! SCALE = 'S' OR 's' RETURNS
+! AI=CEXP(ZTA)*AI(Z) ON DERIV='F' OR
+! AI=CEXP(ZTA)*DAI(Z)/DZ ON DERIV='D' WHERE
+! ZTA=(2/3)*Z*CSQRT(Z)
+!
+! OUTPUT
+! AI - COMPLEX ANSWER DEPENDING ON THE CHOICES FOR DERIV
+! AND SCALE
+! NZ - UNDERFLOW INDICATOR
+! NZ= 0 , NORMAL RETURN
+! NZ= 1 , AI=CMPLX(0.0,0.0) DUE TO UNDERFLOW IN
+! -PI/3.LT.ARG(Z).LT.PI/3 ON SCALE='U'
+! IFAIL - ERROR FLAG
+! IFAIL=0, NORMAL RETURN - COMPUTATION COMPLETED
+! IFAIL=1, INPUT ERROR - NO COMPUTATION
+! IFAIL=2, OVERFLOW - NO COMPUTATION, REAL(ZTA)
+! TOO LARGE WITH SCALE = 'U'
+! IFAIL=3, CABS(Z) LARGE - COMPUTATION COMPLETED
+! LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION
+! PRODUCE LESS THAN HALF OF MACHINE ACCURACY
+! IFAIL=4, CABS(Z) TOO LARGE - NO COMPUTATION
+! COMPLETE LOSS OF ACCURACY BY ARGUMENT
+! REDUCTION
+! IFAIL=5, ERROR - NO COMPUTATION,
+! ALGORITHM TERMINATION CONDITION NOT MET
+!
+! LONG DESCRIPTION
+! ================
+!
+! AI AND DAI ARE COMPUTED FOR CABS(Z).GT.1.0 FROM THE K BESSEL
+! FUNCTIONS BY
+!
+! AI(Z)=C*SQRT(Z)*K(1/3,ZTA) , DAI(Z)=-C*Z*K(2/3,ZTA)
+! C=1.0/(PI*SQRT(3.0))
+! ZTA=(2/3)*Z**(3/2)
+!
+! WITH THE POWER SERIES FOR CABS(Z).LE.1.0.
+!
+! IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+! MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES
+! OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF
+! THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR),
+! THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR
+! FLAG IFAIL=3 IS TRIGGERED WHERE UR=X02AJE()=UNIT ROUNDOFF.
+! ALSO, IF THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN
+! ALL SIGNIFICANCE IS LOST AND IFAIL=4. IN ORDER TO USE THE INT
+! FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE
+! LARGEST INTEGER, U3=X02BBE(). THUS, THE MAGNITUDE OF ZETA
+! MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2,
+! AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE
+! PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE
+! PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT-
+! ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG-
+! NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN
+! DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN
+! EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES,
+! NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE
+! PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER
+! MACHINES.
+!
+! THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+! BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+! ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+! SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+! ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+! ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+! CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+! HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+! ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+! SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+! THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+! 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+! THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+! COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+! BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+! COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+! MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+! THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+! OR -PI/2+P.
+!
+! REFERENCES
+! ==========
+! HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+! AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+! COMMERCE, 1955.
+!
+! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+! AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+!
+! A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+! 1018, MAY, 1985
+!
+! A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+! MATH. SOFTWARE, 1986
+!
+! DATE WRITTEN 830501 (YYMMDD)
+! REVISION DATE 830501 (YYMMDD)
+! AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+!
+! .. Parameters ..
+ CHARACTER*6 SRNAME
+ PARAMETER (SRNAME='S17DGE')
+! .. Scalar Arguments ..
+ COMPLEX AI, Z
+ INTEGER IFAIL, NZ
+ CHARACTER DERIV, SCALE
+! .. Local Scalars ..
+ COMPLEX CONE, CSQ, S1, S2, TRM1, TRM2, Z3, ZTA
+ REAL AA, AD, AK, ALAZ, ALIM, ATRM, AZ, AZ3, BB, BK,
+ * C1, C2, CK, COEF, D1, D2, DIG, DK, ELIM, FID,
+ * FNU, R1M5, RL, SAVAA, SFAC, TOL, TTH, Z3I, Z3R,
+ * ZI, ZR
+ INTEGER ID, IERR, IFL, IFLAG, K, K1, K2, KODE, MR, NN,
+ * NREC
+! .. Local Arrays ..
+ COMPLEX CY(1)
+ CHARACTER*80 REC(1)
+! .. External Functions ..
+ COMPLEX S01EAE
+ REAL X02AHE, X02AJE, X02AME
+ INTEGER P01ABE, X02BBE, X02BHE, X02BJE, X02BKE, X02BLE
+ EXTERNAL S01EAE, X02AHE, X02AJE, X02AME, P01ABE, X02BBE,
+ * X02BHE, X02BJE, X02BKE, X02BLE
+! .. External Subroutines ..
+ EXTERNAL DGXS17, DGZS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, LOG, LOG10, MAX, MIN, REAL,
+ * SQRT
+! .. Data statements ..
+ DATA TTH, C1, C2, COEF/6.66666666666666667E-01,
+ * 3.55028053887817240E-01,
+ * 2.58819403792806799E-01,
+ * 1.83776298473930683E-01/
+ DATA CONE/(1.0E0,0.0E0)/
+! .. Executable Statements ..
+ IERR = 0
+ NREC = 0
+ NZ = 0
+ IF (DERIV.EQ.'F' .OR. DERIV.EQ.'f') THEN
+ ID = 0
+ ELSE IF (DERIV.EQ.'D' .OR. DERIV.EQ.'d') THEN
+ ID = 1
+ ELSE
+ ID = -1
+ END IF
+ IF (SCALE.EQ.'U' .OR. SCALE.EQ.'u') THEN
+ KODE = 1
+ ELSE IF (SCALE.EQ.'S' .OR. SCALE.EQ.'s') THEN
+ KODE = 2
+ ELSE
+ KODE = -1
+ END IF
+ IF (ID.EQ.-1) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99999) DERIV
+ ELSE IF (KODE.EQ.-1) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99998) SCALE
+ END IF
+ IF (IERR.EQ.0) THEN
+ AZ = ABS(Z)
+ TOL = MAX(X02AJE(),1.0E-18)
+ FID = ID
+ IF (AZ.GT.1.0E0) THEN
+! ------------------------------------------------------------
+! CASE FOR CABS(Z).GT.1.0
+! ------------------------------------------------------------
+ FNU = (1.0E0+FID)/3.0E0
+! ------------------------------------------------------------
+! SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+! TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+! ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW
+! LIMIT.
+! EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND
+! EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS
+! NEAR UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC
+! IS DONE.
+! RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR
+! LARGE Z.
+! DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+! ------------------------------------------------------------
+ K1 = X02BKE()
+ K2 = X02BLE()
+ R1M5 = LOG10(REAL(X02BHE()))
+ K = MIN(ABS(K1),ABS(K2))
+ ELIM = 2.303E0*(K*R1M5-3.0E0)
+ K1 = X02BJE() - 1
+ AA = R1M5*K1
+ DIG = MIN(AA,18.0E0)
+ AA = AA*2.303E0
+ ALIM = ELIM + MAX(-AA,-41.45E0)
+ RL = 1.2E0*DIG + 3.0E0
+ ALAZ = LOG(AZ)
+! ------------------------------------------------------------
+! TEST FOR RANGE
+! ------------------------------------------------------------
+ AA = 0.5E0/TOL
+ BB = X02BBE(1.0E0)*0.5E0
+ AA = MIN(AA,BB,X02AHE(1.0E0))
+ AA = AA**TTH
+ IF (AZ.GT.AA) THEN
+ NZ = 0
+ IERR = 4
+ NREC = 1
+ WRITE (REC,FMT=99997) AZ, AA
+ ELSE
+ AA = SQRT(AA)
+ SAVAA = AA
+ IF (AZ.GT.AA) THEN
+ IERR = 3
+ NREC = 1
+ WRITE (REC,FMT=99996) AZ, AA
+ END IF
+ CSQ = SQRT(Z)
+ ZTA = Z*CSQ*CMPLX(TTH,0.0E0)
+! ---------------------------------------------------------
+! RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS
+! SMALL
+! ---------------------------------------------------------
+ IFLAG = 0
+ SFAC = 1.0E0
+ ZI = AIMAG(Z)
+ ZR = REAL(Z)
+ AK = AIMAG(ZTA)
+ IF (ZR.LT.0.0E0) THEN
+ BK = REAL(ZTA)
+ CK = -ABS(BK)
+ ZTA = CMPLX(CK,AK)
+ END IF
+ IF (ZI.EQ.0.0E0) THEN
+ IF (ZR.LE.0.0E0) ZTA = CMPLX(0.0E0,AK)
+ END IF
+ AA = REAL(ZTA)
+ IF (AA.GE.0.0E0 .AND. ZR.GT.0.0E0) THEN
+ IF (KODE.NE.2) THEN
+! ---------------------------------------------------
+! UNDERFLOW TEST
+! ---------------------------------------------------
+ IF (AA.GE.ALIM) THEN
+ AA = -AA - 0.25E0*ALAZ
+ IFLAG = 2
+ SFAC = 1.0E0/TOL
+ IF (AA.LT.(-ELIM)) THEN
+ NZ = 1
+ AI = CMPLX(0.0E0,0.0E0)
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ END IF
+ END IF
+ CALL DGXS17(ZTA,FNU,KODE,1,CY,NZ,TOL,ELIM,ALIM)
+ ELSE
+ IF (KODE.NE.2) THEN
+! ---------------------------------------------------
+! OVERFLOW TEST
+! ---------------------------------------------------
+ IF (AA.LE.(-ALIM)) THEN
+ AA = -AA + 0.25E0*ALAZ
+ IFLAG = 1
+ SFAC = TOL
+ IF (AA.GT.ELIM) GO TO 20
+ END IF
+ END IF
+! ------------------------------------------------------
+! DGXS17 AND DGZS17 RETURN EXP(ZTA)*K(FNU,ZTA) ON KODE=2
+! ------------------------------------------------------
+ MR = 1
+ IF (ZI.LT.0.0E0) MR = -1
+ CALL DGZS17(ZTA,FNU,KODE,MR,1,CY,NN,RL,TOL,ELIM,ALIM)
+ IF (NN.GE.0) THEN
+ NZ = NZ + NN
+ GO TO 40
+ ELSE IF (NN.EQ.(-3)) THEN
+ NZ = 0
+ IERR = 4
+ NREC = 1
+ WRITE (REC,FMT=99997) AZ, SAVAA
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ ELSE IF (NN.NE.(-1)) THEN
+ NZ = 0
+ IERR = 5
+ NREC = 1
+ WRITE (REC,FMT=99995)
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ 20 NZ = 0
+ IERR = 2
+ NREC = 1
+ WRITE (REC,FMT=99994)
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ 40 S1 = CY(1)*CMPLX(COEF,0.0E0)
+ IF (IFLAG.NE.0) THEN
+ S1 = S1*CMPLX(SFAC,0.0E0)
+ IF (ID.EQ.1) THEN
+ S1 = -S1*Z
+ AI = S1*CMPLX(1.0E0/SFAC,0.0E0)
+ ELSE
+ S1 = S1*CSQ
+ AI = S1*CMPLX(1.0E0/SFAC,0.0E0)
+ END IF
+ ELSE IF (ID.EQ.1) THEN
+ AI = -Z*S1
+ ELSE
+ AI = CSQ*S1
+ END IF
+ END IF
+ ELSE
+! ------------------------------------------------------------
+! POWER SERIES FOR CABS(Z).LE.1.
+! ------------------------------------------------------------
+ S1 = CONE
+ S2 = CONE
+ IF (AZ.LT.TOL) THEN
+ AA = 1.0E+3*X02AME()
+ S1 = CMPLX(0.0E0,0.0E0)
+ IF (ID.EQ.1) THEN
+ AI = -CMPLX(C2,0.0E0)
+ AA = SQRT(AA)
+ IF (AZ.GT.AA) S1 = Z*Z*CMPLX(0.5E0,0.0E0)
+ AI = AI + S1*CMPLX(C1,0.0E0)
+ ELSE
+ IF (AZ.GT.AA) S1 = CMPLX(C2,0.0E0)*Z
+ AI = CMPLX(C1,0.0E0) - S1
+ END IF
+ ELSE
+ AA = AZ*AZ
+ IF (AA.GE.TOL/AZ) THEN
+ TRM1 = CONE
+ TRM2 = CONE
+ ATRM = 1.0E0
+ Z3 = Z*Z*Z
+ AZ3 = AZ*AA
+ AK = 2.0E0 + FID
+ BK = 3.0E0 - FID - FID
+ CK = 4.0E0 - FID
+ DK = 3.0E0 + FID + FID
+ D1 = AK*DK
+ D2 = BK*CK
+ AD = MIN(D1,D2)
+ AK = 24.0E0 + 9.0E0*FID
+ BK = 30.0E0 - 9.0E0*FID
+ Z3R = REAL(Z3)
+ Z3I = AIMAG(Z3)
+ DO 60 K = 1, 25
+ TRM1 = TRM1*CMPLX(Z3R/D1,Z3I/D1)
+ S1 = S1 + TRM1
+ TRM2 = TRM2*CMPLX(Z3R/D2,Z3I/D2)
+ S2 = S2 + TRM2
+ ATRM = ATRM*AZ3/AD
+ D1 = D1 + AK
+ D2 = D2 + BK
+ AD = MIN(D1,D2)
+ IF (ATRM.LT.TOL*AD) THEN
+ GO TO 80
+ ELSE
+ AK = AK + 18.0E0
+ BK = BK + 18.0E0
+ END IF
+ 60 CONTINUE
+ END IF
+ 80 IF (ID.EQ.1) THEN
+ AI = -S2*CMPLX(C2,0.0E0)
+ IF (AZ.GT.TOL) AI = AI + Z*Z*S1*CMPLX(C1/(1.0E0+FID),
+ * 0.0E0)
+ IF (KODE.NE.1) THEN
+ ZTA = Z*SQRT(Z)*CMPLX(TTH,0.0E0)
+! AI = AI*EXP(ZTA)
+ IFL = 1
+ AI = AI*S01EAE(ZTA,IFL)
+ END IF
+ ELSE
+ AI = S1*CMPLX(C1,0.0E0) - Z*S2*CMPLX(C2,0.0E0)
+ IF (KODE.NE.1) THEN
+ ZTA = Z*SQRT(Z)*CMPLX(TTH,0.0E0)
+! AI = AI*EXP(ZTA)
+ IFL = 1
+ AI = AI*S01EAE(ZTA,IFL)
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+!
+99999 FORMAT (1X,'** On entry, DERIV has illegal value: DERIV = ''',A,
+ * '''')
+99998 FORMAT (1X,'** On entry, SCALE has illegal value: SCALE = ''',A,
+ * '''')
+99997 FORMAT (1X,'** No computation because abs(Z) =',1P,E13.5,' .GT.',
+ * E13.5)
+99996 FORMAT (1X,'** Results lack precision because abs(Z) =',1P,E13.5,
+ * ' .GT.',E13.5)
+99995 FORMAT (1X,'** No computation - algorithm termination condition ',
+ * 'not met.')
+99994 FORMAT (1X,'** No computation because real(ZTA) too large, where',
+ * ' ZTA = (2/3)*Z**(3/2).')
+ END
+ SUBROUTINE S17DLE(M,FNU,Z,N,SCALE,CY,NZ,IFAIL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-781 (DEC 1989).
+!
+! Original name: CBESH
+!
+! PURPOSE TO COMPUTE THE H-BESSEL FUNCTIONS OF A COMPLEX ARGUMENT
+!
+! DESCRIPTION
+! ===========
+!
+! ON SCALE='U', S17DLE COMPUTES AN N MEMBER SEQUENCE OF COMPLEX
+! HANKEL (BESSEL) FUNCTIONS CY(J)=H(M,FNU+J-1,Z) FOR KINDS M=1
+! OR 2, REAL, NONNEGATIVE ORDERS FNU+J-1, J=1,...,N, AND COMPLEX
+! Z.NE.CMPLX(0.0E0,0.0E0) IN THE CUT PLANE -PI.LT.ARG(Z).LE.PI.
+! ON SCALE='S', S17DLE COMPUTES THE SCALED HANKEL FUNCTIONS
+!
+! CY(I)=H(M,FNU+J-1,Z)*EXP(-MM*Z*I) MM=3-2M, I**2=-1.
+!
+! WHICH REMOVES THE EXPONENTIAL BEHAVIOR IN BOTH THE UPPER
+! AND LOWER HALF PLANES. DEFINITIONS AND NOTATION ARE FOUND IN
+! THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS (REF. 1).
+!
+! INPUT
+! Z - Z=CMPLX(X,Y), Z.NE.CMPLX(0.,0.),-PI.LT.ARG(Z).LE.PI
+! FNU - ORDER OF INITIAL H FUNCTION, FNU.GE.0.0E0
+! SCALE - A PARAMETER TO INDICATE THE SCALING OPTION
+! SCALE = 'U' OR SCALE = 'u' RETURNS
+! CY(J)=H(M,FNU+J-1,Z), J=1,...,N
+! = 'S' OR SCALE = 's' RETURNS
+! CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M))
+! J=1,...,N , I**2=-1
+! M - KIND OF HANKEL FUNCTION, M=1 OR 2
+! N - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1
+!
+! OUTPUT
+! CY - A COMPLEX VECTOR WHOSE FIRST N COMPONENTS CONTAIN
+! VALUES FOR THE SEQUENCE
+! CY(J)=H(M,FNU+J-1,Z) OR
+! CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M)) J=1,...,N
+! DEPENDING ON SCALE, I**2=-1.
+! NZ - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW,
+! NZ= 0 , NORMAL RETURN
+! NZ.GT.0 , FIRST NZ COMPONENTS OF CY SET TO ZERO
+! DUE TO UNDERFLOW, CY(J)=CMPLX(0.0,0.0)
+! J=1,...,NZ WHEN Y.GT.0.0 AND M=1 OR
+! Y.LT.0.0 AND M=2. FOR THE COMPLMENTARY
+! HALF PLANES, NZ STATES ONLY THE NUMBER
+! OF UNDERFLOWS.
+! IERR -ERROR FLAG
+! IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+! IERR=1, INPUT ERROR - NO COMPUTATION
+! IERR=2, OVERFLOW - NO COMPUTATION,
+! CABS(Z) TOO SMALL
+! IERR=3 OVERFLOW - NO COMPUTATION,
+! FNU+N-1 TOO LARGE
+! IERR=4, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE
+! BUT LOSSES OF SIGNIFCANCE BY ARGUMENT
+! REDUCTION PRODUCE LESS THAN HALF OF MACHINE
+! ACCURACY
+! IERR=5, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA-
+! TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI-
+! CANCE BY ARGUMENT REDUCTION
+! IERR=6, ERROR - NO COMPUTATION,
+! ALGORITHM TERMINATION CONDITION NOT MET
+!
+! LONG DESCRIPTION
+! ================
+!
+! THE COMPUTATION IS CARRIED OUT BY THE RELATION
+!
+! H(M,FNU,Z)=(1/MP)*EXP(-MP*FNU)*K(FNU,Z*EXP(-MP))
+! MP=MM*HPI*I, MM=3-2*M, HPI=PI/2, I**2=-1
+!
+! FOR M=1 OR 2 WHERE THE K BESSEL FUNCTION IS COMPUTED FOR THE
+! RIGHT HALF PLANE RE(Z).GE.0.0. THE K FUNCTION IS CONTINUED
+! TO THE LEFT HALF PLANE BY THE RELATION
+!
+! K(FNU,Z*EXP(MP)) = EXP(-MP*FNU)*K(FNU,Z)-MP*I(FNU,Z)
+! MP=MR*PI*I, MR=+1 OR -1, RE(Z).GT.0, I**2=-1
+!
+! WHERE I(FNU,Z) IS THE I BESSEL FUNCTION.
+!
+! EXPONENTIAL DECAY OF H(M,FNU,Z) OCCURS IN THE UPPER HALF Z
+! PLANE FOR M=1 AND THE LOWER HALF Z PLANE FOR M=2. EXPONENTIAL
+! GROWTH OCCURS IN THE COMPLEMENTARY HALF PLANES. SCALING
+! BY EXP(-MM*Z*I) REMOVES THE EXPONENTIAL BEHAVIOR IN THE
+! WHOLE Z PLANE FOR Z TO INFINITY.
+!
+! FOR NEGATIVE ORDERS,THE FORMULAE
+!
+! H(1,-FNU,Z) = H(1,FNU,Z)*CEXP( PI*FNU*I)
+! H(2,-FNU,Z) = H(2,FNU,Z)*CEXP(-PI*FNU*I)
+! I**2=-1
+!
+! CAN BE USED.
+!
+! IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+! MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS
+! LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR.
+! CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN
+! LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG
+! IERR=4 IS TRIGGERED WHERE UR=X02AJE()=UNIT ROUNDOFF. ALSO
+! IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS
+! LOST AND IERR=5. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS
+! MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE
+! INTEGER, U3=X02BBE(). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS
+! RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3
+! ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION
+! ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION
+! ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN
+! THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT
+! TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS
+! IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC.
+! SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES.
+!
+! THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+! BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+! ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+! SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+! ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+! ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+! CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+! HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+! ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+! SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+! THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+! 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+! THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+! COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+! BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+! COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+! MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+! THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+! OR -PI/2+P.
+!
+! REFERENCES
+! ==========
+! HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+! AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+! COMMERCE, 1955.
+!
+! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+! BY D. E. AMOS, SAND83-0083, MAY, 1983.
+!
+! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+! AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+!
+! A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+! 1018, MAY, 1985
+!
+! A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+! MATH. SOFTWARE, 1986
+!
+! DATE WRITTEN 830501 (YYMMDD)
+! REVISION DATE 830501 (YYMMDD)
+! AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+!
+! .. Parameters ..
+ CHARACTER*6 SRNAME
+ PARAMETER (SRNAME='S17DLE')
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL FNU
+ INTEGER IFAIL, M, N, NZ
+ CHARACTER*1 SCALE
+! .. Array Arguments ..
+ COMPLEX CY(N)
+! .. Local Scalars ..
+ COMPLEX CSGN, ZN, ZT
+ REAL AA, ALIM, ALN, ARG, ASCLE, ATOL, AZ, BB, CPN,
+ * DIG, ELIM, FMM, FN, FNUL, HPI, R1M5, RHPI, RL,
+ * RTOL, SGN, SPN, TOL, UFL, XN, XX, YN, YY
+ INTEGER I, IERR, INU, INUH, IR, K, K1, K2, KODE, MM, MR,
+ * NN, NREC, NUF, NW
+! .. Local Arrays ..
+ CHARACTER*80 REC(1)
+! .. External Functions ..
+ REAL X02AHE, X02AJE
+ INTEGER P01ABE, X02BBE, X02BHE, X02BJE, X02BKE, X02BLE
+ EXTERNAL X02AHE, X02AJE, P01ABE, X02BBE, X02BHE, X02BJE,
+ * X02BKE, X02BLE
+! .. External Subroutines ..
+ EXTERNAL DEVS17, DGXS17, DLYS17, DLZS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, INT, LOG, LOG10,
+ * MAX, MIN, MOD, REAL, SIGN, SIN, SQRT
+! .. Data statements ..
+!
+ DATA HPI/1.57079632679489662E0/
+! .. Executable Statements ..
+ NZ = 0
+ NREC = 0
+ XX = REAL(Z)
+ YY = AIMAG(Z)
+ IERR = 0
+ IF (SCALE.EQ.'U' .OR. SCALE.EQ.'u') THEN
+ KODE = 1
+ ELSE IF (SCALE.EQ.'S' .OR. SCALE.EQ.'s') THEN
+ KODE = 2
+ ELSE
+ KODE = -1
+ END IF
+ IF (XX.EQ.0.0E0 .AND. YY.EQ.0.0E0) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99999)
+ ELSE IF (FNU.LT.0.0E0) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99998) FNU
+ ELSE IF (KODE.EQ.-1) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99997) SCALE
+ ELSE IF (N.LT.1) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99996) N
+ ELSE IF (M.LT.1 .OR. M.GT.2) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99995) M
+ END IF
+ IF (IERR.EQ.0) THEN
+ NN = N
+! ---------------------------------------------------------------
+! SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+! TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+! ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+! EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND
+! EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR
+! UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+! RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR
+! LARGE Z.
+! DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+! FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE
+! FNU
+! ---------------------------------------------------------------
+ TOL = MAX(X02AJE(),1.0E-18)
+ K1 = X02BKE()
+ K2 = X02BLE()
+ R1M5 = LOG10(REAL(X02BHE()))
+ K = MIN(ABS(K1),ABS(K2))
+ ELIM = 2.303E0*(K*R1M5-3.0E0)
+ K1 = X02BJE() - 1
+ AA = R1M5*K1
+ DIG = MIN(AA,18.0E0)
+ AA = AA*2.303E0
+ ALIM = ELIM + MAX(-AA,-41.45E0)
+ FNUL = 10.0E0 + 6.0E0*(DIG-3.0E0)
+ RL = 1.2E0*DIG + 3.0E0
+ FN = FNU + NN - 1
+ MM = 3 - M - M
+ FMM = MM
+ ZN = Z*CMPLX(0.0E0,-FMM)
+ XN = REAL(ZN)
+ YN = AIMAG(ZN)
+ AZ = ABS(Z)
+! ---------------------------------------------------------------
+! TEST FOR RANGE
+! ---------------------------------------------------------------
+ AA = 0.5E0/TOL
+ BB = X02BBE(1.0E0)*0.5E0
+ AA = MIN(AA,BB,X02AHE(1.0E0))
+ IF (AZ.LE.AA) THEN
+ IF (FN.LE.AA) THEN
+ AA = SQRT(AA)
+ IF (AZ.GT.AA) THEN
+ IERR = 4
+ NREC = 1
+ WRITE (REC,FMT=99994) AZ, AA
+ ELSE IF (FN.GT.AA) THEN
+ IERR = 4
+ NREC = 1
+ WRITE (REC,FMT=99993) FN, AA
+ END IF
+! ---------------------------------------------------------
+! OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE
+! ---------------------------------------------------------
+ UFL = EXP(-ELIM)
+ IF (AZ.GE.UFL) THEN
+ IF (FNU.GT.FNUL) THEN
+! ---------------------------------------------------
+! UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL
+! ---------------------------------------------------
+ MR = 0
+ IF ((XN.LT.0.0E0) .OR. (XN.EQ.0.0E0 .AND. YN.LT.
+ * 0.0E0 .AND. M.EQ.2)) THEN
+ MR = -MM
+ IF (XN.EQ.0.0E0 .AND. YN.LT.0.0E0) ZN = -ZN
+ END IF
+ CALL DLYS17(ZN,FNU,KODE,MR,NN,CY,NW,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 40
+ ELSE
+ NZ = NZ + NW
+ END IF
+ ELSE
+ IF (FN.GT.1.0E0) THEN
+ IF (FN.GT.2.0E0) THEN
+ CALL DEVS17(ZN,FNU,KODE,2,NN,CY,NUF,TOL,ELIM,
+ * ALIM)
+ IF (NUF.LT.0) THEN
+ GO TO 60
+ ELSE
+ NZ = NZ + NUF
+ NN = NN - NUF
+! ------------------------------------------
+! HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1
+! ON RETURN FROM DEVS17
+! IF NUF=NN, THEN CY(I)=CZERO FOR ALL I
+! ------------------------------------------
+ IF (NN.EQ.0) THEN
+ IF (XN.LT.0.0E0) THEN
+ GO TO 60
+ ELSE
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,
+ * NREC,REC)
+ RETURN
+ END IF
+ END IF
+ END IF
+ ELSE IF (AZ.LE.TOL) THEN
+ ARG = 0.5E0*AZ
+ ALN = -FN*LOG(ARG)
+ IF (ALN.GT.ELIM) GO TO 60
+ END IF
+ END IF
+ IF ((XN.LT.0.0E0) .OR. (XN.EQ.0.0E0 .AND. YN.LT.
+ * 0.0E0 .AND. M.EQ.2)) THEN
+! ------------------------------------------------
+! LEFT HALF PLANE COMPUTATION
+! ------------------------------------------------
+ MR = -MM
+ CALL DLZS17(ZN,FNU,KODE,MR,NN,CY,NW,RL,FNUL,TOL,
+ * ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 40
+ ELSE
+ NZ = NW
+ END IF
+ ELSE
+! ------------------------------------------------
+! RIGHT HALF PLANE COMPUTATION, XN.GE.0. .AND.
+! (XN.NE.0. .OR. YN.GE.0. .OR. M=1)
+! ------------------------------------------------
+ CALL DGXS17(ZN,FNU,KODE,NN,CY,NZ,TOL,ELIM,ALIM)
+ END IF
+ END IF
+! ------------------------------------------------------
+! H(M,FNU,Z) = -FMM*(I/HPI)*(ZT**FNU)*K(FNU,-Z*ZT)
+!
+! ZT=EXP(-FMM*HPI*I) = CMPLX(0.0,-FMM), FMM=3-2*M, M=1,2
+! ------------------------------------------------------
+ SGN = SIGN(HPI,-FMM)
+! ------------------------------------------------------
+! CALCULATE EXP(FNU*HPI*I) TO MINIMIZE LOSSES OF
+! SIGNIFICANCE WHEN FNU IS LARGE
+! ------------------------------------------------------
+ INU = INT(FNU)
+ INUH = INU/2
+ IR = INU - 2*INUH
+ ARG = (FNU-INU+IR)*SGN
+ RHPI = 1.0E0/SGN
+ CPN = RHPI*COS(ARG)
+ SPN = RHPI*SIN(ARG)
+! ZN = CMPLX(-SPN,CPN)
+ CSGN = CMPLX(-SPN,CPN)
+! IF (MOD(INUH,2).EQ.1) ZN = -ZN
+ IF (MOD(INUH,2).EQ.1) CSGN = -CSGN
+ ZT = CMPLX(0.0E0,-FMM)
+ RTOL = 1.0E0/TOL
+ ASCLE = UFL*RTOL
+ DO 20 I = 1, NN
+! CY(I) = CY(I)*ZN
+! ZN = ZN*ZT
+ ZN = CY(I)
+ AA = REAL(ZN)
+ BB = AIMAG(ZN)
+ ATOL = 1.0E0
+ IF (MAX(ABS(AA),ABS(BB)).LE.ASCLE) THEN
+ ZN = ZN*RTOL
+ ATOL = TOL
+ END IF
+ ZN = ZN*CSGN
+ CY(I) = ZN*ATOL
+ CSGN = CSGN*ZT
+ 20 CONTINUE
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ 40 IF (NW.EQ.(-3)) THEN
+ NZ = 0
+ IERR = 5
+ NREC = 1
+ WRITE (REC,FMT=99988) AZ, AA
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ ELSE IF (NW.NE.(-1)) THEN
+ NZ = 0
+ IERR = 6
+ NREC = 1
+ WRITE (REC,FMT=99992)
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ 60 IERR = 3
+ NZ = 0
+ NREC = 1
+ WRITE (REC,FMT=99991) FN
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ ELSE
+ IERR = 2
+ NZ = 0
+ NREC = 1
+ WRITE (REC,FMT=99990) AZ, UFL
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ ELSE
+ NZ = 0
+ IERR = 5
+ NREC = 1
+ WRITE (REC,FMT=99989) FN, AA
+ END IF
+ ELSE
+ NZ = 0
+ IERR = 5
+ NREC = 1
+ WRITE (REC,FMT=99988) AZ, AA
+ END IF
+ END IF
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+!
+99999 FORMAT (1X,'** On entry, Z = (0.0,0.0)')
+99998 FORMAT (1X,'** On entry, FNU .LT. 0: FNU = ',E13.5)
+99997 FORMAT (1X,'** On entry, SCALE has an illegal value: SCALE = ''',
+ * A,'''')
+99996 FORMAT (1X,'** On entry, N .LE. 0: N = ',I16)
+99995 FORMAT (1X,'** On entry, M has illegal value: M = ',I16)
+99994 FORMAT (1X,'** Results lack precision because abs(Z) =',1P,E13.5,
+ * ' .GT.',E13.5)
+99993 FORMAT (1X,'** Results lack precision, FNU+N-1 =',1P,E13.5,
+ * ' .GT.',E13.5)
+99992 FORMAT (1X,'** No computation - algorithm termination condition ',
+ * 'not met.')
+99991 FORMAT (1X,'** No computation because FNU+N-1 =',1P,E13.5,' is t',
+ * 'oo large.')
+99990 FORMAT (1X,'** No computation because abs(Z) =',1P,E13.5,' .LT. ',
+ * E13.5)
+99989 FORMAT (1X,'** No computation because FNU+N-1 =',1P,E13.5,' .GT.',
+ * E13.5)
+99988 FORMAT (1X,'** No computation because abs(Z) =',1P,E13.5,' .GT.',
+ * E13.5)
+ END
+ REAL FUNCTION X02AHE(X)
+! MARK 9 RELEASE. NAG COPYRIGHT 1981.
+! MARK 11.5(F77) REVISED. (SEPT 1985.)
+!
+! * MAXIMUM ARGUMENT FOR SIN AND COS *
+! RETURNS THE LARGEST POSITIVE REAL NUMBER MAXSC SUCH THAT
+! SIN(MAXSC) AND COS(MAXSC) CAN BE SUCCESSFULLY COMPUTED
+! BY THE COMPILER SUPPLIED SIN AND COS ROUTINES.
+!
+! .. Scalar Arguments ..
+ REAL X
+ REAL CONX02
+ DATA CONX02 /1.677721600000E+7 /
+! .. Executable Statements ..
+ X02AHE = CONX02
+ RETURN
+ END
+ REAL FUNCTION X02AJE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS (1/2)*B**(1-P) IF ROUNDS IS .TRUE.
+! RETURNS B**(1-P) OTHERWISE
+!
+ REAL CONX02
+ DATA CONX02 /1.4210854715202E-14 /
+!bc DATA CONX02 /1.421090000020E-14 /
+! .. Executable Statements ..
+ X02AJE = CONX02
+ RETURN
+ END
+ REAL FUNCTION X02ALE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS (1 - B**(-P)) * B**EMAX (THE LARGEST POSITIVE MODEL
+! NUMBER)
+!
+ REAL CONX02
+! DK DK DK DATA CONX02 /0577757777777777777777B /
+ DATA CONX02 /1.e30/
+! .. Executable Statements ..
+ X02ALE = CONX02
+ RETURN
+ END
+ REAL FUNCTION X02AME()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE 'SAFE RANGE' PARAMETER
+! I.E. THE SMALLEST POSITIVE MODEL NUMBER Z SUCH THAT
+! FOR ANY X WHICH SATISFIES X.GE.Z AND X.LE.1/Z
+! THE FOLLOWING CAN BE COMPUTED WITHOUT OVERFLOW, UNDERFLOW OR OTHER
+! ERROR
+!
+! -X
+! 1.0/X
+! SQRT(X)
+! LOG(X)
+! EXP(LOG(X))
+! Y**(LOG(X)/LOG(Y)) FOR ANY Y
+!
+ REAL CONX02
+! DK DK DK DATA CONX02 /0200044000000000000004B /
+ DATA CONX02 /1.e-27/
+! .. Executable Statements ..
+ X02AME = CONX02
+ RETURN
+ END
+ REAL FUNCTION X02ANE()
+! MARK 15 RELEASE. NAG COPYRIGHT 1991.
+!
+! Returns the 'safe range' parameter for complex numbers,
+! i.e. the smallest positive model number Z such that
+! for any X which satisfies X.ge.Z and X.le.1/Z
+! the following can be computed without overflow, underflow or other
+! error
+!
+! -W
+! 1.0/W
+! SQRT(W)
+! LOG(W)
+! EXP(LOG(W))
+! Y**(LOG(W)/LOG(Y)) for any Y
+! ABS(W)
+!
+! where W is any of cmplx(X,0), cmplx(0,X), cmplx(X,X),
+! cmplx(1/X,0), cmplx(0,1/X), cmplx(1/X,1/X).
+!
+ REAL CONX02
+!bc DATA CONX02 /0000006220426276611547B /
+ DATA CONX02 / 2.708212596942E-123 /
+! .. Executable Statements ..
+ X02ANE = CONX02
+ RETURN
+ END
+ INTEGER FUNCTION X02BBE(X)
+! NAG COPYRIGHT 1975
+! MARK 4.5 RELEASE
+! MARK 11.5(F77) REVISED. (SEPT 1985.)
+! * MAXINT *
+! RETURNS THE LARGEST INTEGER REPRESENTABLE ON THE COMPUTER
+! THE X PARAMETER IS NOT USED
+! .. Scalar Arguments ..
+ REAL X
+! .. Executable Statements ..
+! FOR ICL 1900
+! X02BBE = 8388607
+! DK DK DK X02BBE = 70368744177663
+ X02BBE = 744177663
+ RETURN
+ END
+ INTEGER FUNCTION X02BHE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE MODEL PARAMETER, B.
+!
+! .. Executable Statements ..
+ X02BHE = 2
+ RETURN
+ END
+ INTEGER FUNCTION X02BJE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE MODEL PARAMETER, p.
+!
+! .. Executable Statements ..
+ X02BJE = 47
+ RETURN
+ END
+ INTEGER FUNCTION X02BKE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE MODEL PARAMETER, EMIN.
+!
+! .. Executable Statements ..
+ X02BKE = -8192
+ RETURN
+ END
+ INTEGER FUNCTION X02BLE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE MODEL PARAMETER, EMAX.
+!
+! .. Executable Statements ..
+ X02BLE = 8189
+ RETURN
+ END
+ SUBROUTINE X04AAE(I,NERR)
+! MARK 7 RELEASE. NAG COPYRIGHT 1978
+! MARK 7C REVISED IER-190 (MAY 1979)
+! MARK 11.5(F77) REVISED. (SEPT 1985.)
+! MARK 14 REVISED. IER-829 (DEC 1989).
+! IF I = 0, SETS NERR TO CURRENT ERROR MESSAGE UNIT NUMBER
+! (STORED IN NERR1).
+! IF I = 1, CHANGES CURRENT ERROR MESSAGE UNIT NUMBER TO
+! VALUE SPECIFIED BY NERR.
+!
+! .. Scalar Arguments ..
+ INTEGER I, NERR
+! .. Local Scalars ..
+ INTEGER NERR1
+! .. Save statement ..
+ SAVE NERR1
+! .. Data statements ..
+ DATA NERR1/0/
+! .. Executable Statements ..
+ IF (I.EQ.0) NERR = NERR1
+ IF (I.EQ.1) NERR1 = NERR
+ RETURN
+ END
+ SUBROUTINE X04BAE(NOUT,REC)
+! MARK 11.5(F77) RELEASE. NAG COPYRIGHT 1986.
+!
+! X04BAE writes the contents of REC to the unit defined by NOUT.
+!
+! Trailing blanks are not output, except that if REC is entirely
+! blank, a single blank character is output.
+! If NOUT.lt.0, i.e. if NOUT is not a valid Fortran unit identifier,
+! then no output occurs.
+!
+! .. Scalar Arguments ..
+ INTEGER NOUT
+ CHARACTER*(*) REC
+! .. Local Scalars ..
+ INTEGER I
+! .. Intrinsic Functions ..
+ INTRINSIC LEN
+! .. Executable Statements ..
+ IF (NOUT.GE.0) THEN
+! Remove trailing blanks
+ DO 20 I = LEN(REC), 2, -1
+ IF (REC(I:I).NE.' ') GO TO 40
+ 20 CONTINUE
+! Write record to external file
+ 40 WRITE (NOUT,FMT=99999) REC(1:I)
+ END IF
+ RETURN
+!
+99999 FORMAT (A)
+ END
+
Added: seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_ori_with_causality_problem.f
===================================================================
--- seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_ori_with_causality_problem.f (rev 0)
+++ seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_ori_with_causality_problem.f 2012-01-13 17:53:28 UTC (rev 19356)
@@ -0,0 +1,7673 @@
+
+ program analytical_sol
+
+ implicit none
+
+ integer iratio
+ parameter(iratio = 32)
+
+ integer nfreq,nt
+! DK DK parameter (nfreq = 4096)
+ parameter (nfreq = 8*65536)
+ parameter (nt = iratio * nfreq)
+
+ double precision freqmax
+ parameter (freqmax = 80.d0)
+
+ double precision freqseuil
+! DK DK parameter (freqseuil = 0.25d0)
+ parameter (freqseuil = 0.05d0)
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! for the solution in time domain
+ integer it
+ real wsave(4*nt+15)
+ complex c(nt)
+
+! properties of the medium
+ double precision rho
+ parameter(rho = 2000.d0)
+
+! definition position recepteur Carcione
+ double precision x1,x2
+
+! Definition source Dimitri
+ double precision f0,t0,eta
+ parameter(f0 = 18.d0)
+ parameter(t0 = 1.2d0 / f0)
+ parameter(eta = 0.5d0)
+
+! Definition source Carcione
+! double precision f0,t0,eta,epsil
+! parameter(f0 = 50.d0)
+! parameter(t0 = 0.075d0)
+! parameter(epsil = 1.d0)
+! parameter(eta = 0.5d0)
+
+! attenuation constants from Carcione 1988 GJI vol 95 p 604
+! two mechanisms for the moment
+ double precision tau_epsilon_nu1_mech1,
+ . tau_sigma_nu1_mech1,
+ . tau_epsilon_nu2_mech1, tau_sigma_nu2_mech1,
+ . tau_epsilon_nu1_mech2,
+ . tau_sigma_nu1_mech2, tau_epsilon_nu2_mech2,
+ . tau_sigma_nu2_mech2
+
+ parameter(tau_epsilon_nu1_mech1 = 0.0325305d0)
+ parameter(tau_sigma_nu1_mech1 = 0.0311465d0)
+ parameter(tau_epsilon_nu2_mech1 = 0.0332577d0)
+ parameter(tau_sigma_nu2_mech1 = 0.0304655d0)
+ parameter(tau_epsilon_nu1_mech2 = 0.0032530d0)
+ parameter(tau_sigma_nu1_mech2 = 0.0031146d0)
+ parameter(tau_epsilon_nu2_mech2 = 0.0033257d0)
+ parameter(tau_sigma_nu2_mech2 = 0.0030465d0)
+
+ integer Lnu
+
+ double precision M1,M2
+ parameter(M1 = 20.d9)
+ parameter(M2 = 16.d9)
+
+ integer ifreq,ifreq2
+ double precision deltafreq,freq,omega,omega0,deltat,time
+ double complex comparg
+
+! fourier transform of the Ricker wavelet source
+ double complex fomega(0:nfreq)
+
+! real and imaginary parts
+ double precision ra(0:nfreq),rb(0:nfreq)
+
+! spectral amplitude
+ double precision ampli(0:nfreq)
+
+! analytical solution for both components
+ double complex phi1(-nfreq:nfreq)
+ double complex phi2(-nfreq:nfreq)
+
+! external functions
+ double complex u1,u2
+ external u1,u2
+
+! modules elastiques
+ double complex M1C, M2C, E, V1, V2
+
+ logical correction_f0
+
+! ********** fin declarations ************
+
+! lecture des parametres de la simu
+ open(unit=10,file='params_carcione.dat',status='old')
+ read(10,*) x1
+ read(10,*) x2
+ read(10,*) correction_f0
+ close(10)
+
+ print *,'Recepteur en x1,x2 : ',x1,x2
+ print *,'Correction Hankel en f=0 :',correction_f0
+
+! step in frequency
+ deltafreq = freqmax / dble(nfreq)
+
+! define the spectrum of the source
+ do ifreq=0,nfreq
+ freq = deltafreq * dble(ifreq)
+ omega = 2.d0 * pi * freq
+ omega0 = 2.d0 * pi * f0
+ comparg = dcmplx(0.d0,omega*t0)
+
+! definir le spectre du ricker de carcione avec cos()
+! d'apres Carcione GJI vol 93 p 401 (1988)
+! fomega(ifreq) = pi * dsqrt(pi/eta) * (1.d0/omega0)
+! . * cdexp(comparg) *
+! . ( dexp(- (pi*pi/eta) * (epsil/2 - omega/omega0)**2)
+! . + dexp(- (pi*pi/eta) * (epsil/2 + omega/omega0)**2) )
+
+! definir le spectre du ricker de carcione avec cos()
+! d'apres Carcione GJI vol 93 p 401 (1988)
+ fomega(ifreq) = - omega**2 * 2.d0 * (dsqrt(pi)/omega0)
+! DK DK . * cdexp(comparg) * dexp(- (omega/omega0)**2)
+ . * cdexp(-comparg) * dexp(- (omega/omega0)**2)
+
+ ra(ifreq) = dreal(fomega(ifreq))
+ rb(ifreq) = dimag(fomega(ifreq))
+! prendre le module de l'amplitude spectrale
+ ampli(ifreq) = dsqrt(ra(ifreq)**2 + rb(ifreq)**2)
+ enddo
+
+! sauvegarde du spectre d'amplitude de la source en Hz au format Gnuplot
+ open(unit=10,file='spectre.gnu',status='unknown')
+ do ifreq = 0,nfreq
+ freq = deltafreq * dble(ifreq)
+ write(10,*) sngl(freq),sngl(ampli(ifreq))
+ enddo
+ close(10)
+
+! ************** calcul solution analytique ****************
+
+! d'apres Carcione GJI vol 95 p 611 (1988)
+ do ifreq=0,nfreq
+ freq = deltafreq * dble(ifreq)
+ omega = 2.d0 * pi * freq
+
+! critere ad-hoc pour eviter singularite en zero
+ if(freq .lt. freqseuil) omega = 2.d0 * pi * freqseuil
+
+! modules elastiques complexes
+ Lnu = 2
+ M1C = M1 * (1.d0 - Lnu + dcmplx(1.d0,omega*tau_epsilon_nu1_mech1)
+ . / dcmplx(1.d0,omega*tau_sigma_nu1_mech1)
+ . + dcmplx(1.d0,omega*tau_epsilon_nu1_mech2)
+ . / dcmplx(1.d0,omega*tau_sigma_nu1_mech2) )
+ M2C = M2 * (1.d0 - Lnu + dcmplx(1.d0,omega*tau_epsilon_nu2_mech1)
+ . / dcmplx(1.d0,omega*tau_sigma_nu2_mech1)
+ . + dcmplx(1.d0,omega*tau_epsilon_nu2_mech2)
+ . / dcmplx(1.d0,omega*tau_sigma_nu2_mech2) )
+ E = (M1C + M2C) / 2
+ V1 = cdsqrt(E / rho)
+ V2 = cdsqrt(M2C / (2.d0 * rho))
+
+! calcul de la solution analytique en frequence
+ phi1(ifreq) = u1(omega,V1,V2,x1,x2,rho) * fomega(ifreq)
+ phi2(ifreq) = u2(omega,V1,V2,x1,x2,rho) * fomega(ifreq)
+
+! a nouveau critere ad-hoc pour eviter singularite en zero
+ if(freq .lt. freqseuil) then
+ phi1(ifreq) = dcmplx(0.d0,0.d0)
+ phi2(ifreq) = dcmplx(0.d0,0.d0)
+ endif
+
+ enddo
+
+! pour eviter singularite en zero, prendre premiere valeur non nulle
+ if(correction_f0) then
+ do ifreq=0,nfreq
+ if(cdabs(phi1(ifreq)) .gt. 0.d0) goto 180
+ do ifreq2=ifreq,nfreq
+ if(cdabs(phi1(ifreq2)) .gt. 0.d0) goto 181
+ enddo
+ 181 continue
+ phi1(ifreq) = phi1(ifreq2)
+ phi2(ifreq) = phi2(ifreq2)
+ enddo
+ 180 continue
+ endif
+
+! take the conjugate value for negative frequencies
+ do ifreq=-nfreq,-1
+ phi1(ifreq) = dconjg(phi1(-ifreq))
+ phi2(ifreq) = dconjg(phi2(-ifreq))
+ enddo
+
+! save the result in the frequency domain
+ open(unit=11,file='cmplx_phi',status='unknown')
+ do ifreq=-nfreq,nfreq
+ freq = deltafreq * dble(ifreq)
+ write(11,*) sngl(freq),
+ . sngl(dreal(phi1(ifreq))),sngl(dimag(phi1(ifreq))),
+ . sngl(dreal(phi2(ifreq))),sngl(dimag(phi2(ifreq)))
+ enddo
+ close(11)
+
+! Calculation of the time domain solution using Netlib
+
+! initialize FFT arrays
+ call cffti(nt,wsave)
+
+! clear array of Fourier coefficients
+ do it=1,nt
+ c(it) = cmplx(0.,0.)
+ enddo
+
+! enter the fourier values for Ux
+ c(1) = cmplx(phi1(0))
+ do ifreq=1,nfreq-2
+ c(ifreq+1) = cmplx(phi1(ifreq))
+ c(nt+1-ifreq) = conjg(cmplx(phi1(ifreq)))
+ enddo
+
+! perform the inverse FFT for Ux
+ call cfftb(nt,c,wsave)
+
+! valeur d'un pas de temps
+ deltat = 1.d0 / (freqmax*dble(iratio))
+
+! save time result inverse FFT for Ux
+ open(unit=11,file='Ux_time_analytical_solution.dat',
+ . status='unknown')
+ do it=1,nt
+!c DK DK Dec 2011: subtract t0 to be consistent with the SPECFEM2D code
+ time = dble(it)*deltat - t0
+ if(time.le.2.d0)
+ . write(11,*) sngl(time),real(c(it)),imag(c(it))
+ enddo
+ close(11)
+
+! clear array of Fourier coefficients
+ do it=1,nt
+ c(it) = cmplx(0.,0.)
+ enddo
+
+! enter the fourier values for Uz
+ c(1) = cmplx(phi2(0))
+ do ifreq=1,nfreq-2
+ c(ifreq+1) = cmplx(phi2(ifreq))
+ c(nt+1-ifreq) = conjg(cmplx(phi2(ifreq)))
+ enddo
+
+! perform the inverse FFT for Uz
+ call cfftb(nt,c,wsave)
+
+! save time result inverse FFT for Uz
+ open(unit=11,file='Uz_time_analytical_solution.dat',
+ . status='unknown')
+ do it=1,nt
+!c DK DK Dec 2011: subtract t0 to be consistent with the SPECFEM2D code
+ time = dble(it)*deltat - t0
+ if(time.le.2.d0)
+ . write(11,*) sngl(time),real(c(it)),imag(c(it))
+ enddo
+ close(11)
+
+ end
+
+! -----------
+
+ double complex function u1(omega,v1,v2,x1,x2,rho)
+
+ implicit none
+
+ double precision omega
+ double complex v1,v2
+
+ double complex G1,G2
+ external G1,G2
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! amplitude de la force
+ double precision F
+ parameter(F = 1.d10)
+
+ double precision x1,x2,r,rho
+
+! source-receiver distance
+ r = dsqrt(x1**2 + x2**2)
+
+ u1 = F * x1 * x2 * (G1(r,omega,v1,v2) + G2(r,omega,v1,v2))
+ . / (2.d0 * pi * rho * r**2 )
+
+ return
+ end
+
+! -----------
+
+ double complex function u2(omega,v1,v2,x1,x2,rho)
+
+ implicit none
+
+ double precision omega
+ double complex v1,v2
+
+ double complex G1,G2
+ external G1,G2
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! amplitude de la force
+ double precision F
+ parameter(F = 1.d10)
+
+ double precision x1,x2,r,rho
+
+! source-receiver distance
+ r = dsqrt(x1**2 + x2**2)
+
+ u2 = F * (x2*x2*G1(r,omega,v1,v2) - x1*x1*G2(r,omega,v1,v2))
+ . / (2.d0 * pi * rho * r**2 )
+
+ return
+ end
+
+! -----------
+
+ double complex function G1(r,omega,v1,v2)
+
+ implicit none
+
+ double precision r,omega
+ double complex v1,v2
+
+ double complex hankel0,hankel1
+ external hankel0,hankel1
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! bug Carcione corrige : omega/(r*v) -> omega*r/v
+
+ G1 = ( hankel0(omega*r/v1)/(v1**2) +
+ . hankel1(omega*r/v2)/(omega*r*v2) -
+ . hankel1(omega*r/v1)/(omega*r*v1) ) *
+ . dcmplx(0.d0,- pi / 2.d0)
+
+ return
+ end
+
+! -----------
+
+ double complex function G2(r,omega,v1,v2)
+
+ implicit none
+
+ double precision r,omega
+ double complex v1,v2
+
+ double complex hankel0,hankel1
+ external hankel0,hankel1
+
+ double precision pi
+ parameter (pi = 3.141592653589793d0)
+
+! bug Carcione corrige : omega/(r*v) -> omega*r/v
+
+ G2 = ( hankel0(omega*r/v2)/(v2**2) -
+ . hankel1(omega*r/v2)/(omega*r*v2) +
+ . hankel1(omega*r/v1)/(omega*r*v1) ) *
+ . dcmplx(0.d0,+ pi / 2.d0)
+
+ return
+ end
+
+! -----------
+
+ double complex function hankel0(z)
+
+ implicit none
+
+ double complex z
+
+! on utilise la routine NAG appelee S17DLE (simple precision)
+
+ integer ifail,nz
+ complex result
+
+ ifail = -1
+ call S17DLE(2,0.0,cmplx(z),1,'U',result,nz,ifail)
+ if(ifail .ne. 0) stop 'S17DLE failed in hankel0'
+ if(nz .gt. 0) print *,nz,' termes mis a zero par underflow'
+
+ hankel0 = dcmplx(result)
+
+ return
+ end
+
+! -----------
+
+ double complex function hankel1(z)
+
+ implicit none
+
+ double complex z
+
+! on utilise la routine NAG appelee S17DLE (simple precision)
+
+ integer ifail,nz
+ complex result
+
+ ifail = -1
+ call S17DLE(2,1.0,cmplx(z),1,'U',result,nz,ifail)
+ if(ifail .ne. 0) stop 'S17DLE failed in hankel1'
+ if(nz .gt. 0) print *,nz,' termes mis a zero par underflow'
+
+ hankel1 = dcmplx(result)
+
+ return
+ end
+
+! ***************** routine de FFT pour signal en temps ****************
+
+! FFT routine taken from Netlib
+
+ SUBROUTINE CFFTB (N,C,WSAVE)
+ DIMENSION C(1) ,WSAVE(1)
+ IF (N .EQ. 1) RETURN
+ IW1 = N+N+1
+ IW2 = IW1+N+N
+ CALL CFFTB1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2))
+ RETURN
+ END
+ SUBROUTINE CFFTB1 (N,C,CH,WA,IFAC)
+ DIMENSION CH(1) ,C(1) ,WA(1) ,IFAC(1)
+ NF = IFAC(2)
+ NA = 0
+ L1 = 1
+ IW = 1
+ DO 116 K1=1,NF
+ IP = IFAC(K1+2)
+ L2 = IP*L1
+ IDO = N/L2
+ IDOT = IDO+IDO
+ IDL1 = IDOT*L1
+ IF (IP .NE. 4) GO TO 103
+ IX2 = IW+IDOT
+ IX3 = IX2+IDOT
+ IF (NA .NE. 0) GO TO 101
+ CALL PASSB4 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3))
+ GO TO 102
+ 101 CALL PASSB4 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3))
+ 102 NA = 1-NA
+ GO TO 115
+ 103 IF (IP .NE. 2) GO TO 106
+ IF (NA .NE. 0) GO TO 104
+ CALL PASSB2 (IDOT,L1,C,CH,WA(IW))
+ GO TO 105
+ 104 CALL PASSB2 (IDOT,L1,CH,C,WA(IW))
+ 105 NA = 1-NA
+ GO TO 115
+ 106 IF (IP .NE. 3) GO TO 109
+ IX2 = IW+IDOT
+ IF (NA .NE. 0) GO TO 107
+ CALL PASSB3 (IDOT,L1,C,CH,WA(IW),WA(IX2))
+ GO TO 108
+ 107 CALL PASSB3 (IDOT,L1,CH,C,WA(IW),WA(IX2))
+ 108 NA = 1-NA
+ GO TO 115
+ 109 IF (IP .NE. 5) GO TO 112
+ IX2 = IW+IDOT
+ IX3 = IX2+IDOT
+ IX4 = IX3+IDOT
+ IF (NA .NE. 0) GO TO 110
+ CALL PASSB5 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+ GO TO 111
+ 110 CALL PASSB5 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+ 111 NA = 1-NA
+ GO TO 115
+ 112 IF (NA .NE. 0) GO TO 113
+ CALL PASSB (NAC,IDOT,IP,L1,IDL1,C,C,C,CH,CH,WA(IW))
+ GO TO 114
+ 113 CALL PASSB (NAC,IDOT,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW))
+ 114 IF (NAC .NE. 0) NA = 1-NA
+ 115 L1 = L2
+ IW = IW+(IP-1)*IDOT
+ 116 CONTINUE
+ IF (NA .EQ. 0) RETURN
+ N2 = N+N
+ DO 117 I=1,N2
+ C(I) = CH(I)
+ 117 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB (NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA)
+ DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) ,
+ 1 C1(IDO,L1,IP) ,WA(1) ,C2(IDL1,IP),
+ 2 CH2(IDL1,IP)
+ IDOT = IDO/2
+ NT = IP*IDL1
+ IPP2 = IP+2
+ IPPH = (IP+1)/2
+ IDP = IP*IDO
+!
+ IF (IDO .LT. L1) GO TO 106
+ DO 103 J=2,IPPH
+ JC = IPP2-J
+ DO 102 K=1,L1
+ DO 101 I=1,IDO
+ CH(I,K,J) = CC(I,J,K)+CC(I,JC,K)
+ CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K)
+ 101 CONTINUE
+ 102 CONTINUE
+ 103 CONTINUE
+ DO 105 K=1,L1
+ DO 104 I=1,IDO
+ CH(I,K,1) = CC(I,1,K)
+ 104 CONTINUE
+ 105 CONTINUE
+ GO TO 112
+ 106 DO 109 J=2,IPPH
+ JC = IPP2-J
+ DO 108 I=1,IDO
+ DO 107 K=1,L1
+ CH(I,K,J) = CC(I,J,K)+CC(I,JC,K)
+ CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K)
+ 107 CONTINUE
+ 108 CONTINUE
+ 109 CONTINUE
+ DO 111 I=1,IDO
+ DO 110 K=1,L1
+ CH(I,K,1) = CC(I,1,K)
+ 110 CONTINUE
+ 111 CONTINUE
+ 112 IDL = 2-IDO
+ INC = 0
+ DO 116 L=2,IPPH
+ LC = IPP2-L
+ IDL = IDL+IDO
+ DO 113 IK=1,IDL1
+ C2(IK,L) = CH2(IK,1)+WA(IDL-1)*CH2(IK,2)
+ C2(IK,LC) = WA(IDL)*CH2(IK,IP)
+ 113 CONTINUE
+ IDLJ = IDL
+ INC = INC+IDO
+ DO 115 J=3,IPPH
+ JC = IPP2-J
+ IDLJ = IDLJ+INC
+ IF (IDLJ .GT. IDP) IDLJ = IDLJ-IDP
+ WAR = WA(IDLJ-1)
+ WAI = WA(IDLJ)
+ DO 114 IK=1,IDL1
+ C2(IK,L) = C2(IK,L)+WAR*CH2(IK,J)
+ C2(IK,LC) = C2(IK,LC)+WAI*CH2(IK,JC)
+ 114 CONTINUE
+ 115 CONTINUE
+ 116 CONTINUE
+ DO 118 J=2,IPPH
+ DO 117 IK=1,IDL1
+ CH2(IK,1) = CH2(IK,1)+CH2(IK,J)
+ 117 CONTINUE
+ 118 CONTINUE
+ DO 120 J=2,IPPH
+ JC = IPP2-J
+ DO 119 IK=2,IDL1,2
+ CH2(IK-1,J) = C2(IK-1,J)-C2(IK,JC)
+ CH2(IK-1,JC) = C2(IK-1,J)+C2(IK,JC)
+ CH2(IK,J) = C2(IK,J)+C2(IK-1,JC)
+ CH2(IK,JC) = C2(IK,J)-C2(IK-1,JC)
+ 119 CONTINUE
+ 120 CONTINUE
+ NAC = 1
+ IF (IDO .EQ. 2) RETURN
+ NAC = 0
+ DO 121 IK=1,IDL1
+ C2(IK,1) = CH2(IK,1)
+ 121 CONTINUE
+ DO 123 J=2,IP
+ DO 122 K=1,L1
+ C1(1,K,J) = CH(1,K,J)
+ C1(2,K,J) = CH(2,K,J)
+ 122 CONTINUE
+ 123 CONTINUE
+ IF (IDOT .GT. L1) GO TO 127
+ IDIJ = 0
+ DO 126 J=2,IP
+ IDIJ = IDIJ+2
+ DO 125 I=4,IDO,2
+ IDIJ = IDIJ+2
+ DO 124 K=1,L1
+ C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)-WA(IDIJ)*CH(I,K,J)
+ C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)+WA(IDIJ)*CH(I-1,K,J)
+ 124 CONTINUE
+ 125 CONTINUE
+ 126 CONTINUE
+ RETURN
+ 127 IDJ = 2-IDO
+ DO 130 J=2,IP
+ IDJ = IDJ+IDO
+ DO 129 K=1,L1
+ IDIJ = IDJ
+ DO 128 I=4,IDO,2
+ IDIJ = IDIJ+2
+ C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)-WA(IDIJ)*CH(I,K,J)
+ C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)+WA(IDIJ)*CH(I-1,K,J)
+ 128 CONTINUE
+ 129 CONTINUE
+ 130 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB2 (IDO,L1,CC,CH,WA1)
+ DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) ,
+ 1 WA1(1)
+ IF (IDO .GT. 2) GO TO 102
+ DO 101 K=1,L1
+ CH(1,K,1) = CC(1,1,K)+CC(1,2,K)
+ CH(1,K,2) = CC(1,1,K)-CC(1,2,K)
+ CH(2,K,1) = CC(2,1,K)+CC(2,2,K)
+ CH(2,K,2) = CC(2,1,K)-CC(2,2,K)
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ CH(I-1,K,1) = CC(I-1,1,K)+CC(I-1,2,K)
+ TR2 = CC(I-1,1,K)-CC(I-1,2,K)
+ CH(I,K,1) = CC(I,1,K)+CC(I,2,K)
+ TI2 = CC(I,1,K)-CC(I,2,K)
+ CH(I,K,2) = WA1(I-1)*TI2+WA1(I)*TR2
+ CH(I-1,K,2) = WA1(I-1)*TR2-WA1(I)*TI2
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB3 (IDO,L1,CC,CH,WA1,WA2)
+ DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) ,
+ 1 WA1(1) ,WA2(1)
+ DATA TAUR,TAUI /-.5,.866025403784439/
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TR2 = CC(1,2,K)+CC(1,3,K)
+ CR2 = CC(1,1,K)+TAUR*TR2
+ CH(1,K,1) = CC(1,1,K)+TR2
+ TI2 = CC(2,2,K)+CC(2,3,K)
+ CI2 = CC(2,1,K)+TAUR*TI2
+ CH(2,K,1) = CC(2,1,K)+TI2
+ CR3 = TAUI*(CC(1,2,K)-CC(1,3,K))
+ CI3 = TAUI*(CC(2,2,K)-CC(2,3,K))
+ CH(1,K,2) = CR2-CI3
+ CH(1,K,3) = CR2+CI3
+ CH(2,K,2) = CI2+CR3
+ CH(2,K,3) = CI2-CR3
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TR2 = CC(I-1,2,K)+CC(I-1,3,K)
+ CR2 = CC(I-1,1,K)+TAUR*TR2
+ CH(I-1,K,1) = CC(I-1,1,K)+TR2
+ TI2 = CC(I,2,K)+CC(I,3,K)
+ CI2 = CC(I,1,K)+TAUR*TI2
+ CH(I,K,1) = CC(I,1,K)+TI2
+ CR3 = TAUI*(CC(I-1,2,K)-CC(I-1,3,K))
+ CI3 = TAUI*(CC(I,2,K)-CC(I,3,K))
+ DR2 = CR2-CI3
+ DR3 = CR2+CI3
+ DI2 = CI2+CR3
+ DI3 = CI2-CR3
+ CH(I,K,2) = WA1(I-1)*DI2+WA1(I)*DR2
+ CH(I-1,K,2) = WA1(I-1)*DR2-WA1(I)*DI2
+ CH(I,K,3) = WA2(I-1)*DI3+WA2(I)*DR3
+ CH(I-1,K,3) = WA2(I-1)*DR3-WA2(I)*DI3
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB4 (IDO,L1,CC,CH,WA1,WA2,WA3)
+ DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) ,
+ 1 WA1(1) ,WA2(1) ,WA3(1)
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TI1 = CC(2,1,K)-CC(2,3,K)
+ TI2 = CC(2,1,K)+CC(2,3,K)
+ TR4 = CC(2,4,K)-CC(2,2,K)
+ TI3 = CC(2,2,K)+CC(2,4,K)
+ TR1 = CC(1,1,K)-CC(1,3,K)
+ TR2 = CC(1,1,K)+CC(1,3,K)
+ TI4 = CC(1,2,K)-CC(1,4,K)
+ TR3 = CC(1,2,K)+CC(1,4,K)
+ CH(1,K,1) = TR2+TR3
+ CH(1,K,3) = TR2-TR3
+ CH(2,K,1) = TI2+TI3
+ CH(2,K,3) = TI2-TI3
+ CH(1,K,2) = TR1+TR4
+ CH(1,K,4) = TR1-TR4
+ CH(2,K,2) = TI1+TI4
+ CH(2,K,4) = TI1-TI4
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TI1 = CC(I,1,K)-CC(I,3,K)
+ TI2 = CC(I,1,K)+CC(I,3,K)
+ TI3 = CC(I,2,K)+CC(I,4,K)
+ TR4 = CC(I,4,K)-CC(I,2,K)
+ TR1 = CC(I-1,1,K)-CC(I-1,3,K)
+ TR2 = CC(I-1,1,K)+CC(I-1,3,K)
+ TI4 = CC(I-1,2,K)-CC(I-1,4,K)
+ TR3 = CC(I-1,2,K)+CC(I-1,4,K)
+ CH(I-1,K,1) = TR2+TR3
+ CR3 = TR2-TR3
+ CH(I,K,1) = TI2+TI3
+ CI3 = TI2-TI3
+ CR2 = TR1+TR4
+ CR4 = TR1-TR4
+ CI2 = TI1+TI4
+ CI4 = TI1-TI4
+ CH(I-1,K,2) = WA1(I-1)*CR2-WA1(I)*CI2
+ CH(I,K,2) = WA1(I-1)*CI2+WA1(I)*CR2
+ CH(I-1,K,3) = WA2(I-1)*CR3-WA2(I)*CI3
+ CH(I,K,3) = WA2(I-1)*CI3+WA2(I)*CR3
+ CH(I-1,K,4) = WA3(I-1)*CR4-WA3(I)*CI4
+ CH(I,K,4) = WA3(I-1)*CI4+WA3(I)*CR4
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSB5 (IDO,L1,CC,CH,WA1,WA2,WA3,WA4)
+ DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) ,
+ 1 WA1(1) ,WA2(1) ,WA3(1) ,WA4(1)
+ DATA TR11,TI11,TR12,TI12 /.309016994374947,.951056516295154,
+ 1-.809016994374947,.587785252292473/
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TI5 = CC(2,2,K)-CC(2,5,K)
+ TI2 = CC(2,2,K)+CC(2,5,K)
+ TI4 = CC(2,3,K)-CC(2,4,K)
+ TI3 = CC(2,3,K)+CC(2,4,K)
+ TR5 = CC(1,2,K)-CC(1,5,K)
+ TR2 = CC(1,2,K)+CC(1,5,K)
+ TR4 = CC(1,3,K)-CC(1,4,K)
+ TR3 = CC(1,3,K)+CC(1,4,K)
+ CH(1,K,1) = CC(1,1,K)+TR2+TR3
+ CH(2,K,1) = CC(2,1,K)+TI2+TI3
+ CR2 = CC(1,1,K)+TR11*TR2+TR12*TR3
+ CI2 = CC(2,1,K)+TR11*TI2+TR12*TI3
+ CR3 = CC(1,1,K)+TR12*TR2+TR11*TR3
+ CI3 = CC(2,1,K)+TR12*TI2+TR11*TI3
+ CR5 = TI11*TR5+TI12*TR4
+ CI5 = TI11*TI5+TI12*TI4
+ CR4 = TI12*TR5-TI11*TR4
+ CI4 = TI12*TI5-TI11*TI4
+ CH(1,K,2) = CR2-CI5
+ CH(1,K,5) = CR2+CI5
+ CH(2,K,2) = CI2+CR5
+ CH(2,K,3) = CI3+CR4
+ CH(1,K,3) = CR3-CI4
+ CH(1,K,4) = CR3+CI4
+ CH(2,K,4) = CI3-CR4
+ CH(2,K,5) = CI2-CR5
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TI5 = CC(I,2,K)-CC(I,5,K)
+ TI2 = CC(I,2,K)+CC(I,5,K)
+ TI4 = CC(I,3,K)-CC(I,4,K)
+ TI3 = CC(I,3,K)+CC(I,4,K)
+ TR5 = CC(I-1,2,K)-CC(I-1,5,K)
+ TR2 = CC(I-1,2,K)+CC(I-1,5,K)
+ TR4 = CC(I-1,3,K)-CC(I-1,4,K)
+ TR3 = CC(I-1,3,K)+CC(I-1,4,K)
+ CH(I-1,K,1) = CC(I-1,1,K)+TR2+TR3
+ CH(I,K,1) = CC(I,1,K)+TI2+TI3
+ CR2 = CC(I-1,1,K)+TR11*TR2+TR12*TR3
+ CI2 = CC(I,1,K)+TR11*TI2+TR12*TI3
+ CR3 = CC(I-1,1,K)+TR12*TR2+TR11*TR3
+ CI3 = CC(I,1,K)+TR12*TI2+TR11*TI3
+ CR5 = TI11*TR5+TI12*TR4
+ CI5 = TI11*TI5+TI12*TI4
+ CR4 = TI12*TR5-TI11*TR4
+ CI4 = TI12*TI5-TI11*TI4
+ DR3 = CR3-CI4
+ DR4 = CR3+CI4
+ DI3 = CI3+CR4
+ DI4 = CI3-CR4
+ DR5 = CR2+CI5
+ DR2 = CR2-CI5
+ DI5 = CI2-CR5
+ DI2 = CI2+CR5
+ CH(I-1,K,2) = WA1(I-1)*DR2-WA1(I)*DI2
+ CH(I,K,2) = WA1(I-1)*DI2+WA1(I)*DR2
+ CH(I-1,K,3) = WA2(I-1)*DR3-WA2(I)*DI3
+ CH(I,K,3) = WA2(I-1)*DI3+WA2(I)*DR3
+ CH(I-1,K,4) = WA3(I-1)*DR4-WA3(I)*DI4
+ CH(I,K,4) = WA3(I-1)*DI4+WA3(I)*DR4
+ CH(I-1,K,5) = WA4(I-1)*DR5-WA4(I)*DI5
+ CH(I,K,5) = WA4(I-1)*DI5+WA4(I)*DR5
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+
+
+
+ SUBROUTINE CFFTI (N,WSAVE)
+ DIMENSION WSAVE(1)
+ IF (N .EQ. 1) RETURN
+ IW1 = N+N+1
+ IW2 = IW1+N+N
+ CALL CFFTI1 (N,WSAVE(IW1),WSAVE(IW2))
+ RETURN
+ END
+ SUBROUTINE CFFTI1 (N,WA,IFAC)
+ DIMENSION WA(1) ,IFAC(1) ,NTRYH(4)
+ DATA NTRYH(1),NTRYH(2),NTRYH(3),NTRYH(4)/3,4,2,5/
+ NL = N
+ NF = 0
+ J = 0
+ 101 J = J+1
+ IF (J-4) 102,102,103
+ 102 NTRY = NTRYH(J)
+ GO TO 104
+ 103 NTRY = NTRY+2
+ 104 NQ = NL/NTRY
+ NR = NL-NTRY*NQ
+ IF (NR) 101,105,101
+ 105 NF = NF+1
+ IFAC(NF+2) = NTRY
+ NL = NQ
+ IF (NTRY .NE. 2) GO TO 107
+ IF (NF .EQ. 1) GO TO 107
+ DO 106 I=2,NF
+ IB = NF-I+2
+ IFAC(IB+2) = IFAC(IB+1)
+ 106 CONTINUE
+ IFAC(3) = 2
+ 107 IF (NL .NE. 1) GO TO 104
+ IFAC(1) = N
+ IFAC(2) = NF
+ TPI = 6.28318530717959
+ ARGH = TPI/FLOAT(N)
+ I = 2
+ L1 = 1
+ DO 110 K1=1,NF
+ IP = IFAC(K1+2)
+ LD = 0
+ L2 = L1*IP
+ IDO = N/L2
+ IDOT = IDO+IDO+2
+ IPM = IP-1
+ DO 109 J=1,IPM
+ I1 = I
+ WA(I-1) = 1.
+ WA(I) = 0.
+ LD = LD+L1
+ FI = 0.
+ ARGLD = FLOAT(LD)*ARGH
+ DO 108 II=4,IDOT,2
+ I = I+2
+ FI = FI+1.
+ ARG = FI*ARGLD
+ WA(I-1) = COS(ARG)
+ WA(I) = SIN(ARG)
+ 108 CONTINUE
+ IF (IP .LE. 5) GO TO 109
+ WA(I1-1) = WA(I-1)
+ WA(I1) = WA(I)
+ 109 CONTINUE
+ L1 = L2
+ 110 CONTINUE
+ RETURN
+ END
+
+
+
+
+
+ SUBROUTINE CFFTF (N,C,WSAVE)
+ DIMENSION C(1) ,WSAVE(1)
+ IF (N .EQ. 1) RETURN
+ IW1 = N+N+1
+ IW2 = IW1+N+N
+ CALL CFFTF1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2))
+ RETURN
+ END
+ SUBROUTINE CFFTF1 (N,C,CH,WA,IFAC)
+ DIMENSION CH(1) ,C(1) ,WA(1) ,IFAC(1)
+ NF = IFAC(2)
+ NA = 0
+ L1 = 1
+ IW = 1
+ DO 116 K1=1,NF
+ IP = IFAC(K1+2)
+ L2 = IP*L1
+ IDO = N/L2
+ IDOT = IDO+IDO
+ IDL1 = IDOT*L1
+ IF (IP .NE. 4) GO TO 103
+ IX2 = IW+IDOT
+ IX3 = IX2+IDOT
+ IF (NA .NE. 0) GO TO 101
+ CALL PASSF4 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3))
+ GO TO 102
+ 101 CALL PASSF4 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3))
+ 102 NA = 1-NA
+ GO TO 115
+ 103 IF (IP .NE. 2) GO TO 106
+ IF (NA .NE. 0) GO TO 104
+ CALL PASSF2 (IDOT,L1,C,CH,WA(IW))
+ GO TO 105
+ 104 CALL PASSF2 (IDOT,L1,CH,C,WA(IW))
+ 105 NA = 1-NA
+ GO TO 115
+ 106 IF (IP .NE. 3) GO TO 109
+ IX2 = IW+IDOT
+ IF (NA .NE. 0) GO TO 107
+ CALL PASSF3 (IDOT,L1,C,CH,WA(IW),WA(IX2))
+ GO TO 108
+ 107 CALL PASSF3 (IDOT,L1,CH,C,WA(IW),WA(IX2))
+ 108 NA = 1-NA
+ GO TO 115
+ 109 IF (IP .NE. 5) GO TO 112
+ IX2 = IW+IDOT
+ IX3 = IX2+IDOT
+ IX4 = IX3+IDOT
+ IF (NA .NE. 0) GO TO 110
+ CALL PASSF5 (IDOT,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+ GO TO 111
+ 110 CALL PASSF5 (IDOT,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4))
+ 111 NA = 1-NA
+ GO TO 115
+ 112 IF (NA .NE. 0) GO TO 113
+ CALL PASSF (NAC,IDOT,IP,L1,IDL1,C,C,C,CH,CH,WA(IW))
+ GO TO 114
+ 113 CALL PASSF (NAC,IDOT,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW))
+ 114 IF (NAC .NE. 0) NA = 1-NA
+ 115 L1 = L2
+ IW = IW+(IP-1)*IDOT
+ 116 CONTINUE
+ IF (NA .EQ. 0) RETURN
+ N2 = N+N
+ DO 117 I=1,N2
+ C(I) = CH(I)
+ 117 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF (NAC,IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA)
+ DIMENSION CH(IDO,L1,IP) ,CC(IDO,IP,L1) ,
+ 1 C1(IDO,L1,IP) ,WA(1) ,C2(IDL1,IP),
+ 2 CH2(IDL1,IP)
+ IDOT = IDO/2
+ NT = IP*IDL1
+ IPP2 = IP+2
+ IPPH = (IP+1)/2
+ IDP = IP*IDO
+!
+ IF (IDO .LT. L1) GO TO 106
+ DO 103 J=2,IPPH
+ JC = IPP2-J
+ DO 102 K=1,L1
+ DO 101 I=1,IDO
+ CH(I,K,J) = CC(I,J,K)+CC(I,JC,K)
+ CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K)
+ 101 CONTINUE
+ 102 CONTINUE
+ 103 CONTINUE
+ DO 105 K=1,L1
+ DO 104 I=1,IDO
+ CH(I,K,1) = CC(I,1,K)
+ 104 CONTINUE
+ 105 CONTINUE
+ GO TO 112
+ 106 DO 109 J=2,IPPH
+ JC = IPP2-J
+ DO 108 I=1,IDO
+ DO 107 K=1,L1
+ CH(I,K,J) = CC(I,J,K)+CC(I,JC,K)
+ CH(I,K,JC) = CC(I,J,K)-CC(I,JC,K)
+ 107 CONTINUE
+ 108 CONTINUE
+ 109 CONTINUE
+ DO 111 I=1,IDO
+ DO 110 K=1,L1
+ CH(I,K,1) = CC(I,1,K)
+ 110 CONTINUE
+ 111 CONTINUE
+ 112 IDL = 2-IDO
+ INC = 0
+ DO 116 L=2,IPPH
+ LC = IPP2-L
+ IDL = IDL+IDO
+ DO 113 IK=1,IDL1
+ C2(IK,L) = CH2(IK,1)+WA(IDL-1)*CH2(IK,2)
+ C2(IK,LC) = -WA(IDL)*CH2(IK,IP)
+ 113 CONTINUE
+ IDLJ = IDL
+ INC = INC+IDO
+ DO 115 J=3,IPPH
+ JC = IPP2-J
+ IDLJ = IDLJ+INC
+ IF (IDLJ .GT. IDP) IDLJ = IDLJ-IDP
+ WAR = WA(IDLJ-1)
+ WAI = WA(IDLJ)
+ DO 114 IK=1,IDL1
+ C2(IK,L) = C2(IK,L)+WAR*CH2(IK,J)
+ C2(IK,LC) = C2(IK,LC)-WAI*CH2(IK,JC)
+ 114 CONTINUE
+ 115 CONTINUE
+ 116 CONTINUE
+ DO 118 J=2,IPPH
+ DO 117 IK=1,IDL1
+ CH2(IK,1) = CH2(IK,1)+CH2(IK,J)
+ 117 CONTINUE
+ 118 CONTINUE
+ DO 120 J=2,IPPH
+ JC = IPP2-J
+ DO 119 IK=2,IDL1,2
+ CH2(IK-1,J) = C2(IK-1,J)-C2(IK,JC)
+ CH2(IK-1,JC) = C2(IK-1,J)+C2(IK,JC)
+ CH2(IK,J) = C2(IK,J)+C2(IK-1,JC)
+ CH2(IK,JC) = C2(IK,J)-C2(IK-1,JC)
+ 119 CONTINUE
+ 120 CONTINUE
+ NAC = 1
+ IF (IDO .EQ. 2) RETURN
+ NAC = 0
+ DO 121 IK=1,IDL1
+ C2(IK,1) = CH2(IK,1)
+ 121 CONTINUE
+ DO 123 J=2,IP
+ DO 122 K=1,L1
+ C1(1,K,J) = CH(1,K,J)
+ C1(2,K,J) = CH(2,K,J)
+ 122 CONTINUE
+ 123 CONTINUE
+ IF (IDOT .GT. L1) GO TO 127
+ IDIJ = 0
+ DO 126 J=2,IP
+ IDIJ = IDIJ+2
+ DO 125 I=4,IDO,2
+ IDIJ = IDIJ+2
+ DO 124 K=1,L1
+ C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)+WA(IDIJ)*CH(I,K,J)
+ C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)-WA(IDIJ)*CH(I-1,K,J)
+ 124 CONTINUE
+ 125 CONTINUE
+ 126 CONTINUE
+ RETURN
+ 127 IDJ = 2-IDO
+ DO 130 J=2,IP
+ IDJ = IDJ+IDO
+ DO 129 K=1,L1
+ IDIJ = IDJ
+ DO 128 I=4,IDO,2
+ IDIJ = IDIJ+2
+ C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)+WA(IDIJ)*CH(I,K,J)
+ C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)-WA(IDIJ)*CH(I-1,K,J)
+ 128 CONTINUE
+ 129 CONTINUE
+ 130 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF2 (IDO,L1,CC,CH,WA1)
+ DIMENSION CC(IDO,2,L1) ,CH(IDO,L1,2) ,
+ 1 WA1(1)
+ IF (IDO .GT. 2) GO TO 102
+ DO 101 K=1,L1
+ CH(1,K,1) = CC(1,1,K)+CC(1,2,K)
+ CH(1,K,2) = CC(1,1,K)-CC(1,2,K)
+ CH(2,K,1) = CC(2,1,K)+CC(2,2,K)
+ CH(2,K,2) = CC(2,1,K)-CC(2,2,K)
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ CH(I-1,K,1) = CC(I-1,1,K)+CC(I-1,2,K)
+ TR2 = CC(I-1,1,K)-CC(I-1,2,K)
+ CH(I,K,1) = CC(I,1,K)+CC(I,2,K)
+ TI2 = CC(I,1,K)-CC(I,2,K)
+ CH(I,K,2) = WA1(I-1)*TI2-WA1(I)*TR2
+ CH(I-1,K,2) = WA1(I-1)*TR2+WA1(I)*TI2
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF3 (IDO,L1,CC,CH,WA1,WA2)
+ DIMENSION CC(IDO,3,L1) ,CH(IDO,L1,3) ,
+ 1 WA1(1) ,WA2(1)
+ DATA TAUR,TAUI /-.5,-.866025403784439/
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TR2 = CC(1,2,K)+CC(1,3,K)
+ CR2 = CC(1,1,K)+TAUR*TR2
+ CH(1,K,1) = CC(1,1,K)+TR2
+ TI2 = CC(2,2,K)+CC(2,3,K)
+ CI2 = CC(2,1,K)+TAUR*TI2
+ CH(2,K,1) = CC(2,1,K)+TI2
+ CR3 = TAUI*(CC(1,2,K)-CC(1,3,K))
+ CI3 = TAUI*(CC(2,2,K)-CC(2,3,K))
+ CH(1,K,2) = CR2-CI3
+ CH(1,K,3) = CR2+CI3
+ CH(2,K,2) = CI2+CR3
+ CH(2,K,3) = CI2-CR3
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TR2 = CC(I-1,2,K)+CC(I-1,3,K)
+ CR2 = CC(I-1,1,K)+TAUR*TR2
+ CH(I-1,K,1) = CC(I-1,1,K)+TR2
+ TI2 = CC(I,2,K)+CC(I,3,K)
+ CI2 = CC(I,1,K)+TAUR*TI2
+ CH(I,K,1) = CC(I,1,K)+TI2
+ CR3 = TAUI*(CC(I-1,2,K)-CC(I-1,3,K))
+ CI3 = TAUI*(CC(I,2,K)-CC(I,3,K))
+ DR2 = CR2-CI3
+ DR3 = CR2+CI3
+ DI2 = CI2+CR3
+ DI3 = CI2-CR3
+ CH(I,K,2) = WA1(I-1)*DI2-WA1(I)*DR2
+ CH(I-1,K,2) = WA1(I-1)*DR2+WA1(I)*DI2
+ CH(I,K,3) = WA2(I-1)*DI3-WA2(I)*DR3
+ CH(I-1,K,3) = WA2(I-1)*DR3+WA2(I)*DI3
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF4 (IDO,L1,CC,CH,WA1,WA2,WA3)
+ DIMENSION CC(IDO,4,L1) ,CH(IDO,L1,4) ,
+ 1 WA1(1) ,WA2(1) ,WA3(1)
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TI1 = CC(2,1,K)-CC(2,3,K)
+ TI2 = CC(2,1,K)+CC(2,3,K)
+ TR4 = CC(2,2,K)-CC(2,4,K)
+ TI3 = CC(2,2,K)+CC(2,4,K)
+ TR1 = CC(1,1,K)-CC(1,3,K)
+ TR2 = CC(1,1,K)+CC(1,3,K)
+ TI4 = CC(1,4,K)-CC(1,2,K)
+ TR3 = CC(1,2,K)+CC(1,4,K)
+ CH(1,K,1) = TR2+TR3
+ CH(1,K,3) = TR2-TR3
+ CH(2,K,1) = TI2+TI3
+ CH(2,K,3) = TI2-TI3
+ CH(1,K,2) = TR1+TR4
+ CH(1,K,4) = TR1-TR4
+ CH(2,K,2) = TI1+TI4
+ CH(2,K,4) = TI1-TI4
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TI1 = CC(I,1,K)-CC(I,3,K)
+ TI2 = CC(I,1,K)+CC(I,3,K)
+ TI3 = CC(I,2,K)+CC(I,4,K)
+ TR4 = CC(I,2,K)-CC(I,4,K)
+ TR1 = CC(I-1,1,K)-CC(I-1,3,K)
+ TR2 = CC(I-1,1,K)+CC(I-1,3,K)
+ TI4 = CC(I-1,4,K)-CC(I-1,2,K)
+ TR3 = CC(I-1,2,K)+CC(I-1,4,K)
+ CH(I-1,K,1) = TR2+TR3
+ CR3 = TR2-TR3
+ CH(I,K,1) = TI2+TI3
+ CI3 = TI2-TI3
+ CR2 = TR1+TR4
+ CR4 = TR1-TR4
+ CI2 = TI1+TI4
+ CI4 = TI1-TI4
+ CH(I-1,K,2) = WA1(I-1)*CR2+WA1(I)*CI2
+ CH(I,K,2) = WA1(I-1)*CI2-WA1(I)*CR2
+ CH(I-1,K,3) = WA2(I-1)*CR3+WA2(I)*CI3
+ CH(I,K,3) = WA2(I-1)*CI3-WA2(I)*CR3
+ CH(I-1,K,4) = WA3(I-1)*CR4+WA3(I)*CI4
+ CH(I,K,4) = WA3(I-1)*CI4-WA3(I)*CR4
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+ SUBROUTINE PASSF5 (IDO,L1,CC,CH,WA1,WA2,WA3,WA4)
+ DIMENSION CC(IDO,5,L1) ,CH(IDO,L1,5) ,
+ 1 WA1(1) ,WA2(1) ,WA3(1) ,WA4(1)
+ DATA TR11,TI11,TR12,TI12 /.309016994374947,-.951056516295154,
+ 1-.809016994374947,-.587785252292473/
+ IF (IDO .NE. 2) GO TO 102
+ DO 101 K=1,L1
+ TI5 = CC(2,2,K)-CC(2,5,K)
+ TI2 = CC(2,2,K)+CC(2,5,K)
+ TI4 = CC(2,3,K)-CC(2,4,K)
+ TI3 = CC(2,3,K)+CC(2,4,K)
+ TR5 = CC(1,2,K)-CC(1,5,K)
+ TR2 = CC(1,2,K)+CC(1,5,K)
+ TR4 = CC(1,3,K)-CC(1,4,K)
+ TR3 = CC(1,3,K)+CC(1,4,K)
+ CH(1,K,1) = CC(1,1,K)+TR2+TR3
+ CH(2,K,1) = CC(2,1,K)+TI2+TI3
+ CR2 = CC(1,1,K)+TR11*TR2+TR12*TR3
+ CI2 = CC(2,1,K)+TR11*TI2+TR12*TI3
+ CR3 = CC(1,1,K)+TR12*TR2+TR11*TR3
+ CI3 = CC(2,1,K)+TR12*TI2+TR11*TI3
+ CR5 = TI11*TR5+TI12*TR4
+ CI5 = TI11*TI5+TI12*TI4
+ CR4 = TI12*TR5-TI11*TR4
+ CI4 = TI12*TI5-TI11*TI4
+ CH(1,K,2) = CR2-CI5
+ CH(1,K,5) = CR2+CI5
+ CH(2,K,2) = CI2+CR5
+ CH(2,K,3) = CI3+CR4
+ CH(1,K,3) = CR3-CI4
+ CH(1,K,4) = CR3+CI4
+ CH(2,K,4) = CI3-CR4
+ CH(2,K,5) = CI2-CR5
+ 101 CONTINUE
+ RETURN
+ 102 DO 104 K=1,L1
+ DO 103 I=2,IDO,2
+ TI5 = CC(I,2,K)-CC(I,5,K)
+ TI2 = CC(I,2,K)+CC(I,5,K)
+ TI4 = CC(I,3,K)-CC(I,4,K)
+ TI3 = CC(I,3,K)+CC(I,4,K)
+ TR5 = CC(I-1,2,K)-CC(I-1,5,K)
+ TR2 = CC(I-1,2,K)+CC(I-1,5,K)
+ TR4 = CC(I-1,3,K)-CC(I-1,4,K)
+ TR3 = CC(I-1,3,K)+CC(I-1,4,K)
+ CH(I-1,K,1) = CC(I-1,1,K)+TR2+TR3
+ CH(I,K,1) = CC(I,1,K)+TI2+TI3
+ CR2 = CC(I-1,1,K)+TR11*TR2+TR12*TR3
+ CI2 = CC(I,1,K)+TR11*TI2+TR12*TI3
+ CR3 = CC(I-1,1,K)+TR12*TR2+TR11*TR3
+ CI3 = CC(I,1,K)+TR12*TI2+TR11*TI3
+ CR5 = TI11*TR5+TI12*TR4
+ CI5 = TI11*TI5+TI12*TI4
+ CR4 = TI12*TR5-TI11*TR4
+ CI4 = TI12*TI5-TI11*TI4
+ DR3 = CR3-CI4
+ DR4 = CR3+CI4
+ DI3 = CI3+CR4
+ DI4 = CI3-CR4
+ DR5 = CR2+CI5
+ DR2 = CR2-CI5
+ DI5 = CI2-CR5
+ DI2 = CI2+CR5
+ CH(I-1,K,2) = WA1(I-1)*DR2+WA1(I)*DI2
+ CH(I,K,2) = WA1(I-1)*DI2-WA1(I)*DR2
+ CH(I-1,K,3) = WA2(I-1)*DR3+WA2(I)*DI3
+ CH(I,K,3) = WA2(I-1)*DI3-WA2(I)*DR3
+ CH(I-1,K,4) = WA3(I-1)*DR4+WA3(I)*DI4
+ CH(I,K,4) = WA3(I-1)*DI4-WA3(I)*DR4
+ CH(I-1,K,5) = WA4(I-1)*DR5+WA4(I)*DI5
+ CH(I,K,5) = WA4(I-1)*DI5-WA4(I)*DR5
+ 103 CONTINUE
+ 104 CONTINUE
+ RETURN
+ END
+
+! !!!!!!!! DK DK NAG routines included below
+
+! DK DK march99 : routines recuperees sur le Cray (simple precision)
+
+ SUBROUTINE ABZP01
+! MARK 11.5(F77) RELEASE. NAG COPYRIGHT 1986.
+!
+! Terminates execution when a hard failure occurs.
+!
+! ******************** IMPLEMENTATION NOTE ********************
+! The following STOP statement may be replaced by a call to an
+! implementation-dependent routine to display a message and/or
+! to abort the program.
+! *************************************************************
+! .. Executable Statements ..
+ STOP
+ END
+
+ SUBROUTINE DCYS18(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-785 (DEC 1989).
+!
+! Original name: CUNK2
+!
+! DCYS18 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
+! RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
+! UNIFORM ASYMPTOTIC EXPANSIONS FOR H(KIND,FNU,ZN) AND J(FNU,ZN)
+! WHERE ZN IS IN THE RIGHT HALF PLANE, KIND=(3-MR)/2, MR=+1 OR
+! -1. HERE ZN=ZR*I OR -ZR*I WHERE ZR=Z IF Z IS IN THE RIGHT
+! HALF PLANE OR ZR=-Z IF Z IS IN THE LEFT HALF PLANE. MR INDIC-
+! ATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
+! NZ=-1 MEANS AN OVERFLOW WILL OCCUR
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX AI, ARGD, ASUMD, BSUMD, C1, C2, CFN, CI, CK,
+ * CONE, CR1, CR2, CRSC, CS, CSCL, CSGN, CSPN,
+ * CZERO, DAI, PHID, RZ, S1, S2, ZB, ZETA1D,
+ * ZETA2D, ZN, ZR
+ REAL AARG, AIC, ANG, APHI, ASC, ASCLE, C2I, C2M, C2R,
+ * CAR, CPN, FMR, FN, FNF, HPI, PI, RS1, SAR, SGN,
+ * SPN, X, YY
+ INTEGER I, IB, IC, IDUM, IFLAG, IFN, IL, IN, INU, IPARD,
+ * IUF, J, K, KDFLG, KFLAG, KK, NAI, NDAI, NW
+! .. Local Arrays ..
+ COMPLEX ARG(2), ASUM(2), BSUM(2), CIP(4), CSR(3),
+ * CSS(3), CY(2), PHI(2), ZETA1(2), ZETA2(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEUS17, S17DGE, DGSS17, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, CONJG, COS, EXP, INT, LOG,
+ * MAX, MOD, REAL, SIGN, SIN
+! .. Data statements ..
+ DATA CZERO, CONE, CI, CR1, CR2/(0.0E0,0.0E0),
+ * (1.0E0,0.0E0), (0.0E0,1.0E0),
+ * (1.0E0,1.73205080756887729E0),
+ * (-0.5E0,-8.66025403784438647E-01)/
+ DATA HPI, PI, AIC/1.57079632679489662E+00,
+ * 3.14159265358979324E+00,
+ * 1.26551212348464539E+00/
+ DATA CIP(1), CIP(2), CIP(3), CIP(4)/(1.0E0,0.0E0),
+ * (0.0E0,-1.0E0), (-1.0E0,0.0E0), (0.0E0,1.0E0)/
+! .. Executable Statements ..
+!
+ KDFLG = 1
+ NZ = 0
+! ------------------------------------------------------------------
+! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
+! THE UNDERFLOW LIMIT
+! ------------------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ X = REAL(Z)
+ ZR = Z
+ IF (X.LT.0.0E0) ZR = -Z
+ YY = AIMAG(ZR)
+ ZN = -ZR*CI
+ ZB = ZR
+ INU = INT(FNU)
+ FNF = FNU - INU
+ ANG = -HPI*FNF
+ CAR = COS(ANG)
+ SAR = SIN(ANG)
+ CPN = -HPI*CAR
+ SPN = -HPI*SAR
+ C2 = CMPLX(-SPN,CPN)
+ KK = MOD(INU,4) + 1
+ CS = CR1*C2*CIP(KK)
+ IF (YY.LE.0.0E0) THEN
+ ZN = CONJG(-ZN)
+ ZB = CONJG(ZB)
+ END IF
+! ------------------------------------------------------------------
+! K(FNU,Z) IS COMPUTED FROM H(2,FNU,-I*Z) WHERE Z IS IN THE FIRST
+! QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY
+! CONJUGATION SINCE THE K FUNCTION IS REAL ON THE POSITIVE REAL AXIS
+! ------------------------------------------------------------------
+ J = 2
+ DO 40 I = 1, N
+! ---------------------------------------------------------------
+! J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
+! ---------------------------------------------------------------
+ J = 3 - J
+ FN = FNU + I - 1
+ CALL DEUS17(ZN,FN,0,TOL,PHI(J),ARG(J),ZETA1(J),ZETA2(J),ASUM(J)
+ * ,BSUM(J),ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = ZETA1(J) - ZETA2(J)
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = ZETA1(J) - CFN*(CFN/(ZB+ZETA2(J)))
+ END IF
+! ---------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ---------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (KDFLG.EQ.1) KFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ---------------------------------------------------------
+! REFINE TEST AND SCALE
+! ---------------------------------------------------------
+ APHI = ABS(PHI(J))
+ AARG = ABS(ARG(J))
+ RS1 = RS1 + LOG(APHI) - 0.25E0*LOG(AARG) - AIC
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 20
+ ELSE
+ IF (KDFLG.EQ.1) KFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (KDFLG.EQ.1) KFLAG = 3
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------
+! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
+! EXPONENT EXTREMES
+! ------------------------------------------------------------
+ C2 = ARG(J)*CR2
+ IDUM = 1
+! S17DGE assumed not to fail, therefore IDUM set to one.
+ CALL S17DGE('F',C2,'S',AI,NAI,IDUM)
+ IDUM = 1
+ CALL S17DGE('D',C2,'S',DAI,NDAI,IDUM)
+ S2 = CS*PHI(J)*(AI*ASUM(J)+CR2*DAI*BSUM(J))
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(KFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (KFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) GO TO 20
+ END IF
+ IF (YY.LE.0.0E0) S2 = CONJG(S2)
+ CY(KDFLG) = S2
+ Y(I) = S2*CSR(KFLAG)
+ CS = -CI*CS
+ IF (KDFLG.EQ.2) THEN
+ GO TO 60
+ ELSE
+ KDFLG = 2
+ GO TO 40
+ END IF
+ END IF
+ 20 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+! ------------------------------------------------------------
+! FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+! ------------------------------------------------------------
+ ELSE IF (X.LT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ KDFLG = 1
+ Y(I) = CZERO
+ CS = -CI*CS
+ NZ = NZ + 1
+ IF (I.NE.1) THEN
+ IF (Y(I-1).NE.CZERO) THEN
+ Y(I-1) = CZERO
+ NZ = NZ + 1
+ END IF
+ END IF
+ END IF
+ 40 CONTINUE
+ I = N
+ 60 RZ = CMPLX(2.0E0,0.0E0)/ZR
+ CK = CMPLX(FN,0.0E0)*RZ
+ IB = I + 1
+ IF (N.GE.IB) THEN
+! ---------------------------------------------------------------
+! TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW, SET SEQUENCE TO
+! ZERO ON UNDERFLOW
+! ---------------------------------------------------------------
+ FN = FNU + N - 1
+ IPARD = 1
+ IF (MR.NE.0) IPARD = 0
+ CALL DEUS17(ZN,FN,IPARD,TOL,PHID,ARGD,ZETA1D,ZETA2D,ASUMD,
+ * BSUMD,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = ZETA1D - ZETA2D
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = ZETA1D - CFN*(CFN/(ZB+ZETA2D))
+ END IF
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (ABS(RS1).GE.ALIM) THEN
+! ---------------------------------------------------------
+! REFINE ESTIMATE AND TEST
+! ---------------------------------------------------------
+ APHI = ABS(PHID)
+ AARG = ABS(ARGD)
+ RS1 = RS1 + LOG(APHI) - 0.25E0*LOG(AARG) - AIC
+ IF (ABS(RS1).GE.ELIM) GO TO 100
+ END IF
+! ------------------------------------------------------------
+! SCALED FORWARD RECURRENCE FOR REMAINDER OF THE SEQUENCE
+! ------------------------------------------------------------
+ S1 = CY(1)
+ S2 = CY(2)
+ C1 = CSR(KFLAG)
+ ASCLE = BRY(KFLAG)
+ DO 80 I = IB, N
+ C2 = S2
+ S2 = CK*S2 + S1
+ S1 = C2
+ CK = CK + RZ
+ C2 = S2*C1
+ Y(I) = C2
+ IF (KFLAG.LT.3) THEN
+ C2R = REAL(C2)
+ C2I = AIMAG(C2)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ KFLAG = KFLAG + 1
+ ASCLE = BRY(KFLAG)
+ S1 = S1*C1
+ S2 = C2
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ C1 = CSR(KFLAG)
+ END IF
+ END IF
+ 80 CONTINUE
+ GO TO 140
+ END IF
+ 100 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+! ------------------------------------------------------------
+! FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+! ------------------------------------------------------------
+ ELSE IF (X.LT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ NZ = N
+ DO 120 I = 1, N
+ Y(I) = CZERO
+ 120 CONTINUE
+ RETURN
+ END IF
+ END IF
+ 140 IF (MR.EQ.0) THEN
+ RETURN
+ ELSE
+! ---------------------------------------------------------------
+! ANALYTIC CONTINUATION FOR RE(Z).LT.0.0E0
+! ---------------------------------------------------------------
+ NZ = 0
+ FMR = MR
+ SGN = -SIGN(PI,FMR)
+! ---------------------------------------------------------------
+! CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP.
+! ---------------------------------------------------------------
+ CSGN = CMPLX(0.0E0,SGN)
+ IF (YY.LE.0.0E0) CSGN = CONJG(CSGN)
+ IFN = INU + N - 1
+ ANG = FNF*SGN
+ CPN = COS(ANG)
+ SPN = SIN(ANG)
+ CSPN = CMPLX(CPN,SPN)
+ IF (MOD(IFN,2).EQ.1) CSPN = -CSPN
+! ---------------------------------------------------------------
+! CS=COEFF OF THE J FUNCTION TO GET THE I FUNCTION. I(FNU,Z) IS
+! COMPUTED FROM EXP(I*FNU*HPI)*J(FNU,-I*Z) WHERE Z IS IN THE
+! FIRST QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE
+! COMPUTED BY CONJUGATION SINCE THE I FUNCTION IS REAL ON THE
+! POSITIVE REAL AXIS
+! ---------------------------------------------------------------
+ CS = CMPLX(CAR,-SAR)*CSGN
+ IN = MOD(IFN,4) + 1
+ C2 = CIP(IN)
+ CS = CS*CONJG(C2)
+ ASC = BRY(1)
+ KK = N
+ KDFLG = 1
+ IB = IB - 1
+ IC = IB - 1
+ IUF = 0
+ DO 220 K = 1, N
+! ------------------------------------------------------------
+! LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
+! FUNCTION ABOVE
+! ------------------------------------------------------------
+ FN = FNU + KK - 1
+ IF (N.GT.2) THEN
+ IF ((KK.EQ.N) .AND. (IB.LT.N)) THEN
+ GO TO 160
+ ELSE IF ((KK.NE.IB) .AND. (KK.NE.IC)) THEN
+ CALL DEUS17(ZN,FN,0,TOL,PHID,ARGD,ZETA1D,ZETA2D,ASUMD,
+ * BSUMD,ELIM)
+ GO TO 160
+ END IF
+ END IF
+ PHID = PHI(J)
+ ARGD = ARG(J)
+ ZETA1D = ZETA1(J)
+ ZETA2D = ZETA2(J)
+ ASUMD = ASUM(J)
+ BSUMD = BSUM(J)
+ J = 3 - J
+ 160 IF (KODE.EQ.1) THEN
+ S1 = -ZETA1D + ZETA2D
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = -ZETA1D + CFN*(CFN/(ZB+ZETA2D))
+ END IF
+! ------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (KDFLG.EQ.1) IFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ------------------------------------------------------
+! REFINE TEST AND SCALE
+! ------------------------------------------------------
+ APHI = ABS(PHID)
+ AARG = ABS(ARGD)
+ RS1 = RS1 + LOG(APHI) - 0.25E0*LOG(AARG) - AIC
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 180
+ ELSE
+ IF (KDFLG.EQ.1) IFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (KDFLG.EQ.1) IFLAG = 3
+ END IF
+ END IF
+ END IF
+ IDUM = 1
+! S17DGE assumed not to fail, therefore IDUM set to one.
+ CALL S17DGE('F',ARGD,'S',AI,NAI,IDUM)
+ IDUM = 1
+ CALL S17DGE('D',ARGD,'S',DAI,NDAI,IDUM)
+ S2 = CS*PHID*(AI*ASUMD+DAI*BSUMD)
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(IFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (IFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) S2 = CMPLX(0.0E0,0.0E0)
+ END IF
+ GO TO 200
+ END IF
+ 180 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ S2 = CZERO
+ END IF
+ 200 IF (YY.LE.0.0E0) S2 = CONJG(S2)
+ CY(KDFLG) = S2
+ C2 = S2
+ S2 = S2*CSR(IFLAG)
+! ------------------------------------------------------------
+! ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
+! ------------------------------------------------------------
+ S1 = Y(KK)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZR,S1,S2,NW,ASC,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(KK) = S1*CSPN + S2
+ KK = KK - 1
+ CSPN = -CSPN
+ CS = -CS*CI
+ IF (C2.EQ.CZERO) THEN
+ KDFLG = 1
+ ELSE IF (KDFLG.EQ.2) THEN
+ GO TO 240
+ ELSE
+ KDFLG = 2
+ END IF
+ 220 CONTINUE
+ K = N
+ 240 IL = N - K
+ IF (IL.NE.0) THEN
+! ------------------------------------------------------------
+! RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
+! K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO
+! KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT
+! EXTREMES.
+! ------------------------------------------------------------
+ S1 = CY(1)
+ S2 = CY(2)
+ CS = CSR(IFLAG)
+ ASCLE = BRY(IFLAG)
+ FN = INU + IL
+ DO 260 I = 1, IL
+ C2 = S2
+ S2 = S1 + CMPLX(FN+FNF,0.0E0)*RZ*S2
+ S1 = C2
+ FN = FN - 1.0E0
+ C2 = S2*CS
+ CK = C2
+ C1 = Y(KK)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZR,C1,C2,NW,ASC,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(KK) = C1*CSPN + C2
+ KK = KK - 1
+ CSPN = -CSPN
+ IF (IFLAG.LT.3) THEN
+ C2R = REAL(CK)
+ C2I = AIMAG(CK)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*CS
+ S2 = CK
+ S1 = S1*CSS(IFLAG)
+ S2 = S2*CSS(IFLAG)
+ CS = CSR(IFLAG)
+ END IF
+ END IF
+ 260 CONTINUE
+ END IF
+ RETURN
+ END IF
+ 280 NZ = -1
+ RETURN
+ END
+ SUBROUTINE DCZS18(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-786 (DEC 1989).
+!
+! Original name: CUNK1
+!
+! DCZS18 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
+! RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
+! UNIFORM ASYMPTOTIC EXPANSION.
+! MR INDICATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
+! NZ=-1 MEANS AN OVERFLOW WILL OCCUR
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CFN, CK, CONE, CRSC, CS, CSCL, CSGN,
+ * CSPN, CZERO, PHID, RZ, S1, S2, SUMD, ZETA1D,
+ * ZETA2D, ZR
+ REAL ANG, APHI, ASC, ASCLE, C2I, C2M, C2R, CPN, FMR,
+ * FN, FNF, PI, RS1, SGN, SPN, X
+ INTEGER I, IB, IC, IFLAG, IFN, IL, INITD, INU, IPARD,
+ * IUF, J, K, KDFLG, KFLAG, KK, M, NW
+! .. Local Arrays ..
+ COMPLEX CSR(3), CSS(3), CWRK(16,3), CY(2), PHI(2),
+ * SUM(2), ZETA1(2), ZETA2(2)
+ REAL BRY(3)
+ INTEGER INIT(2)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEWS17, DGSS17, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, INT, LOG, MAX, MOD,
+ * REAL, SIGN, SIN
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+ DATA PI/3.14159265358979324E0/
+! .. Executable Statements ..
+!
+ KDFLG = 1
+ NZ = 0
+! ------------------------------------------------------------------
+! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
+! THE UNDERFLOW LIMIT
+! ------------------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ X = REAL(Z)
+ ZR = Z
+ IF (X.LT.0.0E0) ZR = -Z
+ J = 2
+ DO 40 I = 1, N
+! ---------------------------------------------------------------
+! J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
+! ---------------------------------------------------------------
+ J = 3 - J
+ FN = FNU + I - 1
+ INIT(J) = 0
+ CALL DEWS17(ZR,FN,2,0,TOL,INIT(J),PHI(J),ZETA1(J),ZETA2(J),
+ * SUM(J),CWRK(1,J),ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = ZETA1(J) - ZETA2(J)
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = ZETA1(J) - CFN*(CFN/(ZR+ZETA2(J)))
+ END IF
+! ---------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ---------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (KDFLG.EQ.1) KFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ---------------------------------------------------------
+! REFINE TEST AND SCALE
+! ---------------------------------------------------------
+ APHI = ABS(PHI(J))
+ RS1 = RS1 + LOG(APHI)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 20
+ ELSE
+ IF (KDFLG.EQ.1) KFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (KDFLG.EQ.1) KFLAG = 3
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------
+! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
+! EXPONENT EXTREMES
+! ------------------------------------------------------------
+ S2 = PHI(J)*SUM(J)
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(KFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (KFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) GO TO 20
+ END IF
+ CY(KDFLG) = S2
+ Y(I) = S2*CSR(KFLAG)
+ IF (KDFLG.EQ.2) THEN
+ GO TO 60
+ ELSE
+ KDFLG = 2
+ GO TO 40
+ END IF
+ END IF
+ 20 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+! ------------------------------------------------------------
+! FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+! ------------------------------------------------------------
+ ELSE IF (X.LT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ KDFLG = 1
+ Y(I) = CZERO
+ NZ = NZ + 1
+ IF (I.NE.1) THEN
+ IF (Y(I-1).NE.CZERO) THEN
+ Y(I-1) = CZERO
+ NZ = NZ + 1
+ END IF
+ END IF
+ END IF
+ 40 CONTINUE
+ I = N
+ 60 RZ = CMPLX(2.0E0,0.0E0)/ZR
+ CK = CMPLX(FN,0.0E0)*RZ
+ IB = I + 1
+ IF (N.GE.IB) THEN
+! ---------------------------------------------------------------
+! TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW, SET SEQUENCE TO
+! ZERO ON UNDERFLOW
+! ---------------------------------------------------------------
+ FN = FNU + N - 1
+ IPARD = 1
+ IF (MR.NE.0) IPARD = 0
+ INITD = 0
+ CALL DEWS17(ZR,FN,2,IPARD,TOL,INITD,PHID,ZETA1D,ZETA2D,SUMD,
+ * CWRK(1,3),ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = ZETA1D - ZETA2D
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = ZETA1D - CFN*(CFN/(ZR+ZETA2D))
+ END IF
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (ABS(RS1).GE.ALIM) THEN
+! ---------------------------------------------------------
+! REFINE ESTIMATE AND TEST
+! ---------------------------------------------------------
+ APHI = ABS(PHID)
+ RS1 = RS1 + LOG(APHI)
+ IF (ABS(RS1).GE.ELIM) GO TO 100
+ END IF
+! ------------------------------------------------------------
+! RECUR FORWARD FOR REMAINDER OF THE SEQUENCE
+! ------------------------------------------------------------
+ S1 = CY(1)
+ S2 = CY(2)
+ C1 = CSR(KFLAG)
+ ASCLE = BRY(KFLAG)
+ DO 80 I = IB, N
+ C2 = S2
+ S2 = CK*S2 + S1
+ S1 = C2
+ CK = CK + RZ
+ C2 = S2*C1
+ Y(I) = C2
+ IF (KFLAG.LT.3) THEN
+ C2R = REAL(C2)
+ C2I = AIMAG(C2)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ KFLAG = KFLAG + 1
+ ASCLE = BRY(KFLAG)
+ S1 = S1*C1
+ S2 = C2
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ C1 = CSR(KFLAG)
+ END IF
+ END IF
+ 80 CONTINUE
+ GO TO 140
+ END IF
+ 100 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+! ------------------------------------------------------------
+! FOR X.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
+! ------------------------------------------------------------
+ ELSE IF (X.LT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ NZ = N
+ DO 120 I = 1, N
+ Y(I) = CZERO
+ 120 CONTINUE
+ RETURN
+ END IF
+ END IF
+ 140 IF (MR.EQ.0) THEN
+ RETURN
+ ELSE
+! ---------------------------------------------------------------
+! ANALYTIC CONTINUATION FOR RE(Z).LT.0.0E0
+! ---------------------------------------------------------------
+ NZ = 0
+ FMR = MR
+ SGN = -SIGN(PI,FMR)
+! ---------------------------------------------------------------
+! CSPN AND CSGN ARE COEFF OF K AND I FUNCIONS RESP.
+! ---------------------------------------------------------------
+ CSGN = CMPLX(0.0E0,SGN)
+ INU = INT(FNU)
+ FNF = FNU - INU
+ IFN = INU + N - 1
+ ANG = FNF*SGN
+ CPN = COS(ANG)
+ SPN = SIN(ANG)
+ CSPN = CMPLX(CPN,SPN)
+ IF (MOD(IFN,2).EQ.1) CSPN = -CSPN
+ ASC = BRY(1)
+ KK = N
+ IUF = 0
+ KDFLG = 1
+ IB = IB - 1
+ IC = IB - 1
+ DO 220 K = 1, N
+ FN = FNU + KK - 1
+! ------------------------------------------------------------
+! LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
+! FUNCTION ABOVE
+! ------------------------------------------------------------
+ M = 3
+ IF (N.GT.2) THEN
+ IF ((KK.EQ.N) .AND. (IB.LT.N)) THEN
+ GO TO 160
+ ELSE IF ((KK.NE.IB) .AND. (KK.NE.IC)) THEN
+ INITD = 0
+ GO TO 160
+ END IF
+ END IF
+ INITD = INIT(J)
+ PHID = PHI(J)
+ ZETA1D = ZETA1(J)
+ ZETA2D = ZETA2(J)
+ SUMD = SUM(J)
+ M = J
+ J = 3 - J
+ 160 CALL DEWS17(ZR,FN,1,0,TOL,INITD,PHID,ZETA1D,ZETA2D,SUMD,
+ * CWRK(1,M),ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1D + ZETA2D
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = -ZETA1D + CFN*(CFN/(ZR+ZETA2D))
+ END IF
+! ------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ IF (KDFLG.EQ.1) IFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ------------------------------------------------------
+! REFINE TEST AND SCALE
+! ------------------------------------------------------
+ APHI = ABS(PHID)
+ RS1 = RS1 + LOG(APHI)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 180
+ ELSE
+ IF (KDFLG.EQ.1) IFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (KDFLG.EQ.1) IFLAG = 3
+ END IF
+ END IF
+ END IF
+ S2 = CSGN*PHID*SUMD
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(IFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (IFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) S2 = CMPLX(0.0E0,0.0E0)
+ END IF
+ GO TO 200
+ END IF
+ 180 IF (RS1.GT.0.0E0) THEN
+ GO TO 280
+ ELSE
+ S2 = CZERO
+ END IF
+ 200 CY(KDFLG) = S2
+ C2 = S2
+ S2 = S2*CSR(IFLAG)
+! ------------------------------------------------------------
+! ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
+! ------------------------------------------------------------
+ S1 = Y(KK)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZR,S1,S2,NW,ASC,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(KK) = S1*CSPN + S2
+ KK = KK - 1
+ CSPN = -CSPN
+ IF (C2.EQ.CZERO) THEN
+ KDFLG = 1
+ ELSE IF (KDFLG.EQ.2) THEN
+ GO TO 240
+ ELSE
+ KDFLG = 2
+ END IF
+ 220 CONTINUE
+ K = N
+ 240 IL = N - K
+ IF (IL.NE.0) THEN
+! ------------------------------------------------------------
+! RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
+! K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO
+! KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT
+! EXTREMES.
+! ------------------------------------------------------------
+ S1 = CY(1)
+ S2 = CY(2)
+ CS = CSR(IFLAG)
+ ASCLE = BRY(IFLAG)
+ FN = INU + IL
+ DO 260 I = 1, IL
+ C2 = S2
+ S2 = S1 + CMPLX(FN+FNF,0.0E0)*RZ*S2
+ S1 = C2
+ FN = FN - 1.0E0
+ C2 = S2*CS
+ CK = C2
+ C1 = Y(KK)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZR,C1,C2,NW,ASC,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(KK) = C1*CSPN + C2
+ KK = KK - 1
+ CSPN = -CSPN
+ IF (IFLAG.LT.3) THEN
+ C2R = REAL(CK)
+ C2I = AIMAG(CK)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*CS
+ S2 = CK
+ S1 = S1*CSS(IFLAG)
+ S2 = S2*CSS(IFLAG)
+ CS = CSR(IFLAG)
+ END IF
+ END IF
+ 260 CONTINUE
+ END IF
+ RETURN
+ END IF
+ 280 NZ = -1
+ RETURN
+ END
+ SUBROUTINE DERS17(Z,FNU,N,CY,TOL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-761 (DEC 1989).
+!
+! Original name: CRATI
+!
+! DERS17 COMPUTES RATIOS OF I BESSEL FUNCTIONS BY BACKWARD
+! RECURRENCE. THE STARTING INDEX IS DETERMINED BY FORWARD
+! RECURRENCE AS DESCRIBED IN J. RES. OF NAT. BUR. OF STANDARDS-B,
+! MATHEMATICAL SCIENCES, VOL 77B, P111-114, SEPTEMBER, 1973,
+! BESSEL FUNCTIONS I AND J OF COMPLEX ARGUMENT AND INTEGER ORDER,
+! BY D. J. SOOKNE.
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL FNU, TOL
+ INTEGER N
+! .. Array Arguments ..
+ COMPLEX CY(N)
+! .. Local Scalars ..
+ COMPLEX CDFNU, CONE, CZERO, P1, P2, PT, RZ, T1
+ REAL AK, AMAGZ, AP1, AP2, ARG, AZ, DFNU, FDNU, FLAM,
+ * FNUP, RAP1, RHO, TEST, TEST1
+ INTEGER I, ID, IDNU, INU, ITIME, K, KK, MAGZ
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, INT, MAX, MIN, REAL, SQRT
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ AZ = ABS(Z)
+ INU = INT(FNU)
+ IDNU = INU + N - 1
+ FDNU = IDNU
+ MAGZ = INT(AZ)
+ AMAGZ = MAGZ + 1
+ FNUP = MAX(AMAGZ,FDNU)
+ ID = IDNU - MAGZ - 1
+ ITIME = 1
+ K = 1
+ RZ = (CONE+CONE)/Z
+ T1 = CMPLX(FNUP,0.0E0)*RZ
+ P2 = -T1
+ P1 = CONE
+ T1 = T1 + RZ
+ IF (ID.GT.0) ID = 0
+ AP2 = ABS(P2)
+ AP1 = ABS(P1)
+! ------------------------------------------------------------------
+! THE OVERFLOW TEST ON K(FNU+I-1,Z) BEFORE THE CALL TO CBKNX
+! GUARANTEES THAT P2 IS ON SCALE. SCALE TEST1 AND ALL SUBSEQUENT
+! P2 VALUES BY AP1 TO ENSURE THAT AN OVERFLOW DOES NOT OCCUR
+! PREMATURELY.
+! ------------------------------------------------------------------
+ ARG = (AP2+AP2)/(AP1*TOL)
+ TEST1 = SQRT(ARG)
+ TEST = TEST1
+ RAP1 = 1.0E0/AP1
+ P1 = P1*CMPLX(RAP1,0.0E0)
+ P2 = P2*CMPLX(RAP1,0.0E0)
+ AP2 = AP2*RAP1
+ 20 CONTINUE
+ K = K + 1
+ AP1 = AP2
+ PT = P2
+ P2 = P1 - T1*P2
+ P1 = PT
+ T1 = T1 + RZ
+ AP2 = ABS(P2)
+ IF (AP1.LE.TEST) THEN
+ GO TO 20
+ ELSE IF (ITIME.NE.2) THEN
+ AK = ABS(T1)*0.5E0
+ FLAM = AK + SQRT(AK*AK-1.0E0)
+ RHO = MIN(AP2/AP1,FLAM)
+ TEST = TEST1*SQRT(RHO/(RHO*RHO-1.0E0))
+ ITIME = 2
+ GO TO 20
+ END IF
+ KK = K + 1 - ID
+ AK = KK
+ DFNU = FNU + N - 1
+ CDFNU = CMPLX(DFNU,0.0E0)
+ T1 = CMPLX(AK,0.0E0)
+ P1 = CMPLX(1.0E0/AP2,0.0E0)
+ P2 = CZERO
+ DO 40 I = 1, KK
+ PT = P1
+ P1 = RZ*(CDFNU+T1)*P1 + P2
+ P2 = PT
+ T1 = T1 - CONE
+ 40 CONTINUE
+ IF (REAL(P1).EQ.0.0E0 .AND. AIMAG(P1).EQ.0.0E0) P1 = CMPLX(TOL,
+ * TOL)
+ CY(N) = P2/P1
+ IF (N.NE.1) THEN
+ K = N - 1
+ AK = K
+ T1 = CMPLX(AK,0.0E0)
+ CDFNU = CMPLX(FNU,0.0E0)*RZ
+ DO 60 I = 2, N
+ PT = CDFNU + T1*RZ + CY(K+1)
+ IF (REAL(PT).EQ.0.0E0 .AND. AIMAG(PT).EQ.0.0E0)
+ * PT = CMPLX(TOL,TOL)
+ CY(K) = CONE/PT
+ T1 = T1 - CONE
+ K = K - 1
+ 60 CONTINUE
+ END IF
+ RETURN
+ END
+ SUBROUTINE DESS17(ZR,FNU,KODE,N,Y,NZ,CW,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-762 (DEC 1989).
+!
+! Original name: CWRSK
+!
+! DESS17 COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY
+! NORMALIZING THE I FUNCTION RATIOS FROM DERS17 BY THE WRONSKIAN
+!
+! .. Scalar Arguments ..
+ COMPLEX ZR
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX CW(2), Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CINU, CSCL, CT, RCT, ST
+ REAL ACT, ACW, ASCLE, S1, S2, YY
+ INTEGER I, NW
+! .. External Functions ..
+ REAL X02AME
+ EXTERNAL X02AME
+! .. External Subroutines ..
+ EXTERNAL DERS17, DGXS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, CONJG, COS, SIN
+! .. Executable Statements ..
+! ------------------------------------------------------------------
+! I(FNU+I-1,Z) BY BACKWARD RECURRENCE FOR RATIOS
+! Y(I)=I(FNU+I,Z)/I(FNU+I-1,Z) FROM DERS17 NORMALIZED BY THE
+! WRONSKIAN WITH K(FNU,Z) AND K(FNU+1,Z) FROM DGXS17.
+! ------------------------------------------------------------------
+ NZ = 0
+ CALL DGXS17(ZR,FNU,KODE,2,CW,NW,TOL,ELIM,ALIM)
+ IF (NW.NE.0) THEN
+ NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ IF (NW.EQ.(-3)) NZ = -3
+ ELSE
+ CALL DERS17(ZR,FNU,N,Y,TOL)
+! ---------------------------------------------------------------
+! RECUR FORWARD ON I(FNU+1,Z) = R(FNU,Z)*I(FNU,Z),
+! R(FNU+J-1,Z)=Y(J), J=1,...,N
+! ---------------------------------------------------------------
+ CINU = CMPLX(1.0E0,0.0E0)
+ IF (KODE.NE.1) THEN
+ YY = AIMAG(ZR)
+ S1 = COS(YY)
+ S2 = SIN(YY)
+ CINU = CMPLX(S1,S2)
+ END IF
+! ---------------------------------------------------------------
+! ON LOW EXPONENT MACHINES THE K FUNCTIONS CAN BE CLOSE TO BOTH
+! THE UNDER AND OVERFLOW LIMITS AND THE NORMALIZATION MUST BE
+! SCALED TO PREVENT OVER OR UNDERFLOW. DEVS17 HAS DETERMINED THAT
+! THE RESULT IS ON SCALE.
+! ---------------------------------------------------------------
+ ACW = ABS(CW(2))
+ ASCLE = (1.0E+3*X02AME())/TOL
+ CSCL = CMPLX(1.0E0,0.0E0)
+ IF (ACW.GT.ASCLE) THEN
+ ASCLE = 1.0E0/ASCLE
+ IF (ACW.GE.ASCLE) CSCL = CMPLX(TOL,0.0E0)
+ ELSE
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ END IF
+ C1 = CW(1)*CSCL
+ C2 = CW(2)*CSCL
+ ST = Y(1)
+! ---------------------------------------------------------------
+! CINU=CINU*(CONJG(CT)/CABS(CT))*(1.0E0/CABS(CT) PREVENTS
+! UNDER- OR OVERFLOW PREMATURELY BY SQUARING CABS(CT)
+! ---------------------------------------------------------------
+ CT = ZR*(C2+ST*C1)
+ ACT = ABS(CT)
+ RCT = CMPLX(1.0E0/ACT,0.0E0)
+ CT = CONJG(CT)*RCT
+ CINU = CINU*RCT*CT
+ Y(1) = CINU*CSCL
+ IF (N.NE.1) THEN
+ DO 20 I = 2, N
+ CINU = ST*CINU
+ ST = Y(I)
+ Y(I) = CINU*CSCL
+ 20 CONTINUE
+ END IF
+ END IF
+ RETURN
+ END
+ SUBROUTINE DETS17(Z,FNU,KODE,N,Y,NZ,NLAST,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-763 (DEC 1989).
+!
+! Original name: CUNI2
+!
+! DETS17 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF
+! UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I
+! OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO.
+!
+! FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
+! EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
+! NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
+! FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
+! Y(I)=CZERO FOR I=NLAST+1,N
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, TOL
+ INTEGER KODE, N, NLAST, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX AI, ARG, ASUM, BSUM, C1, C2, CFN, CI, CID, CONE,
+ * CRSC, CSCL, CZERO, DAI, PHI, RZ, S1, S2, ZB,
+ * ZETA1, ZETA2, ZN
+ REAL AARG, AIC, ANG, APHI, ASCLE, AY, C2I, C2M, C2R,
+ * CAR, FN, HPI, RS1, SAR, YY
+ INTEGER I, IDUM, IFLAG, IN, INU, J, K, NAI, ND, NDAI,
+ * NN, NUF, NW
+! .. Local Arrays ..
+ COMPLEX CIP(4), CSR(3), CSS(3), CY(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEUS17, DEVS17, S17DGE, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, CONJG, COS, EXP, INT, LOG,
+ * MAX, MIN, MOD, REAL, SIN
+! .. Data statements ..
+ DATA CZERO, CONE, CI/(0.0E0,0.0E0), (1.0E0,0.0E0),
+ * (0.0E0,1.0E0)/
+ DATA CIP(1), CIP(2), CIP(3), CIP(4)/(1.0E0,0.0E0),
+ * (0.0E0,1.0E0), (-1.0E0,0.0E0), (0.0E0,-1.0E0)/
+ DATA HPI, AIC/1.57079632679489662E+00,
+ * 1.265512123484645396E+00/
+! .. Executable Statements ..
+!
+ NZ = 0
+ ND = N
+ NLAST = 0
+! ------------------------------------------------------------------
+! COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
+! NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
+! EXP(ALIM)=EXP(ELIM)*TOL
+! ------------------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ YY = AIMAG(Z)
+! ------------------------------------------------------------------
+! ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI
+! ------------------------------------------------------------------
+ ZN = -Z*CI
+ ZB = Z
+ CID = -CI
+ INU = INT(FNU)
+ ANG = HPI*(FNU-INU)
+ CAR = COS(ANG)
+ SAR = SIN(ANG)
+ C2 = CMPLX(CAR,SAR)
+ IN = INU + N - 1
+ IN = MOD(IN,4)
+ C2 = C2*CIP(IN+1)
+ IF (YY.LE.0.0E0) THEN
+ ZN = CONJG(-ZN)
+ ZB = CONJG(ZB)
+ CID = -CID
+ C2 = CONJG(C2)
+ END IF
+! ------------------------------------------------------------------
+! CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
+! ------------------------------------------------------------------
+ FN = MAX(FNU,1.0E0)
+ CALL DEUS17(ZN,FN,1,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,BSUM,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1 + ZETA2
+ ELSE
+ CFN = CMPLX(FNU,0.0E0)
+ S1 = -ZETA1 + CFN*(CFN/(ZB+ZETA2))
+ END IF
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ 20 CONTINUE
+ NN = MIN(2,ND)
+ DO 40 I = 1, NN
+ FN = FNU + ND - I
+ CALL DEUS17(ZN,FN,0,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,BSUM,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1 + ZETA2
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ AY = ABS(YY)
+ S1 = -ZETA1 + CFN*(CFN/(ZB+ZETA2)) + CMPLX(0.0E0,AY)
+ END IF
+! ------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 60
+ ELSE
+ IF (I.EQ.1) IFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ------------------------------------------------------
+! REFINE TEST AND SCALE
+! ------------------------------------------------------
+! ------------------------------------------------------
+ APHI = ABS(PHI)
+ AARG = ABS(ARG)
+ RS1 = RS1 + LOG(APHI) - 0.25E0*LOG(AARG) - AIC
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 60
+ ELSE
+ IF (I.EQ.1) IFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (I.EQ.1) IFLAG = 3
+ END IF
+ END IF
+ END IF
+! ---------------------------------------------------------
+! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
+! EXPONENT EXTREMES
+! ---------------------------------------------------------
+ IDUM = 1
+! S17DGE assumed not to fail, therefore IDUM set to one.
+ CALL S17DGE('F',ARG,'S',AI,NAI,IDUM)
+ IDUM = 1
+ CALL S17DGE('D',ARG,'S',DAI,NDAI,IDUM)
+ S2 = PHI*(AI*ASUM+DAI*BSUM)
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(IFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (IFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) GO TO 60
+ END IF
+ IF (YY.LE.0.0E0) S2 = CONJG(S2)
+ J = ND - I + 1
+ S2 = S2*C2
+ CY(I) = S2
+ Y(J) = S2*CSR(IFLAG)
+ C2 = C2*CID
+ END IF
+ 40 CONTINUE
+ GO TO 80
+ 60 IF (RS1.GT.0.0E0) THEN
+ GO TO 160
+ ELSE
+! ------------------------------------------------------------
+! SET UNDERFLOW AND UPDATE PARAMETERS
+! ------------------------------------------------------------
+ Y(ND) = CZERO
+ NZ = NZ + 1
+ ND = ND - 1
+ IF (ND.EQ.0) THEN
+ RETURN
+ ELSE
+ CALL DEVS17(Z,FNU,KODE,1,ND,Y,NUF,TOL,ELIM,ALIM)
+ IF (NUF.LT.0) THEN
+ GO TO 160
+ ELSE
+ ND = ND - NUF
+ NZ = NZ + NUF
+ IF (ND.EQ.0) THEN
+ RETURN
+ ELSE
+ FN = FNU + ND - 1
+ IF (FN.LT.FNUL) THEN
+ GO TO 120
+ ELSE
+! FN = AIMAG(CID)
+! J = NUF + 1
+! K = MOD(J,4) + 1
+! S1 = CIP(K)
+! IF (FN.LT.0.0E0) S1 = CONJG(S1)
+! C2 = C2*S1
+! The above 6 lines were replaced by the 5 below
+! to fix a bug discovered during implementation
+! on a Multics machine, whereby some results
+! were returned wrongly scaled by sqrt(-1.0). MWP.
+ C2 = CMPLX(CAR,SAR)
+ IN = INU + ND - 1
+ IN = MOD(IN,4) + 1
+ C2 = C2*CIP(IN)
+ IF (YY.LE.0.0E0) C2 = CONJG(C2)
+ GO TO 20
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+ 80 IF (ND.GT.2) THEN
+ RZ = CMPLX(2.0E0,0.0E0)/Z
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ S1 = CY(1)
+ S2 = CY(2)
+ C1 = CSR(IFLAG)
+ ASCLE = BRY(IFLAG)
+ K = ND - 2
+ FN = K
+ DO 100 I = 3, ND
+ C2 = S2
+ S2 = S1 + CMPLX(FNU+FN,0.0E0)*RZ*S2
+ S1 = C2
+ C2 = S2*C1
+ Y(K) = C2
+ K = K - 1
+ FN = FN - 1.0E0
+ IF (IFLAG.LT.3) THEN
+ C2R = REAL(C2)
+ C2I = AIMAG(C2)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*C1
+ S2 = C2
+ S1 = S1*CSS(IFLAG)
+ S2 = S2*CSS(IFLAG)
+ C1 = CSR(IFLAG)
+ END IF
+ END IF
+ 100 CONTINUE
+ END IF
+ RETURN
+ 120 NLAST = ND
+ RETURN
+ ELSE IF (RS1.LE.0.0E0) THEN
+ NZ = N
+ DO 140 I = 1, N
+ Y(I) = CZERO
+ 140 CONTINUE
+ RETURN
+ END IF
+ 160 NZ = -1
+ RETURN
+ END
+ SUBROUTINE DEUS17(Z,FNU,IPMTR,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,BSUM,
+ * ELIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-764 (DEC 1989).
+!
+! Original name: CUNHJ
+!
+! REFERENCES
+! HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A.
+! STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9.
+!
+! ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC
+! PRESS, N.Y., 1974, PAGE 420
+!
+! ABSTRACT
+! DEUS17 COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) =
+! J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU
+! BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION
+!
+! C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) )
+!
+! FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS
+! AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE.
+!
+! (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2,
+!
+! ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING
+! PURPOSES IN AIRY FUNCTIONS FROM S17DGE OR S17DHE.
+!
+! MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND
+! MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR=
+! 1 COMPUTES ALL EXCEPT ASUM AND BSUM.
+!
+! .. Scalar Arguments ..
+ COMPLEX ARG, ASUM, BSUM, PHI, Z, ZETA1, ZETA2
+ REAL ELIM, FNU, TOL
+ INTEGER IPMTR
+! .. Local Scalars ..
+ COMPLEX CFNU, CONE, CZERO, PRZTH, PTFN, RFN13, RTZTA,
+ * RZTH, SUMA, SUMB, T2, TFN, W, W2, ZA, ZB, ZC,
+ * ZETA, ZTH
+ REAL ANG, ASUMI, ASUMR, ATOL, AW2, AZTH, BSUMI,
+ * BSUMR, BTOL, EX1, EX2, FN13, FN23, HPI, PI, PP,
+ * RFNU, RFNU2, TEST, THPI, TSTI, TSTR, WI, WR,
+ * ZCI, ZCR, ZETAI, ZETAR, ZTHI, ZTHR
+ INTEGER IAS, IBS, IS, J, JR, JU, K, KMAX, KP1, KS, L,
+ * L1, L2, LR, LRP1, M
+! .. Local Arrays ..
+ COMPLEX CR(14), DR(14), P(30), UP(14)
+ REAL ALFA(180), AP(30), AR(14), BETA(210), BR(14),
+ * C(105), GAMA(30)
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, ATAN, CMPLX, COS, EXP, LOG, REAL,
+ * SIN, SQRT
+! .. Data statements ..
+ DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7),
+ * AR(8), AR(9), AR(10), AR(11), AR(12), AR(13),
+ * AR(14)/1.00000000000000000E+00,
+ * 1.04166666666666667E-01,
+ * 8.35503472222222222E-02,
+ * 1.28226574556327160E-01,
+ * 2.91849026464140464E-01,
+ * 8.81627267443757652E-01,
+ * 3.32140828186276754E+00,
+ * 1.49957629868625547E+01,
+ * 7.89230130115865181E+01,
+ * 4.74451538868264323E+02,
+ * 3.20749009089066193E+03,
+ * 2.40865496408740049E+04,
+ * 1.98923119169509794E+05,
+ * 1.79190200777534383E+06/
+ DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7),
+ * BR(8), BR(9), BR(10), BR(11), BR(12), BR(13),
+ * BR(14)/1.00000000000000000E+00,
+ * -1.45833333333333333E-01,
+ * -9.87413194444444444E-02,
+ * -1.43312053915895062E-01,
+ * -3.17227202678413548E-01,
+ * -9.42429147957120249E-01,
+ * -3.51120304082635426E+00,
+ * -1.57272636203680451E+01,
+ * -8.22814390971859444E+01,
+ * -4.92355370523670524E+02,
+ * -3.31621856854797251E+03,
+ * -2.48276742452085896E+04,
+ * -2.04526587315129788E+05,
+ * -1.83844491706820990E+06/
+ DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8),
+ * C(9), C(10), C(11), C(12), C(13), C(14), C(15),
+ * C(16)/1.00000000000000000E+00,
+ * -2.08333333333333333E-01,
+ * 1.25000000000000000E-01,
+ * 3.34201388888888889E-01,
+ * -4.01041666666666667E-01,
+ * 7.03125000000000000E-02,
+ * -1.02581259645061728E+00,
+ * 1.84646267361111111E+00,
+ * -8.91210937500000000E-01,
+ * 7.32421875000000000E-02,
+ * 4.66958442342624743E+00,
+ * -1.12070026162229938E+01,
+ * 8.78912353515625000E+00,
+ * -2.36408691406250000E+00,
+ * 1.12152099609375000E-01,
+ * -2.82120725582002449E+01/
+ DATA C(17), C(18), C(19), C(20), C(21), C(22), C(23),
+ * C(24)/8.46362176746007346E+01,
+ * -9.18182415432400174E+01,
+ * 4.25349987453884549E+01,
+ * -7.36879435947963170E+00,
+ * 2.27108001708984375E-01,
+ * 2.12570130039217123E+02,
+ * -7.65252468141181642E+02,
+ * 1.05999045252799988E+03/
+ DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31),
+ * C(32), C(33), C(34), C(35), C(36), C(37), C(38),
+ * C(39), C(40)/-6.99579627376132541E+02,
+ * 2.18190511744211590E+02,
+ * -2.64914304869515555E+01,
+ * 5.72501420974731445E-01,
+ * -1.91945766231840700E+03,
+ * 8.06172218173730938E+03,
+ * -1.35865500064341374E+04,
+ * 1.16553933368645332E+04,
+ * -5.30564697861340311E+03,
+ * 1.20090291321635246E+03,
+ * -1.08090919788394656E+02,
+ * 1.72772750258445740E+00,
+ * 2.02042913309661486E+04,
+ * -9.69805983886375135E+04,
+ * 1.92547001232531532E+05,
+ * -2.03400177280415534E+05/
+ DATA C(41), C(42), C(43), C(44), C(45), C(46), C(47),
+ * C(48)/1.22200464983017460E+05,
+ * -4.11926549688975513E+04,
+ * 7.10951430248936372E+03,
+ * -4.93915304773088012E+02,
+ * 6.07404200127348304E+00,
+ * -2.42919187900551333E+05,
+ * 1.31176361466297720E+06,
+ * -2.99801591853810675E+06/
+ DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55),
+ * C(56), C(57), C(58), C(59), C(60), C(61), C(62),
+ * C(63), C(64)/3.76327129765640400E+06,
+ * -2.81356322658653411E+06,
+ * 1.26836527332162478E+06,
+ * -3.31645172484563578E+05,
+ * 4.52187689813627263E+04,
+ * -2.49983048181120962E+03,
+ * 2.43805296995560639E+01,
+ * 3.28446985307203782E+06,
+ * -1.97068191184322269E+07,
+ * 5.09526024926646422E+07,
+ * -7.41051482115326577E+07,
+ * 6.63445122747290267E+07,
+ * -3.75671766607633513E+07,
+ * 1.32887671664218183E+07,
+ * -2.78561812808645469E+06,
+ * 3.08186404612662398E+05/
+ DATA C(65), C(66), C(67), C(68), C(69), C(70), C(71),
+ * C(72)/-1.38860897537170405E+04,
+ * 1.10017140269246738E+02,
+ * -4.93292536645099620E+07,
+ * 3.25573074185765749E+08,
+ * -9.39462359681578403E+08,
+ * 1.55359689957058006E+09,
+ * -1.62108055210833708E+09,
+ * 1.10684281682301447E+09/
+ DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79),
+ * C(80), C(81), C(82), C(83), C(84), C(85), C(86),
+ * C(87), C(88)/-4.95889784275030309E+08,
+ * 1.42062907797533095E+08,
+ * -2.44740627257387285E+07,
+ * 2.24376817792244943E+06,
+ * -8.40054336030240853E+04,
+ * 5.51335896122020586E+02,
+ * 8.14789096118312115E+08,
+ * -5.86648149205184723E+09,
+ * 1.86882075092958249E+10,
+ * -3.46320433881587779E+10,
+ * 4.12801855797539740E+10,
+ * -3.30265997498007231E+10,
+ * 1.79542137311556001E+10,
+ * -6.56329379261928433E+09,
+ * 1.55927986487925751E+09,
+ * -2.25105661889415278E+08/
+ DATA C(89), C(90), C(91), C(92), C(93), C(94), C(95),
+ * C(96)/1.73951075539781645E+07,
+ * -5.49842327572288687E+05,
+ * 3.03809051092238427E+03,
+ * -1.46792612476956167E+10,
+ * 1.14498237732025810E+11,
+ * -3.99096175224466498E+11,
+ * 8.19218669548577329E+11,
+ * -1.09837515608122331E+12/
+ DATA C(97), C(98), C(99), C(100), C(101), C(102),
+ * C(103), C(104), C(105)/1.00815810686538209E+12,
+ * -6.45364869245376503E+11,
+ * 2.87900649906150589E+11,
+ * -8.78670721780232657E+10,
+ * 1.76347306068349694E+10,
+ * -2.16716498322379509E+09,
+ * 1.43157876718888981E+08,
+ * -3.87183344257261262E+06,
+ * 1.82577554742931747E+04/
+ DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5),
+ * ALFA(6), ALFA(7), ALFA(8), ALFA(9), ALFA(10),
+ * ALFA(11), ALFA(12), ALFA(13),
+ * ALFA(14)/-4.44444444444444444E-03,
+ * -9.22077922077922078E-04,
+ * -8.84892884892884893E-05,
+ * 1.65927687832449737E-04,
+ * 2.46691372741792910E-04,
+ * 2.65995589346254780E-04,
+ * 2.61824297061500945E-04,
+ * 2.48730437344655609E-04,
+ * 2.32721040083232098E-04,
+ * 2.16362485712365082E-04,
+ * 2.00738858762752355E-04,
+ * 1.86267636637545172E-04,
+ * 1.73060775917876493E-04,
+ * 1.61091705929015752E-04/
+ DATA ALFA(15), ALFA(16), ALFA(17), ALFA(18),
+ * ALFA(19), ALFA(20), ALFA(21),
+ * ALFA(22)/1.50274774160908134E-04,
+ * 1.40503497391269794E-04,
+ * 1.31668816545922806E-04,
+ * 1.23667445598253261E-04,
+ * 1.16405271474737902E-04,
+ * 1.09798298372713369E-04,
+ * 1.03772410422992823E-04,
+ * 9.82626078369363448E-05/
+ DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26),
+ * ALFA(27), ALFA(28), ALFA(29), ALFA(30),
+ * ALFA(31), ALFA(32), ALFA(33), ALFA(34),
+ * ALFA(35), ALFA(36)/9.32120517249503256E-05,
+ * 8.85710852478711718E-05,
+ * 8.42963105715700223E-05,
+ * 8.03497548407791151E-05,
+ * 7.66981345359207388E-05,
+ * 7.33122157481777809E-05,
+ * 7.01662625163141333E-05,
+ * 6.72375633790160292E-05,
+ * 6.93735541354588974E-04,
+ * 2.32241745182921654E-04,
+ * -1.41986273556691197E-05,
+ * -1.16444931672048640E-04,
+ * -1.50803558053048762E-04,
+ * -1.55121924918096223E-04/
+ DATA ALFA(37), ALFA(38), ALFA(39), ALFA(40),
+ * ALFA(41), ALFA(42), ALFA(43),
+ * ALFA(44)/-1.46809756646465549E-04,
+ * -1.33815503867491367E-04,
+ * -1.19744975684254051E-04,
+ * -1.06184319207974020E-04,
+ * -9.37699549891194492E-05,
+ * -8.26923045588193274E-05,
+ * -7.29374348155221211E-05,
+ * -6.44042357721016283E-05/
+ DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48),
+ * ALFA(49), ALFA(50), ALFA(51), ALFA(52),
+ * ALFA(53), ALFA(54), ALFA(55), ALFA(56),
+ * ALFA(57), ALFA(58)/-5.69611566009369048E-05,
+ * -5.04731044303561628E-05,
+ * -4.48134868008882786E-05,
+ * -3.98688727717598864E-05,
+ * -3.55400532972042498E-05,
+ * -3.17414256609022480E-05,
+ * -2.83996793904174811E-05,
+ * -2.54522720634870566E-05,
+ * -2.28459297164724555E-05,
+ * -2.05352753106480604E-05,
+ * -1.84816217627666085E-05,
+ * -1.66519330021393806E-05,
+ * -1.50179412980119482E-05,
+ * -1.35554031379040526E-05/
+ DATA ALFA(59), ALFA(60), ALFA(61), ALFA(62),
+ * ALFA(63), ALFA(64), ALFA(65),
+ * ALFA(66)/-1.22434746473858131E-05,
+ * -1.10641884811308169E-05,
+ * -3.54211971457743841E-04,
+ * -1.56161263945159416E-04,
+ * 3.04465503594936410E-05,
+ * 1.30198655773242693E-04,
+ * 1.67471106699712269E-04,
+ * 1.70222587683592569E-04/
+ DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70),
+ * ALFA(71), ALFA(72), ALFA(73), ALFA(74),
+ * ALFA(75), ALFA(76), ALFA(77), ALFA(78),
+ * ALFA(79), ALFA(80)/1.56501427608594704E-04,
+ * 1.36339170977445120E-04,
+ * 1.14886692029825128E-04,
+ * 9.45869093034688111E-05,
+ * 7.64498419250898258E-05,
+ * 6.07570334965197354E-05,
+ * 4.74394299290508799E-05,
+ * 3.62757512005344297E-05,
+ * 2.69939714979224901E-05,
+ * 1.93210938247939253E-05,
+ * 1.30056674793963203E-05,
+ * 7.82620866744496661E-06,
+ * 3.59257485819351583E-06,
+ * 1.44040049814251817E-07/
+ DATA ALFA(81), ALFA(82), ALFA(83), ALFA(84),
+ * ALFA(85), ALFA(86), ALFA(87),
+ * ALFA(88)/-2.65396769697939116E-06,
+ * -4.91346867098485910E-06,
+ * -6.72739296091248287E-06,
+ * -8.17269379678657923E-06,
+ * -9.31304715093561232E-06,
+ * -1.02011418798016441E-05,
+ * -1.08805962510592880E-05,
+ * -1.13875481509603555E-05/
+ DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92),
+ * ALFA(93), ALFA(94), ALFA(95), ALFA(96),
+ * ALFA(97), ALFA(98), ALFA(99), ALFA(100),
+ * ALFA(101), ALFA(102)/-1.17519675674556414E-05,
+ * -1.19987364870944141E-05,
+ * 3.78194199201772914E-04,
+ * 2.02471952761816167E-04,
+ * -6.37938506318862408E-05,
+ * -2.38598230603005903E-04,
+ * -3.10916256027361568E-04,
+ * -3.13680115247576316E-04,
+ * -2.78950273791323387E-04,
+ * -2.28564082619141374E-04,
+ * -1.75245280340846749E-04,
+ * -1.25544063060690348E-04,
+ * -8.22982872820208365E-05,
+ * -4.62860730588116458E-05/
+ DATA ALFA(103), ALFA(104), ALFA(105), ALFA(106),
+ * ALFA(107), ALFA(108), ALFA(109),
+ * ALFA(110)/-1.72334302366962267E-05,
+ * 5.60690482304602267E-06,
+ * 2.31395443148286800E-05,
+ * 3.62642745856793957E-05,
+ * 4.58006124490188752E-05,
+ * 5.24595294959114050E-05,
+ * 5.68396208545815266E-05,
+ * 5.94349820393104052E-05/
+ DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114),
+ * ALFA(115), ALFA(116), ALFA(117), ALFA(118),
+ * ALFA(119), ALFA(120), ALFA(121),
+ * ALFA(122)/6.06478527578421742E-05,
+ * 6.08023907788436497E-05,
+ * 6.01577894539460388E-05,
+ * 5.89199657344698500E-05,
+ * 5.72515823777593053E-05,
+ * 5.52804375585852577E-05,
+ * 5.31063773802880170E-05,
+ * 5.08069302012325706E-05,
+ * 4.84418647620094842E-05,
+ * 4.60568581607475370E-05,
+ * -6.91141397288294174E-04,
+ * -4.29976633058871912E-04/
+ DATA ALFA(123), ALFA(124), ALFA(125), ALFA(126),
+ * ALFA(127), ALFA(128), ALFA(129),
+ * ALFA(130)/1.83067735980039018E-04,
+ * 6.60088147542014144E-04,
+ * 8.75964969951185931E-04,
+ * 8.77335235958235514E-04,
+ * 7.49369585378990637E-04,
+ * 5.63832329756980918E-04,
+ * 3.68059319971443156E-04,
+ * 1.88464535514455599E-04/
+ DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134),
+ * ALFA(135), ALFA(136), ALFA(137), ALFA(138),
+ * ALFA(139), ALFA(140), ALFA(141),
+ * ALFA(142)/3.70663057664904149E-05,
+ * -8.28520220232137023E-05,
+ * -1.72751952869172998E-04,
+ * -2.36314873605872983E-04,
+ * -2.77966150694906658E-04,
+ * -3.02079514155456919E-04,
+ * -3.12594712643820127E-04,
+ * -3.12872558758067163E-04,
+ * -3.05678038466324377E-04,
+ * -2.93226470614557331E-04,
+ * -2.77255655582934777E-04,
+ * -2.59103928467031709E-04/
+ DATA ALFA(143), ALFA(144), ALFA(145), ALFA(146),
+ * ALFA(147), ALFA(148), ALFA(149),
+ * ALFA(150)/-2.39784014396480342E-04,
+ * -2.20048260045422848E-04,
+ * -2.00443911094971498E-04,
+ * -1.81358692210970687E-04,
+ * -1.63057674478657464E-04,
+ * -1.45712672175205844E-04,
+ * -1.29425421983924587E-04,
+ * -1.14245691942445952E-04/
+ DATA ALFA(151), ALFA(152), ALFA(153), ALFA(154),
+ * ALFA(155), ALFA(156), ALFA(157), ALFA(158),
+ * ALFA(159), ALFA(160), ALFA(161),
+ * ALFA(162)/1.92821964248775885E-03,
+ * 1.35592576302022234E-03,
+ * -7.17858090421302995E-04,
+ * -2.58084802575270346E-03,
+ * -3.49271130826168475E-03,
+ * -3.46986299340960628E-03,
+ * -2.82285233351310182E-03,
+ * -1.88103076404891354E-03,
+ * -8.89531718383947600E-04,
+ * 3.87912102631035228E-06,
+ * 7.28688540119691412E-04,
+ * 1.26566373053457758E-03/
+ DATA ALFA(163), ALFA(164), ALFA(165), ALFA(166),
+ * ALFA(167), ALFA(168), ALFA(169),
+ * ALFA(170)/1.62518158372674427E-03,
+ * 1.83203153216373172E-03,
+ * 1.91588388990527909E-03,
+ * 1.90588846755546138E-03,
+ * 1.82798982421825727E-03,
+ * 1.70389506421121530E-03,
+ * 1.55097127171097686E-03,
+ * 1.38261421852276159E-03/
+ DATA ALFA(171), ALFA(172), ALFA(173), ALFA(174),
+ * ALFA(175), ALFA(176), ALFA(177), ALFA(178),
+ * ALFA(179), ALFA(180)/1.20881424230064774E-03,
+ * 1.03676532638344962E-03,
+ * 8.71437918068619115E-04,
+ * 7.16080155297701002E-04,
+ * 5.72637002558129372E-04,
+ * 4.42089819465802277E-04,
+ * 3.24724948503090564E-04,
+ * 2.20342042730246599E-04,
+ * 1.28412898401353882E-04,
+ * 4.82005924552095464E-05/
+ DATA BETA(1), BETA(2), BETA(3), BETA(4), BETA(5),
+ * BETA(6), BETA(7), BETA(8), BETA(9), BETA(10),
+ * BETA(11), BETA(12), BETA(13),
+ * BETA(14)/1.79988721413553309E-02,
+ * 5.59964911064388073E-03,
+ * 2.88501402231132779E-03,
+ * 1.80096606761053941E-03,
+ * 1.24753110589199202E-03,
+ * 9.22878876572938311E-04,
+ * 7.14430421727287357E-04,
+ * 5.71787281789704872E-04,
+ * 4.69431007606481533E-04,
+ * 3.93232835462916638E-04,
+ * 3.34818889318297664E-04,
+ * 2.88952148495751517E-04,
+ * 2.52211615549573284E-04,
+ * 2.22280580798883327E-04/
+ DATA BETA(15), BETA(16), BETA(17), BETA(18),
+ * BETA(19), BETA(20), BETA(21),
+ * BETA(22)/1.97541838033062524E-04,
+ * 1.76836855019718004E-04,
+ * 1.59316899661821081E-04,
+ * 1.44347930197333986E-04,
+ * 1.31448068119965379E-04,
+ * 1.20245444949302884E-04,
+ * 1.10449144504599392E-04,
+ * 1.01828770740567258E-04/
+ DATA BETA(23), BETA(24), BETA(25), BETA(26),
+ * BETA(27), BETA(28), BETA(29), BETA(30),
+ * BETA(31), BETA(32), BETA(33), BETA(34),
+ * BETA(35), BETA(36)/9.41998224204237509E-05,
+ * 8.74130545753834437E-05,
+ * 8.13466262162801467E-05,
+ * 7.59002269646219339E-05,
+ * 7.09906300634153481E-05,
+ * 6.65482874842468183E-05,
+ * 6.25146958969275078E-05,
+ * 5.88403394426251749E-05,
+ * -1.49282953213429172E-03,
+ * -8.78204709546389328E-04,
+ * -5.02916549572034614E-04,
+ * -2.94822138512746025E-04,
+ * -1.75463996970782828E-04,
+ * -1.04008550460816434E-04/
+ DATA BETA(37), BETA(38), BETA(39), BETA(40),
+ * BETA(41), BETA(42), BETA(43),
+ * BETA(44)/-5.96141953046457895E-05,
+ * -3.12038929076098340E-05,
+ * -1.26089735980230047E-05,
+ * -2.42892608575730389E-07,
+ * 8.05996165414273571E-06,
+ * 1.36507009262147391E-05,
+ * 1.73964125472926261E-05,
+ * 1.98672978842133780E-05/
+ DATA BETA(45), BETA(46), BETA(47), BETA(48),
+ * BETA(49), BETA(50), BETA(51), BETA(52),
+ * BETA(53), BETA(54), BETA(55), BETA(56),
+ * BETA(57), BETA(58)/2.14463263790822639E-05,
+ * 2.23954659232456514E-05,
+ * 2.28967783814712629E-05,
+ * 2.30785389811177817E-05,
+ * 2.30321976080909144E-05,
+ * 2.28236073720348722E-05,
+ * 2.25005881105292418E-05,
+ * 2.20981015361991429E-05,
+ * 2.16418427448103905E-05,
+ * 2.11507649256220843E-05,
+ * 2.06388749782170737E-05,
+ * 2.01165241997081666E-05,
+ * 1.95913450141179244E-05,
+ * 1.90689367910436740E-05/
+ DATA BETA(59), BETA(60), BETA(61), BETA(62),
+ * BETA(63), BETA(64), BETA(65),
+ * BETA(66)/1.85533719641636667E-05,
+ * 1.80475722259674218E-05,
+ * 5.52213076721292790E-04,
+ * 4.47932581552384646E-04,
+ * 2.79520653992020589E-04,
+ * 1.52468156198446602E-04,
+ * 6.93271105657043598E-05,
+ * 1.76258683069991397E-05/
+ DATA BETA(67), BETA(68), BETA(69), BETA(70),
+ * BETA(71), BETA(72), BETA(73), BETA(74),
+ * BETA(75), BETA(76), BETA(77), BETA(78),
+ * BETA(79), BETA(80)/-1.35744996343269136E-05,
+ * -3.17972413350427135E-05,
+ * -4.18861861696693365E-05,
+ * -4.69004889379141029E-05,
+ * -4.87665447413787352E-05,
+ * -4.87010031186735069E-05,
+ * -4.74755620890086638E-05,
+ * -4.55813058138628452E-05,
+ * -4.33309644511266036E-05,
+ * -4.09230193157750364E-05,
+ * -3.84822638603221274E-05,
+ * -3.60857167535410501E-05,
+ * -3.37793306123367417E-05,
+ * -3.15888560772109621E-05/
+ DATA BETA(81), BETA(82), BETA(83), BETA(84),
+ * BETA(85), BETA(86), BETA(87),
+ * BETA(88)/-2.95269561750807315E-05,
+ * -2.75978914828335759E-05,
+ * -2.58006174666883713E-05,
+ * -2.41308356761280200E-05,
+ * -2.25823509518346033E-05,
+ * -2.11479656768912971E-05,
+ * -1.98200638885294927E-05,
+ * -1.85909870801065077E-05/
+ DATA BETA(89), BETA(90), BETA(91), BETA(92),
+ * BETA(93), BETA(94), BETA(95), BETA(96),
+ * BETA(97), BETA(98), BETA(99), BETA(100),
+ * BETA(101), BETA(102)/-1.74532699844210224E-05,
+ * -1.63997823854497997E-05,
+ * -4.74617796559959808E-04,
+ * -4.77864567147321487E-04,
+ * -3.20390228067037603E-04,
+ * -1.61105016119962282E-04,
+ * -4.25778101285435204E-05,
+ * 3.44571294294967503E-05,
+ * 7.97092684075674924E-05,
+ * 1.03138236708272200E-04,
+ * 1.12466775262204158E-04,
+ * 1.13103642108481389E-04,
+ * 1.08651634848774268E-04,
+ * 1.01437951597661973E-04/
+ DATA BETA(103), BETA(104), BETA(105), BETA(106),
+ * BETA(107), BETA(108), BETA(109),
+ * BETA(110)/9.29298396593363896E-05,
+ * 8.40293133016089978E-05,
+ * 7.52727991349134062E-05,
+ * 6.69632521975730872E-05,
+ * 5.92564547323194704E-05,
+ * 5.22169308826975567E-05,
+ * 4.58539485165360646E-05,
+ * 4.01445513891486808E-05/
+ DATA BETA(111), BETA(112), BETA(113), BETA(114),
+ * BETA(115), BETA(116), BETA(117), BETA(118),
+ * BETA(119), BETA(120), BETA(121),
+ * BETA(122)/3.50481730031328081E-05,
+ * 3.05157995034346659E-05,
+ * 2.64956119950516039E-05,
+ * 2.29363633690998152E-05,
+ * 1.97893056664021636E-05,
+ * 1.70091984636412623E-05,
+ * 1.45547428261524004E-05,
+ * 1.23886640995878413E-05,
+ * 1.04775876076583236E-05,
+ * 8.79179954978479373E-06,
+ * 7.36465810572578444E-04,
+ * 8.72790805146193976E-04/
+ DATA BETA(123), BETA(124), BETA(125), BETA(126),
+ * BETA(127), BETA(128), BETA(129),
+ * BETA(130)/6.22614862573135066E-04,
+ * 2.85998154194304147E-04,
+ * 3.84737672879366102E-06,
+ * -1.87906003636971558E-04,
+ * -2.97603646594554535E-04,
+ * -3.45998126832656348E-04,
+ * -3.53382470916037712E-04,
+ * -3.35715635775048757E-04/
+ DATA BETA(131), BETA(132), BETA(133), BETA(134),
+ * BETA(135), BETA(136), BETA(137), BETA(138),
+ * BETA(139), BETA(140), BETA(141),
+ * BETA(142)/-3.04321124789039809E-04,
+ * -2.66722723047612821E-04,
+ * -2.27654214122819527E-04,
+ * -1.89922611854562356E-04,
+ * -1.55058918599093870E-04,
+ * -1.23778240761873630E-04,
+ * -9.62926147717644187E-05,
+ * -7.25178327714425337E-05,
+ * -5.22070028895633801E-05,
+ * -3.50347750511900522E-05,
+ * -2.06489761035551757E-05,
+ * -8.70106096849767054E-06/
+ DATA BETA(143), BETA(144), BETA(145), BETA(146),
+ * BETA(147), BETA(148), BETA(149),
+ * BETA(150)/1.13698686675100290E-06,
+ * 9.16426474122778849E-06,
+ * 1.56477785428872620E-05,
+ * 2.08223629482466847E-05,
+ * 2.48923381004595156E-05,
+ * 2.80340509574146325E-05,
+ * 3.03987774629861915E-05,
+ * 3.21156731406700616E-05/
+ DATA BETA(151), BETA(152), BETA(153), BETA(154),
+ * BETA(155), BETA(156), BETA(157), BETA(158),
+ * BETA(159), BETA(160), BETA(161),
+ * BETA(162)/-1.80182191963885708E-03,
+ * -2.43402962938042533E-03,
+ * -1.83422663549856802E-03,
+ * -7.62204596354009765E-04,
+ * 2.39079475256927218E-04,
+ * 9.49266117176881141E-04,
+ * 1.34467449701540359E-03,
+ * 1.48457495259449178E-03,
+ * 1.44732339830617591E-03,
+ * 1.30268261285657186E-03,
+ * 1.10351597375642682E-03,
+ * 8.86047440419791759E-04/
+ DATA BETA(163), BETA(164), BETA(165), BETA(166),
+ * BETA(167), BETA(168), BETA(169),
+ * BETA(170)/6.73073208165665473E-04,
+ * 4.77603872856582378E-04,
+ * 3.05991926358789362E-04,
+ * 1.60315694594721630E-04,
+ * 4.00749555270613286E-05,
+ * -5.66607461635251611E-05,
+ * -1.32506186772982638E-04,
+ * -1.90296187989614057E-04/
+ DATA BETA(171), BETA(172), BETA(173), BETA(174),
+ * BETA(175), BETA(176), BETA(177), BETA(178),
+ * BETA(179), BETA(180), BETA(181),
+ * BETA(182)/-2.32811450376937408E-04,
+ * -2.62628811464668841E-04,
+ * -2.82050469867598672E-04,
+ * -2.93081563192861167E-04,
+ * -2.97435962176316616E-04,
+ * -2.96557334239348078E-04,
+ * -2.91647363312090861E-04,
+ * -2.83696203837734166E-04,
+ * -2.73512317095673346E-04,
+ * -2.61750155806768580E-04,
+ * 6.38585891212050914E-03,
+ * 9.62374215806377941E-03/
+ DATA BETA(183), BETA(184), BETA(185), BETA(186),
+ * BETA(187), BETA(188), BETA(189),
+ * BETA(190)/7.61878061207001043E-03,
+ * 2.83219055545628054E-03,
+ * -2.09841352012720090E-03,
+ * -5.73826764216626498E-03,
+ * -7.70804244495414620E-03,
+ * -8.21011692264844401E-03,
+ * -7.65824520346905413E-03,
+ * -6.47209729391045177E-03/
+ DATA BETA(191), BETA(192), BETA(193), BETA(194),
+ * BETA(195), BETA(196), BETA(197), BETA(198),
+ * BETA(199), BETA(200), BETA(201),
+ * BETA(202)/-4.99132412004966473E-03,
+ * -3.45612289713133280E-03,
+ * -2.01785580014170775E-03,
+ * -7.59430686781961401E-04,
+ * 2.84173631523859138E-04,
+ * 1.10891667586337403E-03,
+ * 1.72901493872728771E-03,
+ * 2.16812590802684701E-03,
+ * 2.45357710494539735E-03,
+ * 2.61281821058334862E-03,
+ * 2.67141039656276912E-03,
+ * 2.65203073395980430E-03/
+ DATA BETA(203), BETA(204), BETA(205), BETA(206),
+ * BETA(207), BETA(208), BETA(209),
+ * BETA(210)/2.57411652877287315E-03,
+ * 2.45389126236094427E-03,
+ * 2.30460058071795494E-03,
+ * 2.13684837686712662E-03,
+ * 1.95896528478870911E-03,
+ * 1.77737008679454412E-03,
+ * 1.59690280765839059E-03,
+ * 1.42111975664438546E-03/
+ DATA GAMA(1), GAMA(2), GAMA(3), GAMA(4), GAMA(5),
+ * GAMA(6), GAMA(7), GAMA(8), GAMA(9), GAMA(10),
+ * GAMA(11), GAMA(12), GAMA(13),
+ * GAMA(14)/6.29960524947436582E-01,
+ * 2.51984209978974633E-01,
+ * 1.54790300415655846E-01,
+ * 1.10713062416159013E-01,
+ * 8.57309395527394825E-02,
+ * 6.97161316958684292E-02,
+ * 5.86085671893713576E-02,
+ * 5.04698873536310685E-02,
+ * 4.42600580689154809E-02,
+ * 3.93720661543509966E-02,
+ * 3.54283195924455368E-02,
+ * 3.21818857502098231E-02,
+ * 2.94646240791157679E-02,
+ * 2.71581677112934479E-02/
+ DATA GAMA(15), GAMA(16), GAMA(17), GAMA(18),
+ * GAMA(19), GAMA(20), GAMA(21),
+ * GAMA(22)/2.51768272973861779E-02,
+ * 2.34570755306078891E-02,
+ * 2.19508390134907203E-02,
+ * 2.06210828235646240E-02,
+ * 1.94388240897880846E-02,
+ * 1.83810633800683158E-02,
+ * 1.74293213231963172E-02,
+ * 1.65685837786612353E-02/
+ DATA GAMA(23), GAMA(24), GAMA(25), GAMA(26),
+ * GAMA(27), GAMA(28), GAMA(29),
+ * GAMA(30)/1.57865285987918445E-02,
+ * 1.50729501494095594E-02,
+ * 1.44193250839954639E-02,
+ * 1.38184805735341786E-02,
+ * 1.32643378994276568E-02,
+ * 1.27517121970498651E-02,
+ * 1.22761545318762767E-02,
+ * 1.18338262398482403E-02/
+ DATA EX1, EX2, HPI, PI, THPI/3.33333333333333333E-01,
+ * 6.66666666666666667E-01,
+ * 1.57079632679489662E+00,
+ * 3.14159265358979324E+00,
+ * 4.71238898038468986E+00/
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ RFNU = 1.0E0/FNU
+ TSTR = REAL(Z)
+ TSTI = AIMAG(Z)
+ TEST = FNU*EXP(-ELIM)
+ IF (ABS(TSTR).LT.TEST) TSTR = 0.0E0
+ IF (ABS(TSTI).LT.TEST) TSTI = 0.0E0
+ IF (TSTR.EQ.0.0E0 .AND. TSTI.EQ.0.0E0) THEN
+ ZETA1 = CMPLX(ELIM+ELIM+FNU,0.0E0)
+ ZETA2 = CMPLX(FNU,0.0E0)
+ PHI = CONE
+ ARG = CONE
+ RETURN
+ END IF
+ ZB = CMPLX(TSTR,TSTI)*CMPLX(RFNU,0.0E0)
+ RFNU2 = RFNU*RFNU
+! ------------------------------------------------------------------
+! COMPUTE IN THE FOURTH QUADRANT
+! ------------------------------------------------------------------
+ FN13 = FNU**EX1
+ FN23 = FN13*FN13
+ RFN13 = CMPLX(1.0E0/FN13,0.0E0)
+ W2 = CONE - ZB*ZB
+ AW2 = ABS(W2)
+ IF (AW2.GT.0.25E0) THEN
+! ---------------------------------------------------------------
+! CABS(W2).GT.0.25E0
+! ---------------------------------------------------------------
+ W = SQRT(W2)
+ WR = REAL(W)
+ WI = AIMAG(W)
+ IF (WR.LT.0.0E0) WR = 0.0E0
+ IF (WI.LT.0.0E0) WI = 0.0E0
+ W = CMPLX(WR,WI)
+ ZA = (CONE+W)/ZB
+ ZC = LOG(ZA)
+ ZCR = REAL(ZC)
+ ZCI = AIMAG(ZC)
+ IF (ZCI.LT.0.0E0) ZCI = 0.0E0
+ IF (ZCI.GT.HPI) ZCI = HPI
+ IF (ZCR.LT.0.0E0) ZCR = 0.0E0
+ ZC = CMPLX(ZCR,ZCI)
+ ZTH = (ZC-W)*CMPLX(1.5E0,0.0E0)
+ CFNU = CMPLX(FNU,0.0E0)
+ ZETA1 = ZC*CFNU
+ ZETA2 = W*CFNU
+ AZTH = ABS(ZTH)
+ ZTHR = REAL(ZTH)
+ ZTHI = AIMAG(ZTH)
+ ANG = THPI
+ IF (ZTHR.LT.0.0E0 .OR. ZTHI.GE.0.0E0) THEN
+ ANG = HPI
+ IF (ZTHR.NE.0.0E0) THEN
+ ANG = ATAN(ZTHI/ZTHR)
+ IF (ZTHR.LT.0.0E0) ANG = ANG + PI
+ END IF
+ END IF
+ PP = AZTH**EX2
+ ANG = ANG*EX2
+ ZETAR = PP*COS(ANG)
+ ZETAI = PP*SIN(ANG)
+ IF (ZETAI.LT.0.0E0) ZETAI = 0.0E0
+ ZETA = CMPLX(ZETAR,ZETAI)
+ ARG = ZETA*CMPLX(FN23,0.0E0)
+ RTZTA = ZTH/ZETA
+ ZA = RTZTA/W
+ PHI = SQRT(ZA+ZA)*RFN13
+ IF (IPMTR.NE.1) THEN
+ TFN = CMPLX(RFNU,0.0E0)/W
+ RZTH = CMPLX(RFNU,0.0E0)/ZTH
+ ZC = RZTH*CMPLX(AR(2),0.0E0)
+ T2 = CONE/W2
+ UP(2) = (T2*CMPLX(C(2),0.0E0)+CMPLX(C(3),0.0E0))*TFN
+ BSUM = UP(2) + ZC
+ ASUM = CZERO
+ IF (RFNU.GE.TOL) THEN
+ PRZTH = RZTH
+ PTFN = TFN
+ UP(1) = CONE
+ PP = 1.0E0
+ BSUMR = REAL(BSUM)
+ BSUMI = AIMAG(BSUM)
+ BTOL = TOL*(ABS(BSUMR)+ABS(BSUMI))
+ KS = 0
+ KP1 = 2
+ L = 3
+ IAS = 0
+ IBS = 0
+ DO 100 LR = 2, 12, 2
+ LRP1 = LR + 1
+! ------------------------------------------------------
+! COMPUTE TWO ADDITIONAL CR, DR, AND UP FOR TWO MORE
+! TERMS IN NEXT SUMA AND SUMB
+! ------------------------------------------------------
+ DO 40 K = LR, LRP1
+ KS = KS + 1
+ KP1 = KP1 + 1
+ L = L + 1
+ ZA = CMPLX(C(L),0.0E0)
+ DO 20 J = 2, KP1
+ L = L + 1
+ ZA = ZA*T2 + CMPLX(C(L),0.0E0)
+ 20 CONTINUE
+ PTFN = PTFN*TFN
+ UP(KP1) = PTFN*ZA
+ CR(KS) = PRZTH*CMPLX(BR(KS+1),0.0E0)
+ PRZTH = PRZTH*RZTH
+ DR(KS) = PRZTH*CMPLX(AR(KS+2),0.0E0)
+ 40 CONTINUE
+ PP = PP*RFNU2
+ IF (IAS.NE.1) THEN
+ SUMA = UP(LRP1)
+ JU = LRP1
+ DO 60 JR = 1, LR
+ JU = JU - 1
+ SUMA = SUMA + CR(JR)*UP(JU)
+ 60 CONTINUE
+ ASUM = ASUM + SUMA
+ ASUMR = REAL(ASUM)
+ ASUMI = AIMAG(ASUM)
+ TEST = ABS(ASUMR) + ABS(ASUMI)
+ IF (PP.LT.TOL .AND. TEST.LT.TOL) IAS = 1
+ END IF
+ IF (IBS.NE.1) THEN
+ SUMB = UP(LR+2) + UP(LRP1)*ZC
+ JU = LRP1
+ DO 80 JR = 1, LR
+ JU = JU - 1
+ SUMB = SUMB + DR(JR)*UP(JU)
+ 80 CONTINUE
+ BSUM = BSUM + SUMB
+ BSUMR = REAL(BSUM)
+ BSUMI = AIMAG(BSUM)
+ TEST = ABS(BSUMR) + ABS(BSUMI)
+ IF (PP.LT.BTOL .AND. TEST.LT.TOL) IBS = 1
+ END IF
+ IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 120
+ 100 CONTINUE
+ END IF
+ 120 ASUM = ASUM + CONE
+ BSUM = -BSUM*RFN13/RTZTA
+ END IF
+ ELSE
+! ---------------------------------------------------------------
+! POWER SERIES FOR CABS(W2).LE.0.25E0
+! ---------------------------------------------------------------
+ K = 1
+ P(1) = CONE
+ SUMA = CMPLX(GAMA(1),0.0E0)
+ AP(1) = 1.0E0
+ IF (AW2.GE.TOL) THEN
+ DO 140 K = 2, 30
+ P(K) = P(K-1)*W2
+ SUMA = SUMA + P(K)*CMPLX(GAMA(K),0.0E0)
+ AP(K) = AP(K-1)*AW2
+ IF (AP(K).LT.TOL) GO TO 160
+ 140 CONTINUE
+ K = 30
+ END IF
+ 160 KMAX = K
+ ZETA = W2*SUMA
+ ARG = ZETA*CMPLX(FN23,0.0E0)
+ ZA = SQRT(SUMA)
+ ZETA2 = SQRT(W2)*CMPLX(FNU,0.0E0)
+ ZETA1 = ZETA2*(CONE+ZETA*ZA*CMPLX(EX2,0.0E0))
+ ZA = ZA + ZA
+ PHI = SQRT(ZA)*RFN13
+ IF (IPMTR.NE.1) THEN
+! ------------------------------------------------------------
+! SUM SERIES FOR ASUM AND BSUM
+! ------------------------------------------------------------
+ SUMB = CZERO
+ DO 180 K = 1, KMAX
+ SUMB = SUMB + P(K)*CMPLX(BETA(K),0.0E0)
+ 180 CONTINUE
+ ASUM = CZERO
+ BSUM = SUMB
+ L1 = 0
+ L2 = 30
+ BTOL = TOL*ABS(BSUM)
+ ATOL = TOL
+ PP = 1.0E0
+ IAS = 0
+ IBS = 0
+ IF (RFNU2.GE.TOL) THEN
+ DO 280 IS = 2, 7
+ ATOL = ATOL/RFNU2
+ PP = PP*RFNU2
+ IF (IAS.NE.1) THEN
+ SUMA = CZERO
+ DO 200 K = 1, KMAX
+ M = L1 + K
+ SUMA = SUMA + P(K)*CMPLX(ALFA(M),0.0E0)
+ IF (AP(K).LT.ATOL) GO TO 220
+ 200 CONTINUE
+ 220 ASUM = ASUM + SUMA*CMPLX(PP,0.0E0)
+ IF (PP.LT.TOL) IAS = 1
+ END IF
+ IF (IBS.NE.1) THEN
+ SUMB = CZERO
+ DO 240 K = 1, KMAX
+ M = L2 + K
+ SUMB = SUMB + P(K)*CMPLX(BETA(M),0.0E0)
+ IF (AP(K).LT.ATOL) GO TO 260
+ 240 CONTINUE
+ 260 BSUM = BSUM + SUMB*CMPLX(PP,0.0E0)
+ IF (PP.LT.BTOL) IBS = 1
+ END IF
+ IF (IAS.EQ.1 .AND. IBS.EQ.1) THEN
+ GO TO 300
+ ELSE
+ L1 = L1 + 30
+ L2 = L2 + 30
+ END IF
+ 280 CONTINUE
+ END IF
+ 300 ASUM = ASUM + CONE
+ PP = RFNU*REAL(RFN13)
+ BSUM = BSUM*CMPLX(PP,0.0E0)
+ END IF
+ END IF
+ RETURN
+ END
+ SUBROUTINE DEVS17(Z,FNU,KODE,IKFLG,N,Y,NUF,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-765 (DEC 1989).
+!
+! Original name: CUOIK
+!
+! DEVS17 COMPUTES THE LEADING TERMS OF THE UNIFORM ASYMPTOTIC
+! EXPANSIONS FOR THE I AND K FUNCTIONS AND COMPARES THEM
+! (IN LOGARITHMIC FORM) TO ALIM AND ELIM FOR OVER AND UNDERFLOW
+! WHERE ALIM.LT.ELIM. IF THE MAGNITUDE, BASED ON THE LEADING
+! EXPONENTIAL, IS LESS THAN ALIM OR GREATER THAN -ALIM, THEN
+! THE RESULT IS ON SCALE. IF NOT, THEN A REFINED TEST USING OTHER
+! MULTIPLIERS (IN LOGARITHMIC FORM) IS MADE BASED ON ELIM. HERE
+! EXP(-ELIM)=SMALLEST MACHINE NUMBER*1.0E+3 AND EXP(-ALIM)=
+! EXP(-ELIM)/TOL
+!
+! IKFLG=1 MEANS THE I SEQUENCE IS TESTED
+! =2 MEANS THE K SEQUENCE IS TESTED
+! NUF = 0 MEANS THE LAST MEMBER OF THE SEQUENCE IS ON SCALE
+! =-1 MEANS AN OVERFLOW WOULD OCCUR
+! IKFLG=1 AND NUF.GT.0 MEANS THE LAST NUF Y VALUES WERE SET TO ZERO
+! THE FIRST N-NUF VALUES MUST BE SET BY ANOTHER ROUTINE
+! IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO
+! IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY
+! ANOTHER ROUTINE
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER IKFLG, KODE, N, NUF
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX ARG, ASUM, BSUM, CZ, CZERO, PHI, SUM, ZB, ZETA1,
+ * ZETA2, ZN, ZR
+ REAL AARG, AIC, APHI, ASCLE, AX, AY, FNN, GNN, GNU,
+ * RCZ, X, YY
+ INTEGER I, IFORM, INIT, NN, NW
+! .. Local Arrays ..
+ COMPLEX CWRK(16)
+! .. External Functions ..
+ REAL X02AME
+ EXTERNAL X02AME
+! .. External Subroutines ..
+ EXTERNAL DEUS17, DEWS17, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, CONJG, COS, EXP, LOG, MAX,
+ * REAL, SIN
+! .. Data statements ..
+ DATA CZERO/(0.0E0,0.0E0)/
+ DATA AIC/1.265512123484645396E+00/
+! .. Executable Statements ..
+!
+ NUF = 0
+ NN = N
+ X = REAL(Z)
+ ZR = Z
+ IF (X.LT.0.0E0) ZR = -Z
+ ZB = ZR
+ YY = AIMAG(ZR)
+ AX = ABS(X)*1.7321E0
+ AY = ABS(YY)
+ IFORM = 1
+ IF (AY.GT.AX) IFORM = 2
+ GNU = MAX(FNU,1.0E0)
+ IF (IKFLG.NE.1) THEN
+ FNN = NN
+ GNN = FNU + FNN - 1.0E0
+ GNU = MAX(GNN,FNN)
+ END IF
+! ------------------------------------------------------------------
+! ONLY THE MAGNITUDE OF ARG AND PHI ARE NEEDED ALONG WITH THE
+! REAL PARTS OF ZETA1, ZETA2 AND ZB. NO ATTEMPT IS MADE TO GET
+! THE SIGN OF THE IMAGINARY PART CORRECT.
+! ------------------------------------------------------------------
+ IF (IFORM.EQ.2) THEN
+ ZN = -ZR*CMPLX(0.0E0,1.0E0)
+ IF (YY.LE.0.0E0) ZN = CONJG(-ZN)
+ CALL DEUS17(ZN,GNU,1,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,BSUM,ELIM)
+ CZ = -ZETA1 + ZETA2
+ AARG = ABS(ARG)
+ ELSE
+ INIT = 0
+ CALL DEWS17(ZR,GNU,IKFLG,1,TOL,INIT,PHI,ZETA1,ZETA2,SUM,CWRK,
+ * ELIM)
+ CZ = -ZETA1 + ZETA2
+ END IF
+ IF (KODE.EQ.2) CZ = CZ - ZB
+ IF (IKFLG.EQ.2) CZ = -CZ
+ APHI = ABS(PHI)
+ RCZ = REAL(CZ)
+! ------------------------------------------------------------------
+! OVERFLOW TEST
+! ------------------------------------------------------------------
+ IF (RCZ.LE.ELIM) THEN
+ IF (RCZ.LT.ALIM) THEN
+! ------------------------------------------------------------
+! UNDERFLOW TEST
+! ------------------------------------------------------------
+ IF (RCZ.GE.(-ELIM)) THEN
+ IF (RCZ.GT.(-ALIM)) THEN
+ GO TO 40
+ ELSE
+ RCZ = RCZ + LOG(APHI)
+ IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*LOG(AARG) - AIC
+ IF (RCZ.GT.(-ELIM)) THEN
+ ASCLE = (1.0E+3*X02AME())/TOL
+ CZ = CZ + LOG(PHI)
+ IF (IFORM.NE.1) CZ = CZ - CMPLX(0.25E0,0.0E0)
+ * *LOG(ARG) - CMPLX(AIC,0.0E0)
+ AX = EXP(RCZ)/TOL
+ AY = AIMAG(CZ)
+ CZ = CMPLX(AX,0.0E0)*CMPLX(COS(AY),SIN(AY))
+ CALL DGVS17(CZ,NW,ASCLE,TOL)
+ IF (NW.NE.1) GO TO 40
+ END IF
+ END IF
+ END IF
+ DO 20 I = 1, NN
+ Y(I) = CZERO
+ 20 CONTINUE
+ NUF = NN
+ RETURN
+ ELSE
+ RCZ = RCZ + LOG(APHI)
+ IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*LOG(AARG) - AIC
+ IF (RCZ.GT.ELIM) GO TO 80
+ END IF
+ 40 IF (IKFLG.NE.2) THEN
+ IF (N.NE.1) THEN
+ 60 CONTINUE
+! ---------------------------------------------------------
+! SET UNDERFLOWS ON I SEQUENCE
+! ---------------------------------------------------------
+ GNU = FNU + NN - 1
+ IF (IFORM.EQ.2) THEN
+ CALL DEUS17(ZN,GNU,1,TOL,PHI,ARG,ZETA1,ZETA2,ASUM,
+ * BSUM,ELIM)
+ CZ = -ZETA1 + ZETA2
+ AARG = ABS(ARG)
+ ELSE
+ INIT = 0
+ CALL DEWS17(ZR,GNU,IKFLG,1,TOL,INIT,PHI,ZETA1,ZETA2,
+ * SUM,CWRK,ELIM)
+ CZ = -ZETA1 + ZETA2
+ END IF
+ IF (KODE.EQ.2) CZ = CZ - ZB
+ APHI = ABS(PHI)
+ RCZ = REAL(CZ)
+ IF (RCZ.GE.(-ELIM)) THEN
+ IF (RCZ.GT.(-ALIM)) THEN
+ RETURN
+ ELSE
+ RCZ = RCZ + LOG(APHI)
+ IF (IFORM.EQ.2) RCZ = RCZ - 0.25E0*LOG(AARG) - AIC
+ IF (RCZ.GT.(-ELIM)) THEN
+ ASCLE = (1.0E+3*X02AME())/TOL
+ CZ = CZ + LOG(PHI)
+ IF (IFORM.NE.1) CZ = CZ - CMPLX(0.25E0,0.0E0)
+ * *LOG(ARG) - CMPLX(AIC,
+ * 0.0E0)
+ AX = EXP(RCZ)/TOL
+ AY = AIMAG(CZ)
+ CZ = CMPLX(AX,0.0E0)*CMPLX(COS(AY),SIN(AY))
+ CALL DGVS17(CZ,NW,ASCLE,TOL)
+ IF (NW.NE.1) RETURN
+ END IF
+ END IF
+ END IF
+ Y(NN) = CZERO
+ NN = NN - 1
+ NUF = NUF + 1
+ IF (NN.NE.0) GO TO 60
+ END IF
+ END IF
+ RETURN
+ END IF
+ 80 NUF = -1
+ RETURN
+ END
+ SUBROUTINE DEWS17(ZR,FNU,IKFLG,IPMTR,TOL,INIT,PHI,ZETA1,ZETA2,SUM,
+ * CWRK,ELIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-766 (DEC 1989).
+!
+! Original name: CUNIK
+!
+! DEWS17 COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC
+! EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2
+! RESPECTIVELY BY
+!
+! W(FNU,ZR) = PHI*EXP(ZETA)*SUM
+!
+! WHERE ZETA=-ZETA1 + ZETA2 OR
+! ZETA1 - ZETA2
+!
+! THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE
+! SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG=
+! 1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK
+! ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI,
+! ZETA1,ZETA2.
+!
+! .. Scalar Arguments ..
+ COMPLEX PHI, SUM, ZETA1, ZETA2, ZR
+ REAL ELIM, FNU, TOL
+ INTEGER IKFLG, INIT, IPMTR
+! .. Array Arguments ..
+ COMPLEX CWRK(16)
+! .. Local Scalars ..
+ COMPLEX CFN, CONE, CRFN, CZERO, S, SR, T, T2, ZN
+ REAL AC, RFN, TEST, TSTI, TSTR
+ INTEGER I, J, K, L
+! .. Local Arrays ..
+ COMPLEX CON(2)
+ REAL C(120)
+!bc
+! .. external Functions ..
+ real x02ane
+ external x02ane
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, EXP, LOG, REAL, SQRT
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+ DATA CON(1), CON(2)/(3.98942280401432678E-01,0.0E0),
+ * (1.25331413731550025E+00,0.0E0)/
+ DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8),
+ * C(9), C(10), C(11), C(12), C(13), C(14), C(15),
+ * C(16)/1.00000000000000000E+00,
+ * -2.08333333333333333E-01,
+ * 1.25000000000000000E-01,
+ * 3.34201388888888889E-01,
+ * -4.01041666666666667E-01,
+ * 7.03125000000000000E-02,
+ * -1.02581259645061728E+00,
+ * 1.84646267361111111E+00,
+ * -8.91210937500000000E-01,
+ * 7.32421875000000000E-02,
+ * 4.66958442342624743E+00,
+ * -1.12070026162229938E+01,
+ * 8.78912353515625000E+00,
+ * -2.36408691406250000E+00,
+ * 1.12152099609375000E-01,
+ * -2.82120725582002449E+01/
+ DATA C(17), C(18), C(19), C(20), C(21), C(22), C(23),
+ * C(24)/8.46362176746007346E+01,
+ * -9.18182415432400174E+01,
+ * 4.25349987453884549E+01,
+ * -7.36879435947963170E+00,
+ * 2.27108001708984375E-01,
+ * 2.12570130039217123E+02,
+ * -7.65252468141181642E+02,
+ * 1.05999045252799988E+03/
+ DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31),
+ * C(32), C(33), C(34), C(35), C(36), C(37), C(38),
+ * C(39), C(40)/-6.99579627376132541E+02,
+ * 2.18190511744211590E+02,
+ * -2.64914304869515555E+01,
+ * 5.72501420974731445E-01,
+ * -1.91945766231840700E+03,
+ * 8.06172218173730938E+03,
+ * -1.35865500064341374E+04,
+ * 1.16553933368645332E+04,
+ * -5.30564697861340311E+03,
+ * 1.20090291321635246E+03,
+ * -1.08090919788394656E+02,
+ * 1.72772750258445740E+00,
+ * 2.02042913309661486E+04,
+ * -9.69805983886375135E+04,
+ * 1.92547001232531532E+05,
+ * -2.03400177280415534E+05/
+ DATA C(41), C(42), C(43), C(44), C(45), C(46), C(47),
+ * C(48)/1.22200464983017460E+05,
+ * -4.11926549688975513E+04,
+ * 7.10951430248936372E+03,
+ * -4.93915304773088012E+02,
+ * 6.07404200127348304E+00,
+ * -2.42919187900551333E+05,
+ * 1.31176361466297720E+06,
+ * -2.99801591853810675E+06/
+ DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55),
+ * C(56), C(57), C(58), C(59), C(60), C(61), C(62),
+ * C(63), C(64)/3.76327129765640400E+06,
+ * -2.81356322658653411E+06,
+ * 1.26836527332162478E+06,
+ * -3.31645172484563578E+05,
+ * 4.52187689813627263E+04,
+ * -2.49983048181120962E+03,
+ * 2.43805296995560639E+01,
+ * 3.28446985307203782E+06,
+ * -1.97068191184322269E+07,
+ * 5.09526024926646422E+07,
+ * -7.41051482115326577E+07,
+ * 6.63445122747290267E+07,
+ * -3.75671766607633513E+07,
+ * 1.32887671664218183E+07,
+ * -2.78561812808645469E+06,
+ * 3.08186404612662398E+05/
+ DATA C(65), C(66), C(67), C(68), C(69), C(70), C(71),
+ * C(72)/-1.38860897537170405E+04,
+ * 1.10017140269246738E+02,
+ * -4.93292536645099620E+07,
+ * 3.25573074185765749E+08,
+ * -9.39462359681578403E+08,
+ * 1.55359689957058006E+09,
+ * -1.62108055210833708E+09,
+ * 1.10684281682301447E+09/
+ DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79),
+ * C(80), C(81), C(82), C(83), C(84), C(85), C(86),
+ * C(87), C(88)/-4.95889784275030309E+08,
+ * 1.42062907797533095E+08,
+ * -2.44740627257387285E+07,
+ * 2.24376817792244943E+06,
+ * -8.40054336030240853E+04,
+ * 5.51335896122020586E+02,
+ * 8.14789096118312115E+08,
+ * -5.86648149205184723E+09,
+ * 1.86882075092958249E+10,
+ * -3.46320433881587779E+10,
+ * 4.12801855797539740E+10,
+ * -3.30265997498007231E+10,
+ * 1.79542137311556001E+10,
+ * -6.56329379261928433E+09,
+ * 1.55927986487925751E+09,
+ * -2.25105661889415278E+08/
+ DATA C(89), C(90), C(91), C(92), C(93), C(94), C(95),
+ * C(96)/1.73951075539781645E+07,
+ * -5.49842327572288687E+05,
+ * 3.03809051092238427E+03,
+ * -1.46792612476956167E+10,
+ * 1.14498237732025810E+11,
+ * -3.99096175224466498E+11,
+ * 8.19218669548577329E+11,
+ * -1.09837515608122331E+12/
+ DATA C(97), C(98), C(99), C(100), C(101), C(102),
+ * C(103), C(104), C(105), C(106), C(107), C(108),
+ * C(109), C(110)/1.00815810686538209E+12,
+ * -6.45364869245376503E+11,
+ * 2.87900649906150589E+11,
+ * -8.78670721780232657E+10,
+ * 1.76347306068349694E+10,
+ * -2.16716498322379509E+09,
+ * 1.43157876718888981E+08,
+ * -3.87183344257261262E+06,
+ * 1.82577554742931747E+04,
+ * 2.86464035717679043E+11,
+ * -2.40629790002850396E+12,
+ * 9.10934118523989896E+12,
+ * -2.05168994109344374E+13,
+ * 3.05651255199353206E+13/
+ DATA C(111), C(112), C(113), C(114), C(115), C(116),
+ * C(117), C(118), C(119),
+ * C(120)/-3.16670885847851584E+13,
+ * 2.33483640445818409E+13,
+ * -1.23204913055982872E+13,
+ * 4.61272578084913197E+12,
+ * -1.19655288019618160E+12,
+ * 2.05914503232410016E+11,
+ * -2.18229277575292237E+10,
+ * 1.24700929351271032E+09,
+ * -2.91883881222208134E+07,
+ * 1.18838426256783253E+05/
+! .. Executable Statements ..
+!
+ IF (INIT.EQ.0) THEN
+! ---------------------------------------------------------------
+! INITIALIZE ALL VARIABLES
+! ---------------------------------------------------------------
+ RFN = 1.0E0/FNU
+ CRFN = CMPLX(RFN,0.0E0)
+ TSTR = REAL(ZR)
+ TSTI = AIMAG(ZR)
+ TEST = FNU*EXP(-ELIM)
+ IF (ABS(TSTR).LT.TEST) TSTR = 0.0E0
+ IF (ABS(TSTI).LT.TEST) TSTI = 0.0E0
+!bc IF (TSTR.EQ.0.0E0 .AND. TSTI.EQ.0.0E0) THEN
+ IF (abs(tstr).le.x02ane().and.abs(tsti).le.x02ane()) then
+ ZETA1 = CMPLX(ELIM+ELIM+FNU,0.0E0)
+ ZETA2 = CMPLX(FNU,0.0E0)
+ PHI = CONE
+ RETURN
+ END IF
+ T = CMPLX(TSTR,TSTI)*CRFN
+ S = CONE + T*T
+ SR = SQRT(S)
+ CFN = CMPLX(FNU,0.0E0)
+ ZN = (CONE+SR)/T
+ ZETA1 = CFN*LOG(ZN)
+ ZETA2 = CFN*SR
+ T = CONE/SR
+ SR = T*CRFN
+ CWRK(16) = SQRT(SR)
+ PHI = CWRK(16)*CON(IKFLG)
+ IF (IPMTR.NE.0) THEN
+ RETURN
+ ELSE
+ T2 = CONE/S
+ CWRK(1) = CONE
+ CRFN = CONE
+ AC = 1.0E0
+ L = 1
+ DO 40 K = 2, 15
+ S = CZERO
+ DO 20 J = 1, K
+ L = L + 1
+ S = S*T2 + CMPLX(C(L),0.0E0)
+ 20 CONTINUE
+ CRFN = CRFN*SR
+ CWRK(K) = CRFN*S
+ AC = AC*RFN
+ TSTR = REAL(CWRK(K))
+ TSTI = AIMAG(CWRK(K))
+ TEST = ABS(TSTR) + ABS(TSTI)
+ IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 60
+ 40 CONTINUE
+ K = 15
+ 60 INIT = K
+ END IF
+ END IF
+ IF (IKFLG.EQ.2) THEN
+! ---------------------------------------------------------------
+! COMPUTE SUM FOR THE K FUNCTION
+! ---------------------------------------------------------------
+ S = CZERO
+ T = CONE
+ DO 80 I = 1, INIT
+ S = S + T*CWRK(I)
+ T = -T
+ 80 CONTINUE
+ SUM = S
+ PHI = CWRK(16)*CON(2)
+ ELSE
+! ---------------------------------------------------------------
+! COMPUTE SUM FOR THE I FUNCTION
+! ---------------------------------------------------------------
+ S = CZERO
+ DO 100 I = 1, INIT
+ S = S + CWRK(I)
+ 100 CONTINUE
+ SUM = S
+ PHI = CWRK(16)*CON(1)
+ END IF
+ RETURN
+ END
+ SUBROUTINE DEXS17(Z,FNU,KODE,N,Y,NZ,NLAST,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-767 (DEC 1989).
+!
+! Original name: CUNI1
+!
+! DEXS17 COMPUTES I(FNU,Z) BY MEANS OF THE UNIFORM ASYMPTOTIC
+! EXPANSION FOR I(FNU,Z) IN -PI/3.LE.ARG Z.LE.PI/3.
+!
+! FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
+! EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
+! NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
+! FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
+! Y(I)=CZERO FOR I=NLAST+1,N
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, TOL
+ INTEGER KODE, N, NLAST, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CFN, CONE, CRSC, CSCL, CZERO, PHI, RZ,
+ * S1, S2, SUM, ZETA1, ZETA2
+ REAL APHI, ASCLE, C2I, C2M, C2R, FN, RS1, YY
+ INTEGER I, IFLAG, INIT, K, M, ND, NN, NUF, NW
+! .. Local Arrays ..
+ COMPLEX CSR(3), CSS(3), CWRK(16), CY(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEVS17, DEWS17, DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, LOG, MAX, MIN,
+ * REAL, SIN
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ ND = N
+ NLAST = 0
+! ------------------------------------------------------------------
+! COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
+! NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
+! EXP(ALIM)=EXP(ELIM)*TOL
+! ------------------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+! ------------------------------------------------------------------
+! CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
+! ------------------------------------------------------------------
+ FN = MAX(FNU,1.0E0)
+ INIT = 0
+ CALL DEWS17(Z,FN,1,1,TOL,INIT,PHI,ZETA1,ZETA2,SUM,CWRK,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1 + ZETA2
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ S1 = -ZETA1 + CFN*(CFN/(Z+ZETA2))
+ END IF
+ RS1 = REAL(S1)
+ IF (ABS(RS1).LE.ELIM) THEN
+ 20 CONTINUE
+ NN = MIN(2,ND)
+ DO 40 I = 1, NN
+ FN = FNU + ND - I
+ INIT = 0
+ CALL DEWS17(Z,FN,1,0,TOL,INIT,PHI,ZETA1,ZETA2,SUM,CWRK,ELIM)
+ IF (KODE.EQ.1) THEN
+ S1 = -ZETA1 + ZETA2
+ ELSE
+ CFN = CMPLX(FN,0.0E0)
+ YY = AIMAG(Z)
+ S1 = -ZETA1 + CFN*(CFN/(Z+ZETA2)) + CMPLX(0.0E0,YY)
+ END IF
+! ------------------------------------------------------------
+! TEST FOR UNDERFLOW AND OVERFLOW
+! ------------------------------------------------------------
+ RS1 = REAL(S1)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 60
+ ELSE
+ IF (I.EQ.1) IFLAG = 2
+ IF (ABS(RS1).GE.ALIM) THEN
+! ------------------------------------------------------
+! REFINE TEST AND SCALE
+! ------------------------------------------------------
+ APHI = ABS(PHI)
+ RS1 = RS1 + LOG(APHI)
+ IF (ABS(RS1).GT.ELIM) THEN
+ GO TO 60
+ ELSE
+ IF (I.EQ.1) IFLAG = 1
+ IF (RS1.GE.0.0E0) THEN
+ IF (I.EQ.1) IFLAG = 3
+ END IF
+ END IF
+ END IF
+! ---------------------------------------------------------
+! SCALE S1 IF CABS(S1).LT.ASCLE
+! ---------------------------------------------------------
+ S2 = PHI*SUM
+ C2R = REAL(S1)
+ C2I = AIMAG(S1)
+ C2M = EXP(C2R)*REAL(CSS(IFLAG))
+ S1 = CMPLX(C2M,0.0E0)*CMPLX(COS(C2I),SIN(C2I))
+ S2 = S2*S1
+ IF (IFLAG.EQ.1) THEN
+ CALL DGVS17(S2,NW,BRY(1),TOL)
+ IF (NW.NE.0) GO TO 60
+ END IF
+ M = ND - I + 1
+ CY(I) = S2
+ Y(M) = S2*CSR(IFLAG)
+ END IF
+ 40 CONTINUE
+ GO TO 80
+! ---------------------------------------------------------------
+! SET UNDERFLOW AND UPDATE PARAMETERS
+! ---------------------------------------------------------------
+ 60 CONTINUE
+ IF (RS1.GT.0.0E0) THEN
+ GO TO 160
+ ELSE
+ Y(ND) = CZERO
+ NZ = NZ + 1
+ ND = ND - 1
+ IF (ND.EQ.0) THEN
+ RETURN
+ ELSE
+ CALL DEVS17(Z,FNU,KODE,1,ND,Y,NUF,TOL,ELIM,ALIM)
+ IF (NUF.LT.0) THEN
+ GO TO 160
+ ELSE
+ ND = ND - NUF
+ NZ = NZ + NUF
+ IF (ND.EQ.0) THEN
+ RETURN
+ ELSE
+ FN = FNU + ND - 1
+ IF (FN.GE.FNUL) THEN
+ GO TO 20
+ ELSE
+ GO TO 120
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+ 80 IF (ND.GT.2) THEN
+ RZ = CMPLX(2.0E0,0.0E0)/Z
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ S1 = CY(1)
+ S2 = CY(2)
+ C1 = CSR(IFLAG)
+ ASCLE = BRY(IFLAG)
+ K = ND - 2
+ FN = K
+ DO 100 I = 3, ND
+ C2 = S2
+ S2 = S1 + CMPLX(FNU+FN,0.0E0)*RZ*S2
+ S1 = C2
+ C2 = S2*C1
+ Y(K) = C2
+ K = K - 1
+ FN = FN - 1.0E0
+ IF (IFLAG.LT.3) THEN
+ C2R = REAL(C2)
+ C2I = AIMAG(C2)
+ C2R = ABS(C2R)
+ C2I = ABS(C2I)
+ C2M = MAX(C2R,C2I)
+ IF (C2M.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*C1
+ S2 = C2
+ S1 = S1*CSS(IFLAG)
+ S2 = S2*CSS(IFLAG)
+ C1 = CSR(IFLAG)
+ END IF
+ END IF
+ 100 CONTINUE
+ END IF
+ RETURN
+ 120 NLAST = ND
+ RETURN
+ ELSE IF (RS1.LE.0.0E0) THEN
+ NZ = N
+ DO 140 I = 1, N
+ Y(I) = CZERO
+ 140 CONTINUE
+ RETURN
+ END IF
+ 160 NZ = -1
+ RETURN
+ END
+ SUBROUTINE DEYS17(Z,FNU,KODE,N,Y,NZ,NUI,NLAST,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-768 (DEC 1989).
+!
+! Original name: CBUNI
+!
+! DEYS17 COMPUTES THE I BESSEL FUNCTION FOR LARGE CABS(Z).GT.
+! FNUL AND FNU+N-1.LT.FNUL. THE ORDER IS INCREASED FROM
+! FNU+N-1 GREATER THAN FNUL BY ADDING NUI AND COMPUTING
+! ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR I(FNU,Z)
+! ON IFORM=1 AND THE EXPANSION FOR J(FNU,Z) ON IFORM=2
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, TOL
+ INTEGER KODE, N, NLAST, NUI, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX CSCL, CSCR, RZ, S1, S2, ST
+ REAL ASCLE, AX, AY, DFNU, FNUI, GNU, STI, STM, STR,
+ * XX, YY
+ INTEGER I, IFLAG, IFORM, K, NL, NW
+! .. Local Arrays ..
+ COMPLEX CY(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME
+ EXTERNAL X02AME
+! .. External Subroutines ..
+ EXTERNAL DETS17, DEXS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, MAX, REAL
+! .. Executable Statements ..
+!
+ NZ = 0
+ XX = REAL(Z)
+ YY = AIMAG(Z)
+ AX = ABS(XX)*1.7321E0
+ AY = ABS(YY)
+ IFORM = 1
+ IF (AY.GT.AX) IFORM = 2
+ IF (NUI.EQ.0) THEN
+ IF (IFORM.EQ.2) THEN
+! ------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
+! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
+! AND HPI=PI/2
+! ------------------------------------------------------------
+ CALL DETS17(Z,FNU,KODE,N,Y,NW,NLAST,FNUL,TOL,ELIM,ALIM)
+ ELSE
+! ------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
+! -PI/3.LE.ARG(Z).LE.PI/3
+! ------------------------------------------------------------
+ CALL DEXS17(Z,FNU,KODE,N,Y,NW,NLAST,FNUL,TOL,ELIM,ALIM)
+ END IF
+ IF (NW.GE.0) THEN
+ NZ = NW
+ RETURN
+ END IF
+ ELSE
+ FNUI = NUI
+ DFNU = FNU + N - 1
+ GNU = DFNU + FNUI
+ IF (IFORM.EQ.2) THEN
+! ------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
+! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
+! AND HPI=PI/2
+! ------------------------------------------------------------
+ CALL DETS17(Z,GNU,KODE,2,CY,NW,NLAST,FNUL,TOL,ELIM,ALIM)
+ ELSE
+! ------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
+! -PI/3.LE.ARG(Z).LE.PI/3
+! ------------------------------------------------------------
+ CALL DEXS17(Z,GNU,KODE,2,CY,NW,NLAST,FNUL,TOL,ELIM,ALIM)
+ END IF
+ IF (NW.GE.0) THEN
+ IF (NW.NE.0) THEN
+ NLAST = N
+ ELSE
+ AY = ABS(CY(1))
+! ---------------------------------------------------------
+! SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER
+! USED
+! ---------------------------------------------------------
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = BRY(2)
+ IFLAG = 2
+ ASCLE = BRY(2)
+ AX = 1.0E0
+ CSCL = CMPLX(AX,0.0E0)
+ IF (AY.LE.BRY(1)) THEN
+ IFLAG = 1
+ ASCLE = BRY(1)
+ AX = 1.0E0/TOL
+ CSCL = CMPLX(AX,0.0E0)
+ ELSE IF (AY.GE.BRY(2)) THEN
+ IFLAG = 3
+ ASCLE = BRY(3)
+ AX = TOL
+ CSCL = CMPLX(AX,0.0E0)
+ END IF
+ AY = 1.0E0/AX
+ CSCR = CMPLX(AY,0.0E0)
+ S1 = CY(2)*CSCL
+ S2 = CY(1)*CSCL
+ RZ = CMPLX(2.0E0,0.0E0)/Z
+ DO 20 I = 1, NUI
+ ST = S2
+ S2 = CMPLX(DFNU+FNUI,0.0E0)*RZ*S2 + S1
+ S1 = ST
+ FNUI = FNUI - 1.0E0
+ IF (IFLAG.LT.3) THEN
+ ST = S2*CSCR
+ STR = REAL(ST)
+ STI = AIMAG(ST)
+ STR = ABS(STR)
+ STI = ABS(STI)
+ STM = MAX(STR,STI)
+ IF (STM.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*CSCR
+ S2 = ST
+ AX = AX*TOL
+ AY = 1.0E0/AX
+ CSCL = CMPLX(AX,0.0E0)
+ CSCR = CMPLX(AY,0.0E0)
+ S1 = S1*CSCL
+ S2 = S2*CSCL
+ END IF
+ END IF
+ 20 CONTINUE
+ Y(N) = S2*CSCR
+ IF (N.NE.1) THEN
+ NL = N - 1
+ FNUI = NL
+ K = NL
+ DO 40 I = 1, NL
+ ST = S2
+ S2 = CMPLX(FNU+FNUI,0.0E0)*RZ*S2 + S1
+ S1 = ST
+ ST = S2*CSCR
+ Y(K) = ST
+ FNUI = FNUI - 1.0E0
+ K = K - 1
+ IF (IFLAG.LT.3) THEN
+ STR = REAL(ST)
+ STI = AIMAG(ST)
+ STR = ABS(STR)
+ STI = ABS(STI)
+ STM = MAX(STR,STI)
+ IF (STM.GT.ASCLE) THEN
+ IFLAG = IFLAG + 1
+ ASCLE = BRY(IFLAG)
+ S1 = S1*CSCR
+ S2 = ST
+ AX = AX*TOL
+ AY = 1.0E0/AX
+ CSCL = CMPLX(AX,0.0E0)
+ CSCR = CMPLX(AY,0.0E0)
+ S1 = S1*CSCL
+ S2 = S2*CSCL
+ END IF
+ END IF
+ 40 CONTINUE
+ END IF
+ END IF
+ RETURN
+ END IF
+ END IF
+ NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ RETURN
+ END
+ SUBROUTINE DEZS17(Z,FNU,KODE,N,CY,NZ,RL,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-769 (DEC 1989).
+!
+! Original name: CBINU
+!
+! DEZS17 COMPUTES THE I FUNCTION IN THE RIGHT HALF Z PLANE
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, RL, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX CY(N)
+! .. Local Scalars ..
+ COMPLEX CZERO
+ REAL AZ, DFNU
+ INTEGER I, INW, NLAST, NN, NUI, NW
+! .. Local Arrays ..
+ COMPLEX CW(2)
+! .. External Subroutines ..
+ EXTERNAL DESS17, DEVS17, DEYS17, DGRS17, DGTS17, DGYS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, INT, MAX
+! .. Data statements ..
+ DATA CZERO/(0.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ AZ = ABS(Z)
+ NN = N
+ DFNU = FNU + N - 1
+ IF (AZ.GT.2.0E0) THEN
+ IF (AZ*AZ*0.25E0.GT.DFNU+1.0E0) GO TO 20
+ END IF
+! ------------------------------------------------------------------
+! POWER SERIES
+! ------------------------------------------------------------------
+ CALL DGRS17(Z,FNU,KODE,NN,CY,NW,TOL,ELIM,ALIM)
+ INW = ABS(NW)
+ NZ = NZ + INW
+ NN = NN - INW
+ IF (NN.EQ.0) THEN
+ RETURN
+ ELSE IF (NW.GE.0) THEN
+ RETURN
+ ELSE
+ DFNU = FNU + NN - 1
+ END IF
+ 20 IF (AZ.GE.RL) THEN
+ IF (DFNU.GT.1.0E0) THEN
+ IF (AZ+AZ.LT.DFNU*DFNU) GO TO 40
+ END IF
+! ---------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR LARGE Z
+! ---------------------------------------------------------------
+ CALL DGYS17(Z,FNU,KODE,NN,CY,NW,RL,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 120
+ ELSE
+ RETURN
+ END IF
+ ELSE IF (DFNU.LE.1.0E0) THEN
+ GO TO 100
+ END IF
+! ------------------------------------------------------------------
+! OVERFLOW AND UNDERFLOW TEST ON I SEQUENCE FOR MILLER ALGORITHM
+! ------------------------------------------------------------------
+ 40 CALL DEVS17(Z,FNU,KODE,1,NN,CY,NW,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 120
+ ELSE
+ NZ = NZ + NW
+ NN = NN - NW
+ IF (NN.EQ.0) THEN
+ RETURN
+ ELSE
+ DFNU = FNU + NN - 1
+ IF (DFNU.LE.FNUL) THEN
+ IF (AZ.LE.FNUL) GO TO 60
+ END IF
+! ------------------------------------------------------------
+! INCREMENT FNU+NN-1 UP TO FNUL, COMPUTE AND RECUR BACKWARD
+! ------------------------------------------------------------
+ NUI = INT(FNUL-DFNU) + 1
+ NUI = MAX(NUI,0)
+ CALL DEYS17(Z,FNU,KODE,NN,CY,NW,NUI,NLAST,FNUL,TOL,ELIM,
+ * ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 120
+ ELSE
+ NZ = NZ + NW
+ IF (NLAST.EQ.0) THEN
+ RETURN
+ ELSE
+ NN = NLAST
+ END IF
+ END IF
+ 60 IF (AZ.GT.RL) THEN
+! ---------------------------------------------------------
+! MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN
+! ---------------------------------------------------------
+! ---------------------------------------------------------
+! OVERFLOW TEST ON K FUNCTIONS USED IN WRONSKIAN
+! ---------------------------------------------------------
+ CALL DEVS17(Z,FNU,KODE,2,2,CW,NW,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ NZ = NN
+ DO 80 I = 1, NN
+ CY(I) = CZERO
+ 80 CONTINUE
+ RETURN
+ ELSE IF (NW.GT.0) THEN
+ GO TO 120
+ ELSE
+ CALL DESS17(Z,FNU,KODE,NN,CY,NW,CW,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 120
+ ELSE
+ RETURN
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------------
+! MILLER ALGORITHM NORMALIZED BY THE SERIES
+! ------------------------------------------------------------------
+ 100 CALL DGTS17(Z,FNU,KODE,NN,CY,NW,TOL)
+ IF (NW.GE.0) RETURN
+ 120 NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ IF (NW.EQ.(-3)) NZ = -3
+ RETURN
+ END
+ SUBROUTINE DGRS17(Z,FNU,KODE,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-771 (DEC 1989).
+!
+! Original name: CSERI
+!
+! DGRS17 COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY
+! MEANS OF THE POWER SERIES FOR LARGE CABS(Z) IN THE
+! REGION CABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN.
+! NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO
+! DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE
+! CONDITION CABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE
+! COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ).
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX AK1, CK, COEF, CONE, CRSC, CZ, CZERO, HZ, RZ,
+ * S1, S2
+ REAL AA, ACZ, AK, ARM, ASCLE, ATOL, AZ, DFNU, FNUP,
+ * RAK1, RS, RTR1, S, SS, X
+ INTEGER I, IB, IDUM, IFLAG, IL, K, L, M, NN, NW
+! .. Local Arrays ..
+ COMPLEX W(2)
+! .. External Functions ..
+ REAL S14ABE, X02AME
+ EXTERNAL S14ABE, X02AME
+! .. External Subroutines ..
+ EXTERNAL DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, LOG, MIN, REAL,
+ * SIN, SQRT
+! .. Data statements ..
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ AZ = ABS(Z)
+ IF (AZ.NE.0.0E0) THEN
+ X = REAL(Z)
+ ARM = 1.0E+3*X02AME()
+ RTR1 = SQRT(ARM)
+ CRSC = CMPLX(1.0E0,0.0E0)
+ IFLAG = 0
+ IF (AZ.LT.ARM) THEN
+ NZ = N
+ IF (FNU.EQ.0.0E0) NZ = NZ - 1
+ ELSE
+ HZ = Z*CMPLX(0.5E0,0.0E0)
+ CZ = CZERO
+ IF (AZ.GT.RTR1) CZ = HZ*HZ
+ ACZ = ABS(CZ)
+ NN = N
+ CK = LOG(HZ)
+ 20 CONTINUE
+ DFNU = FNU + NN - 1
+ FNUP = DFNU + 1.0E0
+! ------------------------------------------------------------
+! UNDERFLOW TEST
+! ------------------------------------------------------------
+ AK1 = CK*CMPLX(DFNU,0.0E0)
+ IDUM = 0
+! S14ABE assumed not to fail, therefore IDUM set to zero.
+ AK = S14ABE(FNUP,IDUM)
+ AK1 = AK1 - CMPLX(AK,0.0E0)
+ IF (KODE.EQ.2) AK1 = AK1 - CMPLX(X,0.0E0)
+ RAK1 = REAL(AK1)
+ IF (RAK1.GT.(-ELIM)) THEN
+ IF (RAK1.LE.(-ALIM)) THEN
+ IFLAG = 1
+ SS = 1.0E0/TOL
+ CRSC = CMPLX(TOL,0.0E0)
+ ASCLE = ARM*SS
+ END IF
+ AK = AIMAG(AK1)
+ AA = EXP(RAK1)
+ IF (IFLAG.EQ.1) AA = AA*SS
+ COEF = CMPLX(AA,0.0E0)*CMPLX(COS(AK),SIN(AK))
+ ATOL = TOL*ACZ/FNUP
+ IL = MIN(2,NN)
+ DO 60 I = 1, IL
+ DFNU = FNU + NN - I
+ FNUP = DFNU + 1.0E0
+ S1 = CONE
+ IF (ACZ.GE.TOL*FNUP) THEN
+ AK1 = CONE
+ AK = FNUP + 2.0E0
+ S = FNUP
+ AA = 2.0E0
+ 40 CONTINUE
+ RS = 1.0E0/S
+ AK1 = AK1*CZ*CMPLX(RS,0.0E0)
+ S1 = S1 + AK1
+ S = S + AK
+ AK = AK + 2.0E0
+ AA = AA*ACZ*RS
+ IF (AA.GT.ATOL) GO TO 40
+ END IF
+ M = NN - I + 1
+ S2 = S1*COEF
+ W(I) = S2
+ IF (IFLAG.NE.0) THEN
+ CALL DGVS17(S2,NW,ASCLE,TOL)
+ IF (NW.NE.0) GO TO 80
+ END IF
+ Y(M) = S2*CRSC
+ IF (I.NE.IL) COEF = COEF*CMPLX(DFNU,0.0E0)/HZ
+ 60 CONTINUE
+ GO TO 100
+ END IF
+ 80 NZ = NZ + 1
+ Y(NN) = CZERO
+ IF (ACZ.GT.DFNU) THEN
+ GO TO 180
+ ELSE
+ NN = NN - 1
+ IF (NN.EQ.0) THEN
+ RETURN
+ ELSE
+ GO TO 20
+ END IF
+ END IF
+ 100 IF (NN.GT.2) THEN
+ K = NN - 2
+ AK = K
+ RZ = (CONE+CONE)/Z
+ IF (IFLAG.EQ.1) THEN
+! ------------------------------------------------------
+! RECUR BACKWARD WITH SCALED VALUES
+! ------------------------------------------------------
+! ------------------------------------------------------
+! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE
+! THE UNDERFLOW LIMIT = ASCLE = X02AME()*CSCL*1.0E+3
+! ------------------------------------------------------
+ S1 = W(1)
+ S2 = W(2)
+ DO 120 L = 3, NN
+ CK = S2
+ S2 = S1 + CMPLX(AK+FNU,0.0E0)*RZ*S2
+ S1 = CK
+ CK = S2*CRSC
+ Y(K) = CK
+ AK = AK - 1.0E0
+ K = K - 1
+ IF (ABS(CK).GT.ASCLE) GO TO 140
+ 120 CONTINUE
+ RETURN
+ 140 IB = L + 1
+ IF (IB.GT.NN) RETURN
+ ELSE
+ IB = 3
+ END IF
+ DO 160 I = IB, NN
+ Y(K) = CMPLX(AK+FNU,0.0E0)*RZ*Y(K+1) + Y(K+2)
+ AK = AK - 1.0E0
+ K = K - 1
+ 160 CONTINUE
+ END IF
+ RETURN
+! ------------------------------------------------------------
+! RETURN WITH NZ.LT.0 IF CABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE
+! THE CALCULATION IN DEZS17 WITH N=N-IABS(NZ)
+! ------------------------------------------------------------
+ 180 CONTINUE
+ NZ = -NZ
+ RETURN
+ END IF
+ END IF
+ Y(1) = CZERO
+ IF (FNU.EQ.0.0E0) Y(1) = CONE
+ IF (N.NE.1) THEN
+ DO 200 I = 2, N
+ Y(I) = CZERO
+ 200 CONTINUE
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGSS17(ZR,S1,S2,NZ,ASCLE,ALIM,IUF)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-772 (DEC 1989).
+!
+! Original name: CS1S2
+!
+! DGSS17 TESTS FOR A POSSIBLE UNDERFLOW RESULTING FROM THE
+! ADDITION OF THE I AND K FUNCTIONS IN THE ANALYTIC CON-
+! TINUATION FORMULA WHERE S1=K FUNCTION AND S2=I FUNCTION.
+! ON KODE=1 THE I AND K FUNCTIONS ARE DIFFERENT ORDERS OF
+! MAGNITUDE, BUT FOR KODE=2 THEY CAN BE OF THE SAME ORDER
+! OF MAGNITUDE AND THE MAXIMUM MUST BE AT LEAST ONE
+! PRECISION ABOVE THE UNDERFLOW LIMIT.
+!
+! .. Scalar Arguments ..
+ COMPLEX S1, S2, ZR
+ REAL ALIM, ASCLE
+ INTEGER IUF, NZ
+! .. Local Scalars ..
+ COMPLEX C1, CZERO, S1D
+ REAL AA, ALN, AS1, AS2, XX
+ INTEGER IF1
+! .. External Functions ..
+ COMPLEX S01EAE
+ EXTERNAL S01EAE
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, LOG, MAX, REAL
+! .. Data statements ..
+ DATA CZERO/(0.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ AS1 = ABS(S1)
+ AS2 = ABS(S2)
+ AA = REAL(S1)
+ ALN = AIMAG(S1)
+ IF (AA.NE.0.0E0 .OR. ALN.NE.0.0E0) THEN
+ IF (AS1.NE.0.0E0) THEN
+ XX = REAL(ZR)
+ ALN = -XX - XX + LOG(AS1)
+ S1D = S1
+ S1 = CZERO
+ AS1 = 0.0E0
+ IF (ALN.GE.(-ALIM)) THEN
+ C1 = LOG(S1D) - ZR - ZR
+! S1 = EXP(C1)
+ IF1 = 1
+ S1 = S01EAE(C1,IF1)
+ AS1 = ABS(S1)
+ IUF = IUF + 1
+ END IF
+ END IF
+ END IF
+ AA = MAX(AS1,AS2)
+ IF (AA.LE.ASCLE) THEN
+ S1 = CZERO
+ S2 = CZERO
+ NZ = 1
+ IUF = 0
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGTS17(Z,FNU,KODE,N,Y,NZ,TOL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-773 (DEC 1989).
+! Mark 17 REVISED. IER-1703 (JUN 1995).
+!
+! Original name: CMLRI
+!
+! DGTS17 COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY THE
+! MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES.
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL FNU, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX CK, CNORM, CONE, CTWO, CZERO, P1, P2, PT, RZ,
+ * SUM
+ REAL ACK, AK, AP, AT, AZ, BK, FKAP, FKK, FLAM, FNF,
+ * RHO, RHO2, SCLE, TFNF, TST, X
+ INTEGER I, IAZ, IDUM, IFL, IFNU, INU, ITIME, K, KK, KM,
+ * M
+! .. External Functions ..
+ COMPLEX S01EAE
+ REAL S14ABE, X02ANE
+ EXTERNAL S14ABE, S01EAE, X02ANE
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, CMPLX, CONJG, EXP, INT, LOG, MAX, MIN,
+ * REAL, SQRT
+! .. Data statements ..
+ DATA CZERO, CONE, CTWO/(0.0E0,0.0E0), (1.0E0,0.0E0),
+ * (2.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ SCLE = (1.0E+3*X02ANE())/TOL
+ NZ = 0
+ AZ = ABS(Z)
+ X = REAL(Z)
+ IAZ = INT(AZ)
+ IFNU = INT(FNU)
+ INU = IFNU + N - 1
+ AT = IAZ + 1.0E0
+ CK = CMPLX(AT,0.0E0)/Z
+ RZ = CTWO/Z
+ P1 = CZERO
+ P2 = CONE
+ ACK = (AT+1.0E0)/AZ
+ RHO = ACK + SQRT(ACK*ACK-1.0E0)
+ RHO2 = RHO*RHO
+ TST = (RHO2+RHO2)/((RHO2-1.0E0)*(RHO-1.0E0))
+ TST = TST/TOL
+! ------------------------------------------------------------------
+! COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES
+! ------------------------------------------------------------------
+ AK = AT
+ DO 20 I = 1, 80
+ PT = P2
+ P2 = P1 - CK*P2
+ P1 = PT
+ CK = CK + RZ
+ AP = ABS(P2)
+ IF (AP.GT.TST*AK*AK) THEN
+ GO TO 40
+ ELSE
+ AK = AK + 1.0E0
+ END IF
+ 20 CONTINUE
+ GO TO 180
+ 40 I = I + 1
+ K = 0
+ IF (INU.GE.IAZ) THEN
+! ---------------------------------------------------------------
+! COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS
+! ---------------------------------------------------------------
+ P1 = CZERO
+ P2 = CONE
+ AT = INU + 1.0E0
+ CK = CMPLX(AT,0.0E0)/Z
+ ACK = AT/AZ
+ TST = SQRT(ACK/TOL)
+ ITIME = 1
+ DO 60 K = 1, 80
+ PT = P2
+ P2 = P1 - CK*P2
+ P1 = PT
+ CK = CK + RZ
+ AP = ABS(P2)
+ IF (AP.GE.TST) THEN
+ IF (ITIME.EQ.2) THEN
+ GO TO 80
+ ELSE
+ ACK = ABS(CK)
+ FLAM = ACK + SQRT(ACK*ACK-1.0E0)
+ FKAP = AP/ABS(P1)
+ RHO = MIN(FLAM,FKAP)
+ TST = TST*SQRT(RHO/(RHO*RHO-1.0E0))
+ ITIME = 2
+ END IF
+ END IF
+ 60 CONTINUE
+ GO TO 180
+ END IF
+! ------------------------------------------------------------------
+! BACKWARD RECURRENCE AND SUM NORMALIZING RELATION
+! ------------------------------------------------------------------
+ 80 K = K + 1
+ KK = MAX(I+IAZ,K+INU)
+ FKK = KK
+ P1 = CZERO
+! ------------------------------------------------------------------
+! SCALE P2 AND SUM BY SCLE
+! ------------------------------------------------------------------
+ P2 = CMPLX(SCLE,0.0E0)
+ FNF = FNU - IFNU
+ TFNF = FNF + FNF
+ IDUM = 0
+! S14ABE assumed not to fail, therefore IDUM set to zero.
+ BK = S14ABE(FKK+TFNF+1.0E0,IDUM) - S14ABE(FKK+1.0E0,IDUM) -
+ * S14ABE(TFNF+1.0E0,IDUM)
+ BK = EXP(BK)
+ SUM = CZERO
+ KM = KK - INU
+ DO 100 I = 1, KM
+ PT = P2
+ P2 = P1 + CMPLX(FKK+FNF,0.0E0)*RZ*P2
+ P1 = PT
+ AK = 1.0E0 - TFNF/(FKK+TFNF)
+ ACK = BK*AK
+ SUM = SUM + CMPLX(ACK+BK,0.0E0)*P1
+ BK = ACK
+ FKK = FKK - 1.0E0
+ 100 CONTINUE
+ Y(N) = P2
+ IF (N.NE.1) THEN
+ DO 120 I = 2, N
+ PT = P2
+ P2 = P1 + CMPLX(FKK+FNF,0.0E0)*RZ*P2
+ P1 = PT
+ AK = 1.0E0 - TFNF/(FKK+TFNF)
+ ACK = BK*AK
+ SUM = SUM + CMPLX(ACK+BK,0.0E0)*P1
+ BK = ACK
+ FKK = FKK - 1.0E0
+ M = N - I + 1
+ Y(M) = P2
+ 120 CONTINUE
+ END IF
+ IF (IFNU.GT.0) THEN
+ DO 140 I = 1, IFNU
+ PT = P2
+ P2 = P1 + CMPLX(FKK+FNF,0.0E0)*RZ*P2
+ P1 = PT
+ AK = 1.0E0 - TFNF/(FKK+TFNF)
+ ACK = BK*AK
+ SUM = SUM + CMPLX(ACK+BK,0.0E0)*P1
+ BK = ACK
+ FKK = FKK - 1.0E0
+ 140 CONTINUE
+ END IF
+ PT = Z
+ IF (KODE.EQ.2) PT = PT - CMPLX(X,0.0E0)
+ P1 = -CMPLX(FNF,0.0E0)*LOG(RZ) + PT
+ IDUM = 0
+! S14ABE assumed not to fail, therefore IDUM set to zero.
+ AP = S14ABE(1.0E0+FNF,IDUM)
+ PT = P1 - CMPLX(AP,0.0E0)
+! ------------------------------------------------------------------
+! THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW
+! IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES
+! ------------------------------------------------------------------
+ P2 = P2 + SUM
+ AP = ABS(P2)
+ P1 = CMPLX(1.0E0/AP,0.0E0)
+! CK = EXP(PT)*P1
+ IFL = 1
+ CK = S01EAE(PT,IFL)*P1
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 200
+ PT = CONJG(P2)*P1
+ CNORM = CK*PT
+ DO 160 I = 1, N
+ Y(I) = Y(I)*CNORM
+ 160 CONTINUE
+ RETURN
+ 180 NZ = -2
+ RETURN
+ 200 NZ = -3
+ RETURN
+ END
+ SUBROUTINE DGUS17(Z,CSH,CCH)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-774 (DEC 1989).
+!
+! Original name: CSHCH
+!
+! DGUS17 COMPUTES THE COMPLEX HYPERBOLIC FUNCTIONS CSH=SINH(X+I*Y)
+! AND CCH=COSH(X+I*Y), WHERE I**2=-1.
+!
+! .. Scalar Arguments ..
+ COMPLEX CCH, CSH, Z
+! .. Local Scalars ..
+ REAL CCHI, CCHR, CH, CN, CSHI, CSHR, SH, SN, X, Y
+! .. Intrinsic Functions ..
+ INTRINSIC AIMAG, CMPLX, COS, COSH, REAL, SIN, SINH
+! .. Executable Statements ..
+!
+ X = REAL(Z)
+ Y = AIMAG(Z)
+ SH = SINH(X)
+ CH = COSH(X)
+ SN = SIN(Y)
+ CN = COS(Y)
+ CSHR = SH*CN
+ CSHI = CH*SN
+ CSH = CMPLX(CSHR,CSHI)
+ CCHR = CH*CN
+ CCHI = SH*SN
+ CCH = CMPLX(CCHR,CCHI)
+ RETURN
+ END
+ SUBROUTINE DGVS17(Y,NZ,ASCLE,TOL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-775 (DEC 1989).
+!
+! Original name: CUCHK
+!
+! Y ENTERS AS A SCALED QUANTITY WHOSE MAGNITUDE IS GREATER THAN
+! EXP(-ALIM)=ASCLE=1.0E+3*X02AME()/TOL. THE TEST IS MADE TO SEE
+! IF THE MAGNITUDE OF THE REAL OR IMAGINARY PART WOULD UNDERFLOW
+! WHEN Y IS SCALED (BY TOL) TO ITS PROPER VALUE. Y IS ACCEPTED
+! IF THE UNDERFLOW IS AT LEAST ONE PRECISION BELOW THE MAGNITUDE
+! OF THE LARGEST COMPONENT; OTHERWISE THE PHASE ANGLE DOES NOT HAVE
+! ABSOLUTE ACCURACY AND AN UNDERFLOW IS ASSUMED.
+!
+! .. Scalar Arguments ..
+ COMPLEX Y
+ REAL ASCLE, TOL
+ INTEGER NZ
+! .. Local Scalars ..
+ REAL SS, ST, YI, YR
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, MAX, MIN, REAL
+! .. Executable Statements ..
+!
+ NZ = 0
+ YR = REAL(Y)
+ YI = AIMAG(Y)
+ YR = ABS(YR)
+ YI = ABS(YI)
+ ST = MIN(YR,YI)
+ IF (ST.LE.ASCLE) THEN
+ SS = MAX(YR,YI)
+ ST = ST/TOL
+ IF (SS.LT.ST) NZ = 1
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGWS17(ZR,FNU,N,Y,NZ,RZ,ASCLE,TOL,ELIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-776 (DEC 1989).
+!
+! Original name: CKSCL
+!
+! SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE
+! ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN
+! RETURN WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL.
+!
+! .. Scalar Arguments ..
+ COMPLEX RZ, ZR
+ REAL ASCLE, ELIM, FNU, TOL
+ INTEGER N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX CELM, CK, CS, CZERO, S1, S2, ZD
+ REAL AA, ACS, ALAS, AS, CSI, CSR, ELM, FN, HELIM, XX,
+ * ZRI
+ INTEGER I, IC, K, KK, NN, NW
+! .. Local Arrays ..
+ COMPLEX CY(2)
+! .. External Subroutines ..
+ EXTERNAL DGVS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, LOG, MIN, REAL, SIN
+! .. Data statements ..
+ DATA CZERO/(0.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ IC = 0
+ XX = REAL(ZR)
+ NN = MIN(2,N)
+ DO 20 I = 1, NN
+ S1 = Y(I)
+ CY(I) = S1
+ AS = ABS(S1)
+ ACS = -XX + LOG(AS)
+ NZ = NZ + 1
+ Y(I) = CZERO
+ IF (ACS.GE.(-ELIM)) THEN
+ CS = -ZR + LOG(S1)
+ CSR = REAL(CS)
+ CSI = AIMAG(CS)
+ AA = EXP(CSR)/TOL
+ CS = CMPLX(AA,0.0E0)*CMPLX(COS(CSI),SIN(CSI))
+ CALL DGVS17(CS,NW,ASCLE,TOL)
+ IF (NW.EQ.0) THEN
+ Y(I) = CS
+ NZ = NZ - 1
+ IC = I
+ END IF
+ END IF
+ 20 CONTINUE
+ IF (N.NE.1) THEN
+ IF (IC.LE.1) THEN
+ Y(1) = CZERO
+ NZ = 2
+ END IF
+ IF (N.NE.2) THEN
+ IF (NZ.NE.0) THEN
+ FN = FNU + 1.0E0
+ CK = CMPLX(FN,0.0E0)*RZ
+ S1 = CY(1)
+ S2 = CY(2)
+ HELIM = 0.5E0*ELIM
+ ELM = EXP(-ELIM)
+ CELM = CMPLX(ELM,0.0E0)
+ ZRI = AIMAG(ZR)
+ ZD = ZR
+!
+! FIND TWO CONSECUTIVE Y VALUES ON SCALE. SCALE
+! RECURRENCE IF S2 GETS LARGER THAN EXP(ELIM/2)
+!
+ DO 40 I = 3, N
+ KK = I
+ CS = S2
+ S2 = CK*S2 + S1
+ S1 = CS
+ CK = CK + RZ
+ AS = ABS(S2)
+ ALAS = LOG(AS)
+ ACS = -XX + ALAS
+ NZ = NZ + 1
+ Y(I) = CZERO
+ IF (ACS.GE.(-ELIM)) THEN
+ CS = -ZD + LOG(S2)
+ CSR = REAL(CS)
+ CSI = AIMAG(CS)
+ AA = EXP(CSR)/TOL
+ CS = CMPLX(AA,0.0E0)*CMPLX(COS(CSI),SIN(CSI))
+ CALL DGVS17(CS,NW,ASCLE,TOL)
+ IF (NW.EQ.0) THEN
+ Y(I) = CS
+ NZ = NZ - 1
+ IF (IC.EQ.(KK-1)) THEN
+ GO TO 60
+ ELSE
+ IC = KK
+ GO TO 40
+ END IF
+ END IF
+ END IF
+ IF (ALAS.GE.HELIM) THEN
+ XX = XX - ELIM
+ S1 = S1*CELM
+ S2 = S2*CELM
+ ZD = CMPLX(XX,ZRI)
+ END IF
+ 40 CONTINUE
+ NZ = N
+ IF (IC.EQ.N) NZ = N - 1
+ GO TO 80
+ 60 NZ = KK - 2
+ 80 DO 100 K = 1, NZ
+ Y(K) = CZERO
+ 100 CONTINUE
+ END IF
+ END IF
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGXS17(Z,FNU,KODE,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-777 (DEC 1989).
+!
+! Original name: CBKNU
+!
+! DGXS17 COMPUTES THE K BESSEL FUNCTION IN THE RIGHT HALF Z PLANE
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX CCH, CELM, CK, COEF, CONE, CRSC, CS, CSCL, CSH,
+ * CTWO, CZ, CZERO, F, FMU, P, P1, P2, PT, Q, RZ,
+ * S1, S2, SMU, ST, ZD
+ REAL A1, A2, AA, AK, ALAS, AS, ASCLE, BB, BK, CAZ,
+ * DNU, DNU2, ELM, ETEST, FC, FHS, FK, FKS, FPI,
+ * G1, G2, HELIM, HPI, P2I, P2M, P2R, PI, R1, RK,
+ * RTHPI, S, SPI, T1, T2, TM, TTH, XD, XX, YD, YY
+ INTEGER I, IC, IDUM, IFL, IFLAG, INU, INUB, J, K, KFLAG,
+ * KK, KMAX, KODED, NW
+! .. Local Arrays ..
+ COMPLEX CSR(3), CSS(3), CY(2)
+ REAL BRY(3), CC(8)
+! .. External Functions ..
+ COMPLEX S01EAE
+ REAL S14ABE, X02AME, X02ALE
+ INTEGER X02BHE, X02BJE
+ EXTERNAL S14ABE, S01EAE, X02AME, X02ALE, X02BHE, X02BJE
+! .. External Subroutines ..
+ EXTERNAL DGUS17, DGVS17, DGWS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, ATAN, CMPLX, CONJG, COS, EXP, INT,
+ * LOG, LOG10, MAX, MIN, REAL, SIN, SQRT
+! .. Data statements ..
+!
+!
+!
+ DATA KMAX/30/
+ DATA R1/2.0E0/
+ DATA CZERO, CONE, CTWO/(0.0E0,0.0E0), (1.0E0,0.0E0),
+ * (2.0E0,0.0E0)/
+ DATA PI, RTHPI, SPI, HPI, FPI,
+ * TTH/3.14159265358979324E0,
+ * 1.25331413731550025E0, 1.90985931710274403E0,
+ * 1.57079632679489662E0, 1.89769999331517738E0,
+ * 6.66666666666666666E-01/
+ DATA CC(1), CC(2), CC(3), CC(4), CC(5), CC(6), CC(7),
+ * CC(8)/5.77215664901532861E-01,
+ * -4.20026350340952355E-02,
+ * -4.21977345555443367E-02,
+ * 7.21894324666309954E-03,
+ * -2.15241674114950973E-04,
+ * -2.01348547807882387E-05,
+ * 1.13302723198169588E-06,
+ * 6.11609510448141582E-09/
+! .. Executable Statements ..
+!
+ XX = REAL(Z)
+ YY = AIMAG(Z)
+ CAZ = ABS(Z)
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CRSC = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CRSC
+ CSR(1) = CRSC
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = (1.0E+3*X02AME())/TOL
+ BRY(2) = 1.0E0/BRY(1)
+ BRY(3) = X02ALE()
+ NZ = 0
+ IFLAG = 0
+ KODED = KODE
+ RZ = CTWO/Z
+ INU = INT(FNU+0.5E0)
+ DNU = FNU - INU
+ IF (ABS(DNU).NE.0.5E0) THEN
+ DNU2 = 0.0E0
+ IF (ABS(DNU).GT.TOL) DNU2 = DNU*DNU
+ IF (CAZ.LE.R1) THEN
+! ------------------------------------------------------------
+! SERIES FOR CABS(Z).LE.R1
+! ------------------------------------------------------------
+ FC = 1.0E0
+ SMU = LOG(RZ)
+ FMU = SMU*CMPLX(DNU,0.0E0)
+ CALL DGUS17(FMU,CSH,CCH)
+ IF (DNU.NE.0.0E0) THEN
+ FC = DNU*PI
+ FC = FC/SIN(FC)
+ SMU = CSH*CMPLX(1.0E0/DNU,0.0E0)
+ END IF
+ A2 = 1.0E0 + DNU
+! ------------------------------------------------------------
+! GAM(1-Z)*GAM(1+Z)=PI*Z/SIN(PI*Z), T1=1/GAM(1-DNU),
+! T2=1/GAM(1+DNU)
+! ------------------------------------------------------------
+ IDUM = 0
+! S14ABE assumed not to fail, therefore IDUM set to zero.
+ T2 = EXP(-S14ABE(A2,IDUM))
+ T1 = 1.0E0/(T2*FC)
+ IF (ABS(DNU).GT.0.1E0) THEN
+ G1 = (T1-T2)/(DNU+DNU)
+ ELSE
+! ---------------------------------------------------------
+! SERIES FOR F0 TO RESOLVE INDETERMINACY FOR SMALL ABS(DNU)
+! ---------------------------------------------------------
+ AK = 1.0E0
+ S = CC(1)
+ DO 20 K = 2, 8
+ AK = AK*DNU2
+ TM = CC(K)*AK
+ S = S + TM
+ IF (ABS(TM).LT.TOL) GO TO 40
+ 20 CONTINUE
+ 40 G1 = -S
+ END IF
+ G2 = 0.5E0*(T1+T2)*FC
+ G1 = G1*FC
+ F = CMPLX(G1,0.0E0)*CCH + SMU*CMPLX(G2,0.0E0)
+ IFL = 1
+ PT = S01EAE(FMU,IFL)
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 320
+ P = CMPLX(0.5E0/T2,0.0E0)*PT
+ Q = CMPLX(0.5E0/T1,0.0E0)/PT
+ S1 = F
+ S2 = P
+ AK = 1.0E0
+ A1 = 1.0E0
+ CK = CONE
+ BK = 1.0E0 - DNU2
+ IF (INU.GT.0 .OR. N.GT.1) THEN
+! ---------------------------------------------------------
+! GENERATE K(DNU,Z) AND K(DNU+1,Z) FOR FORWARD RECURRENCE
+! ---------------------------------------------------------
+ IF (CAZ.GE.TOL) THEN
+ CZ = Z*Z*CMPLX(0.25E0,0.0E0)
+ T1 = 0.25E0*CAZ*CAZ
+ 60 CONTINUE
+ F = (F*CMPLX(AK,0.0E0)+P+Q)*CMPLX(1.0E0/BK,0.0E0)
+ P = P*CMPLX(1.0E0/(AK-DNU),0.0E0)
+ Q = Q*CMPLX(1.0E0/(AK+DNU),0.0E0)
+ RK = 1.0E0/AK
+ CK = CK*CZ*CMPLX(RK,0.0E0)
+ S1 = S1 + CK*F
+ S2 = S2 + CK*(P-F*CMPLX(AK,0.0E0))
+ A1 = A1*T1*RK
+ BK = BK + AK + AK + 1.0E0
+ AK = AK + 1.0E0
+ IF (A1.GT.TOL) GO TO 60
+ END IF
+ KFLAG = 2
+ BK = REAL(SMU)
+ A1 = FNU + 1.0E0
+ AK = A1*ABS(BK)
+ IF (AK.GT.ALIM) KFLAG = 3
+ P2 = S2*CSS(KFLAG)
+ S2 = P2*RZ
+ S1 = S1*CSS(KFLAG)
+ IF (KODED.NE.1) THEN
+! F = EXP(Z)
+ IFL = 1
+ F = S01EAE(Z,IFL)
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 320
+ S1 = S1*F
+ S2 = S2*F
+ END IF
+ GO TO 160
+ ELSE
+! ---------------------------------------------------------
+! GENERATE K(FNU,Z), 0.0D0 .LE. FNU .LT. 0.5D0 AND N=1
+! ---------------------------------------------------------
+ IF (CAZ.GE.TOL) THEN
+ CZ = Z*Z*CMPLX(0.25E0,0.0E0)
+ T1 = 0.25E0*CAZ*CAZ
+ 80 CONTINUE
+ F = (F*CMPLX(AK,0.0E0)+P+Q)*CMPLX(1.0E0/BK,0.0E0)
+ P = P*CMPLX(1.0E0/(AK-DNU),0.0E0)
+ Q = Q*CMPLX(1.0E0/(AK+DNU),0.0E0)
+ RK = 1.0E0/AK
+ CK = CK*CZ*CMPLX(RK,0.0E0)
+ S1 = S1 + CK*F
+ A1 = A1*T1*RK
+ BK = BK + AK + AK + 1.0E0
+ AK = AK + 1.0E0
+ IF (A1.GT.TOL) GO TO 80
+ END IF
+ Y(1) = S1
+! IF (KODED.NE.1) Y(1) = S1*EXP(Z)
+ IF (KODED.NE.1) THEN
+ IFL = 1
+ Y(1) = S01EAE(Z,IFL)
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 320
+ Y(1) = S1*Y(1)
+ END IF
+ RETURN
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------------
+! IFLAG=0 MEANS NO UNDERFLOW OCCURRED
+! IFLAG=1 MEANS AN UNDERFLOW OCCURRED- COMPUTATION PROCEEDS WITH
+! KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD
+! RECURSION
+! ------------------------------------------------------------------
+ COEF = CMPLX(RTHPI,0.0E0)/SQRT(Z)
+ KFLAG = 2
+ IF (KODED.NE.2) THEN
+ IF (XX.GT.ALIM) THEN
+! ------------------------------------------------------------
+! SCALE BY EXP(Z), IFLAG = 1 CASES
+! ------------------------------------------------------------
+ KODED = 2
+ IFLAG = 1
+ KFLAG = 2
+ ELSE
+! BLANK LINE
+! A1 = EXP(-XX)*REAL(CSS(KFLAG))
+! PT = CMPLX(A1,0.0E0)*CMPLX(COS(YY),-SIN(YY))
+ IFL = 1
+ PT = S01EAE(CMPLX(-XX,-YY),IFL)
+ IF ((IFL.GE.1 .AND. IFL.LE.3) .OR. IFL.EQ.5) GO TO 320
+ PT = PT*REAL(CSS(KFLAG))
+ COEF = COEF*PT
+ END IF
+ END IF
+ IF (ABS(DNU).NE.0.5E0) THEN
+! ---------------------------------------------------------------
+! MILLER ALGORITHM FOR CABS(Z).GT.R1
+! ---------------------------------------------------------------
+ AK = COS(PI*DNU)
+ AK = ABS(AK)
+ IF (AK.NE.0.0E0) THEN
+ FHS = ABS(0.25E0-DNU2)
+ IF (FHS.NE.0.0E0) THEN
+! ---------------------------------------------------------
+! COMPUTE R2=F(E). IF CABS(Z).GE.R2, USE FORWARD RECURRENCE
+! TO DETERMINE THE BACKWARD INDEX K. R2=F(E) IS A STRAIGHT
+! LINE ON 12.LE.E.LE.60. E IS COMPUTED FROM
+! 2**(-E)=B**(1-X02BJE())=TOL WHERE B IS THE BASE OF THE
+! ARITHMETIC.
+! ---------------------------------------------------------
+ T1 = (X02BJE()-1)*LOG10(REAL(X02BHE()))*3.321928094E0
+ T1 = MAX(T1,12.0E0)
+ T1 = MIN(T1,60.0E0)
+ T2 = TTH*T1 - 6.0E0
+ IF (XX.NE.0.0E0) THEN
+ T1 = ATAN(YY/XX)
+ T1 = ABS(T1)
+ ELSE
+ T1 = HPI
+ END IF
+ IF (T2.GT.CAZ) THEN
+! ------------------------------------------------------
+! COMPUTE BACKWARD INDEX K FOR CABS(Z).LT.R2
+! ------------------------------------------------------
+ A2 = SQRT(CAZ)
+ AK = FPI*AK/(TOL*SQRT(A2))
+ AA = 3.0E0*T1/(1.0E0+CAZ)
+ BB = 14.7E0*T1/(28.0E0+CAZ)
+ AK = (LOG(AK)+CAZ*COS(AA)/(1.0E0+0.008E0*CAZ))/COS(BB)
+ FK = 0.12125E0*AK*AK/CAZ + 1.5E0
+ ELSE
+! ------------------------------------------------------
+! FORWARD RECURRENCE LOOP WHEN CABS(Z).GE.R2
+! ------------------------------------------------------
+ ETEST = AK/(PI*CAZ*TOL)
+ FK = 1.0E0
+ IF (ETEST.GE.1.0E0) THEN
+ FKS = 2.0E0
+ RK = CAZ + CAZ + 2.0E0
+ A1 = 0.0E0
+ A2 = 1.0E0
+ DO 100 I = 1, KMAX
+ AK = FHS/FKS
+ BK = RK/(FK+1.0E0)
+ TM = A2
+ A2 = BK*A2 - AK*A1
+ A1 = TM
+ RK = RK + 2.0E0
+ FKS = FKS + FK + FK + 2.0E0
+ FHS = FHS + FK + FK
+ FK = FK + 1.0E0
+ TM = ABS(A2)*FK
+ IF (ETEST.LT.TM) GO TO 120
+ 100 CONTINUE
+ NZ = -2
+ RETURN
+ 120 FK = FK + SPI*T1*SQRT(T2/CAZ)
+ FHS = ABS(0.25E0-DNU2)
+ END IF
+ END IF
+ K = INT(FK)
+! ---------------------------------------------------------
+! BACKWARD RECURRENCE LOOP FOR MILLER ALGORITHM
+! ---------------------------------------------------------
+ FK = K
+ FKS = FK*FK
+ P1 = CZERO
+ P2 = CMPLX(TOL,0.0E0)
+ CS = P2
+ DO 140 I = 1, K
+ A1 = FKS - FK
+ A2 = (FKS+FK)/(A1+FHS)
+ RK = 2.0E0/(FK+1.0E0)
+ T1 = (FK+XX)*RK
+ T2 = YY*RK
+ PT = P2
+ P2 = (P2*CMPLX(T1,T2)-P1)*CMPLX(A2,0.0E0)
+ P1 = PT
+ CS = CS + P2
+ FKS = A1 - FK + 1.0E0
+ FK = FK - 1.0E0
+ 140 CONTINUE
+! ---------------------------------------------------------
+! COMPUTE (P2/CS)=(P2/CABS(CS))*(CONJG(CS)/CABS(CS)) FOR
+! BETTER SCALING
+! ---------------------------------------------------------
+ TM = ABS(CS)
+ PT = CMPLX(1.0E0/TM,0.0E0)
+ S1 = PT*P2
+ CS = CONJG(CS)*PT
+ S1 = COEF*S1*CS
+ IF (INU.GT.0 .OR. N.GT.1) THEN
+! ------------------------------------------------------
+! COMPUTE P1/P2=(P1/CABS(P2)*CONJG(P2)/CABS(P2) FOR
+! SCALING
+! ------------------------------------------------------
+ TM = ABS(P2)
+ PT = CMPLX(1.0E0/TM,0.0E0)
+ P1 = PT*P1
+ P2 = CONJG(P2)*PT
+ PT = P1*P2
+ S2 = S1*(CONE+(CMPLX(DNU+0.5E0,0.0E0)-PT)/Z)
+ GO TO 160
+ ELSE
+ ZD = Z
+ IF (IFLAG.EQ.1) THEN
+ GO TO 240
+ ELSE
+ GO TO 260
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------------
+! FNU=HALF ODD INTEGER CASE, DNU=-0.5
+! ------------------------------------------------------------------
+ S1 = COEF
+ S2 = COEF
+! ------------------------------------------------------------------
+! FORWARD RECURSION ON THE THREE TERM RECURSION RELATION WITH
+! SCALING NEAR EXPONENT EXTREMES ON KFLAG=1 OR KFLAG=3
+! ------------------------------------------------------------------
+ 160 CONTINUE
+ CK = CMPLX(DNU+1.0E0,0.0E0)*RZ
+ IF (N.EQ.1) INU = INU - 1
+ IF (INU.GT.0) THEN
+ INUB = 1
+ IF (IFLAG.EQ.1) THEN
+! ------------------------------------------------------------
+! IFLAG=1 CASES, FORWARD RECURRENCE ON SCALED VALUES ON
+! UNDERFLOW
+! ------------------------------------------------------------
+ HELIM = 0.5E0*ELIM
+ ELM = EXP(-ELIM)
+ CELM = CMPLX(ELM,0.0E0)
+ ASCLE = BRY(1)
+ ZD = Z
+ XD = XX
+ YD = YY
+ IC = -1
+ J = 2
+ DO 180 I = 1, INU
+ ST = S2
+ S2 = CK*S2 + S1
+ S1 = ST
+ CK = CK + RZ
+ AS = ABS(S2)
+ ALAS = LOG(AS)
+ P2R = -XD + ALAS
+ IF (P2R.GE.(-ELIM)) THEN
+ P2 = -ZD + LOG(S2)
+ P2R = REAL(P2)
+ P2I = AIMAG(P2)
+ P2M = EXP(P2R)/TOL
+ P1 = CMPLX(P2M,0.0E0)*CMPLX(COS(P2I),SIN(P2I))
+ CALL DGVS17(P1,NW,ASCLE,TOL)
+ IF (NW.EQ.0) THEN
+ J = 3 - J
+ CY(J) = P1
+ IF (IC.EQ.(I-1)) THEN
+ GO TO 200
+ ELSE
+ IC = I
+ GO TO 180
+ END IF
+ END IF
+ END IF
+ IF (ALAS.GE.HELIM) THEN
+ XD = XD - ELIM
+ S1 = S1*CELM
+ S2 = S2*CELM
+ ZD = CMPLX(XD,YD)
+ END IF
+ 180 CONTINUE
+ IF (N.EQ.1) S1 = S2
+ GO TO 240
+ 200 KFLAG = 1
+ INUB = I + 1
+ S2 = CY(J)
+ J = 3 - J
+ S1 = CY(J)
+ IF (INUB.GT.INU) THEN
+ IF (N.EQ.1) S1 = S2
+ GO TO 260
+ END IF
+ END IF
+ P1 = CSR(KFLAG)
+ ASCLE = BRY(KFLAG)
+ DO 220 I = INUB, INU
+ ST = S2
+ S2 = CK*S2 + S1
+ S1 = ST
+ CK = CK + RZ
+ IF (KFLAG.LT.3) THEN
+ P2 = S2*P1
+ P2R = REAL(P2)
+ P2I = AIMAG(P2)
+ P2R = ABS(P2R)
+ P2I = ABS(P2I)
+ P2M = MAX(P2R,P2I)
+ IF (P2M.GT.ASCLE) THEN
+ KFLAG = KFLAG + 1
+ ASCLE = BRY(KFLAG)
+ S1 = S1*P1
+ S2 = P2
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ P1 = CSR(KFLAG)
+ END IF
+ END IF
+ 220 CONTINUE
+ IF (N.EQ.1) S1 = S2
+ GO TO 260
+ ELSE
+ IF (N.EQ.1) S1 = S2
+ ZD = Z
+ IF (IFLAG.NE.1) GO TO 260
+ END IF
+ 240 Y(1) = S1
+ IF (N.NE.1) Y(2) = S2
+ ASCLE = BRY(1)
+ CALL DGWS17(ZD,FNU,N,Y,NZ,RZ,ASCLE,TOL,ELIM)
+ INU = N - NZ
+ IF (INU.LE.0) THEN
+ RETURN
+ ELSE
+ KK = NZ + 1
+ S1 = Y(KK)
+ Y(KK) = S1*CSR(1)
+ IF (INU.EQ.1) THEN
+ RETURN
+ ELSE
+ KK = NZ + 2
+ S2 = Y(KK)
+ Y(KK) = S2*CSR(1)
+ IF (INU.EQ.2) THEN
+ RETURN
+ ELSE
+ T2 = FNU + KK - 1
+ CK = CMPLX(T2,0.0E0)*RZ
+ KFLAG = 1
+ GO TO 280
+ END IF
+ END IF
+ END IF
+ 260 Y(1) = S1*CSR(KFLAG)
+ IF (N.EQ.1) THEN
+ RETURN
+ ELSE
+ Y(2) = S2*CSR(KFLAG)
+ IF (N.EQ.2) THEN
+ RETURN
+ ELSE
+ KK = 2
+ END IF
+ END IF
+ 280 KK = KK + 1
+ IF (KK.LE.N) THEN
+ P1 = CSR(KFLAG)
+ ASCLE = BRY(KFLAG)
+ DO 300 I = KK, N
+ P2 = S2
+ S2 = CK*S2 + S1
+ S1 = P2
+ CK = CK + RZ
+ P2 = S2*P1
+ Y(I) = P2
+ IF (KFLAG.LT.3) THEN
+ P2R = REAL(P2)
+ P2I = AIMAG(P2)
+ P2R = ABS(P2R)
+ P2I = ABS(P2I)
+ P2M = MAX(P2R,P2I)
+ IF (P2M.GT.ASCLE) THEN
+ KFLAG = KFLAG + 1
+ ASCLE = BRY(KFLAG)
+ S1 = S1*P1
+ S2 = P2
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ P1 = CSR(KFLAG)
+ END IF
+ END IF
+ 300 CONTINUE
+ END IF
+ RETURN
+ 320 NZ = -3
+ RETURN
+ END
+ SUBROUTINE DGYS17(Z,FNU,KODE,N,Y,NZ,RL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-778 (DEC 1989).
+!
+! Original name: CASYI
+!
+! DGYS17 COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY
+! MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE
+! REGION CABS(Z).GT.MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL RETURN.
+! NZ.LT.0 INDICATES AN OVERFLOW ON KODE=1.
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, RL, TOL
+ INTEGER KODE, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX AK1, CK, CONE, CS1, CS2, CZ, CZERO, DK, EZ, P1,
+ * RZ, S2
+ REAL AA, ACZ, AEZ, AK, ARG, ARM, ATOL, AZ, BB, BK,
+ * DFNU, DNU2, FDN, PI, RTPI, RTR1, S, SGN, SQK, X,
+ * YY
+ INTEGER I, IB, IERR1, IL, INU, J, JL, K, KODED, M, NN
+! .. External Functions ..
+ COMPLEX S01EAE
+ REAL X02AME
+ EXTERNAL S01EAE, X02AME
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, INT, MIN, MOD,
+ * REAL, SIN, SQRT
+! .. Data statements ..
+ DATA PI, RTPI/3.14159265358979324E0,
+ * 0.159154943091895336E0/
+ DATA CZERO, CONE/(0.0E0,0.0E0), (1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ AZ = ABS(Z)
+ X = REAL(Z)
+ ARM = 1.0E+3*X02AME()
+ RTR1 = SQRT(ARM)
+ IL = MIN(2,N)
+ DFNU = FNU + N - IL
+! ------------------------------------------------------------------
+! OVERFLOW TEST
+! ------------------------------------------------------------------
+ AK1 = CMPLX(RTPI,0.0E0)/Z
+ AK1 = SQRT(AK1)
+ CZ = Z
+ IF (KODE.EQ.2) CZ = Z - CMPLX(X,0.0E0)
+ ACZ = REAL(CZ)
+ IF (ABS(ACZ).GT.ELIM) THEN
+ NZ = -1
+ ELSE
+ DNU2 = DFNU + DFNU
+ KODED = 1
+ IF ((ABS(ACZ).LE.ALIM) .OR. (N.LE.2)) THEN
+ KODED = 0
+ IERR1 = 1
+ AK1 = AK1*S01EAE(CZ,IERR1)
+! Allow reduced precision from S01EAE, but disallow other errors.
+ IF ((IERR1.GE.1 .AND. IERR1.LE.3) .OR. IERR1.EQ.5) GO TO 140
+ END IF
+ FDN = 0.0E0
+ IF (DNU2.GT.RTR1) FDN = DNU2*DNU2
+ EZ = Z*CMPLX(8.0E0,0.0E0)
+! ---------------------------------------------------------------
+! WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO
+! THE FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF
+! THE EXPANSION FOR THE IMAGINARY PART.
+! ---------------------------------------------------------------
+ AEZ = 8.0E0*AZ
+ S = TOL/AEZ
+ JL = INT(RL+RL) + 2
+ YY = AIMAG(Z)
+ P1 = CZERO
+ IF (YY.NE.0.0E0) THEN
+! ------------------------------------------------------------
+! CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF
+! SIGNIFICANCE WHEN FNU OR N IS LARGE
+! ------------------------------------------------------------
+ INU = INT(FNU)
+ ARG = (FNU-INU)*PI
+ INU = INU + N - IL
+ AK = -SIN(ARG)
+ BK = COS(ARG)
+ IF (YY.LT.0.0E0) BK = -BK
+ P1 = CMPLX(AK,BK)
+ IF (MOD(INU,2).EQ.1) P1 = -P1
+ END IF
+ DO 60 K = 1, IL
+ SQK = FDN - 1.0E0
+ ATOL = S*ABS(SQK)
+ SGN = 1.0E0
+ CS1 = CONE
+ CS2 = CONE
+ CK = CONE
+ AK = 0.0E0
+ AA = 1.0E0
+ BB = AEZ
+ DK = EZ
+ DO 20 J = 1, JL
+ CK = CK*CMPLX(SQK,0.0E0)/DK
+ CS2 = CS2 + CK
+ SGN = -SGN
+ CS1 = CS1 + CK*CMPLX(SGN,0.0E0)
+ DK = DK + EZ
+ AA = AA*ABS(SQK)/BB
+ BB = BB + AEZ
+ AK = AK + 8.0E0
+ SQK = SQK - AK
+ IF (AA.LE.ATOL) GO TO 40
+ 20 CONTINUE
+ GO TO 120
+ 40 S2 = CS1
+ IF (X+X.LT.ELIM) THEN
+ IERR1 = 1
+ S2 = S2 + P1*CS2*S01EAE(-Z-Z,IERR1)
+ IF ((IERR1.GE.1 .AND. IERR1.LE.3) .OR. IERR1.EQ.5)
+ * GO TO 140
+ END IF
+ FDN = FDN + 8.0E0*DFNU + 4.0E0
+ P1 = -P1
+ M = N - IL + K
+ Y(M) = S2*AK1
+ 60 CONTINUE
+ IF (N.GT.2) THEN
+ NN = N
+ K = NN - 2
+ AK = K
+ RZ = (CONE+CONE)/Z
+ IB = 3
+ DO 80 I = IB, NN
+ Y(K) = CMPLX(AK+FNU,0.0E0)*RZ*Y(K+1) + Y(K+2)
+ AK = AK - 1.0E0
+ K = K - 1
+ 80 CONTINUE
+ IF (KODED.NE.0) THEN
+ IERR1 = 1
+ CK = S01EAE(CZ,IERR1)
+ IF ((IERR1.GE.1 .AND. IERR1.LE.3) .OR. IERR1.EQ.5)
+ * GO TO 140
+ DO 100 I = 1, NN
+ Y(I) = Y(I)*CK
+ 100 CONTINUE
+ END IF
+ END IF
+ RETURN
+ 120 NZ = -2
+ RETURN
+ 140 NZ = -3
+ END IF
+ RETURN
+ END
+ SUBROUTINE DGZS17(Z,FNU,KODE,MR,N,Y,NZ,RL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-779 (DEC 1989).
+!
+! Original name: CACAI
+!
+! DGZS17 APPLIES THE ANALYTIC CONTINUATION FORMULA
+!
+! K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
+! MP=PI*MR*CMPLX(0.0,1.0)
+!
+! TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
+! HALF Z PLANE FOR USE WITH S17DGE WHERE FNU=1/3 OR 2/3 AND N=1.
+! DGZS17 IS THE SAME AS DLZS17 WITH THE PARTS FOR LARGER ORDERS AND
+! RECURRENCE REMOVED. A RECURSIVE CALL TO DLZS17 CAN RESULT IF S17DL
+! IS CALLED FROM S17DGE.
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, RL, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CSGN, CSPN, ZN
+ REAL ARG, ASCLE, AZ, CPN, DFNU, FMR, PI, SGN, SPN, YY
+ INTEGER INU, IUF, NN, NW
+! .. Local Arrays ..
+ COMPLEX CY(2)
+! .. External Functions ..
+ REAL X02AME
+ EXTERNAL X02AME
+! .. External Subroutines ..
+ EXTERNAL DGRS17, DGSS17, DGTS17, DGXS17, DGYS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, INT, MOD, SIGN, SIN
+! .. Data statements ..
+ DATA PI/3.14159265358979324E0/
+! .. Executable Statements ..
+!
+ NZ = 0
+ ZN = -Z
+ AZ = ABS(Z)
+ NN = N
+ DFNU = FNU + N - 1
+ IF (AZ.GT.2.0E0) THEN
+ IF (AZ*AZ*0.25E0.GT.DFNU+1.0E0) THEN
+ IF (AZ.LT.RL) THEN
+! ---------------------------------------------------------
+! MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I
+! FUNCTION
+! ---------------------------------------------------------
+ CALL DGTS17(ZN,FNU,KODE,NN,Y,NW,TOL)
+ IF (NW.LT.0) THEN
+ GO TO 40
+ ELSE
+ GO TO 20
+ END IF
+ ELSE
+! ---------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION
+! ---------------------------------------------------------
+ CALL DGYS17(ZN,FNU,KODE,NN,Y,NW,RL,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 40
+ ELSE
+ GO TO 20
+ END IF
+ END IF
+ END IF
+ END IF
+! ------------------------------------------------------------------
+! POWER SERIES FOR THE I FUNCTION
+! ------------------------------------------------------------------
+ CALL DGRS17(ZN,FNU,KODE,NN,Y,NW,TOL,ELIM,ALIM)
+! ------------------------------------------------------------------
+! ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
+! ------------------------------------------------------------------
+ 20 CALL DGXS17(ZN,FNU,KODE,1,CY,NW,TOL,ELIM,ALIM)
+ IF (NW.EQ.0) THEN
+ FMR = MR
+ SGN = -SIGN(PI,FMR)
+ CSGN = CMPLX(0.0E0,SGN)
+ IF (KODE.NE.1) THEN
+ YY = -AIMAG(ZN)
+ CPN = COS(YY)
+ SPN = SIN(YY)
+ CSGN = CSGN*CMPLX(CPN,SPN)
+ END IF
+! ---------------------------------------------------------------
+! CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
+! WHEN FNU IS LARGE
+! ---------------------------------------------------------------
+ INU = INT(FNU)
+ ARG = (FNU-INU)*SGN
+ CPN = COS(ARG)
+ SPN = SIN(ARG)
+ CSPN = CMPLX(CPN,SPN)
+ IF (MOD(INU,2).EQ.1) CSPN = -CSPN
+ C1 = CY(1)
+ C2 = Y(1)
+ IF (KODE.NE.1) THEN
+ IUF = 0
+ ASCLE = (1.0E+3*X02AME())/TOL
+ CALL DGSS17(ZN,C1,C2,NW,ASCLE,ALIM,IUF)
+ NZ = NZ + NW
+ END IF
+ Y(1) = CSPN*C1 + CSGN*C2
+ RETURN
+ END IF
+ 40 NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ IF (NW.EQ.(-3)) NZ = -3
+ RETURN
+ END
+ SUBROUTINE DLYS17(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-782 (DEC 1989).
+!
+! Original name: CBUNK
+!
+! DLYS17 COMPUTES THE K BESSEL FUNCTION FOR FNU.GT.FNUL.
+! ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR K(FNU,Z)
+! IN DCZS18 AND THE EXPANSION FOR H(2,FNU,Z) IN DCYS18
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ REAL AX, AY, XX, YY
+! .. External Subroutines ..
+ EXTERNAL DCYS18, DCZS18
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, REAL
+! .. Executable Statements ..
+!
+ NZ = 0
+ XX = REAL(Z)
+ YY = AIMAG(Z)
+ AX = ABS(XX)*1.7321E0
+ AY = ABS(YY)
+ IF (AY.GT.AX) THEN
+! ---------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR H(2,FNU,Z*EXP(M*HPI)) FOR LARGE FNU
+! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
+! AND HPI=PI/2
+! ---------------------------------------------------------------
+ CALL DCYS18(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+ ELSE
+! ---------------------------------------------------------------
+! ASYMPTOTIC EXPANSION FOR K(FNU,Z) FOR LARGE FNU APPLIED IN
+! -PI/3.LE.ARG(Z).LE.PI/3
+! ---------------------------------------------------------------
+ CALL DCZS18(Z,FNU,KODE,MR,N,Y,NZ,TOL,ELIM,ALIM)
+ END IF
+ RETURN
+ END
+ SUBROUTINE DLZS17(Z,FNU,KODE,MR,N,Y,NZ,RL,FNUL,TOL,ELIM,ALIM)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-783 (DEC 1989).
+!
+! Original name: CACON
+!
+! DLZS17 APPLIES THE ANALYTIC CONTINUATION FORMULA
+!
+! K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
+! MP=PI*MR*CMPLX(0.0,1.0)
+!
+! TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
+! HALF Z PLANE
+!
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL ALIM, ELIM, FNU, FNUL, RL, TOL
+ INTEGER KODE, MR, N, NZ
+! .. Array Arguments ..
+ COMPLEX Y(N)
+! .. Local Scalars ..
+ COMPLEX C1, C2, CK, CONE, CS, CSCL, CSCR, CSGN, CSPN,
+ * RZ, S1, S2, SC1, SC2, ST, ZN
+ REAL ARG, AS2, ASCLE, BSCLE, C1I, C1M, C1R, CPN, FMR,
+ * PI, SGN, SPN, YY
+ INTEGER I, INU, IUF, KFLAG, NN, NW
+! .. Local Arrays ..
+ COMPLEX CSR(3), CSS(3), CY(2)
+ REAL BRY(3)
+! .. External Functions ..
+ REAL X02AME, X02ALE
+ EXTERNAL X02AME, X02ALE
+! .. External Subroutines ..
+ EXTERNAL DEZS17, DGSS17, DGXS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, INT, MAX, MIN, MOD,
+ * REAL, SIGN, SIN
+! .. Data statements ..
+ DATA PI/3.14159265358979324E0/
+ DATA CONE/(1.0E0,0.0E0)/
+! .. Executable Statements ..
+!
+ NZ = 0
+ ZN = -Z
+ NN = N
+ CALL DEZS17(ZN,FNU,KODE,NN,Y,NW,RL,FNUL,TOL,ELIM,ALIM)
+ IF (NW.GE.0) THEN
+! ---------------------------------------------------------------
+! ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
+! ---------------------------------------------------------------
+ NN = MIN(2,N)
+ CALL DGXS17(ZN,FNU,KODE,NN,CY,NW,TOL,ELIM,ALIM)
+ IF (NW.EQ.0) THEN
+ S1 = CY(1)
+ FMR = MR
+ SGN = -SIGN(PI,FMR)
+ CSGN = CMPLX(0.0E0,SGN)
+ IF (KODE.NE.1) THEN
+ YY = -AIMAG(ZN)
+ CPN = COS(YY)
+ SPN = SIN(YY)
+ CSGN = CSGN*CMPLX(CPN,SPN)
+ END IF
+! ------------------------------------------------------------
+! CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF
+! SIGNIFICANCE WHEN FNU IS LARGE
+! ------------------------------------------------------------
+ INU = INT(FNU)
+ ARG = (FNU-INU)*SGN
+ CPN = COS(ARG)
+ SPN = SIN(ARG)
+ CSPN = CMPLX(CPN,SPN)
+ IF (MOD(INU,2).EQ.1) CSPN = -CSPN
+ IUF = 0
+ C1 = S1
+ C2 = Y(1)
+ ASCLE = (1.0E+3*X02AME())/TOL
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZN,C1,C2,NW,ASCLE,ALIM,IUF)
+ NZ = NZ + NW
+ SC1 = C1
+ END IF
+ Y(1) = CSPN*C1 + CSGN*C2
+ IF (N.NE.1) THEN
+ CSPN = -CSPN
+ S2 = CY(2)
+ C1 = S2
+ C2 = Y(2)
+ IF (KODE.NE.1) THEN
+ CALL DGSS17(ZN,C1,C2,NW,ASCLE,ALIM,IUF)
+ NZ = NZ + NW
+ SC2 = C1
+ END IF
+ Y(2) = CSPN*C1 + CSGN*C2
+ IF (N.NE.2) THEN
+ CSPN = -CSPN
+ RZ = CMPLX(2.0E0,0.0E0)/ZN
+ CK = CMPLX(FNU+1.0E0,0.0E0)*RZ
+! ------------------------------------------------------
+! SCALE NEAR EXPONENT EXTREMES DURING RECURRENCE ON
+! K FUNCTIONS
+! ------------------------------------------------------
+ CSCL = CMPLX(1.0E0/TOL,0.0E0)
+ CSCR = CMPLX(TOL,0.0E0)
+ CSS(1) = CSCL
+ CSS(2) = CONE
+ CSS(3) = CSCR
+ CSR(1) = CSCR
+ CSR(2) = CONE
+ CSR(3) = CSCL
+ BRY(1) = ASCLE
+ BRY(2) = 1.0E0/ASCLE
+ BRY(3) = X02ALE()
+ AS2 = ABS(S2)
+ KFLAG = 2
+ IF (AS2.LE.BRY(1)) THEN
+ KFLAG = 1
+ ELSE IF (AS2.GE.BRY(2)) THEN
+ KFLAG = 3
+ END IF
+ BSCLE = BRY(KFLAG)
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ CS = CSR(KFLAG)
+ DO 20 I = 3, N
+ ST = S2
+ S2 = CK*S2 + S1
+ S1 = ST
+ C1 = S2*CS
+ ST = C1
+ C2 = Y(I)
+ IF (KODE.NE.1) THEN
+ IF (IUF.GE.0) THEN
+ CALL DGSS17(ZN,C1,C2,NW,ASCLE,ALIM,IUF)
+ NZ = NZ + NW
+ SC1 = SC2
+ SC2 = C1
+ IF (IUF.EQ.3) THEN
+ IUF = -4
+ S1 = SC1*CSS(KFLAG)
+ S2 = SC2*CSS(KFLAG)
+ ST = SC2
+ END IF
+ END IF
+ END IF
+ Y(I) = CSPN*C1 + CSGN*C2
+ CK = CK + RZ
+ CSPN = -CSPN
+ IF (KFLAG.LT.3) THEN
+ C1R = REAL(C1)
+ C1I = AIMAG(C1)
+ C1R = ABS(C1R)
+ C1I = ABS(C1I)
+ C1M = MAX(C1R,C1I)
+ IF (C1M.GT.BSCLE) THEN
+ KFLAG = KFLAG + 1
+ BSCLE = BRY(KFLAG)
+ S1 = S1*CS
+ S2 = ST
+ S1 = S1*CSS(KFLAG)
+ S2 = S2*CSS(KFLAG)
+ CS = CSR(KFLAG)
+ END IF
+ END IF
+ 20 CONTINUE
+ END IF
+ END IF
+ RETURN
+ END IF
+ END IF
+ NZ = -1
+ IF (NW.EQ.(-2)) NZ = -2
+ IF (NW.EQ.(-3)) NZ = -3
+ RETURN
+ END
+ INTEGER FUNCTION P01ABE(IFAIL,IERROR,SRNAME,NREC,REC)
+! MARK 11.5(F77) RELEASE. NAG COPYRIGHT 1986.
+! MARK 13 REVISED. IER-621 (APR 1988).
+! MARK 13B REVISED. IER-668 (AUG 1988).
+!
+! P01ABE is the error-handling routine for the NAG Library.
+!
+! P01ABE either returns the value of IERROR through the routine
+! name (soft failure), or terminates execution of the program
+! (hard failure). Diagnostic messages may be output.
+!
+! If IERROR = 0 (successful exit from the calling routine),
+! the value 0 is returned through the routine name, and no
+! message is output
+!
+! If IERROR is non-zero (abnormal exit from the calling routine),
+! the action taken depends on the value of IFAIL.
+!
+! IFAIL = 1: soft failure, silent exit (i.e. no messages are
+! output)
+! IFAIL = -1: soft failure, noisy exit (i.e. messages are output)
+! IFAIL =-13: soft failure, noisy exit but standard messages from
+! P01ABE are suppressed
+! IFAIL = 0: hard failure, noisy exit
+!
+! For compatibility with certain routines included before Mark 12
+! P01ABE also allows an alternative specification of IFAIL in which
+! it is regarded as a decimal integer with least significant digits
+! cba. Then
+!
+! a = 0: hard failure a = 1: soft failure
+! b = 0: silent exit b = 1: noisy exit
+!
+! except that hard failure now always implies a noisy exit.
+!
+! S.Hammarling, M.P.Hooper and J.J.du Croz, NAG Central Office.
+!
+! .. Scalar Arguments ..
+ INTEGER IERROR, IFAIL, NREC
+ CHARACTER*(*) SRNAME
+! .. Array Arguments ..
+ CHARACTER*(*) REC(*)
+! .. Local Scalars ..
+ INTEGER I, NERR
+ CHARACTER*72 MESS
+! .. External Subroutines ..
+ EXTERNAL ABZP01, X04AAE, X04BAE
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, MOD
+! .. Executable Statements ..
+ IF (IERROR.NE.0) THEN
+! Abnormal exit from calling routine
+ IF (IFAIL.EQ.-1 .OR. IFAIL.EQ.0 .OR. IFAIL.EQ.-13 .OR.
+ * (IFAIL.GT.0 .AND. MOD(IFAIL/10,10).NE.0)) THEN
+! Noisy exit
+ CALL X04AAE(0,NERR)
+ DO 20 I = 1, NREC
+ CALL X04BAE(NERR,REC(I))
+ 20 CONTINUE
+ IF (IFAIL.NE.-13) THEN
+ WRITE (MESS,FMT=99999) SRNAME, IERROR
+ CALL X04BAE(NERR,MESS)
+ IF (ABS(MOD(IFAIL,10)).NE.1) THEN
+! Hard failure
+ CALL X04BAE(NERR,
+ * ' ** NAG hard failure - execution terminated'
+ * )
+ CALL ABZP01
+ ELSE
+! Soft failure
+ CALL X04BAE(NERR,
+ * ' ** NAG soft failure - control returned')
+ END IF
+ END IF
+ END IF
+ END IF
+ P01ABE = IERROR
+ RETURN
+!
+99999 FORMAT (' ** ABNORMAL EXIT from NAG Library routine ',A,': IFAIL',
+ * ' =',I6)
+ END
+ COMPLEX FUNCTION S01EAE(Z,IFAIL)
+! MARK 14 RELEASE. NAG COPYRIGHT 1989.
+! Returns exp(Z) for complex Z.
+! .. Parameters ..
+ REAL ONE, ZERO
+ PARAMETER (ONE=1.0E0,ZERO=0.0E0)
+ CHARACTER*6 SRNAME
+ PARAMETER (SRNAME='S01EAE')
+! .. Scalar Arguments ..
+ COMPLEX Z
+ INTEGER IFAIL
+! .. Local Scalars ..
+ REAL COSY, EXPX, LNSAFE, RECEPS, RESI, RESR,
+ * RTSAFS, SAFE, SAFSIN, SINY, X, XPLNCY,
+ * XPLNSY, Y
+ INTEGER IER, NREC
+ LOGICAL FIRST
+! .. Local Arrays ..
+ CHARACTER*80 REC(2)
+! .. External Functions ..
+ REAL X02AHE, X02AJE, X02AME
+ INTEGER P01ABE
+ EXTERNAL X02AHE, X02AJE, X02AME, P01ABE
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, LOG, MIN,
+ * REAL, SIGN, SIN, SQRT
+! .. Save statement ..
+ SAVE SAFE, LNSAFE, SAFSIN, RTSAFS, FIRST
+! .. Data statements ..
+ DATA FIRST/.TRUE./
+! .. Executable Statements ..
+ IF (FIRST) THEN
+ FIRST = .FALSE.
+ SAFE = ONE/X02AME()
+ LNSAFE = LOG(SAFE)
+ RECEPS = ONE/X02AJE()
+ SAFSIN = MIN(X02AHE(ONE),RECEPS)
+ IF (SAFSIN.LT.RECEPS**0.75E0) THEN
+! Assume that SAFSIN is approximately sqrt(RECEPS), in which
+! case IFAIL=4 cannot occur.
+ RTSAFS = SAFSIN
+ ELSE
+! Set RTSAFS to the argument above which SINE and COSINE will
+! return results of less than half precision, assuming that
+! SAFSIN is approximately equal to RECEPS.
+ RTSAFS = SQRT(SAFSIN)
+ END IF
+ END IF
+ NREC = 0
+ IER = 0
+ X = REAL(Z)
+ Y = AIMAG(Z)
+ IF (ABS(Y).GT.SAFSIN) THEN
+ IER = 5
+ NREC = 2
+ WRITE (REC,FMT=99995) Z
+ S01EAE = ZERO
+ ELSE
+ COSY = COS(Y)
+ SINY = SIN(Y)
+ IF (X.GT.LNSAFE) THEN
+ IF (COSY.EQ.ZERO) THEN
+ RESR = ZERO
+ ELSE
+ XPLNCY = X + LOG(ABS(COSY))
+ IF (XPLNCY.GT.LNSAFE) THEN
+ IER = 1
+ RESR = SIGN(SAFE,COSY)
+ ELSE
+ RESR = SIGN(EXP(XPLNCY),COSY)
+ END IF
+ END IF
+ IF (SINY.EQ.ZERO) THEN
+ RESI = ZERO
+ ELSE
+ XPLNSY = X + LOG(ABS(SINY))
+ IF (XPLNSY.GT.LNSAFE) THEN
+ IER = IER + 2
+ RESI = SIGN(SAFE,SINY)
+ ELSE
+ RESI = SIGN(EXP(XPLNSY),SINY)
+ END IF
+ END IF
+ ELSE
+ EXPX = EXP(X)
+ RESR = EXPX*COSY
+ RESI = EXPX*SINY
+ END IF
+ S01EAE = CMPLX(RESR,RESI)
+ IF (IER.EQ.3) THEN
+ NREC = 2
+ WRITE (REC,FMT=99997) Z
+ ELSE IF (ABS(Y).GT.RTSAFS) THEN
+ IER = 4
+ NREC = 2
+ WRITE (REC,FMT=99996) Z
+ ELSE IF (IER.EQ.1) THEN
+ NREC = 2
+ WRITE (REC,FMT=99999) Z
+ ELSE IF (IER.EQ.2) THEN
+ NREC = 2
+ WRITE (REC,FMT=99998) Z
+ END IF
+ END IF
+ IFAIL = P01ABE(IFAIL,IER,SRNAME,NREC,REC)
+ RETURN
+!
+99999 FORMAT (1X,'** Argument Z causes overflow in real part of result:'
+ * ,/4X,'Z = (',1P,E13.5,',',E13.5,')')
+99998 FORMAT (1X,'** Argument Z causes overflow in imaginary part of r',
+ * 'esult:',/4X,'Z = (',1P,E13.5,',',E13.5,')')
+99997 FORMAT (1X,'** Argument Z causes overflow in both real and imagi',
+ * 'nary parts of result:',/4X,'Z = (',1P,E13.5,',',E13.5,')')
+99996 FORMAT (1X,'** The imaginary part of argument Z is so large that',
+ * ' the result is',/4X,'accurate to less than half precisio',
+ * 'n: Z = (',1P,E13.5,',',E13.5,')')
+99995 FORMAT (1X,'** The imaginary part of argument Z is so large that',
+ * ' the result has no',/4X,'precision: Z = (',1P,E13.5,',',
+ * E13.5,')')
+ END
+ REAL FUNCTION S14ABE(X,IFAIL)
+! MARK 8 RELEASE. NAG COPYRIGHT 1979.
+! MARK 11.5(F77) REVISED. (SEPT 1985.)
+! LNGAMMA(X) FUNCTION
+! ABRAMOWITZ AND STEGUN CH.6
+!
+! **************************************************************
+!
+! TO EXTRACT THE CORRECT CODE FOR A PARTICULAR MACHINE-RANGE,
+! ACTIVATE THE STATEMENTS CONTAINED IN COMMENTS BEGINNING CDD ,
+! WHERE DD IS THE APPROXIMATE NUMBER OF SIGNIFICANT DECIMAL
+! DIGITS REPRESENTED BY THE MACHINE
+! DELETE THE ILLEGAL DUMMY STATEMENTS OF THE FORM
+! * EXPANSION (NNNN) *
+!
+! ALSO INSERT APPROPRIATE DATA STATEMENTS TO DEFINE CONSTANTS
+! WHICH DEPEND ON THE RANGE OF NUMBERS REPRESENTED BY THE
+! MACHINE, RATHER THAN THE PRECISION (SUITABLE STATEMENTS FOR
+! SOME MACHINES ARE CONTAINED IN COMMENTS BEGINNING CRD WHERE
+! D IS A DIGIT WHICH SIMPLY DISTINGUISHES A GROUP OF MACHINES).
+! DELETE THE ILLEGAL DUMMY DATA STATEMENTS WITH VALUES WRITTEN
+! *VALUE*
+!
+! **************************************************************
+!
+! IMPLEMENTATION DEPENDENT CONSTANTS
+!
+! IF(X.LT.XSMALL)GAMMA(X)=1/X
+! I.E. XSMALL*EULGAM.LE.XRELPR
+! LNGAM(XVBIG)=GBIG.LE.XOVFLO
+! LNR2PI=LN(SQRT(2*PI))
+! IF(X.GT.XBIG)LNGAM(X)=(X-0.5)LN(X)-X+LNR2PI
+!
+! .. Parameters ..
+ CHARACTER*6 SRNAME
+ PARAMETER (SRNAME='S14ABE')
+! .. Scalar Arguments ..
+ REAL X
+ INTEGER IFAIL
+! .. Local Scalars ..
+ REAL G, GBIG, LNR2PI, T, XBIG, XSMALL, XVBIG, Y
+ INTEGER I, M
+! .. Local Arrays ..
+ CHARACTER*1 P01REC(1)
+! .. External Functions ..
+ INTEGER P01ABE
+ EXTERNAL P01ABE
+! .. Intrinsic Functions ..
+ INTRINSIC LOG, REAL
+! .. Data statements ..
+!08 DATA XSMALL,XBIG,LNR2PI/
+!08 *1.0E-8,1.2E+3,9.18938533E-1/
+!09 DATA XSMALL,XBIG,LNR2PI/
+!09 *1.0E-9,4.8E+3,9.189385332E-1/
+!12 DATA XSMALL,XBIG,LNR2PI/
+!12 *1.0E-12,3.7E+5,9.189385332047E-1/
+ DATA XSMALL,XBIG,LNR2PI/
+ *1.0E-15,6.8E+6,9.189385332046727E-1/
+!17 DATA XSMALL,XBIG,LNR2PI/
+!17 *1.0E-17,7.7E+7,9.18938533204672742E-1/
+!19 DATA XSMALL,XBIG,LNR2PI/
+!19 *1.0E-19,3.1E+8,9.189385332046727418E-1/
+!
+! RANGE DEPENDENT CONSTANTS
+! DK DK DATA XVBIG,GBIG/4.81E+2461,2.72E+2465/
+ DATA XVBIG,GBIG/4.08E+36,3.40E+38/
+! FOR IEEE SINGLE PRECISION
+!R0 DATA XVBIG,GBIG/4.08E+36,3.40E+38/
+! FOR IBM 360/370 AND SIMILAR MACHINES
+!R1 DATA XVBIG,GBIG/4.29E+73,7.231E+75/
+! FOR DEC10, HONEYWELL, UNIVAC 1100 (S.P.)
+!R2 DATA XVBIG,GBIG/2.05E36,1.69E38/
+! FOR ICL 1900
+!R3 DATA XVBIG,GBIG/3.39E+74,5.784E+76/
+! FOR CDC 7600/CYBER
+!R4 DATA XVBIG,GBIG/1.72E+319,1.26E+322/
+! FOR UNIVAC 1100 (D.P.)
+!R5 DATA XVBIG,GBIG/1.28E305,8.98E+307/
+! FOR IEEE DOUBLE PRECISION
+!R7 DATA XVBIG,GBIG/2.54D+305,1.79D+308/
+! .. Executable Statements ..
+ IF (X.GT.XSMALL) GO TO 20
+! VERY SMALL RANGE
+ IF (X.LE.0.0) GO TO 160
+ IFAIL = 0
+ S14ABE = -LOG(X)
+ GO TO 200
+!
+ 20 IF (X.GT.15.0) GO TO 120
+! MAIN SMALL X RANGE
+ M = X
+ T = X - FLOAT(M)
+ M = M - 1
+ G = 1.0
+ IF (M) 40, 100, 60
+ 40 G = G/X
+ GO TO 100
+ 60 DO 80 I = 1, M
+ G = (X-FLOAT(I))*G
+ 80 CONTINUE
+ 100 T = 2.0*T - 1.0
+!
+! * EXPANSION (0026) *
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 08E.09
+!08 Y = (((((((((((+1.88278283E-6*T-5.48272091E-6)*T+1.03144033E-5)
+!08 * *T-3.13088821E-5)*T+1.01593694E-4)*T-2.98340924E-4)
+!08 * *T+9.15547391E-4)*T-2.42216251E-3)*T+9.04037536E-3)
+!08 * *T-1.34119055E-2)*T+1.03703361E-1)*T+1.61692007E-2)*T +
+!08 * 8.86226925E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 09E.10
+!09 Y = ((((((((((((-6.463247484E-7*T+1.882782826E-6)
+!09 * *T-3.382165478E-6)*T+1.031440334E-5)*T-3.393457634E-5)
+!09 * *T+1.015936944E-4)*T-2.967655076E-4)*T+9.155473906E-4)
+!09 * *T-2.422622002E-3)*T+9.040375355E-3)*T-1.341184808E-2)
+!09 * *T+1.037033609E-1)*T+1.616919866E-2)*T + 8.862269255E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 12E.13
+!12 Y = ((((((((((((((((-8.965837291520E-9*T+2.612707393536E-8)
+!12 * *T-3.802866827264E-8)*T+1.173294768947E-7)
+!12 * *T-4.275076254106E-7)*T+1.276176602829E-6)
+!12 * *T-3.748495971011E-6)*T+1.123829871408E-5)
+!12 * *T-3.364018663166E-5)*T+1.009331480887E-4)
+!12 * *T-2.968895120407E-4)*T+9.157850115110E-4)
+!12 * *T-2.422595461409E-3)*T+9.040335037321E-3)
+!12 * *T-1.341185056618E-2)*T+1.037033634184E-1)
+!12 * *T+1.616919872437E-2)*T + 8.862269254528E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 15E.16
+ Y = (((((((((((((((-1.243191705600000E-10*T+
+ * 3.622882508800000E-10)*T-4.030909644800000E-10)
+ * *T+1.265236705280000E-9)*T-5.419466096640000E-9)
+ * *T+1.613133578240000E-8)*T-4.620920340480000E-8)
+ * *T+1.387603440435200E-7)*T-4.179652784537600E-7)
+ * *T+1.253148247777280E-6)*T-3.754930502328320E-6)
+ * *T+1.125234962812416E-5)*T-3.363759801664768E-5)
+ * *T+1.009281733953869E-4)*T-2.968901194293069E-4)
+ * *T+9.157859942174304E-4)*T-2.422595384546340E-3
+ Y = ((((Y*T+9.040334940477911E-3)*T-1.341185057058971E-2)
+ * *T+1.037033634220705E-1)*T+1.616919872444243E-2)*T +
+ * 8.862269254527580E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 17E.18
+!17 Y = (((((((((((((((-1.46381209600000000E-11*T+
+!17 * 4.26560716800000000E-11)*T-4.01499750400000000E-11)
+!17 * *T+1.27679856640000000E-10)*T-6.13513953280000000E-10)
+!17 * *T+1.82243164160000000E-9)*T-5.11961333760000000E-9)
+!17 * *T+1.53835215257600000E-8)*T-4.64774927155200000E-8)
+!17 * *T+1.39383522590720000E-7)*T-4.17808776355840000E-7)
+!17 * *T+1.25281466396672000E-6)*T-3.75499034136576000E-6)
+!17 * *T+1.12524642975590400E-5)*T-3.36375833240268800E-5)
+!17 * *T+1.00928148823365120E-4)*T-2.96890121633200000E-4
+!17 Y = ((((((Y*T+9.15785997288933120E-4)*T-2.42259538436268176E-3)
+!17 * *T+9.04033494028101968E-3)*T-1.34118505705967765E-2)
+!17 * *T+1.03703363422075456E-1)*T+1.61691987244425092E-2)*T +
+!17 * 8.86226925452758013E-1
+!
+! EXPANSION (0026) EVALUATED AS Y(T) --PRECISION 19E.19
+!19 Y = (((((((((((((((+6.710886400000000000E-13*T-
+!19 * 1.677721600000000000E-12)*T+6.710886400000000000E-13)
+!19 * *T-4.152360960000000000E-12)*T+2.499805184000000000E-11)
+!19 * *T-6.898581504000000000E-11)*T+1.859597107200000000E-10)
+!19 * *T-5.676387532800000000E-10)*T+1.725556326400000000E-9)
+!19 * *T-5.166307737600000000E-9)*T+1.548131827712000000E-8)
+!19 * *T-4.644574052352000000E-8)*T+1.393195837030400000E-7)
+!19 * *T-4.178233990758400000E-7)*T+1.252842254950400000E-6)
+!19 * *T-3.754985815285760000E-6)*T+1.125245651030528000E-5
+!19 Y = (((((((((Y*T-3.363758423922688000E-5)
+!19 * *T+1.009281502108083200E-4)
+!19 * *T-2.968901215188000000E-4)*T+9.157859971435078400E-4)
+!19 * *T-2.422595384370689760E-3)*T+9.040334940288877920E-3)
+!19 * *T-1.341185057059651648E-2)*T+1.037033634220752902E-1)
+!19 * *T+1.616919872444250674E-2)*T + 8.862269254527580137E-1
+!
+ S14ABE = LOG(Y*G)
+ IFAIL = 0
+ GO TO 200
+!
+ 120 IF (X.GT.XBIG) GO TO 140
+! MAIN LARGE X RANGE
+ T = 450.0/(X*X) - 1.0
+!
+! * EXPANSION (0059) *
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 08E.09
+!08 Y = (+3.89980902E-9*T-6.16502533E-6)*T + 8.33271644E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 09E.10
+!09 Y = (+3.899809019E-9*T-6.165025333E-6)*T + 8.332716441E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 12E.13
+!12 Y = ((-6.451144077930E-12*T+3.899809018958E-9)
+!12 * *T-6.165020494506E-6)*T + 8.332716440658E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 15E.16
+ Y = (((+2.002019273379824E-14*T-6.451144077929628E-12)
+ * *T+3.899788998764847E-9)*T-6.165020494506090E-6)*T +
+ * 8.332716440657866E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 17E.18
+!17 Y = ((((-9.94561064728159347E-17*T+2.00201927337982364E-14)
+!17 * *T-6.45101975779653651E-12)*T+3.89978899876484712E-9)
+!17 * *T-6.16502049453716986E-6)*T + 8.33271644065786580E-2
+!
+! EXPANSION (0059) EVALUATED AS Y(T) --PRECISION 19E.19
+!19 Y = (((((+7.196406678180202240E-19*T-9.945610647281593472E-17)
+!19 * *T+2.001911327279650935E-14)*T-6.451019757796536510E-12)
+!19 * *T+3.899788999169644998E-9)*T-6.165020494537169862E-6)*T +
+!19 * 8.332716440657865795E-2
+!
+ S14ABE = (X-0.5)*LOG(X) - X + LNR2PI + Y/X
+ IFAIL = 0
+ GO TO 200
+!
+ 140 IF (X.GT.XVBIG) GO TO 180
+! ASYMPTOTIC LARGE X RANGE
+ S14ABE = (X-0.5)*LOG(X) - X + LNR2PI
+ IFAIL = 0
+ GO TO 200
+!
+! FAILURE EXITS
+ 160 IFAIL = P01ABE(IFAIL,1,SRNAME,0,P01REC)
+ S14ABE = 0.0
+ GO TO 200
+ 180 IFAIL = P01ABE(IFAIL,2,SRNAME,0,P01REC)
+ S14ABE = GBIG
+!
+ 200 RETURN
+!
+ END
+ SUBROUTINE S17DGE(DERIV,Z,SCALE,AI,NZ,IFAIL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-770 (DEC 1989).
+!
+! Original name: CAIRY
+!
+! PURPOSE TO COMPUTE AIRY FUNCTIONS AI(Z) AND DAI(Z) FOR COMPLEX Z
+!
+! DESCRIPTION
+! ===========
+!
+! ON SCALE='U', S17DGE COMPUTES THE COMPLEX AIRY FUNCTION AI(Z)
+! OR ITS DERIVATIVE DAI(Z)/DZ ON DERIV='F' OR DERIV='D'
+! RESPECTIVELY. ON SCALE='S', A SCALING OPTION
+! CEXP(ZTA)*AI(Z) OR CEXP(ZTA)*DAI(Z)/DZ IS PROVIDED TO REMOVE
+! THE EXPONENTIAL DECAY IN -PI/3.LT.ARG(Z).LT.PI/3 AND THE
+! EXPONENTIAL GROWTH IN PI/3.LT.ABS(ARG(Z)).LT.PI WHERE
+! ZTA=(2/3)*Z*CSQRT(Z)
+!
+! WHILE THE AIRY FUNCTIONS AI(Z) AND DAI(Z)/DZ ARE ANALYTIC IN
+! THE WHOLE Z PLANE, THE CORRESPONDING SCALED FUNCTIONS DEFINED
+! FOR SCALE='S' HAVE A CUT ALONG THE NEGATIVE REAL AXIS.
+! DEFINITIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF
+! MATHEMATICAL FUNCTIONS (REF. 1).
+!
+! INPUT
+! Z - Z=CMPLX(X,Y)
+! DERIV - RETURN FUNCTION (DERIV='F') OR DERIVATIVE
+! (DERIV='D')
+! SCALE - A PARAMETER TO INDICATE THE SCALING OPTION
+! SCALE = 'U' OR 'u' RETURNS
+! AI=AI(Z) ON DERIV='F' OR
+! AI=DAI(Z)/DZ ON DERIV='D'
+! SCALE = 'S' OR 's' RETURNS
+! AI=CEXP(ZTA)*AI(Z) ON DERIV='F' OR
+! AI=CEXP(ZTA)*DAI(Z)/DZ ON DERIV='D' WHERE
+! ZTA=(2/3)*Z*CSQRT(Z)
+!
+! OUTPUT
+! AI - COMPLEX ANSWER DEPENDING ON THE CHOICES FOR DERIV
+! AND SCALE
+! NZ - UNDERFLOW INDICATOR
+! NZ= 0 , NORMAL RETURN
+! NZ= 1 , AI=CMPLX(0.0,0.0) DUE TO UNDERFLOW IN
+! -PI/3.LT.ARG(Z).LT.PI/3 ON SCALE='U'
+! IFAIL - ERROR FLAG
+! IFAIL=0, NORMAL RETURN - COMPUTATION COMPLETED
+! IFAIL=1, INPUT ERROR - NO COMPUTATION
+! IFAIL=2, OVERFLOW - NO COMPUTATION, REAL(ZTA)
+! TOO LARGE WITH SCALE = 'U'
+! IFAIL=3, CABS(Z) LARGE - COMPUTATION COMPLETED
+! LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION
+! PRODUCE LESS THAN HALF OF MACHINE ACCURACY
+! IFAIL=4, CABS(Z) TOO LARGE - NO COMPUTATION
+! COMPLETE LOSS OF ACCURACY BY ARGUMENT
+! REDUCTION
+! IFAIL=5, ERROR - NO COMPUTATION,
+! ALGORITHM TERMINATION CONDITION NOT MET
+!
+! LONG DESCRIPTION
+! ================
+!
+! AI AND DAI ARE COMPUTED FOR CABS(Z).GT.1.0 FROM THE K BESSEL
+! FUNCTIONS BY
+!
+! AI(Z)=C*SQRT(Z)*K(1/3,ZTA) , DAI(Z)=-C*Z*K(2/3,ZTA)
+! C=1.0/(PI*SQRT(3.0))
+! ZTA=(2/3)*Z**(3/2)
+!
+! WITH THE POWER SERIES FOR CABS(Z).LE.1.0.
+!
+! IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+! MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES
+! OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF
+! THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR),
+! THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR
+! FLAG IFAIL=3 IS TRIGGERED WHERE UR=X02AJE()=UNIT ROUNDOFF.
+! ALSO, IF THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN
+! ALL SIGNIFICANCE IS LOST AND IFAIL=4. IN ORDER TO USE THE INT
+! FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE
+! LARGEST INTEGER, U3=X02BBE(). THUS, THE MAGNITUDE OF ZETA
+! MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2,
+! AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE
+! PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE
+! PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT-
+! ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG-
+! NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN
+! DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN
+! EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES,
+! NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE
+! PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER
+! MACHINES.
+!
+! THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+! BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+! ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+! SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+! ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+! ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+! CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+! HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+! ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+! SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+! THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+! 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+! THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+! COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+! BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+! COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+! MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+! THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+! OR -PI/2+P.
+!
+! REFERENCES
+! ==========
+! HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+! AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+! COMMERCE, 1955.
+!
+! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+! AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+!
+! A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+! 1018, MAY, 1985
+!
+! A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+! MATH. SOFTWARE, 1986
+!
+! DATE WRITTEN 830501 (YYMMDD)
+! REVISION DATE 830501 (YYMMDD)
+! AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+!
+! .. Parameters ..
+ CHARACTER*6 SRNAME
+ PARAMETER (SRNAME='S17DGE')
+! .. Scalar Arguments ..
+ COMPLEX AI, Z
+ INTEGER IFAIL, NZ
+ CHARACTER DERIV, SCALE
+! .. Local Scalars ..
+ COMPLEX CONE, CSQ, S1, S2, TRM1, TRM2, Z3, ZTA
+ REAL AA, AD, AK, ALAZ, ALIM, ATRM, AZ, AZ3, BB, BK,
+ * C1, C2, CK, COEF, D1, D2, DIG, DK, ELIM, FID,
+ * FNU, R1M5, RL, SAVAA, SFAC, TOL, TTH, Z3I, Z3R,
+ * ZI, ZR
+ INTEGER ID, IERR, IFL, IFLAG, K, K1, K2, KODE, MR, NN,
+ * NREC
+! .. Local Arrays ..
+ COMPLEX CY(1)
+ CHARACTER*80 REC(1)
+! .. External Functions ..
+ COMPLEX S01EAE
+ REAL X02AHE, X02AJE, X02AME
+ INTEGER P01ABE, X02BBE, X02BHE, X02BJE, X02BKE, X02BLE
+ EXTERNAL S01EAE, X02AHE, X02AJE, X02AME, P01ABE, X02BBE,
+ * X02BHE, X02BJE, X02BKE, X02BLE
+! .. External Subroutines ..
+ EXTERNAL DGXS17, DGZS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, LOG, LOG10, MAX, MIN, REAL,
+ * SQRT
+! .. Data statements ..
+ DATA TTH, C1, C2, COEF/6.66666666666666667E-01,
+ * 3.55028053887817240E-01,
+ * 2.58819403792806799E-01,
+ * 1.83776298473930683E-01/
+ DATA CONE/(1.0E0,0.0E0)/
+! .. Executable Statements ..
+ IERR = 0
+ NREC = 0
+ NZ = 0
+ IF (DERIV.EQ.'F' .OR. DERIV.EQ.'f') THEN
+ ID = 0
+ ELSE IF (DERIV.EQ.'D' .OR. DERIV.EQ.'d') THEN
+ ID = 1
+ ELSE
+ ID = -1
+ END IF
+ IF (SCALE.EQ.'U' .OR. SCALE.EQ.'u') THEN
+ KODE = 1
+ ELSE IF (SCALE.EQ.'S' .OR. SCALE.EQ.'s') THEN
+ KODE = 2
+ ELSE
+ KODE = -1
+ END IF
+ IF (ID.EQ.-1) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99999) DERIV
+ ELSE IF (KODE.EQ.-1) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99998) SCALE
+ END IF
+ IF (IERR.EQ.0) THEN
+ AZ = ABS(Z)
+ TOL = MAX(X02AJE(),1.0E-18)
+ FID = ID
+ IF (AZ.GT.1.0E0) THEN
+! ------------------------------------------------------------
+! CASE FOR CABS(Z).GT.1.0
+! ------------------------------------------------------------
+ FNU = (1.0E0+FID)/3.0E0
+! ------------------------------------------------------------
+! SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+! TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+! ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW
+! LIMIT.
+! EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND
+! EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS
+! NEAR UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC
+! IS DONE.
+! RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR
+! LARGE Z.
+! DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+! ------------------------------------------------------------
+ K1 = X02BKE()
+ K2 = X02BLE()
+ R1M5 = LOG10(REAL(X02BHE()))
+ K = MIN(ABS(K1),ABS(K2))
+ ELIM = 2.303E0*(K*R1M5-3.0E0)
+ K1 = X02BJE() - 1
+ AA = R1M5*K1
+ DIG = MIN(AA,18.0E0)
+ AA = AA*2.303E0
+ ALIM = ELIM + MAX(-AA,-41.45E0)
+ RL = 1.2E0*DIG + 3.0E0
+ ALAZ = LOG(AZ)
+! ------------------------------------------------------------
+! TEST FOR RANGE
+! ------------------------------------------------------------
+ AA = 0.5E0/TOL
+ BB = X02BBE(1.0E0)*0.5E0
+ AA = MIN(AA,BB,X02AHE(1.0E0))
+ AA = AA**TTH
+ IF (AZ.GT.AA) THEN
+ NZ = 0
+ IERR = 4
+ NREC = 1
+ WRITE (REC,FMT=99997) AZ, AA
+ ELSE
+ AA = SQRT(AA)
+ SAVAA = AA
+ IF (AZ.GT.AA) THEN
+ IERR = 3
+ NREC = 1
+ WRITE (REC,FMT=99996) AZ, AA
+ END IF
+ CSQ = SQRT(Z)
+ ZTA = Z*CSQ*CMPLX(TTH,0.0E0)
+! ---------------------------------------------------------
+! RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS
+! SMALL
+! ---------------------------------------------------------
+ IFLAG = 0
+ SFAC = 1.0E0
+ ZI = AIMAG(Z)
+ ZR = REAL(Z)
+ AK = AIMAG(ZTA)
+ IF (ZR.LT.0.0E0) THEN
+ BK = REAL(ZTA)
+ CK = -ABS(BK)
+ ZTA = CMPLX(CK,AK)
+ END IF
+ IF (ZI.EQ.0.0E0) THEN
+ IF (ZR.LE.0.0E0) ZTA = CMPLX(0.0E0,AK)
+ END IF
+ AA = REAL(ZTA)
+ IF (AA.GE.0.0E0 .AND. ZR.GT.0.0E0) THEN
+ IF (KODE.NE.2) THEN
+! ---------------------------------------------------
+! UNDERFLOW TEST
+! ---------------------------------------------------
+ IF (AA.GE.ALIM) THEN
+ AA = -AA - 0.25E0*ALAZ
+ IFLAG = 2
+ SFAC = 1.0E0/TOL
+ IF (AA.LT.(-ELIM)) THEN
+ NZ = 1
+ AI = CMPLX(0.0E0,0.0E0)
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ END IF
+ END IF
+ CALL DGXS17(ZTA,FNU,KODE,1,CY,NZ,TOL,ELIM,ALIM)
+ ELSE
+ IF (KODE.NE.2) THEN
+! ---------------------------------------------------
+! OVERFLOW TEST
+! ---------------------------------------------------
+ IF (AA.LE.(-ALIM)) THEN
+ AA = -AA + 0.25E0*ALAZ
+ IFLAG = 1
+ SFAC = TOL
+ IF (AA.GT.ELIM) GO TO 20
+ END IF
+ END IF
+! ------------------------------------------------------
+! DGXS17 AND DGZS17 RETURN EXP(ZTA)*K(FNU,ZTA) ON KODE=2
+! ------------------------------------------------------
+ MR = 1
+ IF (ZI.LT.0.0E0) MR = -1
+ CALL DGZS17(ZTA,FNU,KODE,MR,1,CY,NN,RL,TOL,ELIM,ALIM)
+ IF (NN.GE.0) THEN
+ NZ = NZ + NN
+ GO TO 40
+ ELSE IF (NN.EQ.(-3)) THEN
+ NZ = 0
+ IERR = 4
+ NREC = 1
+ WRITE (REC,FMT=99997) AZ, SAVAA
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ ELSE IF (NN.NE.(-1)) THEN
+ NZ = 0
+ IERR = 5
+ NREC = 1
+ WRITE (REC,FMT=99995)
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ 20 NZ = 0
+ IERR = 2
+ NREC = 1
+ WRITE (REC,FMT=99994)
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ 40 S1 = CY(1)*CMPLX(COEF,0.0E0)
+ IF (IFLAG.NE.0) THEN
+ S1 = S1*CMPLX(SFAC,0.0E0)
+ IF (ID.EQ.1) THEN
+ S1 = -S1*Z
+ AI = S1*CMPLX(1.0E0/SFAC,0.0E0)
+ ELSE
+ S1 = S1*CSQ
+ AI = S1*CMPLX(1.0E0/SFAC,0.0E0)
+ END IF
+ ELSE IF (ID.EQ.1) THEN
+ AI = -Z*S1
+ ELSE
+ AI = CSQ*S1
+ END IF
+ END IF
+ ELSE
+! ------------------------------------------------------------
+! POWER SERIES FOR CABS(Z).LE.1.
+! ------------------------------------------------------------
+ S1 = CONE
+ S2 = CONE
+ IF (AZ.LT.TOL) THEN
+ AA = 1.0E+3*X02AME()
+ S1 = CMPLX(0.0E0,0.0E0)
+ IF (ID.EQ.1) THEN
+ AI = -CMPLX(C2,0.0E0)
+ AA = SQRT(AA)
+ IF (AZ.GT.AA) S1 = Z*Z*CMPLX(0.5E0,0.0E0)
+ AI = AI + S1*CMPLX(C1,0.0E0)
+ ELSE
+ IF (AZ.GT.AA) S1 = CMPLX(C2,0.0E0)*Z
+ AI = CMPLX(C1,0.0E0) - S1
+ END IF
+ ELSE
+ AA = AZ*AZ
+ IF (AA.GE.TOL/AZ) THEN
+ TRM1 = CONE
+ TRM2 = CONE
+ ATRM = 1.0E0
+ Z3 = Z*Z*Z
+ AZ3 = AZ*AA
+ AK = 2.0E0 + FID
+ BK = 3.0E0 - FID - FID
+ CK = 4.0E0 - FID
+ DK = 3.0E0 + FID + FID
+ D1 = AK*DK
+ D2 = BK*CK
+ AD = MIN(D1,D2)
+ AK = 24.0E0 + 9.0E0*FID
+ BK = 30.0E0 - 9.0E0*FID
+ Z3R = REAL(Z3)
+ Z3I = AIMAG(Z3)
+ DO 60 K = 1, 25
+ TRM1 = TRM1*CMPLX(Z3R/D1,Z3I/D1)
+ S1 = S1 + TRM1
+ TRM2 = TRM2*CMPLX(Z3R/D2,Z3I/D2)
+ S2 = S2 + TRM2
+ ATRM = ATRM*AZ3/AD
+ D1 = D1 + AK
+ D2 = D2 + BK
+ AD = MIN(D1,D2)
+ IF (ATRM.LT.TOL*AD) THEN
+ GO TO 80
+ ELSE
+ AK = AK + 18.0E0
+ BK = BK + 18.0E0
+ END IF
+ 60 CONTINUE
+ END IF
+ 80 IF (ID.EQ.1) THEN
+ AI = -S2*CMPLX(C2,0.0E0)
+ IF (AZ.GT.TOL) AI = AI + Z*Z*S1*CMPLX(C1/(1.0E0+FID),
+ * 0.0E0)
+ IF (KODE.NE.1) THEN
+ ZTA = Z*SQRT(Z)*CMPLX(TTH,0.0E0)
+! AI = AI*EXP(ZTA)
+ IFL = 1
+ AI = AI*S01EAE(ZTA,IFL)
+ END IF
+ ELSE
+ AI = S1*CMPLX(C1,0.0E0) - Z*S2*CMPLX(C2,0.0E0)
+ IF (KODE.NE.1) THEN
+ ZTA = Z*SQRT(Z)*CMPLX(TTH,0.0E0)
+! AI = AI*EXP(ZTA)
+ IFL = 1
+ AI = AI*S01EAE(ZTA,IFL)
+ END IF
+ END IF
+ END IF
+ END IF
+ END IF
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+!
+99999 FORMAT (1X,'** On entry, DERIV has illegal value: DERIV = ''',A,
+ * '''')
+99998 FORMAT (1X,'** On entry, SCALE has illegal value: SCALE = ''',A,
+ * '''')
+99997 FORMAT (1X,'** No computation because abs(Z) =',1P,E13.5,' .GT.',
+ * E13.5)
+99996 FORMAT (1X,'** Results lack precision because abs(Z) =',1P,E13.5,
+ * ' .GT.',E13.5)
+99995 FORMAT (1X,'** No computation - algorithm termination condition ',
+ * 'not met.')
+99994 FORMAT (1X,'** No computation because real(ZTA) too large, where',
+ * ' ZTA = (2/3)*Z**(3/2).')
+ END
+ SUBROUTINE S17DLE(M,FNU,Z,N,SCALE,CY,NZ,IFAIL)
+! MARK 13 RELEASE. NAG COPYRIGHT 1988.
+! MARK 14 REVISED. IER-781 (DEC 1989).
+!
+! Original name: CBESH
+!
+! PURPOSE TO COMPUTE THE H-BESSEL FUNCTIONS OF A COMPLEX ARGUMENT
+!
+! DESCRIPTION
+! ===========
+!
+! ON SCALE='U', S17DLE COMPUTES AN N MEMBER SEQUENCE OF COMPLEX
+! HANKEL (BESSEL) FUNCTIONS CY(J)=H(M,FNU+J-1,Z) FOR KINDS M=1
+! OR 2, REAL, NONNEGATIVE ORDERS FNU+J-1, J=1,...,N, AND COMPLEX
+! Z.NE.CMPLX(0.0E0,0.0E0) IN THE CUT PLANE -PI.LT.ARG(Z).LE.PI.
+! ON SCALE='S', S17DLE COMPUTES THE SCALED HANKEL FUNCTIONS
+!
+! CY(I)=H(M,FNU+J-1,Z)*EXP(-MM*Z*I) MM=3-2M, I**2=-1.
+!
+! WHICH REMOVES THE EXPONENTIAL BEHAVIOR IN BOTH THE UPPER
+! AND LOWER HALF PLANES. DEFINITIONS AND NOTATION ARE FOUND IN
+! THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS (REF. 1).
+!
+! INPUT
+! Z - Z=CMPLX(X,Y), Z.NE.CMPLX(0.,0.),-PI.LT.ARG(Z).LE.PI
+! FNU - ORDER OF INITIAL H FUNCTION, FNU.GE.0.0E0
+! SCALE - A PARAMETER TO INDICATE THE SCALING OPTION
+! SCALE = 'U' OR SCALE = 'u' RETURNS
+! CY(J)=H(M,FNU+J-1,Z), J=1,...,N
+! = 'S' OR SCALE = 's' RETURNS
+! CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M))
+! J=1,...,N , I**2=-1
+! M - KIND OF HANKEL FUNCTION, M=1 OR 2
+! N - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1
+!
+! OUTPUT
+! CY - A COMPLEX VECTOR WHOSE FIRST N COMPONENTS CONTAIN
+! VALUES FOR THE SEQUENCE
+! CY(J)=H(M,FNU+J-1,Z) OR
+! CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M)) J=1,...,N
+! DEPENDING ON SCALE, I**2=-1.
+! NZ - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW,
+! NZ= 0 , NORMAL RETURN
+! NZ.GT.0 , FIRST NZ COMPONENTS OF CY SET TO ZERO
+! DUE TO UNDERFLOW, CY(J)=CMPLX(0.0,0.0)
+! J=1,...,NZ WHEN Y.GT.0.0 AND M=1 OR
+! Y.LT.0.0 AND M=2. FOR THE COMPLMENTARY
+! HALF PLANES, NZ STATES ONLY THE NUMBER
+! OF UNDERFLOWS.
+! IERR -ERROR FLAG
+! IERR=0, NORMAL RETURN - COMPUTATION COMPLETED
+! IERR=1, INPUT ERROR - NO COMPUTATION
+! IERR=2, OVERFLOW - NO COMPUTATION,
+! CABS(Z) TOO SMALL
+! IERR=3 OVERFLOW - NO COMPUTATION,
+! FNU+N-1 TOO LARGE
+! IERR=4, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE
+! BUT LOSSES OF SIGNIFCANCE BY ARGUMENT
+! REDUCTION PRODUCE LESS THAN HALF OF MACHINE
+! ACCURACY
+! IERR=5, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA-
+! TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI-
+! CANCE BY ARGUMENT REDUCTION
+! IERR=6, ERROR - NO COMPUTATION,
+! ALGORITHM TERMINATION CONDITION NOT MET
+!
+! LONG DESCRIPTION
+! ================
+!
+! THE COMPUTATION IS CARRIED OUT BY THE RELATION
+!
+! H(M,FNU,Z)=(1/MP)*EXP(-MP*FNU)*K(FNU,Z*EXP(-MP))
+! MP=MM*HPI*I, MM=3-2*M, HPI=PI/2, I**2=-1
+!
+! FOR M=1 OR 2 WHERE THE K BESSEL FUNCTION IS COMPUTED FOR THE
+! RIGHT HALF PLANE RE(Z).GE.0.0. THE K FUNCTION IS CONTINUED
+! TO THE LEFT HALF PLANE BY THE RELATION
+!
+! K(FNU,Z*EXP(MP)) = EXP(-MP*FNU)*K(FNU,Z)-MP*I(FNU,Z)
+! MP=MR*PI*I, MR=+1 OR -1, RE(Z).GT.0, I**2=-1
+!
+! WHERE I(FNU,Z) IS THE I BESSEL FUNCTION.
+!
+! EXPONENTIAL DECAY OF H(M,FNU,Z) OCCURS IN THE UPPER HALF Z
+! PLANE FOR M=1 AND THE LOWER HALF Z PLANE FOR M=2. EXPONENTIAL
+! GROWTH OCCURS IN THE COMPLEMENTARY HALF PLANES. SCALING
+! BY EXP(-MM*Z*I) REMOVES THE EXPONENTIAL BEHAVIOR IN THE
+! WHOLE Z PLANE FOR Z TO INFINITY.
+!
+! FOR NEGATIVE ORDERS,THE FORMULAE
+!
+! H(1,-FNU,Z) = H(1,FNU,Z)*CEXP( PI*FNU*I)
+! H(2,-FNU,Z) = H(2,FNU,Z)*CEXP(-PI*FNU*I)
+! I**2=-1
+!
+! CAN BE USED.
+!
+! IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE-
+! MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS
+! LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR.
+! CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN
+! LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG
+! IERR=4 IS TRIGGERED WHERE UR=X02AJE()=UNIT ROUNDOFF. ALSO
+! IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS
+! LOST AND IERR=5. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS
+! MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE
+! INTEGER, U3=X02BBE(). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS
+! RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3
+! ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION
+! ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION
+! ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN
+! THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT
+! TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS
+! IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC.
+! SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES.
+!
+! THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX
+! BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT
+! ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE-
+! SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE
+! ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))),
+! ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF
+! CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY
+! HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN
+! ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY
+! SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER
+! THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K,
+! 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS
+! THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER
+! COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY
+! BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER
+! COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE
+! MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES,
+! THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P,
+! OR -PI/2+P.
+!
+! REFERENCES
+! ==========
+! HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ
+! AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF
+! COMMERCE, 1955.
+!
+! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+! BY D. E. AMOS, SAND83-0083, MAY, 1983.
+!
+! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
+! AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983
+!
+! A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85-
+! 1018, MAY, 1985
+!
+! A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX
+! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS.
+! MATH. SOFTWARE, 1986
+!
+! DATE WRITTEN 830501 (YYMMDD)
+! REVISION DATE 830501 (YYMMDD)
+! AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
+!
+! .. Parameters ..
+ CHARACTER*6 SRNAME
+ PARAMETER (SRNAME='S17DLE')
+! .. Scalar Arguments ..
+ COMPLEX Z
+ REAL FNU
+ INTEGER IFAIL, M, N, NZ
+ CHARACTER*1 SCALE
+! .. Array Arguments ..
+ COMPLEX CY(N)
+! .. Local Scalars ..
+ COMPLEX CSGN, ZN, ZT
+ REAL AA, ALIM, ALN, ARG, ASCLE, ATOL, AZ, BB, CPN,
+ * DIG, ELIM, FMM, FN, FNUL, HPI, R1M5, RHPI, RL,
+ * RTOL, SGN, SPN, TOL, UFL, XN, XX, YN, YY
+ INTEGER I, IERR, INU, INUH, IR, K, K1, K2, KODE, MM, MR,
+ * NN, NREC, NUF, NW
+! .. Local Arrays ..
+ CHARACTER*80 REC(1)
+! .. External Functions ..
+ REAL X02AHE, X02AJE
+ INTEGER P01ABE, X02BBE, X02BHE, X02BJE, X02BKE, X02BLE
+ EXTERNAL X02AHE, X02AJE, P01ABE, X02BBE, X02BHE, X02BJE,
+ * X02BKE, X02BLE
+! .. External Subroutines ..
+ EXTERNAL DEVS17, DGXS17, DLYS17, DLZS17
+! .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, COS, EXP, INT, LOG, LOG10,
+ * MAX, MIN, MOD, REAL, SIGN, SIN, SQRT
+! .. Data statements ..
+!
+ DATA HPI/1.57079632679489662E0/
+! .. Executable Statements ..
+ NZ = 0
+ NREC = 0
+ XX = REAL(Z)
+ YY = AIMAG(Z)
+ IERR = 0
+ IF (SCALE.EQ.'U' .OR. SCALE.EQ.'u') THEN
+ KODE = 1
+ ELSE IF (SCALE.EQ.'S' .OR. SCALE.EQ.'s') THEN
+ KODE = 2
+ ELSE
+ KODE = -1
+ END IF
+ IF (XX.EQ.0.0E0 .AND. YY.EQ.0.0E0) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99999)
+ ELSE IF (FNU.LT.0.0E0) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99998) FNU
+ ELSE IF (KODE.EQ.-1) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99997) SCALE
+ ELSE IF (N.LT.1) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99996) N
+ ELSE IF (M.LT.1 .OR. M.GT.2) THEN
+ IERR = 1
+ NREC = 1
+ WRITE (REC,FMT=99995) M
+ END IF
+ IF (IERR.EQ.0) THEN
+ NN = N
+! ---------------------------------------------------------------
+! SET PARAMETERS RELATED TO MACHINE CONSTANTS.
+! TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18.
+! ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT.
+! EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND
+! EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR
+! UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE.
+! RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR
+! LARGE Z.
+! DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG).
+! FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE
+! FNU
+! ---------------------------------------------------------------
+ TOL = MAX(X02AJE(),1.0E-18)
+ K1 = X02BKE()
+ K2 = X02BLE()
+ R1M5 = LOG10(REAL(X02BHE()))
+ K = MIN(ABS(K1),ABS(K2))
+ ELIM = 2.303E0*(K*R1M5-3.0E0)
+ K1 = X02BJE() - 1
+ AA = R1M5*K1
+ DIG = MIN(AA,18.0E0)
+ AA = AA*2.303E0
+ ALIM = ELIM + MAX(-AA,-41.45E0)
+ FNUL = 10.0E0 + 6.0E0*(DIG-3.0E0)
+ RL = 1.2E0*DIG + 3.0E0
+ FN = FNU + NN - 1
+ MM = 3 - M - M
+ FMM = MM
+ ZN = Z*CMPLX(0.0E0,-FMM)
+ XN = REAL(ZN)
+ YN = AIMAG(ZN)
+ AZ = ABS(Z)
+! ---------------------------------------------------------------
+! TEST FOR RANGE
+! ---------------------------------------------------------------
+ AA = 0.5E0/TOL
+ BB = X02BBE(1.0E0)*0.5E0
+ AA = MIN(AA,BB,X02AHE(1.0E0))
+ IF (AZ.LE.AA) THEN
+ IF (FN.LE.AA) THEN
+ AA = SQRT(AA)
+ IF (AZ.GT.AA) THEN
+ IERR = 4
+ NREC = 1
+ WRITE (REC,FMT=99994) AZ, AA
+ ELSE IF (FN.GT.AA) THEN
+ IERR = 4
+ NREC = 1
+ WRITE (REC,FMT=99993) FN, AA
+ END IF
+! ---------------------------------------------------------
+! OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE
+! ---------------------------------------------------------
+ UFL = EXP(-ELIM)
+ IF (AZ.GE.UFL) THEN
+ IF (FNU.GT.FNUL) THEN
+! ---------------------------------------------------
+! UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL
+! ---------------------------------------------------
+ MR = 0
+ IF ((XN.LT.0.0E0) .OR. (XN.EQ.0.0E0 .AND. YN.LT.
+ * 0.0E0 .AND. M.EQ.2)) THEN
+ MR = -MM
+ IF (XN.EQ.0.0E0 .AND. YN.LT.0.0E0) ZN = -ZN
+ END IF
+ CALL DLYS17(ZN,FNU,KODE,MR,NN,CY,NW,TOL,ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 40
+ ELSE
+ NZ = NZ + NW
+ END IF
+ ELSE
+ IF (FN.GT.1.0E0) THEN
+ IF (FN.GT.2.0E0) THEN
+ CALL DEVS17(ZN,FNU,KODE,2,NN,CY,NUF,TOL,ELIM,
+ * ALIM)
+ IF (NUF.LT.0) THEN
+ GO TO 60
+ ELSE
+ NZ = NZ + NUF
+ NN = NN - NUF
+! ------------------------------------------
+! HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1
+! ON RETURN FROM DEVS17
+! IF NUF=NN, THEN CY(I)=CZERO FOR ALL I
+! ------------------------------------------
+ IF (NN.EQ.0) THEN
+ IF (XN.LT.0.0E0) THEN
+ GO TO 60
+ ELSE
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,
+ * NREC,REC)
+ RETURN
+ END IF
+ END IF
+ END IF
+ ELSE IF (AZ.LE.TOL) THEN
+ ARG = 0.5E0*AZ
+ ALN = -FN*LOG(ARG)
+ IF (ALN.GT.ELIM) GO TO 60
+ END IF
+ END IF
+ IF ((XN.LT.0.0E0) .OR. (XN.EQ.0.0E0 .AND. YN.LT.
+ * 0.0E0 .AND. M.EQ.2)) THEN
+! ------------------------------------------------
+! LEFT HALF PLANE COMPUTATION
+! ------------------------------------------------
+ MR = -MM
+ CALL DLZS17(ZN,FNU,KODE,MR,NN,CY,NW,RL,FNUL,TOL,
+ * ELIM,ALIM)
+ IF (NW.LT.0) THEN
+ GO TO 40
+ ELSE
+ NZ = NW
+ END IF
+ ELSE
+! ------------------------------------------------
+! RIGHT HALF PLANE COMPUTATION, XN.GE.0. .AND.
+! (XN.NE.0. .OR. YN.GE.0. .OR. M=1)
+! ------------------------------------------------
+ CALL DGXS17(ZN,FNU,KODE,NN,CY,NZ,TOL,ELIM,ALIM)
+ END IF
+ END IF
+! ------------------------------------------------------
+! H(M,FNU,Z) = -FMM*(I/HPI)*(ZT**FNU)*K(FNU,-Z*ZT)
+!
+! ZT=EXP(-FMM*HPI*I) = CMPLX(0.0,-FMM), FMM=3-2*M, M=1,2
+! ------------------------------------------------------
+ SGN = SIGN(HPI,-FMM)
+! ------------------------------------------------------
+! CALCULATE EXP(FNU*HPI*I) TO MINIMIZE LOSSES OF
+! SIGNIFICANCE WHEN FNU IS LARGE
+! ------------------------------------------------------
+ INU = INT(FNU)
+ INUH = INU/2
+ IR = INU - 2*INUH
+ ARG = (FNU-INU+IR)*SGN
+ RHPI = 1.0E0/SGN
+ CPN = RHPI*COS(ARG)
+ SPN = RHPI*SIN(ARG)
+! ZN = CMPLX(-SPN,CPN)
+ CSGN = CMPLX(-SPN,CPN)
+! IF (MOD(INUH,2).EQ.1) ZN = -ZN
+ IF (MOD(INUH,2).EQ.1) CSGN = -CSGN
+ ZT = CMPLX(0.0E0,-FMM)
+ RTOL = 1.0E0/TOL
+ ASCLE = UFL*RTOL
+ DO 20 I = 1, NN
+! CY(I) = CY(I)*ZN
+! ZN = ZN*ZT
+ ZN = CY(I)
+ AA = REAL(ZN)
+ BB = AIMAG(ZN)
+ ATOL = 1.0E0
+ IF (MAX(ABS(AA),ABS(BB)).LE.ASCLE) THEN
+ ZN = ZN*RTOL
+ ATOL = TOL
+ END IF
+ ZN = ZN*CSGN
+ CY(I) = ZN*ATOL
+ CSGN = CSGN*ZT
+ 20 CONTINUE
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ 40 IF (NW.EQ.(-3)) THEN
+ NZ = 0
+ IERR = 5
+ NREC = 1
+ WRITE (REC,FMT=99988) AZ, AA
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ ELSE IF (NW.NE.(-1)) THEN
+ NZ = 0
+ IERR = 6
+ NREC = 1
+ WRITE (REC,FMT=99992)
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ 60 IERR = 3
+ NZ = 0
+ NREC = 1
+ WRITE (REC,FMT=99991) FN
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ ELSE
+ IERR = 2
+ NZ = 0
+ NREC = 1
+ WRITE (REC,FMT=99990) AZ, UFL
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+ END IF
+ ELSE
+ NZ = 0
+ IERR = 5
+ NREC = 1
+ WRITE (REC,FMT=99989) FN, AA
+ END IF
+ ELSE
+ NZ = 0
+ IERR = 5
+ NREC = 1
+ WRITE (REC,FMT=99988) AZ, AA
+ END IF
+ END IF
+ IFAIL = P01ABE(IFAIL,IERR,SRNAME,NREC,REC)
+ RETURN
+!
+99999 FORMAT (1X,'** On entry, Z = (0.0,0.0)')
+99998 FORMAT (1X,'** On entry, FNU .LT. 0: FNU = ',E13.5)
+99997 FORMAT (1X,'** On entry, SCALE has an illegal value: SCALE = ''',
+ * A,'''')
+99996 FORMAT (1X,'** On entry, N .LE. 0: N = ',I16)
+99995 FORMAT (1X,'** On entry, M has illegal value: M = ',I16)
+99994 FORMAT (1X,'** Results lack precision because abs(Z) =',1P,E13.5,
+ * ' .GT.',E13.5)
+99993 FORMAT (1X,'** Results lack precision, FNU+N-1 =',1P,E13.5,
+ * ' .GT.',E13.5)
+99992 FORMAT (1X,'** No computation - algorithm termination condition ',
+ * 'not met.')
+99991 FORMAT (1X,'** No computation because FNU+N-1 =',1P,E13.5,' is t',
+ * 'oo large.')
+99990 FORMAT (1X,'** No computation because abs(Z) =',1P,E13.5,' .LT. ',
+ * E13.5)
+99989 FORMAT (1X,'** No computation because FNU+N-1 =',1P,E13.5,' .GT.',
+ * E13.5)
+99988 FORMAT (1X,'** No computation because abs(Z) =',1P,E13.5,' .GT.',
+ * E13.5)
+ END
+ REAL FUNCTION X02AHE(X)
+! MARK 9 RELEASE. NAG COPYRIGHT 1981.
+! MARK 11.5(F77) REVISED. (SEPT 1985.)
+!
+! * MAXIMUM ARGUMENT FOR SIN AND COS *
+! RETURNS THE LARGEST POSITIVE REAL NUMBER MAXSC SUCH THAT
+! SIN(MAXSC) AND COS(MAXSC) CAN BE SUCCESSFULLY COMPUTED
+! BY THE COMPILER SUPPLIED SIN AND COS ROUTINES.
+!
+! .. Scalar Arguments ..
+ REAL X
+ REAL CONX02
+ DATA CONX02 /1.677721600000E+7 /
+! .. Executable Statements ..
+ X02AHE = CONX02
+ RETURN
+ END
+ REAL FUNCTION X02AJE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS (1/2)*B**(1-P) IF ROUNDS IS .TRUE.
+! RETURNS B**(1-P) OTHERWISE
+!
+ REAL CONX02
+ DATA CONX02 /1.4210854715202E-14 /
+!bc DATA CONX02 /1.421090000020E-14 /
+! .. Executable Statements ..
+ X02AJE = CONX02
+ RETURN
+ END
+ REAL FUNCTION X02ALE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS (1 - B**(-P)) * B**EMAX (THE LARGEST POSITIVE MODEL
+! NUMBER)
+!
+ REAL CONX02
+! DK DK DK DATA CONX02 /0577757777777777777777B /
+ DATA CONX02 /1.e30/
+! .. Executable Statements ..
+ X02ALE = CONX02
+ RETURN
+ END
+ REAL FUNCTION X02AME()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE 'SAFE RANGE' PARAMETER
+! I.E. THE SMALLEST POSITIVE MODEL NUMBER Z SUCH THAT
+! FOR ANY X WHICH SATISFIES X.GE.Z AND X.LE.1/Z
+! THE FOLLOWING CAN BE COMPUTED WITHOUT OVERFLOW, UNDERFLOW OR OTHER
+! ERROR
+!
+! -X
+! 1.0/X
+! SQRT(X)
+! LOG(X)
+! EXP(LOG(X))
+! Y**(LOG(X)/LOG(Y)) FOR ANY Y
+!
+ REAL CONX02
+! DK DK DK DATA CONX02 /0200044000000000000004B /
+ DATA CONX02 /1.e-27/
+! .. Executable Statements ..
+ X02AME = CONX02
+ RETURN
+ END
+ REAL FUNCTION X02ANE()
+! MARK 15 RELEASE. NAG COPYRIGHT 1991.
+!
+! Returns the 'safe range' parameter for complex numbers,
+! i.e. the smallest positive model number Z such that
+! for any X which satisfies X.ge.Z and X.le.1/Z
+! the following can be computed without overflow, underflow or other
+! error
+!
+! -W
+! 1.0/W
+! SQRT(W)
+! LOG(W)
+! EXP(LOG(W))
+! Y**(LOG(W)/LOG(Y)) for any Y
+! ABS(W)
+!
+! where W is any of cmplx(X,0), cmplx(0,X), cmplx(X,X),
+! cmplx(1/X,0), cmplx(0,1/X), cmplx(1/X,1/X).
+!
+ REAL CONX02
+!bc DATA CONX02 /0000006220426276611547B /
+ DATA CONX02 / 2.708212596942E-1233 /
+! .. Executable Statements ..
+ X02ANE = CONX02
+ RETURN
+ END
+ INTEGER FUNCTION X02BBE(X)
+! NAG COPYRIGHT 1975
+! MARK 4.5 RELEASE
+! MARK 11.5(F77) REVISED. (SEPT 1985.)
+! * MAXINT *
+! RETURNS THE LARGEST INTEGER REPRESENTABLE ON THE COMPUTER
+! THE X PARAMETER IS NOT USED
+! .. Scalar Arguments ..
+ REAL X
+! .. Executable Statements ..
+! FOR ICL 1900
+! X02BBE = 8388607
+! DK DK DK X02BBE = 70368744177663
+ X02BBE = 744177663
+ RETURN
+ END
+ INTEGER FUNCTION X02BHE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE MODEL PARAMETER, B.
+!
+! .. Executable Statements ..
+ X02BHE = 2
+ RETURN
+ END
+ INTEGER FUNCTION X02BJE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE MODEL PARAMETER, p.
+!
+! .. Executable Statements ..
+ X02BJE = 47
+ RETURN
+ END
+ INTEGER FUNCTION X02BKE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE MODEL PARAMETER, EMIN.
+!
+! .. Executable Statements ..
+ X02BKE = -8192
+ RETURN
+ END
+ INTEGER FUNCTION X02BLE()
+! MARK 12 RELEASE. NAG COPYRIGHT 1986.
+!
+! RETURNS THE MODEL PARAMETER, EMAX.
+!
+! .. Executable Statements ..
+ X02BLE = 8189
+ RETURN
+ END
+ SUBROUTINE X04AAE(I,NERR)
+! MARK 7 RELEASE. NAG COPYRIGHT 1978
+! MARK 7C REVISED IER-190 (MAY 1979)
+! MARK 11.5(F77) REVISED. (SEPT 1985.)
+! MARK 14 REVISED. IER-829 (DEC 1989).
+! IF I = 0, SETS NERR TO CURRENT ERROR MESSAGE UNIT NUMBER
+! (STORED IN NERR1).
+! IF I = 1, CHANGES CURRENT ERROR MESSAGE UNIT NUMBER TO
+! VALUE SPECIFIED BY NERR.
+!
+! .. Scalar Arguments ..
+ INTEGER I, NERR
+! .. Local Scalars ..
+ INTEGER NERR1
+! .. Save statement ..
+ SAVE NERR1
+! .. Data statements ..
+ DATA NERR1/0/
+! .. Executable Statements ..
+ IF (I.EQ.0) NERR = NERR1
+ IF (I.EQ.1) NERR1 = NERR
+ RETURN
+ END
+ SUBROUTINE X04BAE(NOUT,REC)
+! MARK 11.5(F77) RELEASE. NAG COPYRIGHT 1986.
+!
+! X04BAE writes the contents of REC to the unit defined by NOUT.
+!
+! Trailing blanks are not output, except that if REC is entirely
+! blank, a single blank character is output.
+! If NOUT.lt.0, i.e. if NOUT is not a valid Fortran unit identifier,
+! then no output occurs.
+!
+! .. Scalar Arguments ..
+ INTEGER NOUT
+ CHARACTER*(*) REC
+! .. Local Scalars ..
+ INTEGER I
+! .. Intrinsic Functions ..
+ INTRINSIC LEN
+! .. Executable Statements ..
+ IF (NOUT.GE.0) THEN
+! Remove trailing blanks
+ DO 20 I = LEN(REC), 2, -1
+ IF (REC(I:I).NE.' ') GO TO 40
+ 20 CONTINUE
+! Write record to external file
+ 40 WRITE (NOUT,FMT=99999) REC(1:I)
+ END IF
+ RETURN
+!
+99999 FORMAT (A)
+ END
+
Modified: seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/plot_compare_to_analytical_solution.gnu
===================================================================
--- seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/plot_compare_to_analytical_solution.gnu 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/EXAMPLES/attenuation/plot_compare_to_analytical_solution.gnu 2012-01-13 17:53:28 UTC (rev 19356)
@@ -6,9 +6,9 @@
set xrange [0:1.4]
-plot "OUTPUT_FILES/S0001.AA.BXX.semd" t 'Numerical Ux' w l lc 1, "Ux_time_analytical_solution.dat" t 'Quasi-analytical Ux' w l lc 3
+plot "OUTPUT_FILES/S0001.AA.BXX.semd" t 'Numerical Ux' w l lc 1, "Ux_time_analytical_solution_viscoelastic.dat" t 'Quasi-analytical Ux' w l lc 3
pause -1 "Hit any key..."
-plot "OUTPUT_FILES/S0001.AA.BXZ.semd" t 'Numerical Uz' w l lc 1, "Uz_time_analytical_solution.dat" t 'Quasi-analytical Uz' w l lc 3
+plot "OUTPUT_FILES/S0001.AA.BXZ.semd" t 'Numerical Uz' w l lc 1, "Uz_time_analytical_solution_viscoelastic.dat" t 'Quasi-analytical Uz' w l lc 3
pause -1 "Hit any key..."
Modified: seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/bibliography.bib
===================================================================
--- seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/bibliography.bib 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/bibliography.bib 2012-01-13 17:53:28 UTC (rev 19356)
@@ -43,11937 +43,11999 @@
@STRING{pepi = {Phys. Earth Planet. In.}}
- at ARTICLE{PeKoLuMaLeCaLeMaLiBlNiBaTr11,
-author = {Daniel Peter and Dimitri Komatitsch and Yang Luo and Roland Martin and Nicolas {Le Goff} and Emanuele Casarotti and Pieyre {Le Loher} and Federica Magnoni and Qinya Liu and C\'eline Blitz and Tarje Nissen-Meyer and Piero Basini and Jeroen Tromp},
-title = {Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes},
-journal = gji,
-year = {2011},
-volume = {186},
-pages = {721-739},
-number = {2},
-doi = {10.1111/j.1365-246X.2011.05044.x}
-}
-
@ARTICLE{arnadottiretal2001,
-author = {T. \'Arnad\'ottir and S. Hreinsd\'ottir and G. Gudmunsson and P.
-Einarsson and M. Heinert and C. V\"olksen},
-title = {Crustal deformation measured by {GPS} in the {S}outh {I}celand {S}eismic
-{Z}one due to two large earthquakes in {J}une 2000},
-journal = grl,
-year = {2001},
-volume = {28},
-pages = {4031-4033}
+ author = {T. \'Arnad\'ottir and S. Hreinsd\'ottir and G. Gudmunsson and P.
+ Einarsson and M. Heinert and C. V\"olksen},
+ title = {Crustal deformation measured by {GPS} in the {S}outh {I}celand {S}eismic
+ {Z}one due to two large earthquakes in {J}une 2000},
+ journal = grl,
+ year = {2001},
+ volume = {28},
+ pages = {4031-4033}
}
@ARTICLE{EtChViGl10,
-author = {\'Etienne, V. and Chaljub, E. and Virieux, J. and Glinsky, N.},
-title = {An hp-adaptive discontinuous {G}alerkin finite-element method for
-3-{D} elastic wave modelling},
-journal = gji,
-year = {2010},
-volume = {183},
-pages = {941-962},
-number = {2},
-doi = {10.1111/j.1365-246X.2010.04764.x}
+ author = {\'Etienne, V. and Chaljub, E. and Virieux, J. and Glinsky, N.},
+ title = {An hp-adaptive discontinuous {G}alerkin finite-element method for
+ 3-{D} elastic wave modelling},
+ journal = gji,
+ year = {2010},
+ volume = {183},
+ pages = {941-962},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2010.04764.x}
}
@ARTICLE{AaHaHe2001,
-author = {Brad T. Aagaard and John F. Hall and Thomas H. Heaton},
-title = {Characterization of Near-Source Ground Motions with Earthquake Simulations},
-journal = {Earthquake Spectra},
-year = {2001},
-volume = {17},
-pages = {177-207},
-number = {2}
+ author = {Brad T. Aagaard and John F. Hall and Thomas H. Heaton},
+ title = {Characterization of Near-Source Ground Motions with Earthquake Simulations},
+ journal = {Earthquake Spectra},
+ year = {2001},
+ volume = {17},
+ pages = {177-207},
+ number = {2}
}
@ARTICLE{AaHeHa2001,
-author = {Brad T. Aagaard and Thomas H. Heaton and John F. Hall},
-title = {Dynamic earthquake ruptures in the presence of lithostatic normal
-stresses: implications for Friction Models and Heat Production},
-journal = bssa,
-year = {2001},
-volume = {91},
-pages = {1765-1796},
-number = {6}
+ author = {Brad T. Aagaard and Thomas H. Heaton and John F. Hall},
+ title = {Dynamic earthquake ruptures in the presence of lithostatic normal
+ stresses: implications for Friction Models and Heat Production},
+ journal = bssa,
+ year = {2001},
+ volume = {91},
+ pages = {1765-1796},
+ number = {6}
}
@ARTICLE{AbGo98,
-author = {S. Abarbanel and D. Gottlieb},
-title = {On the construction of absorbing layers in {CEM}},
-journal = {Applied Numerical Mathematics},
-year = {1998},
-volume = {27},
-pages = {331-340}
+ author = {S. Abarbanel and D. Gottlieb},
+ title = {On the construction of absorbing layers in {CEM}},
+ journal = {Applied Numerical Mathematics},
+ year = {1998},
+ volume = {27},
+ pages = {331-340}
}
@ARTICLE{AbGoHe02,
-author = {S. Abarbanel and D. Gottlieb and J. S. Hesthaven},
-title = {Long time behavior of the perfectly matched layer equations in computational
-electromagnetics},
-journal = {Journal of Scientific Computing},
-year = {2002},
-volume = {17},
-pages = {405-422},
-number = {1-4},
-doi = {10.1023/A:1015141823608}
+ author = {S. Abarbanel and D. Gottlieb and J. S. Hesthaven},
+ title = {Long time behavior of the perfectly matched layer equations in computational
+ electromagnetics},
+ journal = {Journal of Scientific Computing},
+ year = {2002},
+ volume = {17},
+ pages = {405-422},
+ number = {1-4},
+ doi = {10.1023/A:1015141823608}
}
@ARTICLE{AbGoHe99,
-author = {S. Abarbanel and D. Gottlieb and J. S. Hesthaven},
-title = {Well-posed Perfectly Matched Layers for Advective Acoustics},
-journal = jcp,
-year = {1999},
-volume = {154},
-pages = {266-283},
-number = {2},
-doi = {10.1006/jcph.1999.6313}
+ author = {S. Abarbanel and D. Gottlieb and J. S. Hesthaven},
+ title = {Well-posed Perfectly Matched Layers for Advective Acoustics},
+ journal = jcp,
+ year = {1999},
+ volume = {154},
+ pages = {266-283},
+ number = {2},
+ doi = {10.1006/jcph.1999.6313}
}
@MASTERSTHESIS{Abd07,
-author = {Rached Abdelkhalek},
-title = {{\'E}valuation des acc\'el\'erateurs de calcul {GPGPU} pour la mod\'elisation
-sismique},
-school = {ENSEIRB, Bordeaux, France},
-year = {2007}
+ author = {Rached Abdelkhalek},
+ title = {{\'E}valuation des acc\'el\'erateurs de calcul {GPGPU} pour la mod\'elisation
+ sismique},
+ school = {ENSEIRB, Bordeaux, France},
+ year = {2007}
}
@CONFERENCE{AbCaCoRoLa09,
-author = {Abdelkhalek, Rached and Calandra, Henri and Coulaud, Olivier and
-Roman, Jean and Latu, Guillaume},
-title = {Fast Seismic Modeling and Reverse Time Migration on a {GPU} Cluster},
-booktitle = {High Performance Computing \& Simulation 2009},
-year = {2009},
-editor = {Waleed W. Smari and John P. McIntire},
-pages = {36--44},
-address = {Leipzig, Germany},
-month = jun,
-note = {http://hal.inria.fr/docs/00/40/39/33/PDF/hpcs.pdf}
+ author = {Abdelkhalek, Rached and Calandra, Henri and Coulaud, Olivier and
+ Roman, Jean and Latu, Guillaume},
+ title = {Fast Seismic Modeling and Reverse Time Migration on a {GPU} Cluster},
+ booktitle = {High Performance Computing \& Simulation 2009},
+ year = {2009},
+ editor = {Waleed W. Smari and John P. McIntire},
+ pages = {36--44},
+ address = {Leipzig, Germany},
+ month = jun,
+ note = {http://hal.inria.fr/docs/00/40/39/33/PDF/hpcs.pdf}
}
@ARTICLE{AbMaSoCa08,
-author = {A. I. Abreu and W. J. Mansur and D. {Soares Jr.} and J. A. M. Carrer},
-title = {Numerical Computation of Space Derivatives by the Complex-Variable-Differentiation
-Method in the Convolution Quadrature-Method-Based {BEM} Formulation},
-journal = cmes,
-year = {2008},
-volume = {30},
-pages = {123-132},
-number = {3}
+ author = {A. I. Abreu and W. J. Mansur and D. {Soares Jr.} and J. A. M. Carrer},
+ title = {Numerical Computation of Space Derivatives by the Complex-Variable-Differentiation
+ Method in the Convolution Quadrature-Method-Based {BEM} Formulation},
+ journal = cmes,
+ year = {2008},
+ volume = {30},
+ pages = {123-132},
+ number = {3}
}
@BOOK{Ach73,
-title = {Wave Propagation in Elastic Solids},
-publisher = {North-Holland},
-year = {1973},
-author = {J. D. Achenbach},
-address = {Amsterdam, The Netherlands}
+ title = {Wave Propagation in Elastic Solids},
+ publisher = {North-Holland},
+ year = {1973},
+ author = {J. D. Achenbach},
+ address = {Amsterdam, The Netherlands}
}
@ARTICLE{AcKo11,
-author = {Acosta Minolia, Cesar A. and David A. Kopriva},
-title = {Discontinuous {G}alerkin spectral element approximations on moving
-meshes},
-journal = jcp,
-year = {2011},
-volume = {230},
-pages = {1876-1902},
-number = {5},
-doi = {10.1016/j.jcp.2010.11.038}
+ author = {Acosta Minolia, Cesar A. and David A. Kopriva},
+ title = {Discontinuous {G}alerkin spectral element approximations on moving
+ meshes},
+ journal = jcp,
+ year = {2011},
+ volume = {230},
+ pages = {1876-1902},
+ number = {5},
+ doi = {10.1016/j.jcp.2010.11.038}
}
@INPROCEEDINGS{AdPaBo07,
-author = {S. Adams and J. Payne and R. Boppana},
-title = {Finite Difference Time Domain ({FDTD}) Simulations Using Graphics
-Processors},
-booktitle = {Proceedings of the Department of Defense High Performance Computing
-Modernization Program Users Group Conference},
-year = {2007},
-pages = {334-338},
-address = {Pittsburgh, Pennsylvania, USA},
-publisher = {IEEE Computer Society, Washington, DC, USA},
-doi = {10.1109/HPCMP-UGC.2007.34}
+ author = {S. Adams and J. Payne and R. Boppana},
+ title = {Finite Difference Time Domain ({FDTD}) Simulations Using Graphics
+ Processors},
+ booktitle = {Proceedings of the Department of Defense High Performance Computing
+ Modernization Program Users Group Conference},
+ year = {2007},
+ pages = {334-338},
+ address = {Pittsburgh, Pennsylvania, USA},
+ publisher = {IEEE Computer Society, Washington, DC, USA},
+ doi = {10.1109/HPCMP-UGC.2007.34}
}
@ARTICLE{AgDeDoHaKuLaLtLuTo09,
-author = {Emmanuel Agullo and Jim Demmel and Jack Dongarra and Bilel Hadri
-and Jakub Kurzak and Julien Langou and Hatem Ltaief and Piotr Luszczek
-and Stanimire Tomov},
-title = {Numerical linear algebra on emerging architectures: The {PLASMA}
-and {MAGMA} projects},
-journal = {Journal of Physics: Conference Series},
-year = {2009},
-volume = {180},
-pages = {012037},
-doi = {10.1088/1742-6596/180/1/012037}
+ author = {Emmanuel Agullo and Jim Demmel and Jack Dongarra and Bilel Hadri
+ and Jakub Kurzak and Julien Langou and Hatem Ltaief and Piotr Luszczek
+ and Stanimire Tomov},
+ title = {Numerical linear algebra on emerging architectures: The {PLASMA}
+ and {MAGMA} projects},
+ journal = {Journal of Physics: Conference Series},
+ year = {2009},
+ volume = {180},
+ pages = {012037},
+ doi = {10.1088/1742-6596/180/1/012037}
}
@ARTICLE{AiMoMu06,
-author = {Ainsworth, M. and Monk, P. and Muniz, W.},
-title = {Dispersive and Dissipative Properties of Discontinuous {G}alerkin
-Finite Element Methods for the Second-Order Wave Equation},
-journal = {Journal of Scientific Computing},
-year = {2006},
-volume = {27},
-pages = {5-40},
-number = {1},
-doi = {10.1007/s10915-005-9044-x}
+ author = {Ainsworth, M. and Monk, P. and Muniz, W.},
+ title = {Dispersive and Dissipative Properties of Discontinuous {G}alerkin
+ Finite Element Methods for the Second-Order Wave Equation},
+ journal = {Journal of Scientific Computing},
+ year = {2006},
+ volume = {27},
+ pages = {5-40},
+ number = {1},
+ doi = {10.1007/s10915-005-9044-x}
}
@INCOLLECTION{Aki88,
-author = {K. Aki},
-title = {Local site effects on strong ground motion},
-booktitle = {Earthquake Engineering and Soil Dynamics II- Recent advances in ground
-motion evaluation},
-publisher = {American Society of Civil Engineering},
-year = {1988},
-editor = {J. L. Von Thun},
-volume = {20},
-series = {Geothechnical Special Publication},
-pages = {103-155},
-address = {New York, USA}
+ author = {K. Aki},
+ title = {Local site effects on strong ground motion},
+ booktitle = {Earthquake Engineering and Soil Dynamics II- Recent advances in ground
+ motion evaluation},
+ publisher = {American Society of Civil Engineering},
+ year = {1988},
+ editor = {J. L. Von Thun},
+ volume = {20},
+ series = {Geothechnical Special Publication},
+ pages = {103-155},
+ address = {New York, USA}
}
@ARTICLE{AkLa70,
-author = {K. Aki and K. L. Larner},
-title = {Surface motion of a layered medium having an irregular interface,
-due to incident plane {{\it SH}} waves},
-journal = jgr,
-year = {1970},
-volume = {75},
-pages = {933-954}
+ author = {K. Aki and K. L. Larner},
+ title = {Surface motion of a layered medium having an irregular interface,
+ due to incident plane {{\it SH}} waves},
+ journal = jgr,
+ year = {1970},
+ volume = {75},
+ pages = {933-954}
}
@BOOK{AkRi80,
-title = {Quantitative seismology, theory and methods},
-publisher = {W. H. Freeman},
-year = {1980},
-author = {K. Aki and P. G. Richards},
-address = {San Francisco, USA}
+ title = {Quantitative seismology, theory and methods},
+ publisher = {W. H. Freeman},
+ year = {1980},
+ author = {K. Aki and P. G. Richards},
+ address = {San Francisco, USA}
}
@ARTICLE{AlWo08,
-author = {David Al-Attar and John H. Woodhouse},
-title = {Calculation of seismic displacement fields in self-gravitating earth
-models: applications of minors vectors and symplectic structure},
-journal = gji,
-year = {2008},
-volume = {175},
-pages = {1176-1208},
-number = {3},
-doi = {10.1111/j.1365-246X.2008.03961.x}
+ author = {David Al-Attar and John H. Woodhouse},
+ title = {Calculation of seismic displacement fields in self-gravitating earth
+ models: applications of minors vectors and symplectic structure},
+ journal = gji,
+ year = {2008},
+ volume = {175},
+ pages = {1176-1208},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2008.03961.x}
}
@ARTICLE{AlOl98,
-author = {C. M. Alex and K. B. Olsen},
-title = {Lens effect in {S}anta {M}onica?},
-journal = grl,
-year = {1998},
-volume = {25},
-pages = {3441-3444}
+ author = {C. M. Alex and K. B. Olsen},
+ title = {Lens effect in {S}anta {M}onica?},
+ journal = grl,
+ year = {1998},
+ volume = {25},
+ pages = {3441-3444}
}
@ARTICLE{AlZeLaBeBeSeKoJu94,
-author = {F. Alexandre and D. Zerguine and P. Launay and J. L. Benchimol and
-M. Berz and B. Sermage and D. Komatitsch and M. Juhel},
-title = {Quasi-planar {G}allium {A}rsenide heterojunction bipolar transistor
-device entirely grown by {C}hemical {B}eam {E}pitaxy},
-journal = {J. Crystal Growth},
-year = {1994},
-volume = {136},
-pages = {235-240},
-number = {1-4},
-doi = {10.1016/0022-0248(94)90416-2}
+ author = {F. Alexandre and D. Zerguine and P. Launay and J. L. Benchimol and
+ M. Berz and B. Sermage and D. Komatitsch and M. Juhel},
+ title = {Quasi-planar {G}allium {A}rsenide heterojunction bipolar transistor
+ device entirely grown by {C}hemical {B}eam {E}pitaxy},
+ journal = {J. Crystal Growth},
+ year = {1994},
+ volume = {136},
+ pages = {235-240},
+ number = {1-4},
+ doi = {10.1016/0022-0248(94)90416-2}
}
@ARTICLE{AlKeBo74,
-author = {R. Alford and K. Kelly and D. Boore},
-title = {Accuracy of finite difference modeling of the acoustic wave equation},
-journal = geophysics,
-year = {1974},
-volume = {39},
-pages = {834-842}
+ author = {R. Alford and K. Kelly and D. Boore},
+ title = {Accuracy of finite difference modeling of the acoustic wave equation},
+ journal = geophysics,
+ year = {1974},
+ volume = {39},
+ pages = {834-842}
}
@ARTICLE{AlsLot04,
-author = {V. I. Alshits and J. Lothe},
-title = {Some basic properties of bulk elastic waves in anisotropic media},
-journal = {Wave Motion},
-year = {2004},
-volume = {40},
-pages = {297-313}
+ author = {V. I. Alshits and J. Lothe},
+ title = {Some basic properties of bulk elastic waves in anisotropic media},
+ journal = {Wave Motion},
+ year = {2004},
+ volume = {40},
+ pages = {297-313}
}
@ARTICLE{AlsLot81,
-author = {V. I. Alshits and J. Lothe},
-title = {Comments on the relation between surface wave theory and the theory
-of reflection},
-journal = {Wave Motion},
-year = {1981},
-volume = {3},
-pages = {297-310}
+ author = {V. I. Alshits and J. Lothe},
+ title = {Comments on the relation between surface wave theory and the theory
+ of reflection},
+ journal = {Wave Motion},
+ year = {1981},
+ volume = {3},
+ pages = {297-310}
}
@ARTICLE{AlsLot79a,
-author = {V. I. Alshits and J. Lothe},
-title = {Elastic waves in triclinic crystals: ({I}) {G}eneral theory and the
-degeneracy problem},
-journal = {Soviet Physics Crystallography},
-year = {1979},
-volume = {24},
-pages = {387-392}
+ author = {V. I. Alshits and J. Lothe},
+ title = {Elastic waves in triclinic crystals: ({I}) {G}eneral theory and the
+ degeneracy problem},
+ journal = {Soviet Physics Crystallography},
+ year = {1979},
+ volume = {24},
+ pages = {387-392}
}
@ARTICLE{AlsLot79b,
-author = {V. I. Alshits and J. Lothe},
-title = {Elastic waves in triclinic crystals: ({II}) {T}opology of polarization
-fields and some general theorems},
-journal = {Soviet Physics Crystallography},
-year = {1979},
-volume = {24},
-pages = {393-398}
+ author = {V. I. Alshits and J. Lothe},
+ title = {Elastic waves in triclinic crystals: ({II}) {T}opology of polarization
+ fields and some general theorems},
+ journal = {Soviet Physics Crystallography},
+ year = {1979},
+ volume = {24},
+ pages = {393-398}
}
@ARTICLE{AlsLot79c,
-author = {V. I. Alshits and J. Lothe},
-title = {Elastic waves in triclinic crystals: ({III}) {T}he problem of existence
-and some general properties of exceptional surface waves},
-journal = {Soviet Physics Crystallography},
-year = {1979},
-volume = {24},
-pages = {644-648}
+ author = {V. I. Alshits and J. Lothe},
+ title = {Elastic waves in triclinic crystals: ({III}) {T}he problem of existence
+ and some general properties of exceptional surface waves},
+ journal = {Soviet Physics Crystallography},
+ year = {1979},
+ volume = {24},
+ pages = {644-648}
}
@ARTICLE{AlsLot78,
-author = {V. I. Alshits and J. Lothe},
-title = {Surface waves in hexagonal crystals},
-journal = {Soviet Physics Crystallography},
-year = {1978},
-volume = {23},
-pages = {509-515}
+ author = {V. I. Alshits and J. Lothe},
+ title = {Surface waves in hexagonal crystals},
+ journal = {Soviet Physics Crystallography},
+ year = {1978},
+ volume = {23},
+ pages = {509-515}
}
@ARTICLE{AlsLyu83,
-author = {V. I. Alshits and V. N. Lyubimov},
-title = {Leaky elastic waves in hexagonal crystals},
-journal = {Soviet Physics of Crystallograpy},
-year = {1983},
-volume = {28},
-pages = {130-135},
-number = {2}
+ author = {V. I. Alshits and V. N. Lyubimov},
+ title = {Leaky elastic waves in hexagonal crystals},
+ journal = {Soviet Physics of Crystallograpy},
+ year = {1983},
+ volume = {28},
+ pages = {130-135},
+ number = {2}
}
@ARTICLE{AlsLyuNauPerShu85,
-author = {V. I. Alshits and V. N. Lyubimov and N. F. Naumenko and N. V. Perelomova
-and A. L. Shuvalov},
-title = {Exceptional elastic body waves in crystals of various symmetries},
-journal = {Soviet Physics Crystallography},
-year = {1985},
-volume = {30},
-pages = {123-126}
+ author = {V. I. Alshits and V. N. Lyubimov and N. F. Naumenko and N. V. Perelomova
+ and A. L. Shuvalov},
+ title = {Exceptional elastic body waves in crystals of various symmetries},
+ journal = {Soviet Physics Crystallography},
+ year = {1985},
+ volume = {30},
+ pages = {123-126}
}
@ARTICLE{AlKa68,
-author = {Z. Alterman and F. C. Karal},
-title = {Propagation of elastic waves in layered media by finite difference
-methods},
-journal = bssa,
-year = {1968},
-volume = {58},
-pages = {367-398}
+ author = {Z. Alterman and F. C. Karal},
+ title = {Propagation of elastic waves in layered media by finite difference
+ methods},
+ journal = bssa,
+ year = {1968},
+ volume = {58},
+ pages = {367-398}
}
@ARTICLE{amaradjelloulifarhat2006,
-author = {M. Amara and R. Djellouli and C. Farhat},
-title = {Convergence analysis of a discontinuous {G}alerkin method with plane
-waves and {L}agrange multipliers for the solution of {H}elmholtz
-problems},
-journal = {SIAM Journal on Numerical Analysis},
-year = {2006},
-note = {Submitted}
+ author = {M. Amara and R. Djellouli and C. Farhat},
+ title = {Convergence analysis of a discontinuous {G}alerkin method with plane
+ waves and {L}agrange multipliers for the solution of {H}elmholtz
+ problems},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {2006},
+ note = {Submitted}
}
@ARTICLE{AmWi94,
-author = {K. Amaratunga and J. R. Williams},
-title = {Wavelet-{G}alerkin solutions for one-dimensional partial differential
-equations},
-journal = ijnme,
-year = {1994},
-volume = {37},
-pages = {999998-999999}
+ author = {K. Amaratunga and J. R. Williams},
+ title = {Wavelet-{G}alerkin solutions for one-dimensional partial differential
+ equations},
+ journal = ijnme,
+ year = {1994},
+ volume = {37},
+ pages = {999998-999999}
}
@ARTICLE{AmDuKoEx01,
-author = {P. R. Amestoy and I. S. Duff and J. Koster and J.-Y. L'Excellent},
-title = {A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic
-Scheduling},
-journal = {SIAM Journal on Matrix Analysis and Applications},
-year = {2001},
-volume = {23},
-pages = {15-41},
-number = {1}
+ author = {P. R. Amestoy and I. S. Duff and J. Koster and J.-Y. L'Excellent},
+ title = {A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic
+ Scheduling},
+ journal = {SIAM Journal on Matrix Analysis and Applications},
+ year = {2001},
+ volume = {23},
+ pages = {15-41},
+ number = {1}
}
@ARTICLE{AmmonJiThio2005,
-author = {C. J. Ammon and C. Ji and H. K. Thio and D. Robinson and S. D. Ni
-and V. Hjorleifsdottir and H. Kanamori and T. Lay and S. Das and
-D. Helmberger and G. Ichinose and J. Polet and D. Wald},
-title = {Rupture process of the 2004 {S}umatra-{A}ndaman earthquake},
-journal = {Science},
-year = {2005},
-volume = {3},
-pages = {1133-1139},
-number = {5725}
+ author = {C. J. Ammon and C. Ji and H. K. Thio and D. Robinson and S. D. Ni
+ and V. Hjorleifsdottir and H. Kanamori and T. Lay and S. Das and
+ D. Helmberger and G. Ichinose and J. Polet and D. Wald},
+ title = {Rupture process of the 2004 {S}umatra-{A}ndaman earthquake},
+ journal = {Science},
+ year = {2005},
+ volume = {3},
+ pages = {1133-1139},
+ number = {5725}
}
@PHDTHESIS{Amp02,
-author = {Jean-Paul Ampuero},
-title = {\'Etude physique et num\'erique de la nucl\'eation des s\'eismes
-({A} physical and numerical study of earthquake nucleation)},
-school = {Institut de Physique du Globe},
-year = {2002},
-address = {Paris, France}
+ author = {Jean-Paul Ampuero},
+ title = {\'Etude physique et num\'erique de la nucl\'eation des s\'eismes
+ ({A} physical and numerical study of earthquake nucleation)},
+ school = {Institut de Physique du Globe},
+ year = {2002},
+ address = {Paris, France}
}
@ARTICLE{anderson1987,
-author = {D. L. Anderson},
-title = {A seismic equation of state, {P}art~{II}: {S}hear properties and
-thermodynamics of the lower mantle},
-journal = pepi,
-year = {1987},
-volume = {45},
-pages = {307-323}
+ author = {D. L. Anderson},
+ title = {A seismic equation of state, {P}art~{II}: {S}hear properties and
+ thermodynamics of the lower mantle},
+ journal = pepi,
+ year = {1987},
+ volume = {45},
+ pages = {307-323}
}
@ARTICLE{anderson_lorenz_travesset_2008,
-author = {Joshua A. Anderson and Chris D. Lorenz and Alex Travesset},
-title = {General purpose molecular dynamics simulations fully implemented
-on graphics processing units},
-journal = jcp,
-year = {2008},
-volume = {227},
-pages = {5342--5359},
-number = {10},
-month = may,
-doi = {10.1016/j.jcp.2008.01.047}
+ author = {Joshua A. Anderson and Chris D. Lorenz and Alex Travesset},
+ title = {General purpose molecular dynamics simulations fully implemented
+ on graphics processing units},
+ journal = jcp,
+ year = {2008},
+ volume = {227},
+ pages = {5342--5359},
+ number = {10},
+ month = may,
+ doi = {10.1016/j.jcp.2008.01.047}
}
@ARTICLE{AnLeZeDa96,
-author = {J. G. Anderson and Y. Lee and Y. Zeng and S. M. Day},
-title = {Control of strong motion by the upper 30~meters},
-journal = bssa,
-year = {1996},
-volume = {86},
-pages = {1749-1759}
+ author = {J. G. Anderson and Y. Lee and Y. Zeng and S. M. Day},
+ title = {Control of strong motion by the upper 30~meters},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1749-1759}
}
@ARTICLE{AnBa204,
-author = {X. Antoine and H. Barucq},
-title = {Approximation by generalized impedance boundary conditions of a transmission
-problem in acoustic scattering},
-journal = {Math. Model. Numer. Anal.},
-year = {2005},
-volume = {39},
-pages = {1041-1059},
-number = {5}
+ author = {X. Antoine and H. Barucq},
+ title = {Approximation by generalized impedance boundary conditions of a transmission
+ problem in acoustic scattering},
+ journal = {Math. Model. Numer. Anal.},
+ year = {2005},
+ volume = {39},
+ pages = {1041-1059},
+ number = {5}
}
@INPROCEEDINGS{AnBa104,
-author = {X. Antoine and H. Barucq},
-title = {On the construction of approximate boundary conditions for solving
-the interior problem of the acoustic scattering transmission problem},
-booktitle = {Methods in Science and Engineering},
-year = {2004},
-volume = {40},
-series = {Lecture Notes in computational science and engineering},
-pages = {133-140}
+ author = {X. Antoine and H. Barucq},
+ title = {On the construction of approximate boundary conditions for solving
+ the interior problem of the acoustic scattering transmission problem},
+ booktitle = {Methods in Science and Engineering},
+ year = {2004},
+ volume = {40},
+ series = {Lecture Notes in computational science and engineering},
+ pages = {133-140}
}
@ARTICLE{AnBa01,
-author = {X. Antoine and H. Barucq},
-title = {Microlocal diagonalization of strictly hyperbolic pseudodifferential
-systems and application to the design of radiation conditions in
-electromagnetism},
-journal = {SIAM J. Appl. Math.},
-year = {2001},
-volume = {6},
-pages = {1877-1905}
+ author = {X. Antoine and H. Barucq},
+ title = {Microlocal diagonalization of strictly hyperbolic pseudodifferential
+ systems and application to the design of radiation conditions in
+ electromagnetism},
+ journal = {SIAM J. Appl. Math.},
+ year = {2001},
+ volume = {6},
+ pages = {1877-1905}
}
@ARTICLE{AnBaBe99,
-author = {X. Antoine and H. Barucq and A. Bendali},
-title = {Bayliss-{T}urkel-like radiation conditions on surfaces of arbitrary
-shape},
-journal = {J. Math. Anal. Appl.},
-year = {1999},
-volume = {229},
-pages = {184-211}
+ author = {X. Antoine and H. Barucq and A. Bendali},
+ title = {Bayliss-{T}urkel-like radiation conditions on surfaces of arbitrary
+ shape},
+ journal = {J. Math. Anal. Appl.},
+ year = {1999},
+ volume = {229},
+ pages = {184-211}
}
@ARTICLE{AnBaVe01,
-author = {X. Antoine and H. Barucq and L. Vernhet},
-title = {High-frequency asymptotic analysis of a dissipative transmission
-problem resulting in generalized impedance boundary conditions},
-journal = {Asymptotic Analysis},
-year = {2001},
-volume = {3},
-pages = {257-284},
-number = {4}
+ author = {X. Antoine and H. Barucq and L. Vernhet},
+ title = {High-frequency asymptotic analysis of a dissipative transmission
+ problem resulting in generalized impedance boundary conditions},
+ journal = {Asymptotic Analysis},
+ year = {2001},
+ volume = {3},
+ pages = {257-284},
+ number = {4}
}
@ARTICLE{AnBeDa04,
-author = {X. Antoine and A. Bendali and M. Darbas},
-title = {Analytic Preconditioners for the boundary integral solution of the
-scattering of acoustic waves by open surfaces},
-journal = jca,
-year = {2005},
-volume = {13},
-pages = {477-498},
-number = {3}
+ author = {X. Antoine and A. Bendali and M. Darbas},
+ title = {Analytic Preconditioners for the boundary integral solution of the
+ scattering of acoustic waves by open surfaces},
+ journal = jca,
+ year = {2005},
+ volume = {13},
+ pages = {477-498},
+ number = {3}
}
@ARTICLE{AnLaDrRo96,
-author = {M. Antolik and S. Larsen and D. Dreger and B. Romanowicz},
-title = {Modeling broadband waveforms in central {C}alifornia using finite
-differences},
-journal = {Seis. Res. Lett.},
-year = {1996},
-volume = {67},
-pages = {30}
+ author = {M. Antolik and S. Larsen and D. Dreger and B. Romanowicz},
+ title = {Modeling broadband waveforms in central {C}alifornia using finite
+ differences},
+ journal = {Seis. Res. Lett.},
+ year = {1996},
+ volume = {67},
+ pages = {30}
}
@ARTICLE{antonionietal2002,
-author = {A. Antonioli and M. Cocco and S. Das and C. Henry},
-title = {Dynamic stress triggering during the great 25~{M}arch 1998 {A}ntarctic
-{P}late earthquake},
-journal = bssa,
-year = {2002},
-volume = {92},
-pages = {896-903}
+ author = {A. Antonioli and M. Cocco and S. Das and C. Henry},
+ title = {Dynamic stress triggering during the great 25~{M}arch 1998 {A}ntarctic
+ {P}late earthquake},
+ journal = bssa,
+ year = {2002},
+ volume = {92},
+ pages = {896-903}
}
@ARTICLE{AoDo06,
-author = {H. Aochi and J. Douglas},
-title = {Testing the validity of simulated strong ground motion from the dynamic
-rupture of a finite fault by using empirical equations},
-journal = {Bull. Earthq. Eng.},
-year = {2006},
-volume = {4},
-pages = {211-229},
-number = {3},
-doi = {10.1007/s10518-006-0001-3}
+ author = {H. Aochi and J. Douglas},
+ title = {Testing the validity of simulated strong ground motion from the dynamic
+ rupture of a finite fault by using empirical equations},
+ journal = {Bull. Earthq. Eng.},
+ year = {2006},
+ volume = {4},
+ pages = {211-229},
+ number = {3},
+ doi = {10.1007/s10518-006-0001-3}
}
@ARTICLE{ApKr06,
-author = {Daniel Appel\"o and Gunilla Kreiss},
-title = {A new absorbing layer for elastic waves},
-journal = jcp,
-year = {2006},
-volume = {215},
-pages = {642-660},
-number = {2},
-doi = {10.1016/j.jcp.2005.11.006}
+ author = {Daniel Appel\"o and Gunilla Kreiss},
+ title = {A new absorbing layer for elastic waves},
+ journal = jcp,
+ year = {2006},
+ volume = {215},
+ pages = {642-660},
+ number = {2},
+ doi = {10.1016/j.jcp.2005.11.006}
}
@PHDTHESIS{da,
-author = {D. Apprato},
-title = {Approximation de surfaces param\'etr\'ees par \'el\'ements finis},
-school = {Universit\'e de Pau et des Pays de l'Adour},
-year = {1987},
-address = {Pau, France},
-note = {Th\`ese d'Etat, 142 p.}
+ author = {D. Apprato},
+ title = {Approximation de surfaces param\'etr\'ees par \'el\'ements finis},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {1987},
+ address = {Pau, France},
+ note = {Th\`ese d'Etat, 142 p.}
}
@ARTICLE{GoKo02,
-author = {D. Apprato and C. Gout and D. Komatitsch},
-title = {A new method for {{$C^k$-}}surface approximation from a set of curves,
-with application to ship track data in the {M}arianas trench},
-journal = {Math. Geol.},
-year = {2002},
-volume = {34},
-pages = {831-843},
-number = {7},
-doi = {10.1023/A:1020976611029}
+ author = {D. Apprato and C. Gout and D. Komatitsch},
+ title = {A new method for {{$C^k$-}}surface approximation from a set of curves,
+ with application to ship track data in the {M}arianas trench},
+ journal = {Math. Geol.},
+ year = {2002},
+ volume = {34},
+ pages = {831-843},
+ number = {7},
+ doi = {10.1023/A:1020976611029}
}
@ARTICLE{ApLu83,
-author = {R. J. Apsel and J. E. Luco},
-title = {On the {G}reen's functions for a layered half-space},
-journal = bssa,
-year = {1983},
-volume = {73},
-pages = {931-951}
+ author = {R. J. Apsel and J. E. Luco},
+ title = {On the {G}reen's functions for a layered half-space},
+ journal = bssa,
+ year = {1983},
+ volume = {73},
+ pages = {931-951}
}
@INCOLLECTION{ra1,
-author = {R. Arcang\'eli},
-title = {Some Applications of Discrete {$D^m$}-splines},
-booktitle = {Mathematical Methods in Computer Aided Geometric Design},
-publisher = {Academic Press, New York, USA},
-year = {1989},
-editor = {T. Lyche and L. L. Schumaker},
-pages = {35-44}
+ author = {R. Arcang\'eli},
+ title = {Some Applications of Discrete {$D^m$}-splines},
+ booktitle = {Mathematical Methods in Computer Aided Geometric Design},
+ publisher = {Academic Press, New York, USA},
+ year = {1989},
+ editor = {T. Lyche and L. L. Schumaker},
+ pages = {35-44}
}
@TECHREPORT{ra,
-author = {R. Arcang\'eli},
-title = {{$D^m$}-splines sur un domaine born\'e de {$R$}},
-institution = {UA 1204 CNRS, Universit\'e de Pau et des Pays de l'Adour},
-year = {1986},
-number = {1986/2},
-address = {Pau, France},
-note = {47 p.}
+ author = {R. Arcang\'eli},
+ title = {{$D^m$}-splines sur un domaine born\'e de {$R$}},
+ institution = {UA 1204 CNRS, Universit\'e de Pau et des Pays de l'Adour},
+ year = {1986},
+ number = {1986/2},
+ address = {Pau, France},
+ note = {47 p.}
}
@ARTICLE{Arn82,
-author = {Douglas N. Arnold},
-title = {An Interior Penalty Finite Element Method with Discontinuous Elements},
-journal = {SIAM Journal on Numerical Analysis},
-year = {1982},
-volume = {19},
-pages = {742-760},
-number = {4},
-doi = {10.1137/0719052}
+ author = {Douglas N. Arnold},
+ title = {An Interior Penalty Finite Element Method with Discontinuous Elements},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1982},
+ volume = {19},
+ pages = {742-760},
+ number = {4},
+ doi = {10.1137/0719052}
}
@BOOK{AtPr90,
-title = {\'El\'ements d'analyse num\'erique},
-publisher = {C\'epadues \'Editions},
-year = {1990},
-author = {Marc Atteia and Michel Pradel},
-address = {Toulouse}
+ title = {\'El\'ements d'analyse num\'erique},
+ publisher = {C\'epadues \'Editions},
+ year = {1990},
+ author = {Marc Atteia and Michel Pradel},
+ address = {Toulouse}
}
@INCOLLECTION{AuChMoMo85,
-author = {D. Aubry and D. Chouvet and H. Modaressi and P. Mouroux},
-title = {Local amplification of a seismic incident field through an elastoplastic
-sedimentary valley},
-booktitle = {Numerical methods in geomechanics},
-publisher = {Balkema},
-year = {1985},
-editor = {T. Kawamoto and Y. Ichikawa},
-pages = {421-428}
+ author = {D. Aubry and D. Chouvet and H. Modaressi and P. Mouroux},
+ title = {Local amplification of a seismic incident field through an elastoplastic
+ sedimentary valley},
+ booktitle = {Numerical methods in geomechanics},
+ publisher = {Balkema},
+ year = {1985},
+ editor = {T. Kawamoto and Y. Ichikawa},
+ pages = {421-428}
}
+ at ARTICLE{AuHoVaCe11,
+ author = {Aubry, R. and Houzeaux, G. and V\'azquez, M. and Cela, J. M.},
+ title = {Some useful strategies for unstructured edge-based solvers on shared
+ memory machines},
+ journal = ijnme,
+ year = {2011},
+ volume = {85},
+ pages = {537-561},
+ number = {5},
+ doi = {10.1002/nme.2973}
+}
+
@INPROCEEDINGS{AuThNaWa09Europar,
-author = {C{\'e}dric Augonnet and Samuel Thibault and Raymond Namyst and Pierre-Andr{\'e}
-Wacrenier},
-title = {{StarPU}: {A} Unified Platform for Task Scheduling on Heterogeneous
-Multicore Architectures},
-booktitle = {Proceedings of the 15th EuroPar Conference},
-year = {2009},
-volume = {5704},
-series = {Lecture Notes in Computer Science},
-pages = {863-874},
-address = {Delft, The Netherlands},
-month = aug,
-publisher = {Springer},
-bdsk-url-2 = {http://dx.doi.org/10.1007/978-3-642-03869-3%5C_80},
-doi = {10.1007/978-3-642-03869-3\_80},
-url = {http://hal.inria.fr/inria-00384363}
+ author = {C{\'e}dric Augonnet and Samuel Thibault and Raymond Namyst and Pierre-Andr{\'e}
+ Wacrenier},
+ title = {{StarPU}: {A} Unified Platform for Task Scheduling on Heterogeneous
+ Multicore Architectures},
+ booktitle = {Proceedings of the 15th EuroPar Conference},
+ year = {2009},
+ volume = {5704},
+ series = {Lecture Notes in Computer Science},
+ pages = {863-874},
+ address = {Delft, The Netherlands},
+ month = aug,
+ publisher = {Springer},
+ bdsk-url-2 = {http://dx.doi.org/10.1007/978-3-642-03869-3%5C_80},
+ doi = {10.1007/978-3-642-03869-3\_80},
+ url = {http://hal.inria.fr/inria-00384363}
}
@BOOK{Aul90,
-title = {Acoustic fields and waves in solids},
-publisher = {Krieger Publishing},
-year = {1990},
-author = {B. A. Auld},
-volume = {1},
-edition = {2nd}
+ title = {Acoustic fields and waves in solids},
+ publisher = {Krieger Publishing},
+ year = {1990},
+ author = {B. A. Auld},
+ volume = {1},
+ edition = {2nd}
}
@ARTICLE{Aus93,
-author = {P. Auscher},
-title = {Ondelettes \`a support compact et conditions aux limites},
-journal = {J. Funct. Anal.},
-year = {1993},
-volume = {111},
-pages = {9999998-9999999}
+ author = {P. Auscher},
+ title = {Ondelettes \`a support compact et conditions aux limites},
+ journal = {J. Funct. Anal.},
+ year = {1993},
+ volume = {111},
+ pages = {9999998-9999999}
}
@ARTICLE{AuzaZiol,
-author = {F. Auzanneau and R. W. Ziolkowski},
-title = {{{\'E}}tude th\'eorique de mat\'eriaux bianisotropes synth\'etiques
-contr\^olables},
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+ author = {F. Auzanneau and R. W. Ziolkowski},
+ title = {{{\'E}}tude th\'eorique de mat\'eriaux bianisotropes synth\'etiques
+ contr\^olables},
+ journal = {J. Phys. III},
+ year = {1997},
+ volume = {7},
+ pages = {2405-2418}
}
@TECHREPORT{AzDaMa94,
-author = {Mejdi Azaiez and Monique Dauge and Yvon Maday},
-title = {M\'ethodes spectrales et des \'el\'ements spectraux},
-institution = {Institut de Recherche Math\'ematique de Rennes},
-year = {1994},
-address = {Universit\'e de Rennes, France}
+ author = {Mejdi Azaiez and Monique Dauge and Yvon Maday},
+ title = {M\'ethodes spectrales et des \'el\'ements spectraux},
+ institution = {Institut de Recherche Math\'ematique de Rennes},
+ year = {1994},
+ address = {Universit\'e de Rennes, France}
}
@ARTICLE{BaBiPr98,
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-year = {1998},
-volume = {34},
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-number = {5}
+ author = {I. B\'ardi and O. B\'{\i}r\'o and K. Preis},
+ title = {{P}erfectly {M}atched {L}ayers in static fields},
+ journal = {IEEE transactions on Magnetics},
+ year = {1998},
+ volume = {34},
+ pages = {2433-2436},
+ number = {5}
}
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+ author = {E. B\'ecache and S. Fauqueux and P. Joly},
+ title = {Stability of {P}erfectly {M}atched {L}ayers, group velocities and
+ anisotropic waves},
+ journal = jcp,
+ year = {2003},
+ volume = {188},
+ pages = {399-433},
+ number = {2}
}
@ARTICLE{BeJo02,
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-equations},
-journal = {Mathematical Modelling and Numerical Analysis},
-year = {2002},
-volume = {36},
-pages = {87-120},
-number = {1}
+ author = {E. B\'ecache and P. Joly},
+ title = {On the analysis of {B}\'erenger's perfectly matched layers for {M}axwell's
+ equations},
+ journal = {Mathematical Modelling and Numerical Analysis},
+ year = {2002},
+ volume = {36},
+ pages = {87-120},
+ number = {1}
}
@ARTICLE{BeJoTs2001,
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-{L}ayers for {2-D} Elastic Wave Propagation},
-journal = jca,
-year = {2001},
-volume = {9},
-pages = {1175-1203},
-number = {3}
+ author = {E. B\'ecache and P. Joly and C. Tsogka},
+ title = {Fictitious Domains, Mixed Finite Elements and {P}erfectly {M}atched
+ {L}ayers for {2-D} Elastic Wave Propagation},
+ journal = jca,
+ year = {2001},
+ volume = {9},
+ pages = {1175-1203},
+ number = {3}
}
@ARTICLE{BePeGe04,
-author = {E. B\'ecache and P. G. Petropoulos and S. G. Gedney},
-title = {On the Long-Time Behavior of Unsplit Perfectly Matched Layers},
-journal = {IEEE Transactions on Antennas and Propagation},
-year = {2004},
-volume = {52},
-pages = {1335-1342},
-number = {5},
-doi = {10.1109/TAP.2004.827253}
+ author = {E. B\'ecache and P. G. Petropoulos and S. G. Gedney},
+ title = {On the Long-Time Behavior of Unsplit Perfectly Matched Layers},
+ journal = {IEEE Transactions on Antennas and Propagation},
+ year = {2004},
+ volume = {52},
+ pages = {1335-1342},
+ number = {5},
+ doi = {10.1109/TAP.2004.827253}
}
@ARTICLE{Ber02a,
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-in waveguides},
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-year = {2002},
-volume = {12},
-pages = {218-220},
-number = {6},
-doi = {10.1109/LMWC.2002.1010000}
+ author = {J. P. B\'erenger},
+ title = {Application of the {CFS} {PML} to the absorption of evanescent waves
+ in waveguides},
+ journal = {IEEE Microwave and Wireless Components Letters},
+ year = {2002},
+ volume = {12},
+ pages = {218-220},
+ number = {6},
+ doi = {10.1109/LMWC.2002.1010000}
}
@ARTICLE{Ber02b,
-author = {J. P. B\'erenger},
-title = {Numerical reflection from {FDTD-PML}s: A comparison of the split
-{PML} with the unsplit and {CFS PML}s},
-journal = {IEEE Transactions on Antennas and Propagation},
-year = {2002},
-volume = {50},
-pages = {258-265},
-number = {3},
-doi = {10.1109/8.999615}
+ author = {J. P. B\'erenger},
+ title = {Numerical reflection from {FDTD-PML}s: A comparison of the split
+ {PML} with the unsplit and {CFS PML}s},
+ journal = {IEEE Transactions on Antennas and Propagation},
+ year = {2002},
+ volume = {50},
+ pages = {258-265},
+ number = {3},
+ doi = {10.1109/8.999615}
}
@ARTICLE{Ber96,
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-of electromagnetic waves},
-journal = jcp,
-year = {1996},
-volume = {127},
-pages = {363-379}
+ author = {J. P. B\'erenger},
+ title = {Three-dimensional {P}erfectly {M}atched {L}ayer for the absorption
+ of electromagnetic waves},
+ journal = jcp,
+ year = {1996},
+ volume = {127},
+ pages = {363-379}
}
@ARTICLE{Ber94,
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-waves},
-journal = jcp,
-year = {1994},
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-pages = {185-200}
+ author = {J. P. B\'erenger},
+ title = {A {P}erfectly {M}atched {L}ayer for the absorption of electromagnetic
+ waves},
+ journal = jcp,
+ year = {1994},
+ volume = {114},
+ pages = {185-200}
}
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+ author = {I. Babu\u{s}ka and M. R. Dorr},
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+ element method},
+ journal = {Numer. Math.},
+ year = {1981},
+ volume = {37},
+ pages = {257-277}
}
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+ author = {I. Babu\u{s}ka and B. A. Szab\'o and I. N. Katz},
+ title = {The $p$ version of the finite element method},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1981},
+ volume = {18},
+ pages = {512-545}
}
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+ author = {I. Babuska and F. Ihlenburg and E. T. Paik and S. A. Sauter},
+ title = {A generalized finite element method for solving the {H}elmholtz equation
+ in two dimensions with minimal pollution},
+ journal = cmame,
+ year = {1995},
+ volume = {128},
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+ number = {3-4}
}
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+ author = {G. A. Backer},
+ title = {Error estimates for the finite element method for second order hyperbolic
+ equations},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1976},
+ volume = {13},
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}
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+ year = {1962},
+ volume = {67},
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}
@INPROCEEDINGS{BaRoLiHiSiTaPaGo08,
-author = {Balevic, A. and Rockstroh, L. and Li, W. and Hillebrand, J. and Simon,
-S. and Tausendfreund, A. and Patzelt, S. and Goch, G.},
-title = {Acceleration of a finite-difference method with general purpose {GPU}s:
-{L}esson learned},
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-and Information Technology},
-year = {2008},
-pages = {291-294},
-address = {Sydney, Australia},
-publisher = {IEEE Computer Society, Washington, DC, USA},
-doi = {10.1109/CIT.2008.4594689}
+ author = {Balevic, A. and Rockstroh, L. and Li, W. and Hillebrand, J. and Simon,
+ S. and Tausendfreund, A. and Patzelt, S. and Goch, G.},
+ title = {Acceleration of a finite-difference method with general purpose {GPU}s:
+ {L}esson learned},
+ booktitle = {Proceedings of the 8th IEEE International Conference on Computer
+ and Information Technology},
+ year = {2008},
+ pages = {291-294},
+ address = {Sydney, Australia},
+ publisher = {IEEE Computer Society, Washington, DC, USA},
+ doi = {10.1109/CIT.2008.4594689}
}
@INPROCEEDINGS{BaRoTaPaGoSi08,
-author = {A. Balevic and L. Rockstroh and A. Tausendfreund and S. Patzelt and
-G. Goch and S. Simon},
-title = {Accelerating Simulations of Light Scattering Based on a Finite-Difference
-Time-Domain Method with General Purpose {GPU}s},
-booktitle = {Proceedings of the 11th IEEE International Conference on Computational
-Science and Engineering},
-year = {2008},
-pages = {327-334},
-address = {Sao Paulo, Brazil},
-publisher = {IEEE Computer Society, Washington, DC, USA}
+ author = {A. Balevic and L. Rockstroh and A. Tausendfreund and S. Patzelt and
+ G. Goch and S. Simon},
+ title = {Accelerating Simulations of Light Scattering Based on a Finite-Difference
+ Time-Domain Method with General Purpose {GPU}s},
+ booktitle = {Proceedings of the 11th IEEE International Conference on Computational
+ Science and Engineering},
+ year = {2008},
+ pages = {327-334},
+ address = {Sao Paulo, Brazil},
+ publisher = {IEEE Computer Society, Washington, DC, USA}
}
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-media},
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-year = {1988},
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+ author = {A. Bamberger and B. Engquist and L. Halpern and P. Joly},
+ title = {Higher order paraxial wave equation approximations in heterogeneous
+ media},
+ journal = {SIAM J. Appl. Math.},
+ year = {1988},
+ volume = {48},
+ pages = {129-154}
}
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-a solution for the corner problem},
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-year = {1990},
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+ author = {A. Bamberger and P. Joly and J. E. Roberts},
+ title = {Second order absorbing boundary conditions for the wave equation:
+ a solution for the corner problem},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1990},
+ volume = {27},
+ pages = {323-352}
}
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-media on parallel computers},
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+ author = {H. Bao and J. Bielak and O. Ghattas and L. F. Kallivokas and D. R.
+ O'Hallaron and J. R. Shewchuk and J. Xu},
+ title = {Large-scale simulation of elastic wave propagation in heterogeneous
+ media on parallel computers},
+ journal = cmame,
+ year = {1998},
+ volume = {152},
+ pages = {85-102}
}
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-year = {1982},
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+ author = {P. Y. Bard},
+ title = {Diffracted waves and displacement field over two dimensional topographies},
+ journal = gjras,
+ year = {1982},
+ volume = {71},
+ pages = {731-760}
}
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-year = {1985},
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+ author = {Pierre-Yves Bard and Michel Bouchon},
+ title = {The two-dimensional resonance of sediment-filled valleys},
+ journal = bssa,
+ year = {1985},
+ volume = {75},
+ pages = {519-541}
}
@ARTICLE{BaBo80a,
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-of incident {SH} waves},
-journal = bssa,
-year = {1980},
-volume = {70},
-pages = {1263-1286}
+ author = {Pierre-Yves Bard and Michel Bouchon},
+ title = {The seismic response of sediment-filled valleys, {P}art 1: The case
+ of incident {SH} waves},
+ journal = bssa,
+ year = {1980},
+ volume = {70},
+ pages = {1263-1286}
}
@ARTICLE{BaBo80b,
-author = {Pierre-Yves Bard and Michel Bouchon},
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-of incident {P} and {SV} waves},
-journal = bssa,
-year = {1980},
-volume = {70},
-pages = {1921-1941}
+ author = {Pierre-Yves Bard and Michel Bouchon},
+ title = {The seismic response of sediment-filled valleys, {P}art 2: The case
+ of incident {P} and {SV} waves},
+ journal = bssa,
+ year = {1980},
+ volume = {70},
+ pages = {1921-1941}
}
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+ author = {C. Bardos and G. Lebeau and J. Rauch},
+ title = {Gevrey regularity and distribution of the scattering frequencies},
+ journal = {Invent. Math.},
+ year = {1987},
+ volume = {90},
+ pages = {77-114}
}
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+ author = {D. M. Barnett},
+ title = {Bulk, surface, and interfacial waves in anisotropic linear elastic
+ solids},
+ journal = {International Journal of Solids and Structures},
+ year = {2000},
+ volume = {37},
+ pages = {45-54}
}
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-free surface waves},
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-pages = {98-103}
+ author = {D. M. Barnett},
+ title = {On the non-existence of subsonic boundary-polarized two-component
+ free surface waves},
+ journal = {Physica Scripta},
+ year = {1992},
+ volume = {T44},
+ pages = {98-103}
}
@INCOLLECTION{BarCha91,
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-editor = {J. J. Wu and T. C. T. Ting and D. M. Barnett},
-pages = {199-214},
-address = {Philadelphia, USA}
+ author = {D. M. Barnett and P. Chadwick},
+ title = {The existence of one-component surface waves and exceptional transonic
+ states of types 2, 4 and {E}1 in anisotropic elastic media},
+ booktitle = {Modern Theory of Anisotropic Elasticity and Applications},
+ publisher = {SIAM},
+ year = {1991},
+ editor = {J. J. Wu and T. C. T. Ting and D. M. Barnett},
+ pages = {199-214},
+ address = {Philadelphia, USA}
}
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-symmetry. {I}. {A}ddendum},
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-year = {1991},
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-pages = {699-710}
+ author = {D. M. Barnett and P. Chadwick and J. Lothe},
+ title = {The behaviour of elastic surface waves polarized in a plane of material
+ symmetry. {I}. {A}ddendum},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1991},
+ volume = {A433},
+ pages = {699-710}
}
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-year = {1988},
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+ author = {D. M. Barnett and S. D. Gavazza and J. Lothe},
+ title = {Slip waves along the interface between two anisotropic elastic half-spaces
+ in sliding contact},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1988},
+ volume = {A415},
+ pages = {389-419}
}
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-year = {1985},
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+ author = {D. M. Barnett and J. Lothe},
+ title = {Free surface ({R}ayleigh) waves in anisotropic elastic halfspaces:
+ the surface impedance method},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1985},
+ volume = {A402},
+ pages = {135-152}
}
@ARTICLE{BarLot74,
-author = {D. M. Barnett and J. Lothe},
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-solutions in anisotropic elastic crystals},
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-year = {1974},
-volume = {4},
-pages = {671-686}
+ author = {D. M. Barnett and J. Lothe},
+ title = {Consideration of the existence of surface wave ({R}ayleigh wave)
+ solutions in anisotropic elastic crystals},
+ journal = {Journal of Physics F: Metal Physics},
+ year = {1974},
+ volume = {4},
+ pages = {671-686}
}
@ARTICLE{BarLot73,
-author = {D. M. Barnett and J. Lothe},
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-{G}reens functions, and surface waves in anisotropic elastic solids},
-journal = {Physica Norvegica},
-year = {1973},
-volume = {7},
-pages = {13-22}
+ author = {D. M. Barnett and J. Lothe},
+ title = {Synthesis of the {S}extic and the {I}ntegral {F}ormalism for dislocations,
+ {G}reens functions, and surface waves in anisotropic elastic solids},
+ journal = {Physica Norvegica},
+ year = {1973},
+ volume = {7},
+ pages = {13-22}
}
@ARTICLE{BarLotNisAsa73,
-author = {D. M. Barnett and J. Lothe and K. Nishioka and R. J. Asaro},
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-for calculating {R}ayleigh velocities using dislocation theory},
-journal = {Journal of Physics F: Metal Physics},
-year = {1973},
-volume = {3},
-pages = {1083-1096}
+ author = {D. M. Barnett and J. Lothe and K. Nishioka and R. J. Asaro},
+ title = {Elastic surface waves in anisotropic crystals: a simplified method
+ for calculating {R}ayleigh velocities using dislocation theory},
+ journal = {Journal of Physics F: Metal Physics},
+ year = {1973},
+ volume = {3},
+ pages = {1083-1096}
}
@INPROCEEDINGS{BaSaFiRo05,
-author = {Baron, G. S. and Sarris, C. D. and Fiume, E. and Rogers Sr., Edward
-S.},
-title = {Fast and accurate time-domain simulations with commodity graphics
-hardware},
-booktitle = {Proceedings of the 2005 IEEE Antennas and Propagation Society International
-Symposium},
-year = {2005},
-volume = {4A},
-pages = {193-196},
-address = {Seoul, Korea},
-publisher = {IEEE Computer Society, Washington, DC, USA},
-doi = {10.1109/APS.2005.1552619}
+ author = {Baron, G. S. and Sarris, C. D. and Fiume, E. and Rogers Sr., Edward
+ S.},
+ title = {Fast and accurate time-domain simulations with commodity graphics
+ hardware},
+ booktitle = {Proceedings of the 2005 IEEE Antennas and Propagation Society International
+ Symposium},
+ year = {2005},
+ volume = {4A},
+ pages = {193-196},
+ address = {Seoul, Korea},
+ publisher = {IEEE Computer Society, Washington, DC, USA},
+ doi = {10.1109/APS.2005.1552619}
}
@INPROCEEDINGS{Ba03,
-author = {H. Barucq},
-title = {A family of first-order conditions for the long-time stability of
-the {M}axwell system},
-booktitle = {Mathematical and Numerical Aspects of Wave Propagation: Waves 2003},
-year = {2003},
-editor = {Gary Cohen and Erkki Heikkola and Patrick Joly and Pekka Neittaanm\"aki},
-series = {Proceedings of the Sixth International Conference on Mathematical
-and Numerical Aspects of Wave Propagation},
-address = {Jyv\"askyl\"a, Finland},
-publisher = {Springer-Verlag}
+ author = {H. Barucq},
+ title = {A family of first-order conditions for the long-time stability of
+ the {M}axwell system},
+ booktitle = {Mathematical and Numerical Aspects of Wave Propagation: Waves 2003},
+ year = {2003},
+ editor = {Gary Cohen and Erkki Heikkola and Patrick Joly and Pekka Neittaanm\"aki},
+ series = {Proceedings of the Sixth International Conference on Mathematical
+ and Numerical Aspects of Wave Propagation},
+ address = {Jyv\"askyl\"a, Finland},
+ publisher = {Springer-Verlag}
}
@ARTICLE{Bar02,
-author = {H. Barucq},
-title = {A new family of first-order boundary conditions for the {M}axwell
-system: derivation, well-posedness and long-time behavior},
-journal = {J. Math. Pures Appl.},
-year = {2002},
-volume = {82},
-pages = {67-88}
+ author = {H. Barucq},
+ title = {A new family of first-order boundary conditions for the {M}axwell
+ system: derivation, well-posedness and long-time behavior},
+ journal = {J. Math. Pures Appl.},
+ year = {2002},
+ volume = {82},
+ pages = {67-88}
}
@ARTICLE{BaBeDj04,
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+ author = {H. Barucq and C. Bekkey and R. Djellouli},
+ title = {Construction of local boundary conditions for an eigenvalue problem
+ using micro-local analysis. Application to optical waveguide problem},
+ journal = {J. Comp. Phys.},
+ year = {2004},
+ volume = {193},
+ pages = {666-696},
+ number = {2},
+ note = {to appear}
}
@ARTICLE{BaDeHa98,
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-journal = {SIAM Journal on Numerical Analysis},
-year = {1998},
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-pages = {1113-1129}
+ author = {H. Barucq and F. Delaurens and B. Hanouzet},
+ title = {Method of Absorbing Boundary conditions: Phenomena of error stabilization},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1998},
+ volume = {35},
+ pages = {1113-1129}
}
@ARTICLE{b0.4,
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-title = {Analysis of the three-dimensional {M}axwell system coupled with strongly
-absorbing layers},
-journal = {Journal de Math\'ematiques Pures et Appliqu\'ees},
-year = {2006}
+ author = {H. Barucq and M. Fontes},
+ title = {Analysis of the three-dimensional {M}axwell system coupled with strongly
+ absorbing layers},
+ journal = {Journal de Math\'ematiques Pures et Appliqu\'ees},
+ year = {2006}
}
@ARTICLE{BaHa97,
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-{S}ilver-{M}uller condition on the exterior boundary},
-journal = {Asympt. Anal.},
-year = {1997},
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+ author = {H. Barucq and B. Hanouzet},
+ title = {Asymptotic Behavior of solutions to {M}axwell's system with absorbing
+ {S}ilver-{M}uller condition on the exterior boundary},
+ journal = {Asympt. Anal.},
+ year = {1997},
+ volume = {15},
+ pages = {465-473}
}
@ARTICLE{BaMaSm204,
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-journal = {Advances in Differential Equations},
-year = {2006},
-volume = {11},
-pages = {61-90},
-number = {1}
+ author = {H. Barucq and M. Madaune-Tort and P. Saint-Macary},
+ title = {Asymptotic models in porous media arising from a {B}iot system},
+ journal = {Advances in Differential Equations},
+ year = {2006},
+ volume = {11},
+ pages = {61-90},
+ number = {1}
}
@ARTICLE{BarucqMadauneSaintMacary12005,
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-nonlinear {B}iot models},
-journal = {Nonlinear Analysis: Theory, Methods and Applications},
-year = {2005},
-volume = {61},
-pages = {591-612},
-number = {4}
+ author = {H. Barucq and M. Madaune-Tort and P. Saint-Macary},
+ title = {Some existence-uniqueness results for a class of one-dimensional
+ nonlinear {B}iot models},
+ journal = {Nonlinear Analysis: Theory, Methods and Applications},
+ year = {2005},
+ volume = {61},
+ pages = {591-612},
+ number = {4}
}
@ARTICLE{BarucqMadauneSaintMacary22005,
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-title = {On nonlinear {B}iot consolidation models},
-journal = {Nonlinear Analysis: Theory, Methods and Applications},
-year = {2005},
-volume = {63},
-pages = {e985-e995},
-number = {5-7}
+ author = {H. Barucq and M. Madaune-Tort and P. Saint-Macary},
+ title = {On nonlinear {B}iot consolidation models},
+ journal = {Nonlinear Analysis: Theory, Methods and Applications},
+ year = {2005},
+ volume = {63},
+ pages = {e985-e995},
+ number = {5-7}
}
@ARTICLE{BaLaMa00,
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-{A}merica},
-journal = {EOS},
-year = {2000},
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-pages = {F897}
+ author = {C. Bassin and G. Laske and G. Masters},
+ title = {The Current Limits of Resolution for Surface Wave Tomography in {N}orth
+ {A}merica},
+ journal = {EOS},
+ year = {2000},
+ volume = {81},
+ pages = {F897}
}
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-elastic waves},
-journal = ijnme,
-year = {2009},
-volume = {77},
-pages = {151-176},
-doi = {10.1002/nme.2397}
+ author = {Ushnish Basu},
+ title = {Explicit finite-element perfectly matched layer for transient three-dimensional
+ elastic waves},
+ journal = ijnme,
+ year = {2009},
+ volume = {77},
+ pages = {151-176},
+ doi = {10.1002/nme.2397}
}
@ARTICLE{BaCh04,
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-domains},
-journal = ijnme,
-year = {2004},
-volume = {59},
-pages = {1039-1074}
+ author = {U. Basu and A. K. Chopra},
+ title = {Perfectly matched layers for transient elastodynamics of unbounded
+ domains},
+ journal = ijnme,
+ year = {2004},
+ volume = {59},
+ pages = {1039-1074}
}
@ARTICLE{BaCh03,
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-domains: theory and finite-element implementation},
-journal = cmame,
-year = {2003},
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-pages = {1337-1375}
+ author = {U. Basu and A. K. Chopra},
+ title = {Perfectly matched layers for time-harmonic elastodynamics of unbounded
+ domains: theory and finite-element implementation},
+ journal = cmame,
+ year = {2003},
+ volume = {192},
+ pages = {1337-1375}
}
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+ pages = {9999998-9999999}
}
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+ title = {A fourth-order accurate finite-difference scheme for the computation
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+ year = {1986},
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}
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}
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+ author = {E. Baysal and D. D. Kosloff and J. W. C. Sherwood},
+ title = {Reverse-time migration},
+ journal = {Geophysics},
+ year = {1983},
+ volume = {48},
+ pages = {1514-1524}
}
@ARTICLE{beckerboschi2002,
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+ author = {T. W. Becker and L. Boschi},
+ title = {A comparison of tomographic and geodynamic mantle models},
+ journal = {Geochem. Geophys. Geosyst.},
+ year = {2002},
+ volume = {3},
+ pages = {1003},
+ number = {1},
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}
@INPROCEEDINGS{Bell:2009:ISM,
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-address = {New York, USA},
-month = nov,
-publisher = {ACM},
-doi = {10.1145/1654059.1654078},
-location = {Portland, Oregon, USA}
+ author = {Nathan Bell and Michael Garland},
+ title = {Implementing sparse matrix-vector multiplication on throughput-oriented
+ processors},
+ booktitle = {SC'09: Proceedings of the 2009 ACM/IEEE conference on Supercomputing},
+ year = {2009},
+ pages = {1--11},
+ address = {New York, USA},
+ month = nov,
+ publisher = {ACM},
+ doi = {10.1145/1654059.1654078},
+ location = {Portland, Oregon, USA}
}
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+ title = {On dispersive properties of finite element solutions},
+ booktitle = {Modern problems in elastic wave propagation},
+ publisher = {John Wiley and Sons},
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+ volume = {67},
+ address = {New York}
}
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+ author = {Ted Belytschko and E. J. Plaskacz and J. M. Kennedy and D. L. Greenwell},
+ title = {Finite element analysis on the {C}onnection {M}achine},
+ journal = cmame,
+ year = {1990},
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}
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+ publisher = {Springer-Verlag},
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@ARTICLE{BeOl05,
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+ author = {Rafael Benites and Kim B. Olsen},
+ title = {Modeling Strong Ground Motion in the {W}ellington Metropolitan Area,
+ {N}ew {Z}ealand},
+ journal = bssa,
+ year = {2005},
+ volume = {95},
+ pages = {2180-2196},
+ number = {6},
+ doi = {10.1785/0120040223}
}
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+ author = {M. Benjemaa and Glinsky-Olivier, N. and Cruz-Atienza, V. M. and Virieux,
+ J.},
+ title = {3{D} dynamic rupture simulation by a finite volume method},
+ journal = gji,
+ year = {2009},
+ volume = {178},
+ pages = {541-560},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2009.04088.x}
}
@ARTICLE{BeGlCrViPi07,
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-year = {2007},
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-pages = {271-285},
-number = {1},
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+ author = {Benjemaa, M. and Glinsky-Olivier, N. and Cruz-Atienza, V. M. and
+ Virieux, J. and Piperno, S.},
+ title = {{D}ynamic non-planar crack rupture by a finite volume method},
+ journal = gji,
+ year = {2007},
+ volume = {171},
+ pages = {271-285},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2006.03500.x}
}
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+ author = {P. Berg and F. If and P. Nielsen and O. Skovegaard},
+ title = {Analytic reference solutions},
+ booktitle = {Modeling the Earth for oil exploration, Final report of the CEC's
+ GEOSCIENCE~I Program 1990-1993},
+ publisher = {Pergamon Press, Oxford, United Kingdom},
+ year = {1994},
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+ pages = {421-427}
}
@INCOLLECTION{BeBrSy82,
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+ element problems},
+ booktitle = {Proceedings of the International Conference on Parallel Processing,
+ ICPP'82, August 24-27, 1982, Bellaire, Michigan, USA},
+ publisher = {IEEE Computer Society},
+ year = {1982},
+ pages = {41-46}
}
@INPROCEEDINGS{BeHePrRo06b,
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-Rodolfo Rodr\'{\i}guez},
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-year = {2006},
-editor = {E. Taroco and E. A. de Souza Neto and A. A. Novotny},
-address = {Barcelona, Spain},
-publisher = {CIMNE}
+ author = {Alfredo Berm\'udez and Luis Hervella-Nieto and Andr\'es Prieto and
+ Rodolfo Rodr\'{\i}guez},
+ title = {An optimal finite-element/{PML} method for the simulation of acoustic
+ wave propagation phenomena},
+ booktitle = {Variational Formulations in Mechanics: Theory and Applications},
+ year = {2006},
+ editor = {E. Taroco and E. A. de Souza Neto and A. A. Novotny},
+ address = {Barcelona, Spain},
+ publisher = {CIMNE}
}
@ARTICLE{BeHePrRo06,
-author = {Alfredo Berm\'udez and Luis Hervella-Nieto and Andr\'es Prieto and
-Rodolfo Rodr\'{\i}guez},
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-journal = jcp,
-year = {2007},
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-pages = {469-488},
-number = {2},
-doi = {10.1016/j.jcp.2006.09.018}
+ author = {Alfredo Berm\'udez and Luis Hervella-Nieto and Andr\'es Prieto and
+ Rodolfo Rodr\'{\i}guez},
+ title = {An optimal perfectly matched layer with unbounded absorbing function
+ for time-harmonic acoustic scattering problems},
+ journal = jcp,
+ year = {2007},
+ volume = {223},
+ pages = {469-488},
+ number = {2},
+ doi = {10.1016/j.jcp.2006.09.018}
}
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+ author = {A. Berm\'udez and L. Hervella-Nieto and R. Rodriguez},
+ title = {Finite-element computation of three-dimensional elastoacoustic vibrations},
+ journal = {J. Sound Vibr.},
+ year = {1999},
+ volume = {219},
+ pages = {279-306}
}
@ARTICLE{BeRo94,
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+ title = {Finite-element computation of the vibration modes of a fluid-solid
+ system},
+ journal = cmame,
+ year = {1994},
+ volume = {119},
+ pages = {355-370}
}
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+ author = {Marc Bernacki and St\'ephane Lanteri and Serge Piperno},
+ title = {Time-Domain Parallel Simulation Of Heterogeneous Wave Propagation
+ On Unstructured Grids Using Explicit, Nondiffusive, Discontinuous
+ {G}alerkin Methods},
+ journal = jca,
+ year = {2006},
+ volume = {14},
+ pages = {57-81},
+ number = {1}
}
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+ author = {C. Bernardi and Y. Maday and A. T. Patera},
+ title = {A new nonconforming approach to domain decomposition: the {M}ortar
+ element method},
+ booktitle = {Nonlinear partial differential equations and their applications},
+ year = {1994},
+ editor = {H. Brezis and J. L. Lions},
+ series = {S\'eminaires du Coll\`ege de France},
+ pages = {13-51},
+ address = {Paris},
+ publisher = {Pitman}
}
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+ author = {C. Bescond and M. Deschamps},
+ title = {Dynamical surface response of a semi-infinite anisotropic elastic
+ medium to an impulsive force},
+ journal = jasa,
+ year = {1998},
+ volume = {103},
+ pages = {114-124},
+ number = {1}
}
@ARTICLE{BesDes98b,
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+ author = {C. Bescond and M. Deschamps},
+ title = {Erratum to `{D}ynamical surface response of a semi-infinite anisotropic
+ elastic medium to an impulsive force'},
+ journal = jasa,
+ year = {1998},
+ volume = {104},
+ pages = {599},
+ number = {1}
}
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+ year = {1984},
+ volume = {12},
+ pages = {107-119}
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+ author = {J. Bielak and O. Ghattas and E. J. Kim},
+ title = {Parallel Octree-Based Finite Element Method for Large-Scale Earthquake
+ Ground Motion Simulation},
+ journal = cmes,
+ year = {2005},
+ volume = {10},
+ pages = {99-112},
+ number = {2}
}
@ARTICLE{BiXuGh99,
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+ author = {J. Bielak and J. Xu and O. Ghattas},
+ title = {Earthquake ground motion and structural response in alluvial valleys},
+ journal = {J. Geotech. Geoenv. Eng.},
+ year = {1999},
+ volume = {125},
+ pages = {413-423}
}
@ARTICLE{Biot56a,
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+ author = {M. A. Biot},
+ title = {Theory of propagation of elastic waves in a fluid-saturated porous
+ solid. {I: L}ow-frequency range},
+ journal = jasa,
+ year = {1956},
+ volume = {28},
+ pages = {168-178}
}
@ARTICLE{Biot56b,
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-title = {Theory of propagation of elastic waves in a fluid-saturated porous
-solid. {II: H}igher-frequency range},
-journal = jasa,
-year = {1956},
-volume = {28},
-pages = {179-191}
+ author = {M. A. Biot},
+ title = {Theory of propagation of elastic waves in a fluid-saturated porous
+ solid. {II: H}igher-frequency range},
+ journal = jasa,
+ year = {1956},
+ volume = {28},
+ pages = {179-191}
}
@ARTICLE{Bio52,
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-journal = bssa,
-year = {1952},
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+ author = {M. A. Biot},
+ title = {The interaction of {R}ayleigh and {S}toneley waves in the ocean bottom},
+ journal = bssa,
+ year = {1952},
+ volume = {42},
+ pages = {81-93}
}
@BOOK{BirGulKryPle95,
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-volume = {20},
-series = {Springer Series on Wave Phenomena},
-address = {Berlin, Germany}
+ title = {Surface acoustic waves in inhomogeneous media},
+ publisher = {Springer-Verlag},
+ year = {1995},
+ author = {S. V. Biryukov and Y. V. Gulyaev and V. V. Krylov and V. P. Plessky},
+ volume = {20},
+ series = {Springer Series on Wave Phenomena},
+ address = {Berlin, Germany}
}
@ARTICLE{Bit05,
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-journal = ijnme,
-year = {2005},
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-pages = {1530-1558},
-number = {11},
-doi = {10.1002/nme.1325}
+ author = {M. L. Bittencourt},
+ title = {Fully tensorial nodal and modal shape functions for triangles and
+ tetrahedra},
+ journal = ijnme,
+ year = {2005},
+ volume = {63},
+ pages = {1530-1558},
+ number = {11},
+ doi = {10.1002/nme.1325}
}
@MANUAL{Bl94,
-title = {{CUBIT} Mesh Generation Environment Users Manual Vol. 1},
-author = {T.D. Blacker and P. Knupp and R. r. Lober and D. Melander and G.
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-B. McRae and M. Panthaki},
-organization = {Sandia National Laboratories},
-address = {Albuquerque, NM},
-year = {1994}
+ title = {{CUBIT} Mesh Generation Environment Users Manual Vol. 1},
+ author = {T.D. Blacker and P. Knupp and R. r. Lober and D. Melander and G.
+ D. Sjaardema and W. A. Sample and M. K. Smith and T. J. Tautges and
+ D. R. White and S. Benzley and R. Kerr and S. R. Jankovich and D.
+ B. McRae and M. Panthaki},
+ organization = {Sandia National Laboratories},
+ address = {Albuquerque, NM},
+ year = {1994}
}
@ARTICLE{BlLoKoBa09,
-author = {C\'eline Blitz and Philippe Lognonn\'e and Dimitri Komatitsch and
-David Baratoux},
-title = {Effects of ejecta accumulation on the crater population of asteroid
-433 {E}ros},
-journal = jgr,
-year = {2009},
-volume = {114},
-pages = {E06006},
-doi = {10.1029/2008JE003229}
+ author = {C\'eline Blitz and Philippe Lognonn\'e and Dimitri Komatitsch and
+ David Baratoux},
+ title = {Effects of ejecta accumulation on the crater population of asteroid
+ 433 {E}ros},
+ journal = jgr,
+ year = {2009},
+ volume = {114},
+ pages = {E06006},
+ doi = {10.1029/2008JE003229}
}
@ARTICLE{BoSaenger06,
-author = {Thomas Bohlen and Erik H. Saenger},
-title = {Accuracy of heterogeneous staggered-grid finite-difference modeling
-of {R}ayleigh waves},
-journal = geophysics,
-year = {2006},
-volume = {71},
-pages = {T109-T115},
-number = {4},
-doi = {10.1190/1.2213051}
+ author = {Thomas Bohlen and Erik H. Saenger},
+ title = {Accuracy of heterogeneous staggered-grid finite-difference modeling
+ of {R}ayleigh waves},
+ journal = geophysics,
+ year = {2006},
+ volume = {71},
+ pages = {T109-T115},
+ number = {4},
+ doi = {10.1190/1.2213051}
}
@ARTICLE{BoHa77,
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-title = {The upthrow of objects in earthquakes},
-journal = bssa,
-year = {1977},
-volume = {67},
-pages = {1415-1427}
+ author = {B. A. Bolt and R. A. Hansen},
+ title = {The upthrow of objects in earthquakes},
+ journal = bssa,
+ year = {1977},
+ volume = {67},
+ pages = {1415-1427}
}
@ARTICLE{Bolz:2003:SMS,
-author = {Jeff Bolz and Ian Farmer and Eitan Grinspun and Peter Schr{\"o}der},
-title = {Sparse matrix solvers on the {GPU}: {C}onjugate Gradients and Multigrid},
-journal = {ACM Transactions on Graphics},
-year = {2003},
-volume = {22},
-pages = {917--924},
-number = {3},
-month = jul,
-doi = {10.1145/882262.882364}
+ author = {Jeff Bolz and Ian Farmer and Eitan Grinspun and Peter Schr{\"o}der},
+ title = {Sparse matrix solvers on the {GPU}: {C}onjugate Gradients and Multigrid},
+ journal = {ACM Transactions on Graphics},
+ year = {2003},
+ volume = {22},
+ pages = {917--924},
+ number = {3},
+ month = jul,
+ doi = {10.1145/882262.882364}
}
@ARTICLE{BoVi91,
-author = {O. Bonamassa and J. E. Vidale},
-title = {Directional site resonances observed from aftershocks of the 18 october
-1989 {L}oma {P}rieta earthquake},
-journal = bssa,
-year = {1991},
-volume = {81},
-pages = {1945-1957}
+ author = {O. Bonamassa and J. E. Vidale},
+ title = {Directional site resonances observed from aftershocks of the 18 october
+ 1989 {L}oma {P}rieta earthquake},
+ journal = bssa,
+ year = {1991},
+ volume = {81},
+ pages = {1945-1957}
}
@BOOK{Bon95,
-title = {\'Equations int\'egrales et \'el\'ements de fronti\`ere},
-publisher = {CNRS \'Editions, Eyrolles},
-year = {1995},
-author = {M. Bonnet},
-address = {Paris}
+ title = {\'Equations int\'egrales et \'el\'ements de fronti\`ere},
+ publisher = {CNRS \'Editions, Eyrolles},
+ year = {1995},
+ author = {M. Bonnet},
+ address = {Paris}
}
@INCOLLECTION{Boo72a,
-author = {D. M. Boore},
-title = {Finite difference methods for seismic wave propagation in heterogeneous
-materials},
-booktitle = {Methods in Computational Physics},
-publisher = {Academic Press},
-year = {1972},
-volume = {11},
-address = {New York}
+ author = {D. M. Boore},
+ title = {Finite difference methods for seismic wave propagation in heterogeneous
+ materials},
+ booktitle = {Methods in Computational Physics},
+ publisher = {Academic Press},
+ year = {1972},
+ volume = {11},
+ address = {New York}
}
@ARTICLE{Boo72b,
-author = {D. M. Boore},
-title = {A note on the effect of simple topography on seismic {{\it SH}} waves},
-journal = bssa,
-year = {1972},
-volume = {62},
-pages = {275-284}
+ author = {D. M. Boore},
+ title = {A note on the effect of simple topography on seismic {{\it SH}} waves},
+ journal = bssa,
+ year = {1972},
+ volume = {62},
+ pages = {275-284}
}
@ARTICLE{BoHaHa81,
-author = {D. M. Boore and S. C. Harmsen and S. T. Harding},
-title = {Wave scattering from a steep change in surface topography},
-journal = bssa,
-year = {1981},
-volume = {71},
-pages = {117-125}
+ author = {D. M. Boore and S. C. Harmsen and S. T. Harding},
+ title = {Wave scattering from a steep change in surface topography},
+ journal = bssa,
+ year = {1981},
+ volume = {71},
+ pages = {117-125}
}
@ARTICLE{BoCr83,
-author = {D. C. Booth and S. Crampin},
-title = {The anisotropic reflectivity technique: theory},
-journal = {Geophys. J. R. Astr. Soc.},
-year = {1983},
-volume = {72},
-pages = {755-766}
+ author = {D. C. Booth and S. Crampin},
+ title = {The anisotropic reflectivity technique: theory},
+ journal = {Geophys. J. R. Astr. Soc.},
+ year = {1983},
+ volume = {72},
+ pages = {755-766}
}
@ARTICLE{Bos91,
-author = {L. Bos},
-title = {On certain configurations of points in {{\rm I\kern -0.18 em R}$^n$}
-which are unisolvent for polynomial interpolation},
-journal = {J. Approx. Theory},
-year = {1991},
-volume = {64},
-pages = {271-280}
+ author = {L. Bos},
+ title = {On certain configurations of points in {{\rm I\kern -0.18 em R}$^n$}
+ which are unisolvent for polynomial interpolation},
+ journal = {J. Approx. Theory},
+ year = {1991},
+ volume = {64},
+ pages = {271-280}
}
@ARTICLE{BoTaWi01,
-author = {L. P. Bos and M. A. Taylor and B. A. Wingate},
-title = {Tensor Product {G}auss-{L}obatto Points are {F}ekete Points for the
-Cube},
-journal = {Math. Comp.},
-year = {2001},
-volume = {70},
-pages = {1543-1547}
+ author = {L. P. Bos and M. A. Taylor and B. A. Wingate},
+ title = {Tensor Product {G}auss-{L}obatto Points are {F}ekete Points for the
+ Cube},
+ journal = {Math. Comp.},
+ year = {2001},
+ volume = {70},
+ pages = {1543-1547}
}
@ARTICLE{BoGriMia,
-author = {A. Bossavit and G. Griso and B. Miara},
-title = {Modelling of periodic electromagnetic structures bianosotropic materials
-with memory effects},
-journal = {Journal de Math\'ematiques Pures et Appliqu\'ees},
-year = {2005},
-volume = {84},
-pages = {819-850},
-number = {7}
+ author = {A. Bossavit and G. Griso and B. Miara},
+ title = {Modelling of periodic electromagnetic structures bianosotropic materials
+ with memory effects},
+ journal = {Journal de Math\'ematiques Pures et Appliqu\'ees},
+ year = {2005},
+ volume = {84},
+ pages = {819-850},
+ number = {7}
}
@ARTICLE{Bos02,
-author = {M. G. Bostock},
-title = {Kirchhoff-approximate inversion of teleseismic wavefields},
-journal = gji,
-year = {2002},
-volume = {149},
-pages = {787-795}
+ author = {M. G. Bostock},
+ title = {Kirchhoff-approximate inversion of teleseismic wavefields},
+ journal = gji,
+ year = {2002},
+ volume = {149},
+ pages = {787-795}
}
@ARTICLE{BoRo99,
-author = {M. G. Bostock and S. Rondenay},
-title = {Migration of scattered teleseismic body waves},
-journal = gji,
-year = {1999},
-volume = {137},
-pages = {732-746}
+ author = {M. G. Bostock and S. Rondenay},
+ title = {Migration of scattered teleseismic body waves},
+ journal = gji,
+ year = {1999},
+ volume = {137},
+ pages = {732-746}
}
@ARTICLE{BoRoSh01,
-author = {M. G. Bostock and S. Rondenay and J. Shragge},
-title = {Multiparameter two-dimensional inversion of scattered teleseismic
-body waves - 1. {T}heory for oblique incidence},
-journal = jgr,
-year = {2001},
-volume = {106},
-pages = {30771-30782}
+ author = {M. G. Bostock and S. Rondenay and J. Shragge},
+ title = {Multiparameter two-dimensional inversion of scattered teleseismic
+ body waves - 1. {T}heory for oblique incidence},
+ journal = jgr,
+ year = {2001},
+ volume = {106},
+ pages = {30771-30782}
}
@ARTICLE{Bou96,
-author = {M. Bouchon},
-title = {The discrete wave number formulation of boundary integral equations
-and boundary element methods: a review with applications to the simulation
-of seismic wave propagation in complex geological structures},
-journal = pageoph,
-year = {1996},
-volume = {148},
-pages = {3-20},
-number = {1}
+ author = {M. Bouchon},
+ title = {The discrete wave number formulation of boundary integral equations
+ and boundary element methods: a review with applications to the simulation
+ of seismic wave propagation in complex geological structures},
+ journal = pageoph,
+ year = {1996},
+ volume = {148},
+ pages = {3-20},
+ number = {1}
}
@ARTICLE{Bou85,
-author = {M. Bouchon},
-title = {A simple complete numerical solution of the problem of diffraction
-of {{\it SH}} waves by an irregular surface},
-journal = jasa,
-year = {1985},
-volume = {77},
-pages = {1-5}
+ author = {M. Bouchon},
+ title = {A simple complete numerical solution of the problem of diffraction
+ of {{\it SH}} waves by an irregular surface},
+ journal = jasa,
+ year = {1985},
+ volume = {77},
+ pages = {1-5}
}
@ARTICLE{Bou81,
-author = {M. Bouchon},
-title = {A simple method to calculate {G}reen's functions for elastic layered
-media},
-journal = bssa,
-year = {1981},
-volume = {71},
-pages = {959-971}
+ author = {M. Bouchon},
+ title = {A simple method to calculate {G}reen's functions for elastic layered
+ media},
+ journal = bssa,
+ year = {1981},
+ volume = {71},
+ pages = {959-971}
}
@ARTICLE{Bou79,
-author = {M. Bouchon},
-title = {Discrete wavenumber representation of elastic wave fields in three
-space dimensions},
-journal = jgr,
-year = {1979},
-volume = {84},
-pages = {3609-3614}
+ author = {M. Bouchon},
+ title = {Discrete wavenumber representation of elastic wave fields in three
+ space dimensions},
+ journal = jgr,
+ year = {1979},
+ volume = {84},
+ pages = {3609-3614}
}
@ARTICLE{Bou78,
-author = {M. Bouchon},
-title = {The importance of the surface interface {{\it P}} wave in near-earthquake
-studies},
-journal = bssa,
-year = {1978},
-volume = {68},
-pages = {1293-1311}
+ author = {M. Bouchon},
+ title = {The importance of the surface interface {{\it P}} wave in near-earthquake
+ studies},
+ journal = bssa,
+ year = {1978},
+ volume = {68},
+ pages = {1293-1311}
}
@ARTICLE{Bou73,
-author = {M. Bouchon},
-title = {Effect of topography on surface motion},
-journal = bssa,
-year = {1973},
-volume = {63},
-pages = {615-632}
+ author = {M. Bouchon},
+ title = {Effect of topography on surface motion},
+ journal = bssa,
+ year = {1973},
+ volume = {63},
+ pages = {615-632}
}
@ARTICLE{BoAk77,
-author = {M. Bouchon and K. Aki},
-title = {Discrete wavenumber representation of seismic-source wave fields},
-journal = bssa,
-year = {1977},
-volume = {67},
-pages = {259-277}
+ author = {M. Bouchon and K. Aki},
+ title = {Discrete wavenumber representation of seismic-source wave fields},
+ journal = bssa,
+ year = {1977},
+ volume = {67},
+ pages = {259-277}
}
@ARTICLE{BoBa96,
-author = {M. Bouchon and J. S. Barker},
-title = {Seismic response of a hill: the example of {T}arzana, {C}alifornia},
-journal = bssa,
-year = {1996},
-volume = {86},
-pages = {66-72},
-number = {1A}
+ author = {M. Bouchon and J. S. Barker},
+ title = {Seismic response of a hill: the example of {T}arzana, {C}alifornia},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {66-72},
+ number = {1A}
}
@ARTICLE{BoCaGa89,
-author = {M. Bouchon and M. Campillo and S. Gaffet},
-title = {A boundary integral equation-discrete wavenumber representation method
-to study wave propagation in multilayered media having irregular
-interfaces},
-journal = geophysics,
-year = {1989},
-volume = {54},
-pages = {1134-1140}
+ author = {M. Bouchon and M. Campillo and S. Gaffet},
+ title = {A boundary integral equation-discrete wavenumber representation method
+ to study wave propagation in multilayered media having irregular
+ interfaces},
+ journal = geophysics,
+ year = {1989},
+ volume = {54},
+ pages = {1134-1140}
}
@INCOLLECTION{BoSanchez06,
-author = {M. Bouchon and F. J. S\'anchez-Sesma},
-title = {Boundary-integral equations and boundary-element methods in elastodynamics},
-booktitle = {Advances in wave propagation in heterogeneous media},
-publisher = {Elsevier},
-year = {2006},
-editor = {Ru-Shan Wu and Val\'erie Maupin},
-series = {Advances in Geophysics}
+ author = {M. Bouchon and F. J. S\'anchez-Sesma},
+ title = {Boundary-integral equations and boundary-element methods in elastodynamics},
+ booktitle = {Advances in wave propagation in heterogeneous media},
+ publisher = {Elsevier},
+ year = {2006},
+ editor = {Ru-Shan Wu and Val\'erie Maupin},
+ series = {Advances in Geophysics}
}
@ARTICLE{BoScTo96,
-author = {M. Bouchon and C. A. Schultz and M. Nafi T\"oksoz},
-title = {Effect of three-dimensional topography on seismic motion},
-journal = jgr,
-year = {1996},
-volume = {101},
-pages = {5835-5846}
+ author = {M. Bouchon and C. A. Schultz and M. Nafi T\"oksoz},
+ title = {Effect of three-dimensional topography on seismic motion},
+ journal = jgr,
+ year = {1996},
+ volume = {101},
+ pages = {5835-5846}
}
@ARTICLE{BoScTo95,
-author = {M. Bouchon and C. A. Schultz and M. Nafi T\"oksoz},
-title = {A fast implementation of boundary integral equation methods to calculate
-the propagation of seismic waves in laterally varying layered media},
-journal = bssa,
-year = {1995},
-volume = {85},
-pages = {1679-1687}
+ author = {M. Bouchon and C. A. Schultz and M. Nafi T\"oksoz},
+ title = {A fast implementation of boundary integral equation methods to calculate
+ the propagation of seismic waves in laterally varying layered media},
+ journal = bssa,
+ year = {1995},
+ volume = {85},
+ pages = {1679-1687}
}
@PHDTHESIS{ab,
-author = {A. Bouhamidi},
-title = {Interpolation et approximation par des fonctions splines radiales
-\`a plusieurs variables},
-school = {Universit\'e de Nantes},
-year = {1992},
-address = {Nantes, France},
-note = {190 p.}
+ author = {A. Bouhamidi},
+ title = {Interpolation et approximation par des fonctions splines radiales
+ \`a plusieurs variables},
+ school = {Universit\'e de Nantes},
+ year = {1992},
+ address = {Nantes, France},
+ note = {190 p.}
}
@BOOK{BouHay93,
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-publisher = {Chapman and Hall},
-year = {1993},
-author = {Ph. Boulanger and M. Hayes},
-address = {London, United Kingdom}
+ title = {Bivectors and waves in {M}echanics and {O}ptics},
+ publisher = {Chapman and Hall},
+ year = {1993},
+ author = {Ph. Boulanger and M. Hayes},
+ address = {London, United Kingdom}
}
@ARTICLE{brandvik_pullan_euler_2d,
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-of Mechanical Engineering Science},
-year = {2007},
-volume = {221},
-pages = {1745--1748},
-number = {12},
-doi = {10.1243/09544062JMES813FT}
+ author = {Tobias Brandvik and Graham Pullan},
+ title = {Acceleration of a two-dimensional {E}uler flow solver using commodity
+ Graphics Hardware},
+ journal = {Proceedings of the Institution of Mechanical Engineers, Part C: Journal
+ of Mechanical Engineering Science},
+ year = {2007},
+ volume = {221},
+ pages = {1745--1748},
+ number = {12},
+ doi = {10.1243/09544062JMES813FT}
}
@BOOK{BreGod90,
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-series = {Springer Series on Wave phenomena},
-address = {Berlin, Germany}
+ title = {Acoustics of layered media {I}},
+ publisher = {Springer-Verlag},
+ year = {1990},
+ author = {L. M. Brekhovskikh and O. A. Godin},
+ volume = {5},
+ series = {Springer Series on Wave phenomena},
+ address = {Berlin, Germany}
}
@ARTICLE{Bremmer,
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-year = {1951},
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+ author = {H. Bremmer},
+ title = {The {WKB} approximation as the first term of a geometric-optical
+ series},
+ journal = {Comm. Pure Appl. Math.},
+ year = {1951},
+ volume = {9999999},
+ pages = {105-115}
}
@INCOLLECTION{brezzifortin,
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-booktitle = {Springer Series in Computational Mathematics},
-publisher = {Springer},
-year = {1991},
-volume = {15},
-address = {New York, USA}
+ author = {F. Brezzi and M. Fortin},
+ title = {Mixed and Hybrid Finite Element Methods},
+ booktitle = {Springer Series in Computational Mathematics},
+ publisher = {Springer},
+ year = {1991},
+ volume = {15},
+ address = {New York, USA}
}
@BOOK{Bri64,
-title = {Tensors in Mechanics and Elasticity},
-publisher = {Academic Press},
-year = {1964},
-author = {L. Brillouin},
-address = {New York, USA},
-edition = {3rd}
+ title = {Tensors in Mechanics and Elasticity},
+ publisher = {Academic Press},
+ year = {1964},
+ author = {L. Brillouin},
+ address = {New York, USA},
+ edition = {3rd}
}
@ARTICLE{Buc61,
-author = {V. T. Buchwald},
-title = {Rayleigh waves in anisotropic media},
-journal = {Quarterly Journal of Mechanics and Applied Mathematics},
-year = {1961},
-volume = {14},
-pages = {461-468},
-number = {4}
+ author = {V. T. Buchwald},
+ title = {Rayleigh waves in anisotropic media},
+ journal = {Quarterly Journal of Mechanics and Applied Mathematics},
+ year = {1961},
+ volume = {14},
+ pages = {461-468},
+ number = {4}
}
@ARTICLE{Buc59,
-author = {V. T. Buchwald},
-title = {Elastic waves in anisotropic media},
-journal = {Proceedings of the Royal Society of London, United Kingdom},
-year = {1959},
-volume = {A253},
-pages = {563-580}
+ author = {V. T. Buchwald},
+ title = {Elastic waves in anisotropic media},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1959},
+ volume = {A253},
+ pages = {563-580}
}
@ARTICLE{BucDav63,
-author = {V. T. Buchwald and A. Davis},
-title = {Surface waves in elastic media with cubic symmetry},
-journal = {Quarterly Journal of Mechanics and Applied Mathematics},
-year = {1963},
-volume = {16},
-pages = {283-293}
+ author = {V. T. Buchwald and A. Davis},
+ title = {Surface waves in elastic media with cubic symmetry},
+ journal = {Quarterly Journal of Mechanics and Applied Mathematics},
+ year = {1963},
+ volume = {16},
+ pages = {283-293}
}
@INPROCEEDINGS{Buc06,
-author = {Ian Buck},
-title = {Ge{F}orce 8800 and {NVIDIA CUDA}: A New Architecture for Computing
-on the {GPU}},
-booktitle = {Proceedings of the Supercomputing'06 Workshop on "General-Purpose
-GPU Computing: Practice And Experience"},
-year = {2006},
-pages = {1-29},
-url = {www.gpgpu.org/sc2006/workshop/presentations/Buck\_NVIDIA\_Cuda.pdf}
+ author = {Ian Buck},
+ title = {Ge{F}orce 8800 and {NVIDIA CUDA}: A New Architecture for Computing
+ on the {GPU}},
+ booktitle = {Proceedings of the Supercomputing'06 Workshop on "General-Purpose
+ GPU Computing: Practice And Experience"},
+ year = {2006},
+ pages = {1-29},
+ url = {www.gpgpu.org/sc2006/workshop/presentations/Buck\_NVIDIA\_Cuda.pdf}
}
@ARTICLE{Buck:2004:BFG,
-author = {Ian Buck and Tim Foley and Daniel R. Horn and Jeremy Sugerman and
-Kayvon Fatahalian and Mike Houston and Pat Hanrahan},
-title = {Brook for {GPUs}: {S}tream computing on graphics hardware},
-journal = {ACM Transactions on Graphics},
-year = {2004},
-volume = {23},
-pages = {777--786},
-number = {3},
-month = aug,
-doi = {10.1145/1015706.1015800}
+ author = {Ian Buck and Tim Foley and Daniel R. Horn and Jeremy Sugerman and
+ Kayvon Fatahalian and Mike Houston and Pat Hanrahan},
+ title = {Brook for {GPUs}: {S}tream computing on graphics hardware},
+ journal = {ACM Transactions on Graphics},
+ year = {2004},
+ volume = {23},
+ pages = {777--786},
+ number = {3},
+ month = aug,
+ doi = {10.1145/1015706.1015800}
}
@ARTICLE{Bur71,
-author = {R. Burridge},
-title = {Lamb's problem for an anisotropic half-space},
-journal = {Quarterly Journal of Mechanics and Applied Mathematics},
-year = {1971},
-volume = {24},
-pages = {81-98},
-number = {1}
+ author = {R. Burridge},
+ title = {Lamb's problem for an anisotropic half-space},
+ journal = {Quarterly Journal of Mechanics and Applied Mathematics},
+ year = {1971},
+ volume = {24},
+ pages = {81-98},
+ number = {1}
}
@ARTICLE{Bur70,
-author = {R. Burridge},
-title = {The directions in which {R}ayleigh waves may be propagated on crystals},
-journal = {Quarterly Journal of Mechanics and Applied Mathematics},
-year = {1970},
-volume = {23},
-pages = {217-224},
-number = {2}
+ author = {R. Burridge},
+ title = {The directions in which {R}ayleigh waves may be propagated on crystals},
+ journal = {Quarterly Journal of Mechanics and Applied Mathematics},
+ year = {1970},
+ volume = {23},
+ pages = {217-224},
+ number = {2}
}
@BOOK{Cag39,
-title = {R\'eflexion et R\'efraction des Ondes Sismiques Progressives},
-publisher = {Gauthiers-Villars},
-year = {1939},
-author = {L. Cagniard},
-address = {Paris}
+ title = {R\'eflexion et R\'efraction des Ondes Sismiques Progressives},
+ publisher = {Gauthiers-Villars},
+ year = {1939},
+ author = {L. Cagniard},
+ address = {Paris}
}
@PHDTHESIS{Calvet_thesis,
-author = {M. Calvet},
-title = {Apport des noyaux de sensibilit\'e des ondes {PKP} et {P} diffract\'ees
-pour l'\'etude de la graine anisotrope et de la couche {D}''},
-school = {Universit\'e Paul Sabatier, Toulouse, France},
-year = {2006}
+ author = {M. Calvet},
+ title = {Apport des noyaux de sensibilit\'e des ondes {PKP} et {P} diffract\'ees
+ pour l'\'etude de la graine anisotrope et de la couche {D}''},
+ school = {Universit\'e Paul Sabatier, Toulouse, France},
+ year = {2006}
}
@ARTICLE{Calvet05,
-author = {M. Calvet and S. Chevrot},
-title = {Traveltime sensitivity kernels for {PKP} phases in the mantle},
-journal = pepi,
-year = {2005},
-volume = {153},
-pages = {21-31}
+ author = {M. Calvet and S. Chevrot},
+ title = {Traveltime sensitivity kernels for {PKP} phases in the mantle},
+ journal = pepi,
+ year = {2005},
+ volume = {153},
+ pages = {21-31}
}
@ARTICLE{Calvet06a,
-author = {M. Calvet and S. Chevrot and A. Souriau},
-title = {P wave propagation in transversely isotropic media: {I}. {F}inite-frequency
-theory},
-journal = pepi,
-year = {2006},
-volume = {156},
-pages = {12-20}
+ author = {M. Calvet and S. Chevrot and A. Souriau},
+ title = {P wave propagation in transversely isotropic media: {I}. {F}inite-frequency
+ theory},
+ journal = pepi,
+ year = {2006},
+ volume = {156},
+ pages = {12-20}
}
@ARTICLE{Calvet06b,
-author = {M. Calvet and S. Chevrot and A. Souriau},
-title = {P wave propagation in transversely isotropic media: {II}. {A}pplication
-to inner core anisotropy: {E}ffects of data averaging, parameterization
-and a priori information},
-journal = pepi,
-year = {2006},
-volume = {156},
-pages = {21-40}
+ author = {M. Calvet and S. Chevrot and A. Souriau},
+ title = {P wave propagation in transversely isotropic media: {II}. {A}pplication
+ to inner core anisotropy: {E}ffects of data averaging, parameterization
+ and a priori information},
+ journal = pepi,
+ year = {2006},
+ volume = {156},
+ pages = {21-40}
}
@ARTICLE{CamMar83,
-author = {R. E. Camley and A. A. Maradudin},
-title = {Phonon focusing at surfaces},
-journal = {Physical Review B},
-year = {1983},
-volume = {27},
-pages = {1959-1964},
-number = {4}
+ author = {R. E. Camley and A. A. Maradudin},
+ title = {Phonon focusing at surfaces},
+ journal = {Physical Review B},
+ year = {1983},
+ volume = {27},
+ pages = {1959-1964},
+ number = {4}
}
@ARTICLE{Cam87,
-author = {M. Campillo},
-title = {{$L_g$} wave propagation in a laterally varying crust and the distribution
-of the apparent quality factor in {C}entre {F}rance},
-journal = jgr,
-year = {1987},
-volume = {92},
-pages = {12604-12614}
+ author = {M. Campillo},
+ title = {{$L_g$} wave propagation in a laterally varying crust and the distribution
+ of the apparent quality factor in {C}entre {F}rance},
+ journal = jgr,
+ year = {1987},
+ volume = {92},
+ pages = {12604-12614}
}
@ARTICLE{CaBo85,
-author = {M. Campillo and M. Bouchon},
-title = {Synthetic {{\it SH}} seismograms in laterally varying medium by discrete
-wavenumber method},
-journal = gjras,
-year = {1985},
-volume = {83},
-pages = {307-317}
+ author = {M. Campillo and M. Bouchon},
+ title = {Synthetic {{\it SH}} seismograms in laterally varying medium by discrete
+ wavenumber method},
+ journal = gjras,
+ year = {1985},
+ volume = {83},
+ pages = {307-317}
}
@INCOLLECTION{CaDo99,
-author = {E. J. Cand\`es and D. L. Donoho},
-title = {Curvelets: A Surprisingly Effective Nonadaptive Representation for
-Objects with Edges, Curves and Surfaces},
-booktitle = {Curve and Surface Fitting},
-publisher = {Vanderbilt University Press},
-year = {1999},
-editor = {A. Cohen and C. Rabut and L. L. Schumaker},
-address = {Nashville, Tennessee, USA}
+ author = {E. J. Cand\`es and D. L. Donoho},
+ title = {Curvelets: A Surprisingly Effective Nonadaptive Representation for
+ Objects with Edges, Curves and Surfaces},
+ booktitle = {Curve and Surface Fitting},
+ publisher = {Vanderbilt University Press},
+ year = {1999},
+ editor = {A. Cohen and C. Rabut and L. L. Schumaker},
+ address = {Nashville, Tennessee, USA}
}
@ARTICLE{CaFu88,
-author = {C. Canuto and D. Funaro},
-title = {The {S}chwarz algorithm for spectral methods},
-journal = {SIAM Journal on Numerical Analysis},
-year = {1988},
-volume = {25},
-pages = {24-40}
+ author = {C. Canuto and D. Funaro},
+ title = {The {S}chwarz algorithm for spectral methods},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1988},
+ volume = {25},
+ pages = {24-40}
}
@BOOK{CaHuQuZa88,
-title = {Spectral methods in fluid dynamics},
-publisher = {Springer-Verlag},
-year = {1988},
-author = {C. Canuto and M. Y. Hussaini and A. Quarteroni and T. A. Zang},
-address = {New York, USA}
+ title = {Spectral methods in fluid dynamics},
+ publisher = {Springer-Verlag},
+ year = {1988},
+ author = {C. Canuto and M. Y. Hussaini and A. Quarteroni and T. A. Zang},
+ address = {New York, USA}
}
@ARTICLE{CaQu82,
-author = {C. Canuto and A. Quarteroni},
-title = {Approximation results for orthogonal polynomials in {S}obolev spaces},
-journal = {Math. Comp.},
-year = {1982},
-volume = {38},
-pages = {67-86}
+ author = {C. Canuto and A. Quarteroni},
+ title = {Approximation results for orthogonal polynomials in {S}obolev spaces},
+ journal = {Math. Comp.},
+ year = {1982},
+ volume = {38},
+ pages = {67-86}
}
@PHDTHESIS{Ca00,
-author = {Y. Capdeville},
-title = {M\'ethode coupl\'ee \'el\'ements spectraux - solution modale pour
-la propagation d'ondes dans la {T}erre \`a l'\'echelle globale ({A}
-coupled method using spectral elements and normal modes for global
-wave propagation in the {E}arth)},
-school = {Universit\'e Paris {\sc VII} Denis Diderot},
-year = {2000},
-address = {Paris, France}
+ author = {Y. Capdeville},
+ title = {M\'ethode coupl\'ee \'el\'ements spectraux - solution modale pour
+ la propagation d'ondes dans la {T}erre \`a l'\'echelle globale ({A}
+ coupled method using spectral elements and normal modes for global
+ wave propagation in the {E}arth)},
+ school = {Universit\'e Paris {\sc VII} Denis Diderot},
+ year = {2000},
+ address = {Paris, France}
}
@ARTICLE{CaChViMo03,
-author = {Y. Capdeville and E. Chaljub and J. P. Vilotte and J. P. Montagner},
-title = {Coupling the spectral element method with a modal solution for elastic
-wave propagation in global {E}arth models},
-journal = gji,
-year = {2003},
-volume = {152},
-pages = {34-67}
+ author = {Y. Capdeville and E. Chaljub and J. P. Vilotte and J. P. Montagner},
+ title = {Coupling the spectral element method with a modal solution for elastic
+ wave propagation in global {E}arth models},
+ journal = gji,
+ year = {2003},
+ volume = {152},
+ pages = {34-67}
}
@ARTICLE{CaGuRo05,
-author = {Y. Capdeville and Y. Gung and B. Romanowicz},
-title = {Towards global {E}arth tomography using the spectral element method:
-a technique based on source stacking},
-journal = gji,
-year = {2005},
-volume = {162},
-pages = {541-554}
+ author = {Y. Capdeville and Y. Gung and B. Romanowicz},
+ title = {Towards global {E}arth tomography using the spectral element method:
+ a technique based on source stacking},
+ journal = gji,
+ year = {2005},
+ volume = {162},
+ pages = {541-554}
}
@ARTICLE{Caetal00,
-author = {Y. Capdeville and E. Stutzmann and J.P. Montagner},
-title = {Effect of a plume on long-period surface waves computed with normal-mode
-coupling},
-journal = pepi,
-year = {2000},
-volume = {119},
-pages = {54-71}
+ author = {Y. Capdeville and E. Stutzmann and J.P. Montagner},
+ title = {Effect of a plume on long-period surface waves computed with normal-mode
+ coupling},
+ journal = pepi,
+ year = {2000},
+ volume = {119},
+ pages = {54-71}
}
@ARTICLE{CaToRo03,
-author = {Yann Capdeville and A. To and Barbara Romanowicz},
-title = {Coupling spectral elements and modes in a spherical {E}arth: an extension
-to the `sandwich' case},
-journal = gji,
-year = {2003},
-volume = {154},
-pages = {44-57}
+ author = {Yann Capdeville and A. To and Barbara Romanowicz},
+ title = {Coupling spectral elements and modes in a spherical {E}arth: an extension
+ to the `sandwich' case},
+ journal = gji,
+ year = {2003},
+ volume = {154},
+ pages = {44-57}
}
@BOOK{Car07,
-title = {Wave fields in real media: {T}heory and numerical simulation of wave
-propagation in anisotropic, anelastic, porous and electromagnetic
-media},
-publisher = {Elsevier Science},
-year = {2007},
-author = {Jos\'e M. Carcione},
-address = {Amsterdam, The Netherlands},
-edition = {Second}
+ title = {Wave fields in real media: {T}heory and numerical simulation of wave
+ propagation in anisotropic, anelastic, porous and electromagnetic
+ media},
+ publisher = {Elsevier Science},
+ year = {2007},
+ author = {Jos\'e M. Carcione},
+ address = {Amsterdam, The Netherlands},
+ edition = {Second}
}
@ARTICLE{Car99,
-author = {J. M. Carcione},
-title = {Staggered mesh for the anisotropic and viscoelastic wave equation},
-journal = geophysics,
-year = {1999},
-volume = {64},
-pages = {1863-1866}
+ author = {J. M. Carcione},
+ title = {Staggered mesh for the anisotropic and viscoelastic wave equation},
+ journal = geophysics,
+ year = {1999},
+ volume = {64},
+ pages = {1863-1866}
}
@ARTICLE{Car96,
-author = {J. M. Carcione},
-title = {A 2{D} {C}hebyshev differential operator for the elastic wave equation},
-journal = cmame,
-year = {1996},
-volume = {130},
-pages = {33-45}
+ author = {J. M. Carcione},
+ title = {A 2{D} {C}hebyshev differential operator for the elastic wave equation},
+ journal = cmame,
+ year = {1996},
+ volume = {130},
+ pages = {33-45}
}
@ARTICLE{Carcio96,
-author = {J. M. Carcione},
-title = {Elastodynamic of a non-ideal interface: application to crack and
-fracture scattering},
-journal = jgr,
-year = {1996},
-volume = {101},
-pages = {28177-28188},
-number = {B12}
+ author = {J. M. Carcione},
+ title = {Elastodynamic of a non-ideal interface: application to crack and
+ fracture scattering},
+ journal = jgr,
+ year = {1996},
+ volume = {101},
+ pages = {28177-28188},
+ number = {B12}
}
@ARTICLE{Car94,
-author = {J. M. Carcione},
-title = {The wave equation in generalized coordinates},
-journal = geophysics,
-year = {1994},
-volume = {59},
-pages = {1911-1919}
+ author = {J. M. Carcione},
+ title = {The wave equation in generalized coordinates},
+ journal = geophysics,
+ year = {1994},
+ volume = {59},
+ pages = {1911-1919}
}
@ARTICLE{Car93,
-author = {Jos\'e M. Carcione},
-title = {Seismic modeling in viscoelastic media},
-journal = geophysics,
-year = {1993},
-volume = {58},
-pages = {110-120},
-number = {1},
-doi = {10.1190/1.1443340}
+ author = {Jos\'e M. Carcione},
+ title = {Seismic modeling in viscoelastic media},
+ journal = geophysics,
+ year = {1993},
+ volume = {58},
+ pages = {110-120},
+ number = {1},
+ doi = {10.1190/1.1443340}
}
@ARTICLE{Car92,
-author = {J. M. Carcione},
-title = {Modeling anelastic singular surface waves in the {E}arth},
-journal = {Geophysics},
-year = {1992},
-volume = {57},
-pages = {781-792},
-number = {6}
+ author = {J. M. Carcione},
+ title = {Modeling anelastic singular surface waves in the {E}arth},
+ journal = {Geophysics},
+ year = {1992},
+ volume = {57},
+ pages = {781-792},
+ number = {6}
}
@ARTICLE{Car91,
-author = {J. M. Carcione},
-title = {Domain decomposition for wave propagation problems},
-journal = {J. Sci. Comp.},
-year = {1991},
-volume = {6},
-pages = {453-472},
-number = {4}
+ author = {J. M. Carcione},
+ title = {Domain decomposition for wave propagation problems},
+ journal = {J. Sci. Comp.},
+ year = {1991},
+ volume = {6},
+ pages = {453-472},
+ number = {4}
}
@ARTICLE{Car90,
-author = {J. M. Carcione},
-title = {Wave propagation in anisotropic linear viscoelastic media: theory
-and simulated wavefields},
-journal = gji,
-year = {1990},
-volume = {101},
-pages = {739-750}
+ author = {J. M. Carcione},
+ title = {Wave propagation in anisotropic linear viscoelastic media: theory
+ and simulated wavefields},
+ journal = gji,
+ year = {1990},
+ volume = {101},
+ pages = {739-750}
}
@ARTICLE{CarHel04,
-author = {J. M. Carcione and H. B. Helle},
-title = {On the physics and simulation of wave propagation at the ocean bottom},
-journal = {Geophysics},
-year = {2004},
-volume = {69},
-pages = {825-839}
+ author = {J. M. Carcione and H. B. Helle},
+ title = {On the physics and simulation of wave propagation at the ocean bottom},
+ journal = {Geophysics},
+ year = {2004},
+ volume = {69},
+ pages = {825-839}
}
@ARTICLE{CaHeKr02,
-author = {J. M. Carcione and G. Herman and F. P. E. {ten Kroode}},
-title = {Seismic modeling},
-journal = geophysics,
-year = {2002},
-volume = {67},
-pages = {1304-1325}
+ author = {J. M. Carcione and G. Herman and F. P. E. {ten Kroode}},
+ title = {Seismic modeling},
+ journal = geophysics,
+ year = {2002},
+ volume = {67},
+ pages = {1304-1325}
}
@ARTICLE{CaKoBeSe92,
-author = {J. M. Carcione and D. Kosloff and A. Behle and G. Seriani},
-title = {A spectral scheme for wave propagation simulation in 3-{D} elastic-anisotropic
-media},
-journal = geophysics,
-year = {1992},
-volume = {57},
-pages = {1593-1607},
-number = {12}
+ author = {J. M. Carcione and D. Kosloff and A. Behle and G. Seriani},
+ title = {A spectral scheme for wave propagation simulation in 3-{D} elastic-anisotropic
+ media},
+ journal = geophysics,
+ year = {1992},
+ volume = {57},
+ pages = {1593-1607},
+ number = {12}
}
@ARTICLE{CaKoKo88,
-author = {J. M. Carcione and D. Kosloff and R. Kosloff},
-title = {Wave propagation simulation in an elastic anisotropic (transversely
-isotropic) solid},
-journal = {Q. J. Mech. Appl. Math.},
-year = {1988},
-volume = {41},
-pages = {319-345},
-number = {3}
+ author = {J. M. Carcione and D. Kosloff and R. Kosloff},
+ title = {Wave propagation simulation in an elastic anisotropic (transversely
+ isotropic) solid},
+ journal = {Q. J. Mech. Appl. Math.},
+ year = {1988},
+ volume = {41},
+ pages = {319-345},
+ number = {3}
}
@ARTICLE{CaKoKo88b,
-author = {J. M. Carcione and D. Kosloff and R. Kosloff},
-title = {Wave propagation simulation in a linear viscoelastic medium},
-journal = gji,
-year = {1988},
-volume = {95},
-pages = {597-611}
+ author = {J. M. Carcione and D. Kosloff and R. Kosloff},
+ title = {Wave propagation simulation in a linear viscoelastic medium},
+ journal = gji,
+ year = {1988},
+ volume = {95},
+ pages = {597-611}
}
@ARTICLE{CaPoGe04,
-author = {J. M. Carcione and F. Poletto and D. Gei},
-title = {3-{D} wave simulation in anelastic media using the {K}elvin-{V}oigt
-constitutive equation},
-journal = jcp,
-year = {2004},
-volume = {196},
-pages = {282-297}
+ author = {J. M. Carcione and F. Poletto and D. Gei},
+ title = {3-{D} wave simulation in anelastic media using the {K}elvin-{V}oigt
+ constitutive equation},
+ journal = jcp,
+ year = {2004},
+ volume = {196},
+ pages = {282-297}
}
@ARTICLE{CaWa93,
-author = {J. M. Carcione and P. J. Wang},
-title = {A {C}hebyshev Collocation Method for the Wave Equation in Generalized
-Coordinates},
-journal = {Comp. Fluid Dyn. J.},
-year = {1993},
-volume = {2},
-pages = {269-290}
+ author = {J. M. Carcione and P. J. Wang},
+ title = {A {C}hebyshev Collocation Method for the Wave Equation in Generalized
+ Coordinates},
+ journal = {Comp. Fluid Dyn. J.},
+ year = {1993},
+ volume = {2},
+ pages = {269-290}
}
@ARTICLE{CaKoLaTiMiLeSnTr08,
-author = {Laura Carrington and Dimitri Komatitsch and Michael Laurenzano and
-Mustafa Tikir and David Mich\'ea and Nicolas {Le Goff} and Allan
-Snavely and Jeroen Tromp},
-title = {High-frequency simulations of global seismic wave propagation using
-{SPECFEM3D\_GLOBE} on 62 thousand processor cores},
-journal = {Proceedings of the ACM/IEEE Supercomputing SC'2008 conference},
-year = {2008},
-pages = {1-11},
-note = {Article \#60, {G}ordon {B}ell {P}rize finalist article},
-doi = {10.1145/1413370.1413432}
+ author = {Laura Carrington and Dimitri Komatitsch and Michael Laurenzano and
+ Mustafa Tikir and David Mich\'ea and Nicolas {Le Goff} and Allan
+ Snavely and Jeroen Tromp},
+ title = {High-frequency simulations of global seismic wave propagation using
+ {SPECFEM3D\_GLOBE} on 62 thousand processor cores},
+ journal = {Proceedings of the ACM/IEEE Supercomputing SC'2008 conference},
+ year = {2008},
+ pages = {1-11},
+ note = {Article \#60, {G}ordon {B}ell {P}rize finalist article},
+ doi = {10.1145/1413370.1413432}
}
@ARTICLE{CaKiCrWoSpMu90,
-author = {D. L. Carver and K. W. King and E. Cranswick and D. W. Worley and
-P. Spudich and C. Mueller},
-title = {Digital recordings of aftershocks of the {O}ctober 17, 1989, {L}oma
-{P}rieta, {C}alifornia, earthquake: {S}anta {C}ruz, {L}os {G}atos,
-and surrounding areas},
-journal = {U.S. Geol. Surv. Open File Rep.},
-year = {1990},
-volume = {90},
-pages = {90-683}
+ author = {D. L. Carver and K. W. King and E. Cranswick and D. W. Worley and
+ P. Spudich and C. Mueller},
+ title = {Digital recordings of aftershocks of the {O}ctober 17, 1989, {L}oma
+ {P}rieta, {C}alifornia, earthquake: {S}anta {C}ruz, {L}os {G}atos,
+ and surrounding areas},
+ journal = {U.S. Geol. Surv. Open File Rep.},
+ year = {1990},
+ volume = {90},
+ pages = {90-683}
}
@TECHREPORT{CaGa97,
-author = {F. Casadei and E. Gabellini},
-title = {Implementation of a 3{D} coupled {S}pectral {E}lement solver for
-wave propagation and soil-structure interaction simulations},
-institution = {European Commission Joint Research Center Report EUR17730EN},
-year = {1997},
-address = {Ispra, Italy}
+ author = {F. Casadei and E. Gabellini},
+ title = {Implementation of a 3{D} coupled {S}pectral {E}lement solver for
+ wave propagation and soil-structure interaction simulations},
+ institution = {European Commission Joint Research Center Report EUR17730EN},
+ year = {1997},
+ address = {Ispra, Italy}
}
@ARTICLE{CaHa09,
-author = {Folco Casadei and Jean-Pierre Halleux},
-title = {Binary spatial partitioning of the central-difference time integration
-scheme for explicit fast transient dynamics},
-journal = ijnme,
-year = {2009},
-volume = {78},
-pages = {1436-1473},
-number = {12},
-doi = {10.1002/nme.2533}
+ author = {Folco Casadei and Jean-Pierre Halleux},
+ title = {Binary spatial partitioning of the central-difference time integration
+ scheme for explicit fast transient dynamics},
+ journal = ijnme,
+ year = {2009},
+ volume = {78},
+ pages = {1436-1473},
+ number = {12},
+ doi = {10.1002/nme.2533}
}
@INPROCEEDINGS{CaStLeKoPiTr08,
-author = {E. Casarotti and M. Stupazzini and S. Lee and D. Komatitsch and A.
-Piersanti and J. Tromp},
-title = {CUBIT and Seismic Wave Propagation Based Upon the Spectral-Element
-Method: An Advanced Unstructured Mesher for Complex 3D Geological
-Media},
-booktitle = {Proceedings of the 16th International Meshing Roundtable},
-year = {2008},
-volume = {5B.4},
-pages = {579-597}
+ author = {E. Casarotti and M. Stupazzini and S. Lee and D. Komatitsch and A.
+ Piersanti and J. Tromp},
+ title = {CUBIT and Seismic Wave Propagation Based Upon the Spectral-Element
+ Method: An Advanced Unstructured Mesher for Complex 3D Geological
+ Media},
+ booktitle = {Proceedings of the 16th International Meshing Roundtable},
+ year = {2008},
+ volume = {5B.4},
+ pages = {579-597}
}
@ARTICLE{CaKiSa97,
-author = {V. Caselles and R. Kimmel and G. Sapiro},
-title = {Geodesic {A}ctive {C}ontours},
-journal = {Int. J. Comput. Vis.},
-year = {1997},
-volume = {22},
-pages = {61-79},
-number = {1}
+ author = {V. Caselles and R. Kimmel and G. Sapiro},
+ title = {Geodesic {A}ctive {C}ontours},
+ journal = {Int. J. Comput. Vis.},
+ year = {1997},
+ volume = {22},
+ pages = {61-79},
+ number = {1}
}
@ARTICLE{CasBer92,
-author = {B. Castagn\`ede and Y. Berthelot},
-title = {Photoacoustic interactions by modulation and laser impact: applications
-in mechanics and physics of anisotropic solids},
-journal = {Journal d'Acoustique},
-year = {1992},
-volume = {5},
-pages = {417-453}
+ author = {B. Castagn\`ede and Y. Berthelot},
+ title = {Photoacoustic interactions by modulation and laser impact: applications
+ in mechanics and physics of anisotropic solids},
+ journal = {Journal d'Acoustique},
+ year = {1992},
+ volume = {5},
+ pages = {417-453}
}
@ARTICLE{CaKaBr10,
-author = {C. E. Castro and M. K\"aser and G. B. Brietzke},
-title = {Seismic waves in heterogeneous material: subcell resolution of the
-discontinuous Galerkin method},
-journal = gji,
-year = {2010},
-volume = {182},
-pages = {250-264},
-number = {1}
+ author = {C. E. Castro and M. K\"aser and G. B. Brietzke},
+ title = {Seismic waves in heterogeneous material: subcell resolution of the
+ discontinuous Galerkin method},
+ journal = gji,
+ year = {2010},
+ volume = {182},
+ pages = {250-264},
+ number = {1}
}
@ARTICLE{CaLe96,
-author = {R. D. Catchings and W. H. K. Lee},
-title = {Shallow velocity structure and {P}oisson's ratio at the {T}arzana,
-{C}alifornia, strong-motion accelerometer site},
-journal = bssa,
-year = {1996},
-volume = {86},
-pages = {1704-1713}
+ author = {R. D. Catchings and W. H. K. Lee},
+ title = {Shallow velocity structure and {P}oisson's ratio at the {T}arzana,
+ {C}alifornia, strong-motion accelerometer site},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1704-1713}
}
@ARTICLE{CeMcMcOwQuWr09,
-author = {Elena Celledoni and Robert I. McLachlan and David I. McLaren and
-Brynjulf Owren and G. Reinout W. Quispel and William M. Wright},
-title = {Energy-preserving {R}unge-{K}utta methods},
-journal = {M2AN},
-year = {2009},
-volume = {43},
-pages = {645-649},
-doi = {10.1051/m2an/2009020}
+ author = {Elena Celledoni and Robert I. McLachlan and David I. McLaren and
+ Brynjulf Owren and G. Reinout W. Quispel and William M. Wright},
+ title = {Energy-preserving {R}unge-{K}utta methods},
+ journal = {M2AN},
+ year = {2009},
+ volume = {43},
+ pages = {645-649},
+ doi = {10.1051/m2an/2009020}
}
@ARTICLE{CeKoKoRe85,
-author = {C. Cerjan and D. Kosloff and R. Kosloff and M. Reshef},
-title = {A nonreflecting boundary condition for discrete acoustic and elastic
-wave equation},
-journal = geophysics,
-year = {1985},
-volume = {50},
-pages = {705-708}
+ author = {C. Cerjan and D. Kosloff and R. Kosloff and M. Reshef},
+ title = {A nonreflecting boundary condition for discrete acoustic and elastic
+ wave equation},
+ journal = geophysics,
+ year = {1985},
+ volume = {50},
+ pages = {705-708}
}
@BOOK{cerveny01,
-title = {Seismic Ray Theory},
-publisher = {Cambridge University Press},
-year = {2001},
-author = {V. Cerven\'{y}},
-address = {Cambridge, UK}
+ title = {Seismic Ray Theory},
+ publisher = {Cambridge University Press},
+ year = {2001},
+ author = {V. Cerven\'{y}},
+ address = {Cambridge, UK}
}
@ARTICLE{CeNuMa10,
-author = {Ali Cevahir and Akira Nukada and Satoshi Matsuoka},
-title = {High performance conjugate gradient solver on multi-{GPU} clusters
-using hypergraph partitioning},
-journal = {Computer Science Research and Development},
-year = {2010},
-volume = {25},
-pages = {83-91},
-number = {1-2},
-doi = {10.1007/s00450-010-0112-6}
+ author = {Ali Cevahir and Akira Nukada and Satoshi Matsuoka},
+ title = {High performance conjugate gradient solver on multi-{GPU} clusters
+ using hypergraph partitioning},
+ journal = {Computer Science Research and Development},
+ year = {2010},
+ volume = {25},
+ pages = {83-91},
+ number = {1-2},
+ doi = {10.1007/s00450-010-0112-6}
}
@ARTICLE{ChSaHa96,
-author = {F. J. Ch\'avez-Garc\'{\i}a and L. S\'anchez and D. Hatzfeld},
-title = {Topographic site effects and HVSR. A comparison between observation
-and theory},
-journal = bssa,
-year = {1996},
-volume = {86},
-pages = {1559-1573}
+ author = {F. J. Ch\'avez-Garc\'{\i}a and L. S\'anchez and D. Hatzfeld},
+ title = {Topographic site effects and HVSR. A comparison between observation
+ and theory},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1559-1573}
}
@ARTICLE{Cha92,
-author = {P. Chadwick},
-title = {Some remarks on the existence of one-component surface waves in elastic
-materials with symmetry},
-journal = {Physica Scripta},
-year = {1992},
-volume = {T44},
-pages = {94-97}
+ author = {P. Chadwick},
+ title = {Some remarks on the existence of one-component surface waves in elastic
+ materials with symmetry},
+ journal = {Physica Scripta},
+ year = {1992},
+ volume = {T44},
+ pages = {94-97}
}
@ARTICLE{Cha90,
-author = {P. Chadwick},
-title = {The behaviour of elastic surface waves polarized in a plane of material
-symmetry. {I}. {G}eneral analysis},
-journal = {Proceedings of the Royal Society of London, United Kingdom},
-year = {1990},
-volume = {A430},
-pages = {213-240}
+ author = {P. Chadwick},
+ title = {The behaviour of elastic surface waves polarized in a plane of material
+ symmetry. {I}. {G}eneral analysis},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1990},
+ volume = {A430},
+ pages = {213-240}
}
@ARTICLE{Cha89,
-author = {P. Chadwick},
-title = {Wave propagation in transversely isotropic elastic media. {II}. {S}urface
-waves},
-journal = {Proceedings of the Royal Society of London, United Kingdom},
-year = {1989},
-volume = {A422},
-pages = {67-101}
+ author = {P. Chadwick},
+ title = {Wave propagation in transversely isotropic elastic media. {II}. {S}urface
+ waves},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1989},
+ volume = {A422},
+ pages = {67-101}
}
@INCOLLECTION{ChaSmi82,
-author = {P. Chadwick and G. D. Smith},
-title = {Surface waves in cubic elastic materials},
-booktitle = {Mechanics of solids},
-publisher = {Pergamon Press},
-year = {1982},
-editor = {H. G. Hopkins and M. J. Sewell},
-pages = {47-100},
-address = {Oxford, United Kingdom}
+ author = {P. Chadwick and G. D. Smith},
+ title = {Surface waves in cubic elastic materials},
+ booktitle = {Mechanics of solids},
+ publisher = {Pergamon Press},
+ year = {1982},
+ editor = {H. G. Hopkins and M. J. Sewell},
+ pages = {47-100},
+ address = {Oxford, United Kingdom}
}
@INCOLLECTION{ChaSmi77,
-author = {P. Chadwick and G. D. Smith},
-title = {Foundations of the theory of surface waves in anisotropic elastic
-materials},
-booktitle = {Advances in Applied Mechanics},
-publisher = {Academic Press, New York, USA},
-year = {1977},
-editor = {C. S. Yih},
-volume = {17},
-pages = {303-376}
+ author = {P. Chadwick and G. D. Smith},
+ title = {Foundations of the theory of surface waves in anisotropic elastic
+ materials},
+ booktitle = {Advances in Applied Mechanics},
+ publisher = {Academic Press, New York, USA},
+ year = {1977},
+ editor = {C. S. Yih},
+ volume = {17},
+ pages = {303-376}
}
@ARTICLE{ChaWil92a,
-author = {P. Chadwick and N. J. Wilson},
-title = {The behaviour of elastic surface waves polarized in a plane of material
-symmetry. {II}. {M}onoclinic media},
-journal = {Proceedings of the Royal Society of London, United Kingdom},
-year = {1992},
-volume = {A438},
-pages = {207-223}
+ author = {P. Chadwick and N. J. Wilson},
+ title = {The behaviour of elastic surface waves polarized in a plane of material
+ symmetry. {II}. {M}onoclinic media},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1992},
+ volume = {A438},
+ pages = {207-223}
}
@ARTICLE{ChaWil92b,
-author = {P. Chadwick and N. J. Wilson},
-title = {The behaviour of elastic surface waves polarized in a plane of material
-symmetry. {III}. {O}rthorhombic and cubic media},
-journal = {Proceedings of the Royal Society of London, United Kingdom},
-year = {1992},
-volume = {A438},
-pages = {225-247}
+ author = {P. Chadwick and N. J. Wilson},
+ title = {The behaviour of elastic surface waves polarized in a plane of material
+ symmetry. {III}. {O}rthorhombic and cubic media},
+ journal = {Proceedings of the Royal Society of London, United Kingdom},
+ year = {1992},
+ volume = {A438},
+ pages = {225-247}
}
@ARTICLE{ChaWu94,
-author = {J. F. Chai and T. T. Wu},
-title = {Determination of anisotropic elastic constants using laser-generated
-surface waves},
-journal = jasa,
-year = {1994},
-volume = {95},
-pages = {3232-3241}
+ author = {J. F. Chai and T. T. Wu},
+ title = {Determination of anisotropic elastic constants using laser-generated
+ surface waves},
+ journal = jasa,
+ year = {1994},
+ volume = {95},
+ pages = {3232-3241}
}
@ARTICLE{ChBoSe08,
-author = {St\'{e}phanie Chaillat and Marc Bonnet and Jean-Fran\c{c}ois Semblat},
-title = {A multi-level fast multipole {BEM} for {3-D} elastodynamics in the
-frequency domain},
-journal = cmame,
-year = {2008},
-volume = {197},
-pages = {4233-4249},
-number = {49-50},
-doi = {10.1016/j.cma.2008.04.024}
+ author = {St\'{e}phanie Chaillat and Marc Bonnet and Jean-Fran\c{c}ois Semblat},
+ title = {A multi-level fast multipole {BEM} for {3-D} elastodynamics in the
+ frequency domain},
+ journal = cmame,
+ year = {2008},
+ volume = {197},
+ pages = {4233-4249},
+ number = {49-50},
+ doi = {10.1016/j.cma.2008.04.024}
}
@PHDTHESIS{Ch00,
-author = {E. Chaljub},
-title = {Mod\'elisation num\'erique de la propagation d'ondes sismiques en
-g\'eom\'etrie sph\'erique : application \`a la sismologie globale
-({N}umerical modeling of the propagation of seismic waves in spherical
-geometry: {a}pplication to global seismology)},
-school = {Universit\'e Paris {\sc VII} Denis Diderot},
-year = {2000},
-address = {Paris, France}
+ author = {E. Chaljub},
+ title = {Mod\'elisation num\'erique de la propagation d'ondes sismiques en
+ g\'eom\'etrie sph\'erique : application \`a la sismologie globale
+ ({N}umerical modeling of the propagation of seismic waves in spherical
+ geometry: {a}pplication to global seismology)},
+ school = {Universit\'e Paris {\sc VII} Denis Diderot},
+ year = {2000},
+ address = {Paris, France}
}
@ARTICLE{ChCaVi03,
-author = {E. Chaljub and Y. Capdeville and J. P. Vilotte},
-title = {Solving Elastodynamics in a Fluid-Solid Heterogeneous Sphere: a Parallel
-Spectral-Element Approximation on Non-Conforming Grids},
-journal = jcp,
-year = {2003},
-volume = {187},
-pages = {457-491},
-number = {2}
+ author = {E. Chaljub and Y. Capdeville and J. P. Vilotte},
+ title = {Solving Elastodynamics in a Fluid-Solid Heterogeneous Sphere: a Parallel
+ Spectral-Element Approximation on Non-Conforming Grids},
+ journal = jcp,
+ year = {2003},
+ volume = {187},
+ pages = {457-491},
+ number = {2}
}
@INPROCEEDINGS{CCGCK05,
-author = {Emmanuel Chaljub and C\'ecile Cornou and Philippe Gu\'eguen and Mathieu
-Causse and Dimitri Komatitsch},
-title = {Spectral-element modeling of 3{D} wave propagation in the alpine
-valley of {G}renoble, {F}rance},
-booktitle = {Geophysical Research Abstracts},
-year = {2005},
-volume = {7, 05225},
-publisher = {EGU 2nd general assembly, Wien, Austria}
+ author = {Emmanuel Chaljub and C\'ecile Cornou and Philippe Gu\'eguen and Mathieu
+ Causse and Dimitri Komatitsch},
+ title = {Spectral-element modeling of 3{D} wave propagation in the alpine
+ valley of {G}renoble, {F}rance},
+ booktitle = {Geophysical Research Abstracts},
+ year = {2005},
+ volume = {7, 05225},
+ publisher = {EGU 2nd general assembly, Wien, Austria}
}
@INCOLLECTION{ChKoViCaVaFe07,
-author = {Emmanuel Chaljub and Dimitri Komatitsch and Jean Pierre Vilotte and
-Yann Capdeville and Bernard Valette and Gaetano Festa},
-title = {Spectral Element Analysis in Seismology},
-booktitle = {Advances in wave propagation in heterogeneous media},
-publisher = {Elsevier - Academic Press, London, UK},
-year = {2007},
-editor = {Ru-Shan Wu and Val\'erie Maupin},
-volume = {48},
-series = {Advances in Geophysics},
-pages = {365-419}
+ author = {Emmanuel Chaljub and Dimitri Komatitsch and Jean Pierre Vilotte and
+ Yann Capdeville and Bernard Valette and Gaetano Festa},
+ title = {Spectral Element Analysis in Seismology},
+ booktitle = {Advances in wave propagation in heterogeneous media},
+ publisher = {Elsevier - Academic Press, London, UK},
+ year = {2007},
+ editor = {Ru-Shan Wu and Val\'erie Maupin},
+ volume = {48},
+ series = {Advances in Geophysics},
+ pages = {365-419}
}
@ARTICLE{ChMoTsBaKrKaStKr10,
-author = {E. Chaljub and P. Moczo and S. Tsuno and P.-Y. Bard and J. Kristek
-and M. K\"aser and M. Stupazzini and M. Kristekova},
-title = {Quantitative Comparison of Four Numerical Predictions of 3D Ground
-Motion in the Grenoble Valley, France},
-journal = {Bull. Seismol. Soc. Am.},
-year = {2010},
-volume = {100},
-pages = {1427-1455},
-number = {4}
+ author = {E. Chaljub and P. Moczo and S. Tsuno and P.-Y. Bard and J. Kristek
+ and M. K\"aser and M. Stupazzini and M. Kristekova},
+ title = {Quantitative Comparison of Four Numerical Predictions of 3D Ground
+ Motion in the Grenoble Valley, France},
+ journal = {Bull. Seismol. Soc. Am.},
+ year = {2010},
+ volume = {100},
+ pages = {1427-1455},
+ number = {4}
}
@ARTICLE{ChTa97,
-author = {E. Chaljub and A. Tarantola},
-title = {Sensitivity of {SS} precursors to topography on the upper-mantle
-660-km discontinuity},
-journal = grl,
-year = {1997},
-volume = {24},
-pages = {2613-2616},
-number = {21}
+ author = {E. Chaljub and A. Tarantola},
+ title = {Sensitivity of {SS} precursors to topography on the upper-mantle
+ 660-km discontinuity},
+ journal = grl,
+ year = {1997},
+ volume = {24},
+ pages = {2613-2616},
+ number = {21}
}
@ARTICLE{ChVa04,
-author = {E. Chaljub and B. Valette},
-title = {Spectral element modelling of three-dimensional wave propagation
-in a self-gravitating {E}arth with an arbitrarily stratified outer
-core},
-journal = gji,
-year = {2004},
-volume = {158},
-pages = {131-141}
+ author = {E. Chaljub and B. Valette},
+ title = {Spectral element modelling of three-dimensional wave propagation
+ in a self-gravitating {E}arth with an arbitrarily stratified outer
+ core},
+ journal = gji,
+ year = {2004},
+ volume = {158},
+ pages = {131-141}
}
@BOOK{openmp,
-title = {Parallel Programming in {O}pen{MP}},
-publisher = {Morgan Kaufmann, Elsevier},
-year = {2000},
-author = {Rohit Chandra and Ramesh Menon and Leo Dagum and David Kohr and Dror
-Maydan and Jeff McDonald},
-address = {San Francisco, USA}
+ title = {Parallel Programming in {O}pen{MP}},
+ publisher = {Morgan Kaufmann, Elsevier},
+ year = {2000},
+ author = {Rohit Chandra and Ramesh Menon and Leo Dagum and David Kohr and Dror
+ Maydan and Jeff McDonald},
+ address = {San Francisco, USA}
}
@ARTICLE{ChPr92,
-author = {C. Chapman and R. G. Pratt},
-title = {Traveltime tomography in anisotropic media -{I}: Theory},
-journal = gji,
-year = {1992},
-volume = {109},
-pages = {1-19}
+ author = {C. Chapman and R. G. Pratt},
+ title = {Traveltime tomography in anisotropic media -{I}: Theory},
+ journal = gji,
+ year = {1992},
+ volume = {109},
+ pages = {1-19}
}
@ARTICLE{ChPh72,
-author = {C. H. Chapman and R. A. Phinney},
-title = {Diffracted seismic signals and their numerical solution},
-journal = {Methods Comput. Phys.},
-year = {1972},
-volume = {12},
-pages = {165-230}
+ author = {C. H. Chapman and R. A. Phinney},
+ title = {Diffracted seismic signals and their numerical solution},
+ journal = {Methods Comput. Phys.},
+ year = {1972},
+ volume = {12},
+ pages = {165-230}
}
@ARTICLE{Che:2008:APS,
-author = {Shuai Che and Michael Boyer and Jiayuan Meng and David Tarjan and
-Jeremy W. Sheaffer and Kevin Skadron},
-title = {A performance study of general-purpose applications on graphics processors
-using {CUDA}},
-journal = {Journal of Parallel and Distributed Computing},
-year = {2008},
-volume = {68},
-pages = {1370--1380},
-number = {10},
-month = jun,
-doi = {10.1016/j.jpdc.2008.05.014}
+ author = {Shuai Che and Michael Boyer and Jiayuan Meng and David Tarjan and
+ Jeremy W. Sheaffer and Kevin Skadron},
+ title = {A performance study of general-purpose applications on graphics processors
+ using {CUDA}},
+ journal = {Journal of Parallel and Distributed Computing},
+ year = {2008},
+ volume = {68},
+ pages = {1370--1380},
+ number = {10},
+ month = jun,
+ doi = {10.1016/j.jpdc.2008.05.014}
}
@ARTICLE{ChTr07,
-author = {Min Chen and Jeroen Tromp},
-title = {Theoretical and numerical investigations of global and regional seismic
-wave propagation in weakly anisotropic earth models},
-journal = gji,
-year = {2007},
-volume = {168},
-pages = {1130-1152},
-number = {3},
-doi = {10.1111/j.1365-246X.2006.03218.x}
+ author = {Min Chen and Jeroen Tromp},
+ title = {Theoretical and numerical investigations of global and regional seismic
+ wave propagation in weakly anisotropic earth models},
+ journal = gji,
+ year = {2007},
+ volume = {168},
+ pages = {1130-1152},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2006.03218.x}
}
@ARTICLE{ChTrHeKa07,
-author = {M. Chen and J. Tromp and D. Helmberger and H. Kanamori},
-title = {Waveform modeling of the slab beneath {J}apan},
-journal = jgr,
-year = {2007},
-volume = {112},
-pages = {B02305},
-doi = {10.1029/2006JB004394}
+ author = {M. Chen and J. Tromp and D. Helmberger and H. Kanamori},
+ title = {Waveform modeling of the slab beneath {J}apan},
+ journal = jgr,
+ year = {2007},
+ volume = {112},
+ pages = {B02305},
+ doi = {10.1029/2006JB004394}
}
@ARTICLE{ChenBabu96,
-author = {Q. Chen and I. Babu{\v s}ka},
-title = {The optimal symmetrical points for polynomial interpolation of real
-functions in the tetrahedron},
-journal = cmame,
-year = {1996},
-volume = {137},
-pages = {89-94}
+ author = {Q. Chen and I. Babu{\v s}ka},
+ title = {The optimal symmetrical points for polynomial interpolation of real
+ functions in the tetrahedron},
+ journal = cmame,
+ year = {1996},
+ volume = {137},
+ pages = {89-94}
}
@ARTICLE{ChenBabu95,
-author = {Q. Chen and I. Babu{\v s}ka},
-title = {Approximate optimal points for polynomial interpolation of real functions
-in an interval and in a triangle},
-journal = cmame,
-year = {1995},
-volume = {128},
-pages = {405-417}
+ author = {Q. Chen and I. Babu{\v s}ka},
+ title = {Approximate optimal points for polynomial interpolation of real functions
+ in an interval and in a triangle},
+ journal = cmame,
+ year = {1995},
+ volume = {128},
+ pages = {405-417}
}
@INCOLLECTION{Che06,
-author = {X. Chen},
-title = {Generation and propagation of seismic {SH} waves in multilayered
-media with irregular interfaces},
-booktitle = {Advances in wave propagation in heterogeneous media},
-publisher = {Elsevier},
-year = {2006},
-editor = {Ru-Shan Wu and Val\'erie Maupin},
-series = {Advances in Geophysics}
+ author = {X. Chen},
+ title = {Generation and propagation of seismic {SH} waves in multilayered
+ media with irregular interfaces},
+ booktitle = {Advances in wave propagation in heterogeneous media},
+ publisher = {Elsevier},
+ year = {2006},
+ editor = {Ru-Shan Wu and Val\'erie Maupin},
+ series = {Advances in Geophysics}
}
@ARTICLE{ChPe08,
-author = {C. Chevalier and F. Pellegrini},
-title = {{PT-SCOTCH}: a tool for efficient parallel graph ordering},
-journal = {Parallel Computing},
-year = {2008},
-volume = {34},
-pages = {318-331},
-number = {6-8}
+ author = {C. Chevalier and F. Pellegrini},
+ title = {{PT-SCOTCH}: a tool for efficient parallel graph ordering},
+ journal = {Parallel Computing},
+ year = {2008},
+ volume = {34},
+ pages = {318-331},
+ number = {6-8}
}
@ARTICLE{Che06b,
-author = {S. Chevrot},
-title = {Finite-frequency vectorial tomography: a new method for high-resolution
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+ author = {S. Chevrot},
+ title = {Finite-frequency vectorial tomography: a new method for high-resolution
+ imaging of upper mantle anisotropy},
+ journal = gji,
+ year = {2006},
+ volume = {165},
+ pages = {641-657},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2006.02982.x}
}
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+ author = {S. Chevrot and N. Favier and D. Komatitsch},
+ title = {Shear wave splitting in three-dimensional anisotropic media},
+ journal = gji,
+ year = {2004},
+ volume = {159},
+ pages = {711-720},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2004.02432.x}
}
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+ Philippe Lognonn\'e},
+ title = {Seismic waveform modeling and surface wave tomography in a three-dimensional
+ {E}arth: asymptotic and non-asymptotic approaches},
+ journal = pepi,
+ year = {2000},
+ volume = {119(1)},
+ pages = {37-56}
}
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+ title = {Close in {ScS} and {sScS} reverberations from the 9 {J}une 1994 {B}olivian
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+ journal = grl,
+ year = {1995},
+ volume = {22},
+ pages = {2313-2316},
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}
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+ year = {1977},
+ volume = {67},
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+ author = {R. H. Clouser and C. A. Langston},
+ title = {Modeling observed {$P$-$R_g$} conversions from isolated topographic
+ features near the {NORESS} array},
+ journal = bssa,
+ year = {1995},
+ volume = {85},
+ pages = {859-873}
}
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+ author = {R. T. Coates and M. Schoenberg},
+ title = {Finite-difference modelling of faults and fractures},
+ journal = geophysics,
+ year = {1995},
+ volume = {60},
+ pages = {1514-1526}
}
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+ author = {M. Cocco and J. R. Rice},
+ title = {Pore pressure and poroelasticity effects in {C}oulomb stress analysis
+ of earthquake interaction},
+ journal = jgr,
+ year = {2002},
+ volume = {107},
+ pages = {2-1 - 2-17}
}
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+ title = {Discontinuous {G}alerkin Methods: Theory, Computation and Applications},
+ publisher = {Springer},
+ year = {2000},
+ author = {Bernardo Cockburn and George E. Karniadakis and Chi-Wang Shu},
+ address = {Heidelberg, Germany}
}
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+ address = {Paris}
}
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+ publisher = {Springer-Verlag},
+ year = {2002},
+ author = {Gary Cohen},
+ address = {Berlin, Germany}
}
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+ title = {Schemes fourth-order in time and space for 2{D} elastodynamics equations},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1988},
+ pages = {1288-1291},
+ note = {58th international meeting of the SEG}
}
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+ author = {G. Cohen and S. Fauqueux},
+ title = {Mixed Spectral Finite Elements for the Linear Elasticity System in
+ Unbounded Domains},
+ journal = {SIAM Journal on Scientific Computing},
+ year = {2005},
+ volume = {26},
+ pages = {864-884},
+ number = {3},
+ doi = {10.1137/S1064827502407457}
}
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+ author = {G. Cohen and S. Fauqueux},
+ title = {Mixed finite elements with mass lumping for the transient wave equation},
+ journal = jca,
+ year = {2000},
+ volume = {8},
+ pages = {171-188},
+ number = {1},
+ doi = {10.1142/S0218396X0000011X}
}
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+ author = {G. Cohen and P. Joly and J. E. Roberts and N. Tordjman},
+ title = {Higher-Order Triangular Finite Elements with Mass Lumping for the
+ Wave Equation},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {2001},
+ volume = {38},
+ pages = {2047-2078},
+ number = {6},
+ doi = {10.1137/S0036142997329554}
}
@INPROCEEDINGS{CoJoTo93,
-author = {G. Cohen and P. Joly and N. Tordjman},
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-lumping for the wave equation},
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-and numerical aspects of wave propagation},
-year = {1993},
-editor = {R. Kleinman},
-pages = {152-160},
-publisher = {SIAM, Philadelphia, Pennsylvania, USA}
+ author = {G. Cohen and P. Joly and N. Tordjman},
+ title = {Construction and analysis of higher-order finite elements with mass
+ lumping for the wave equation},
+ booktitle = {Proceedings of the second international conference on mathematical
+ and numerical aspects of wave propagation},
+ year = {1993},
+ editor = {R. Kleinman},
+ pages = {152-160},
+ publisher = {SIAM, Philadelphia, Pennsylvania, USA}
}
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+ author = {F. Collino},
+ title = {{P}erfectly matched absorbing layers for the paraxial equations},
+ journal = jcp,
+ year = {1997},
+ volume = {131},
+ pages = {164-180}
}
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+ author = {Collino, F. and Fouquet, T. and Joly, P.},
+ title = {A conservative space-time mesh refinement method for the 1-{D} wave
+ equation. {I}. {C}onstruction},
+ journal = {Numerische Mathematik},
+ year = {2003},
+ volume = {95},
+ pages = {197-221},
+ number = {2}
}
@ARTICLE{CoFoJo03b,
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+ author = {Collino, F. and Fouquet, T. and Joly, P.},
+ title = {A conservative space-time mesh refinement method for the 1-{D} wave
+ equation. {II}. {A}nalysis},
+ journal = {Numerische Mathematik},
+ year = {2003},
+ volume = {95},
+ pages = {223-251},
+ number = {2}
}
@TECHREPORT{CoFoJo98,
-author = {F. Collino and T. Fouquet and P. Joly},
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-pour l'\'equation des ondes},
-institution = {INRIA},
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-note = {Research report RR-3474}
+ author = {F. Collino and T. Fouquet and P. Joly},
+ title = {Analyse num\'erique d'une m\'ethode de raffinement de maillage espace-temps
+ pour l'\'equation des ondes},
+ institution = {INRIA},
+ year = {1998},
+ note = {Research report RR-3474}
}
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+ author = {F. Collino and P. Monk},
+ title = {Optimizing the {P}erfectly {M}atched {L}ayer},
+ journal = cmame,
+ year = {1998},
+ volume = {164},
+ pages = {157-171}
}
@ARTICLE{CoMo98b,
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+ author = {F. Collino and P. Monk},
+ title = {The {P}erfectly {M}atched {L}ayer in curvilinear coordinates},
+ journal = {SIAM J. Sci. Comput.},
+ year = {1998},
+ volume = {19},
+ pages = {2061-2090},
+ number = {6}
}
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+ author = {F. Collino and C. Tsogka},
+ title = {Application of the {PML} absorbing layer model to the linear elastodynamic
+ problem in anisotropic heterogeneous media},
+ journal = geophysics,
+ year = {2001},
+ volume = {66},
+ pages = {294-307},
+ number = {1}
}
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+ author = {V. F. Cormier},
+ title = {Anisotropy of heterogeneity scale lengths in the lower mantle from
+ PKIKP precursors},
+ journal = gji,
+ year = {1999},
+ volume = {136},
+ pages = {373-384}
}
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+ year = {1986},
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+ year = {2003},
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+ author = {Andrew Corrigan and Fernando Camelli and Rainald L{\"o}hner and John
+ Wallin},
+ title = {Running unstructured grid based {CFD} solvers on modern graphics
+ hardware},
+ booktitle = {19th AIAA Computational Fluid Dynamics Conference},
+ year = {2009},
+ pages = {1-11},
+ month = jun,
+ note = {AIAA 2009-4001}
}
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+ author = {R. Courant and K. O. Friedrichs and H. Lewy},
+ title = {\"{U}ber die partiellen {D}ifferenzengleichungen der mathematischen
+ {P}hysik},
+ journal = {Mathematische Annalen},
+ year = {1928},
+ volume = {100},
+ pages = {32-74}
}
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+ title = {On the solution of nonlinear hyperbolic differential equations by
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+ year = {1952},
+ volume = {5},
+ pages = {243-255}
}
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+ journal = gjras,
+ year = {1984},
+ volume = {76},
+ pages = {17-28}
}
@ARTICLE{CrChHi84,
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+ author = {S. Crampin and E. M. Chesnokov and R. G. Hipkin},
+ title = {Seismic anisotropy - the state of the art {II}},
+ journal = gjras,
+ year = {1984},
+ volume = {76},
+ pages = {1-16}
}
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+ author = {S. Crampin and D. B. Taylor},
+ title = {The propagation of surface waves in anisotropic media},
+ journal = gji,
+ year = {1977},
+ volume = {25},
+ pages = {71-87},
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@ARTICLE{CrPiNoMcTa90,
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+ title = {Robust elastic non-linear waveform inversion: application to real
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+ journal = geophysics,
+ year = {1990},
+ volume = {55},
+ pages = {527-538}
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+ author = {P. Cristini and F. Jensen and D. Morisset and J. Piraux and J. P.
+ Sessarego},
+ title = {Experimental benchmarks for numerical propagation models: comparison
+ between numerical results and tank experiments for deep and shallow
+ water environments},
+ booktitle = {Theoretical and Computational Acoustics' 97},
+ publisher = {World Scientific Publisher},
+ year = {1999},
+ editor = {Y H Pao and E C Shang and Y C Teng},
+ pages = {999998-999999}
}
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+ author = {K. T. Danielson and R. R. Namburu},
+ title = {Nonlinear dynamic finite element analysis on parallel computers using
+ {F}ortran90 and {MPI}},
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+ year = {1998},
+ volume = {29},
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}
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+ solid layer interface. {II} {L}eaky waves given rise to by exceptional
+ bulk waves},
+ journal = jasa,
+ year = {1998},
+ volume = {103},
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}
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+ author = {A. N. Darinskii},
+ title = {On the theory of leaky waves in crystals},
+ journal = {Wave Motion},
+ year = {1997},
+ volume = {25},
+ pages = {35-49}
}
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+ author = {A. N. Darinskii and V. I. Alshits and J. Lothe},
+ title = {Simple reflection and leaky waves in the vicinity of a line of exceptional
+ bulk waves},
+ journal = {Wave Motion},
+ year = {1999},
+ volume = {30},
+ pages = {253-274}
}
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+ author = {A. N. Darinskii and V. I. Alshits and J. Lothe and V. N. Lyubimov
+ and A. L. Shuvalov},
+ title = {An existence criterion for the branch of two-component surface waves
+ in anisotropic elastic media},
+ journal = {Wave Motion},
+ year = {1998},
+ volume = {28},
+ pages = {241-257}
}
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+ author = {A. N. Darinskii and M. Weihnacht},
+ title = {Acoustic waves in bounded anisotropic media: theorems, estimations,
+ and computations},
+ journal = {IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control},
+ year = {2005},
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+ pages = {792-801},
+ number = {5}
}
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+ author = {E. Darrigrand},
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+ year = {2003},
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+ author = {I. Daubechies},
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}
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+ belt, the 1987 {W}hittier {N}arrows Earthquake and earthquake hazard},
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+ author = {De Basabe, J. D. and Sen, M. K. and Wheeler, M. F.},
+ title = {The interior penalty discontinuous {G}alerkin method for elastic
+ wave propagation: grid dispersion},
+ journal = gji,
+ year = {2008},
+ volume = {175},
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}
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+ author = {Jon{\'a}s D. {De Basabe} and Mrinal K. Sen},
+ title = {Stability of the high-order finite elements for acoustic or elastic
+ wave propagation with high-order time stepping},
+ journal = gji,
+ year = {2010},
+ volume = {181},
+ pages = {577-590},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2010.04536.x}
}
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+ author = {Jon{\'a}s D. {De Basabe} and Mrinal K. Sen},
+ title = {Grid dispersion and stability criteria of some common finite-element
+ methods for acoustic and elastic wave equations},
+ journal = geophysics,
+ year = {2007},
+ volume = {72},
+ pages = {T81-T95},
+ number = {6},
+ doi = {10.1190/1.2785046}
}
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+ year = {1958},
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}
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+ author = {E. Delavaud and P. Cupillard and G. Festa and J.-P. Vilotte},
+ title = {3{D} Spectral Element Method simulations of the seismic response
+ in the Caracas basin},
+ booktitle = {Proc. of the Third International Symposium on the Effects of Surface
+ Geology on Seismic Motion},
+ year = {2006},
+ volume = {1},
+ pages = {512-522},
+ address = {Grenoble, France}
}
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+ title = {Analyse num\'erique et \'equations diff\'erentielles},
+ publisher = {Presses Universitaires de Grenoble},
+ year = {1991},
+ author = {Jean-Pierre Demailly},
+ address = {Grenoble}
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+ author = {H. Deresiewicz and R. D. Mindlin},
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}
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+ waves},
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+ author = {M. Deschamps and O. Poncelet},
+ title = {Inhomogeneous plane wave and the most energetic complex ray},
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+ year = {2002},
+ volume = {40},
+ pages = {293-296}
}
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+ author = {J. X. Dessa and G. Pascal},
+ title = {Combined traveltime and frequency-domain seismic waveform inversion:
+ a case study on multi-offset ultrasonic data},
+ journal = gji,
+ year = {2003},
+ volume = {154},
+ pages = {117-133},
+ number = {1},
+ doi = {10.1046/j.1365-246X.2003.01956.x}
}
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+ title = {Rayleigh waves in symmetry planes of crystals: explicit secular equations
+ and some explicit wave speeds},
+ journal = {Mechanics of Materials},
+ year = {2003},
+ volume = {35},
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}
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+ title = {The finite element method displayed},
+ publisher = {John Wiley and sons},
+ year = {1984},
+ author = {Gouri Dhatt and Gilbert Touzot},
+ address = {New York}
}
@ARTICLE{DiEz08,
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-medium},
-journal = jcp,
-year = {2008},
-note = {In preparation.}
+ author = {Julien Diaz and Abdela\^aziz Ezziani},
+ title = {A semi-analytical solution for a two-layer non dissipative poroelastic
+ medium},
+ journal = jcp,
+ year = {2008},
+ note = {In preparation.}
}
@ARTICLE{DiGr09,
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-Equations},
-journal = {SIAM J. Sci. Comput.},
-year = {2009},
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-pages = {1985-2014},
-number = {3}
+ author = {Julien Diaz and Marcus J. Grote},
+ title = {Energy Conserving Explicit Local Time Stepping for Second-Order Wave
+ Equations},
+ journal = {SIAM J. Sci. Comput.},
+ year = {2009},
+ volume = {31},
+ pages = {1985-2014},
+ number = {3}
}
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-author = {J. Diaz and P. Joly},
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-year = {2006},
-volume = {195},
-pages = {3820-3853},
-number = {29-32},
-doi = {10.1016/j.cma.2005.02.031}
+ author = {J. Diaz and P. Joly},
+ title = {A time-domain analysis of {PML} models in acoustics},
+ journal = cmame,
+ year = {2006},
+ volume = {195},
+ pages = {3820-3853},
+ number = {29-32},
+ doi = {10.1016/j.cma.2005.02.031}
}
@ARTICLE{DiJo05,
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-time domain fluid-structure interaction},
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-year = {2005},
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-number = {3}
+ author = {J. Diaz and P. Joly},
+ title = {A robust high-order non-conforming finite-element formulation for
+ time domain fluid-structure interaction},
+ journal = jca,
+ year = {2005},
+ volume = {13},
+ pages = {403-431},
+ number = {3}
}
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-month = {March},
-year = {2008},
-note = {{D}r. Dobb's Portal web site},
-url = {www.ddj.com/hpc-high-performance-computing/207200659}
+ author = {Dr. Dobb's},
+ month = {March},
+ year = {2008},
+ note = {{D}r. Dobb's Portal web site},
+ url = {www.ddj.com/hpc-high-performance-computing/207200659}
}
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-year = {2007},
-pages = {1-5},
-address = {Boston, Massachusetts, USA},
-month = {October},
-url = {www.irisa.fr/caps/projects/Astex}
+ author = {R. Dolbeau and S. Bihan and F. Bodin},
+ title = {{HMPP: A} Hybrid Multi-core Parallel Programming Environment},
+ booktitle = {Proceedings of the Workshop on General Purpose Processing on Graphics
+ Processing Units (GPGPU'2007)},
+ year = {2007},
+ pages = {1-5},
+ address = {Boston, Massachusetts, USA},
+ month = {October},
+ url = {www.irisa.fr/caps/projects/Astex}
}
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-conditions for acoustic and elastic wave equations},
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-year = {2005},
-volume = {2},
-pages = {192-198},
-doi = {10.1088/1742-2132/2/3/003}
+ author = {Liangguo Dong and Deping She and Luping Guan and Zaitian Ma},
+ title = {An eigenvalue decomposition method to construct absorbing boundary
+ conditions for acoustic and elastic wave equations},
+ journal = {J. Geophys. Eng.},
+ year = {2005},
+ volume = {2},
+ pages = {192-198},
+ doi = {10.1088/1742-2132/2/3/003}
}
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+ journal = {Geophys. J. R. astr. Soc.},
+ year = {1983},
+ volume = {75},
+ pages = {693-711}
}
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+ journal = {Geophys. J. R. astr. Soc.},
+ year = {1979},
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}
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+ boundary layer},
+ journal = pepi,
+ year = {1986},
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}
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+ year = {1995},
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}
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+ author = {Christophe Doursat},
+ title = {Qualit\'es, d\'efauts et am\'eliorations des maillages alg\'ebriques
+ et elliptiques},
+ school = {Universit\'e Paris {\sc VI} Jussieu},
+ year = {1994},
+ address = {Paris}
}
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+ author = {L. A. Drake},
+ title = {Love and {R}ayleigh waves in nonhorizontally layered media},
+ journal = bssa,
+ year = {1972},
+ volume = {62},
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+ number = {5}
}
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+ author = {M. Dravinski and T. K. Mossessian},
+ title = {Scattering of plane harmonic {{\it P}}, {{\it SV}} and {R}ayleigh
+ waves by dipping layers of arbitrary shape},
+ journal = bssa,
+ year = {1987},
+ volume = {77},
+ pages = {212-235}
}
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+ journal = bssa,
+ year = {1990},
+ volume = {80},
+ pages = {1162-1179}
}
@ARTICLE{DrGi07a,
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-year = {2007},
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-pages = {T9-T17},
-number = {2},
-doi = {10.1190/1.2424888}
+ author = {Francis H. Drossaert and Antonios Giannopoulos},
+ title = {A nonsplit complex frequency-shifted {PML} based on recursive integration
+ for {FDTD} modeling of elastic waves},
+ journal = geophysics,
+ year = {2007},
+ volume = {72},
+ pages = {T9-T17},
+ number = {2},
+ doi = {10.1190/1.2424888}
}
@ARTICLE{DrGi07b,
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-volume = {44},
-pages = {593-604},
-number = {7-8},
-doi = {10.1016/j.wavemoti.2007.03.003}
+ author = {F. H. Drossaert and A. Giannopoulos},
+ title = {Complex frequency shifted convolution {PML} for {FDTD} modelling
+ of elastic waves},
+ journal = {Wave Motion},
+ year = {2007},
+ volume = {44},
+ pages = {593-604},
+ number = {7-8},
+ doi = {10.1016/j.wavemoti.2007.03.003}
}
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+ author = {Jean-Jacques Droux},
+ title = {An algorithm to optimally color a mesh},
+ journal = cmame,
+ year = {1993},
+ volume = {104},
+ pages = {249-260},
+ number = {2},
+ doi = {10.1016/0045-7825(93)90199-8}
}
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+ volume = {6},
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}
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-and Freysteinn Sigmundsson},
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-sequence in the south {I}celand seismic zone},
-journal = {Tectonophysics},
-year = {2008},
-volume = {457},
-pages = {12-29},
-doi = {10.1016/j.tecto.2008.05.020}
+ author = {L. Dubois and Kurt L. Feigl and Dimitri Komatitsch and T. \'Arnad\'ottir
+ and Freysteinn Sigmundsson},
+ title = {Three-dimensional mechanical models for the {J}une 2000 earthquake
+ sequence in the south {I}celand seismic zone},
+ journal = {Tectonophysics},
+ year = {2008},
+ volume = {457},
+ pages = {12-29},
+ doi = {10.1016/j.tecto.2008.05.020}
}
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-journal = {Bull. Soc. G\'eol. Fr.},
-year = {2003},
-volume = {174},
-pages = {33-44},
-number = {1}
+ author = {N. Dubos and A. Souriau and C. Ponsolles and J. F. Fels and G. S\'en\'echal},
+ title = {{\'E}tude des effets de sites dans la ville de {L}ourdes ({P}yr\'en\'ees,
+ {F}rance) par la m\'ethode des rapports spectraux},
+ journal = {Bull. Soc. G\'eol. Fr.},
+ year = {2003},
+ volume = {174},
+ pages = {33-44},
+ number = {1}
}
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-year = {2008},
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-doi = {10-1098/rsta.2008.0172}
+ author = {Th. S. Duffy},
+ title = {Some recent advances in understanding the mineralogy of {E}arth's
+ deep mantle},
+ journal = {Phil. Trans. R. Soc. A},
+ year = {2008},
+ volume = {366},
+ pages = {4273-4293},
+ doi = {10-1098/rsta.2008.0172}
}
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-number = {1},
-doi = {10.1111/j.1365-246X.2006.03120.x}
+ author = {M. Dumbser and M. K\"aser},
+ title = {An arbitrary high-order discontinuous {G}alerkin method for elastic
+ waves on unstructured meshes-{II}. {T}he three-dimensional isotropic
+ case},
+ journal = gji,
+ year = {2006},
+ volume = {167},
+ pages = {319-336},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2006.03120.x}
}
@ARTICLE{DuKaTo07,
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+ author = {Michael Dumbser and Martin K\"aser and Eleuterio Toro},
+ title = {An arbitrary high-order discontinuous {G}alerkin method for elastic
+ waves on unstructured meshes, {P}art {V}: Local time stepping and
+ $p$-adaptivity},
+ journal = gji,
+ year = {2007},
+ volume = {171},
+ pages = {695-717},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2007.03427.x}
}
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+ author = {T. Dupond},
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+ equations},
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+ volume = {10},
+ pages = {880-891}
}
@ARTICLE{DuDeFoKoRo10,
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-number = {5-6},
-doi = {10.1016/j.parco.2009.12.011}
+ author = {Fabrice Dupros and de Martin, Florent and Evelyne Foerster and Dimitri
+ Komatitsch and Jean Roman},
+ title = {High-performance finite-element simulations of seismic wave propagation
+ in three-dimensional non linear inelastic geological media},
+ journal = {Parallel Computing},
+ year = {2010},
+ volume = {36},
+ pages = {308-325},
+ number = {5-6},
+ doi = {10.1016/j.parco.2009.12.011}
}
@ARTICLE{DuPoAoMeKoRo11,
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-to the finite-difference method for seismic wave propagation},
-journal = {Concurrency Computation Practice and Experience},
-year = {2011},
-note = {Submitted in October 2010.}
+ author = {Fabrice Dupros and Christiane Pousa-Ribeiro and Hideo Aochi and Jean-Fran\c{c}ois
+ M\'{e}haut and Dimitri Komatitsch and Jean Roman},
+ title = {Efficient stencil computation on multicore architectures: {A}pplication
+ to the finite-difference method for seismic wave propagation},
+ journal = {Concurrency Computation Practice and Experience},
+ year = {2011},
+ note = {Submitted in October 2010.}
}
@ARTICLE{DuJoGuKeKo10,
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-year = {2010},
-volume = {42},
-pages = {129-138},
-number = {2},
-doi = {10.1016/j.cad.2009.04.016}
+ author = {Guilhem Dupuy and Bruno Jobard and Sebastien Guillon and Noomane
+ Keskes and Dimitri Komatitsch},
+ title = {Parallel extraction and simplification of large isosurfaces using
+ an extended tandem algorithm},
+ journal = {Computer-Aided Design},
+ year = {2010},
+ volume = {42},
+ pages = {129-138},
+ number = {2},
+ doi = {10.1016/j.cad.2009.04.016}
}
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+ author = {B. Duquet and B. Lavaud and F. Prat},
+ title = {Improving {GSP} Extrapolators},
+ booktitle = {Proceedings of the SEG},
+ year = {2003},
+ note = {submitted.}
}
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+ address = {Paris}
}
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}
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+ author = {A. M. Dziewo\'nski},
+ title = {Global seismic tomography: past, present, and future},
+ booktitle = {Problems in Geophysics for the New Millennium},
+ publisher = {INGV},
+ year = {2000},
+ editor = {E. Boschi and G. Ekstr\"{o}m and A. Morelli},
+ pages = {289-350},
+ address = {Roma, Italy}
}
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+ journal = pepi,
+ year = {1981},
+ volume = {25},
+ pages = {297-356}
}
@ARTICLE{Dziewonski77,
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+ author = {Dziewo\'nski, A. M. and B. H. Hager and R. J. O'Connell},
+ title = {Large-scale heterogeneities in the lower mantle},
+ journal = jgr,
+ year = {1977},
+ volume = {82},
+ pages = {239--255}
}
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+ author = {D. Eberhart-Phillips and P. J. Haeussler and J. T. Freymueller and
+ A. D. Frankel and C. M. Rubin and P. Craw and N. A. Ratchkovski and
+ G. Anderson and G. A. Carver and A. J. Crone and T. E. Dawson and
+ H. Fletcher and R. Hansen and E. L. Harp and R. A. Harris and D.
+ P. Hill and S. Hreinsdottir and R. W. Jibson and L. M. Jones and
+ R. Kayen and D. K. Keefer and C. F. Larsen and S. C. Moran and S.
+ F. Personius and G. Plafker and B. Sherrod and K. Sieh and N. Sitar
+ and W. K. Wallace},
+ title = {The 2002 {D}enali Fault Earthquake, {A}laska: a Large Magnitude,
+ Slip-Partitioned Event},
+ journal = {Science},
+ year = {2003},
+ volume = {300},
+ pages = {1113-1118}
}
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+ author = {L. Eisner and R. W. Clayton},
+ title = {A full waveform test of the southern {C}alifornia velocity model
+ by the reciprocity method},
+ journal = pageoph,
+ year = {2002},
+ volume = {159},
+ pages = {1691-1706}
}
@ARTICLE{Eks95,
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+ title = {Solving the advection-diffusion equation on unstructured meshes with
+ discontinuous/mixed finite elements and a local time stepping procedure},
+ journal = ijnme,
+ year = {2009},
+ volume = {79},
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+ author = {Erich Elsen and Patrick LeGresley and Eric Darve},
+ title = {Large calculation of the flow over a hypersonic vehicle using a {GPU}},
+ journal = jcp,
+ year = {2008},
+ volume = {227},
+ pages = {10148--10161},
+ number = {24},
+ month = dec,
+ doi = {10.1016/j.jcp.2008.08.023}
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+ signature {V}(z) of an anisotropic solid},
+ journal = {Ultrasonics},
+ year = {2003},
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}
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+ title = {Surface dynamic response functions of anisotropic solids},
+ journal = {Ultrasonics},
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+ author = {A. G. Every and K. Y. Kim and A. A. Maznev},
+ title = {The elastodynamic response of a semi-infinite anisotropic solid to
+ sudden surface loading},
+ journal = jasa,
+ year = {1997},
+ volume = {102},
+ pages = {1346-1354},
+ number = {3}
}
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-Appliqu\'ees ARIMA},
-year = {2006},
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+ author = {A. Ezziani},
+ title = {Ondes dans les milieux poro\'elastiques : analyse du mod\`ele de
+ {B}iot},
+ journal = {Revue Africaine de la Recherche en Informatique et Math\'ematiques
+ Appliqu\'ees ARIMA},
+ year = {2006},
+ volume = {5},
+ pages = {95-109}
}
@PHDTHESIS{Ez2005,
-author = {A. Ezziani},
-title = {Mod\'elisation math\'ematique et num\'erique de la propagation d'ondes
-dans des milieux visco\'elastiques et poro\'elastiques},
-school = {Universit\'e Paris IX, France},
-year = {2005},
-address = {Paris, France}
+ author = {A. Ezziani},
+ title = {Mod\'elisation math\'ematique et num\'erique de la propagation d'ondes
+ dans des milieux visco\'elastiques et poro\'elastiques},
+ school = {Universit\'e Paris IX, France},
+ year = {2005},
+ address = {Paris, France}
}
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+ author = {E. Faccioli and F. Maggio and R. Paolucci and A. Quarteroni},
+ title = {2{D} and 3{D} elastic wave propagation by a pseudo-spectral domain
+ decomposition method},
+ journal = {J. Seismol.},
+ year = {1997},
+ volume = {1},
+ pages = {237-251}
}
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+ author = {E. Faccioli and F. Maggio and A. Quarteroni and A. Tagliani},
+ title = {Spectral-domain decomposition methods for the solution of acoustic
+ and elastic wave equations},
+ journal = geophysics,
+ year = {1996},
+ volume = {61},
+ pages = {1160-1174},
+ number = {4}
}
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+ author = {Falk, Richard S. and Richter, Gerard R.},
+ title = {Explicit Finite Element Methods for Symmetric Hyperbolic Equations},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1999},
+ volume = {36},
+ pages = {935-952},
+ number = {3},
+ doi = {10.1137/S0036142997329463}
}
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+ title = {Multidomain pseudospectral time-domain simulations of scattering
+ by objects buried in lossy media},
+ journal = {IEEE Trans. Geosci. Remote Sens.},
+ year = {2002},
+ volume = {GE-40},
+ pages = {1366-1373}
}
@INPROCEEDINGS{FaQiKa08,
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-and Visualization (EGPGV'08)},
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-editor = {G. Drettakis and R. Scopigno},
-volume = {27(2)},
-pages = {341-350},
-address = {Hersonissos, Crete, Greece},
-month = {April}
+ author = {Zhe Fan and Feng Qiu and Arie E. Kaufman},
+ title = {Zippy: A Framework for Computation and Visualization on a {GPU} Cluster},
+ booktitle = {Proceedings of the Eurographics'2008 Symposium on Parallel Graphics
+ and Visualization (EGPGV'08)},
+ year = {2008},
+ editor = {G. Drettakis and R. Scopigno},
+ volume = {27(2)},
+ pages = {341-350},
+ address = {Hersonissos, Crete, Greece},
+ month = {April}
}
@INPROCEEDINGS{Fan:2004:GCF,
-author = {Zhe Fan and Feng Qiu and Arie E. Kaufman and Suzanne Yoakum-Stover},
-title = {{GPU} Cluster for High Performance Computing},
-booktitle = {{SC '04}: Proceedings of the 2004 {ACM/IEEE} conference on Supercomputing},
-year = {2004},
-pages = {47},
-month = nov,
-doi = {10.1109/SC.2004.26}
+ author = {Zhe Fan and Feng Qiu and Arie E. Kaufman and Suzanne Yoakum-Stover},
+ title = {{GPU} Cluster for High Performance Computing},
+ booktitle = {{SC '04}: Proceedings of the 2004 {ACM/IEEE} conference on Supercomputing},
+ year = {2004},
+ pages = {47},
+ month = nov,
+ doi = {10.1109/SC.2004.26}
}
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+ multiprocessors},
+ journal = cmame,
+ year = {1989},
+ volume = {72},
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-year = {2001},
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+ author = {C. Farhat and I. Harari and L. P. Franca},
+ title = {The discontinuous enrichment method},
+ journal = cmame,
+ year = {2001},
+ volume = {190},
+ pages = {6455-6479}
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+ author = {C. Farhat and I. Harari and U. Hetmaniuk},
+ title = {A discontinuous {G}alerkin method with {L}agrange multipliers for
+ the solution of {H}elmholtz problems in the mid-frequency regime},
+ journal = cmame,
+ year = {2003},
+ volume = {192},
+ pages = {1389-1419}
}
@ARTICLE{farhathararihetmaniuk20032,
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-journal = cmame,
-year = {2003},
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+ author = {C. Farhat and I. Harari and U. Hetmaniuk},
+ title = {The discontinuous enrichment method for multiscale analysis},
+ journal = cmame,
+ year = {2003},
+ volume = {192},
+ pages = {3195-3209}
}
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+ author = {C. H. Farhat},
+ title = {A simple and efficient automatic {FEM} domain decomposer},
+ institution = {University of Colorado},
+ year = {1987},
+ address = {Boulder, Colorado}
}
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+ author = {G. W. Farnell},
+ title = {Properties of elastic surface waves},
+ booktitle = {Physical Acoustics},
+ publisher = {Academic Press, New York, USA},
+ year = {1970},
+ editor = {W. P. Mason and R. N. Thurston},
+ volume = {6},
+ chapter = {3},
+ pages = {109-166}
}
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+ author = {G. W. Farnell},
+ title = {Review of pseudo-surface waves},
+ booktitle = {Proceedings of the "Surface waves in solids and layered structures
+ (ISSWAS86)" International Symposium},
+ year = {1986},
+ volume = {3},
+ pages = {7-20},
+ address = {Novosibirsk, Russia}
}
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+ author = {V. Farra},
+ title = {Computation of second-order travel-time perturbation by {H}amiltonian
+ ray theory},
+ journal = gji,
+ year = {1999},
+ volume = {136},
+ pages = {205-217}
}
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+ author = {V. Farra},
+ title = {Ray tracing in complex media},
+ journal = {J. Appl. Geophys.},
+ year = {1993},
+ volume = {30},
+ pages = {55-73}
}
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+ year = {1990},
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@ARTICLE{Fatahalian:2008:ACL,
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-year = {2008},
-volume = {51},
-pages = {50--57},
-number = {10},
-month = oct,
-doi = {10.1145/1400181.1400197}
+ author = {Kayvon Fatahalian and Mike Houston},
+ title = {A Closer Look at {GPUs}},
+ journal = {Communications of the ACM},
+ year = {2008},
+ volume = {51},
+ pages = {50--57},
+ number = {10},
+ month = oct,
+ doi = {10.1145/1400181.1400197}
}
@INPROCEEDINGS{Fatica:2009:ALW,
-author = {Massimiliano Fatica},
-title = {Accelerating {L}inpack with {CUDA} on heterogenous clusters},
-booktitle = {GPGPU-2: Proceedings of 2nd Workshop on General Purpose Processing
-on Graphics Processing Units},
-year = {2009},
-editor = {David Kaeli and Miriam Leeser},
-number = {383},
-series = {ACM International Conference Proceeding Series},
-pages = {46--51},
-month = mar,
-doi = {10.1145/1513895.1513901}
+ author = {Massimiliano Fatica},
+ title = {Accelerating {L}inpack with {CUDA} on heterogenous clusters},
+ booktitle = {GPGPU-2: Proceedings of 2nd Workshop on General Purpose Processing
+ on Graphics Processing Units},
+ year = {2009},
+ editor = {David Kaeli and Miriam Leeser},
+ number = {383},
+ series = {ACM International Conference Proceeding Series},
+ pages = {46--51},
+ month = mar,
+ doi = {10.1145/1513895.1513901}
}
@PHDTHESIS{Fau03,
-author = {Sandrine Fauqueux},
-title = {El\'ements finis mixtes spectraux et couches absorbantes parfaitement
-adapt\'ees pour la propagation d'ondes \'elastiques en r\'egime transitoire},
-school = {Universit\'e Paris-Dauphine},
-year = {2003},
-address = {Paris, France},
-month = {February}
+ author = {Sandrine Fauqueux},
+ title = {El\'ements finis mixtes spectraux et couches absorbantes parfaitement
+ adapt\'ees pour la propagation d'ondes \'elastiques en r\'egime transitoire},
+ school = {Universit\'e Paris-Dauphine},
+ year = {2003},
+ address = {Paris, France},
+ month = {February}
}
@ARTICLE{FaCh03,
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-title = {Sensitivity kernels for shear wave splitting in transverse isotropic
-media},
-journal = gji,
-year = {2003},
-volume = {153},
-pages = {213-228},
-number = {1}
+ author = {N. Favier and S. Chevrot},
+ title = {Sensitivity kernels for shear wave splitting in transverse isotropic
+ media},
+ journal = gji,
+ year = {2003},
+ volume = {153},
+ pages = {213-228},
+ number = {1}
}
@ARTICLE{FaChKo04,
-author = {N. Favier and S. Chevrot and D. Komatitsch},
-title = {Near-field influences on shear wave splitting and traveltime sensitivity
-kernels},
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-year = {2004},
-volume = {156},
-pages = {467-482},
-number = {3},
-doi = {10.1111/j.1365-246X.2004.02178.x}
+ author = {N. Favier and S. Chevrot and D. Komatitsch},
+ title = {Near-field influences on shear wave splitting and traveltime sensitivity
+ kernels},
+ journal = gji,
+ year = {2004},
+ volume = {156},
+ pages = {467-482},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2004.02178.x}
}
@ARTICLE{gp03,
-author = {N. Favretto-Cristini and E. de Bazelaire},
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-waves guilty?},
-journal = {Geophysical Prospecting},
-year = {2003},
-volume = {51},
-pages = {99-115}
+ author = {N. Favretto-Cristini and E. de Bazelaire},
+ title = {P{P} amplitude bias caused by interface scattering: are diffracted
+ waves guilty?},
+ journal = {Geophysical Prospecting},
+ year = {2003},
+ volume = {51},
+ pages = {99-115}
}
@ARTICLE{FaKoCaCa11,
-author = {Nathalie Favretto-Cristini and Dimitri Komatitsch and Jos\'e Carcione
-and Fabio Cavallini},
-title = {Elastic surface waves in crystals: {R}eview of the physics and cross-check
-of two full-wave modeling methods},
-journal = jasa,
-year = {2011},
-note = {Submitted in October 2010.}
+ author = {Nathalie Favretto-Cristini and Dimitri Komatitsch and Jos\'e Carcione
+ and Fabio Cavallini},
+ title = {Elastic surface waves in crystals: {P}art {I} : Review of the physics},
+ journal = {Ultrasonics},
+ year = {2011},
+ volume = {51},
+ pages = {653-660},
+ number = {6},
+ doi = {10.1016/j.ultras.2011.02.007}
}
@ARTICLE{Fejer32,
-author = {L. Fej\'er},
-title = {Bestimmung derjenigen {A}bszissen eines {I}ntervalles f\"ur welche
-die {Q}uadratsumme der {G}rundfunktionen der {L}agrangeschen {I}nterpolation
-im {I}ntervalle $[-1,1]$ ein m\"oglichst kleines {M}aximum besitzt},
-journal = {Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mt. Ser. II},
-year = {1932},
-volume = {1},
-pages = {263-276}
+ author = {L. Fej\'er},
+ title = {Bestimmung derjenigen {A}bszissen eines {I}ntervalles f\"ur welche
+ die {Q}uadratsumme der {G}rundfunktionen der {L}agrangeschen {I}nterpolation
+ im {I}ntervalle $[-1,1]$ ein m\"oglichst kleines {M}aximum besitzt},
+ journal = {Ann. Scuola Norm. Sup. Pisa Sci. Fis. Mt. Ser. II},
+ year = {1932},
+ volume = {1},
+ pages = {263-276}
}
@ARTICLE{FeDe84,
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-title = {Finite-element analysis of shock-induced hull cavitation},
-journal = cmame,
-year = {1984},
-volume = {44},
-pages = {297-337}
+ author = {C. A. Felippa and J. A. Deruntz},
+ title = {Finite-element analysis of shock-induced hull cavitation},
+ journal = cmame,
+ year = {1984},
+ volume = {44},
+ pages = {297-337}
}
@ARTICLE{Felsen,
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-and {G}aussian Beams},
-journal = gjras,
-year = {1984},
-volume = {79},
-pages = {77-88}
+ author = {L. B. Felsen},
+ title = {Geometrical Theory of Diffraction, Evanescent Waves, Complex Rays
+ and {G}aussian Beams},
+ journal = gjras,
+ year = {1984},
+ volume = {79},
+ pages = {77-88}
}
@ARTICLE{FeBo06,
-author = {Clark H. Fenton and Julian J. Bommer},
-title = {The {M}w7 {M}achaze, {M}ozambique, Earthquake of 23 {F}ebruary 2006},
-journal = {Seismological Research Letters},
-year = {2006},
-volume = {77},
-pages = {426-439},
-number = {4}
+ author = {Clark H. Fenton and Julian J. Bommer},
+ title = {The {M}w7 {M}achaze, {M}ozambique, Earthquake of 23 {F}ebruary 2006},
+ journal = {Seismological Research Letters},
+ year = {2006},
+ volume = {77},
+ pages = {426-439},
+ number = {4}
}
@ARTICLE{FeDeVi05,
-author = {G. Festa and E. Delavaud and J. P. Vilotte},
-title = {Interaction between surface waves and absorbing boundaries for wave
-propagation in geological basins: {2D} numerical simulations},
-journal = grl,
-year = {2005},
-volume = {32},
-pages = {L20306},
-number = {20},
-doi = {10.1029/2005GL024091}
+ author = {G. Festa and E. Delavaud and J. P. Vilotte},
+ title = {Interaction between surface waves and absorbing boundaries for wave
+ propagation in geological basins: {2D} numerical simulations},
+ journal = grl,
+ year = {2005},
+ volume = {32},
+ pages = {L20306},
+ number = {20},
+ doi = {10.1029/2005GL024091}
}
@ARTICLE{FeNi03,
-author = {Gaetano Festa and Stefan Nielsen},
-title = {{PML} absorbing boundaries},
-journal = bssa,
-year = {2003},
-volume = {93},
-pages = {891-903}
+ author = {Gaetano Festa and Stefan Nielsen},
+ title = {{PML} absorbing boundaries},
+ journal = bssa,
+ year = {2003},
+ volume = {93},
+ pages = {891-903}
}
@ARTICLE{FeVi05,
-author = {G. Festa and J. P. Vilotte},
-title = {The {N}ewmark scheme as velocity-stress time-staggering: an efficient
-{PML} implementation for spectral-element simulations of elastodynamics},
-journal = gji,
-year = {2005},
-volume = {161},
-pages = {789-812},
-doi = {10.1111/j.1365-246X.2005.02601.x}
+ author = {G. Festa and J. P. Vilotte},
+ title = {The {N}ewmark scheme as velocity-stress time-staggering: an efficient
+ {PML} implementation for spectral-element simulations of elastodynamics},
+ journal = gji,
+ year = {2005},
+ volume = {161},
+ pages = {789-812},
+ doi = {10.1111/j.1365-246X.2005.02601.x}
}
@ARTICLE{FiIgBuKe09,
-author = {Andreas Fichtner and Heiner Igel and Hans-Peter Bunge and Brian L.
-N. Kennett},
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-scales based on a spectral-element method},
-journal = {Journal of Numerical Analysis, Industrial and Applied Mathematics},
-year = {2009},
-volume = {4},
-pages = {11-22},
-number = {1-2}
+ author = {Andreas Fichtner and Heiner Igel and Hans-Peter Bunge and Brian L.
+ N. Kennett},
+ title = {Simulation and inversion of seismic wave propagation on continental
+ scales based on a spectral-element method},
+ journal = {Journal of Numerical Analysis, Industrial and Applied Mathematics},
+ year = {2009},
+ volume = {4},
+ pages = {11-22},
+ number = {1-2}
}
@ARTICLE{fink99,
-author = {M. Fink},
-title = {Time-reversed acoutics},
-journal = {Scientific American},
-year = {1999},
-pages = {91-97},
-month = {November}
+ author = {M. Fink},
+ title = {Time-reversed acoutics},
+ journal = {Scientific American},
+ year = {1999},
+ pages = {91-97},
+ month = {November}
}
@ARTICLE{Fis90,
-author = {P. F. Fischer},
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-the solution of the {N}avier-{S}tokes equations},
-journal = cmame,
-year = {1990},
-volume = {80},
-pages = {483-491}
+ author = {P. F. Fischer},
+ title = {Analysis and application of a parallel spectral element method for
+ the solution of the {N}avier-{S}tokes equations},
+ journal = cmame,
+ year = {1990},
+ volume = {80},
+ pages = {483-491}
}
@PHDTHESIS{Fis89,
-author = {P. F. Fischer},
-title = {Spectral element solution of the {N}avier-{S}tokes equations on high
-performance distributed-memory parallel processors},
-school = {Massachusetts Institute of Technology},
-year = {1989},
-address = {Cambridge, Massachusetts}
+ author = {P. F. Fischer},
+ title = {Spectral element solution of the {N}avier-{S}tokes equations on high
+ performance distributed-memory parallel processors},
+ school = {Massachusetts Institute of Technology},
+ year = {1989},
+ address = {Cambridge, Massachusetts}
}
@ARTICLE{FiHoKaRoPa88,
-author = {P. F. Fischer and L. W. Ho and G. E. Karniadakis and E. M. R{\o}nquist
-and A. T. Patera},
-title = {Recent advances in parallel spectral element simulation of unsteady
-incompressible flows},
-journal = {Computers and Structures},
-year = {1988},
-volume = {30},
-pages = {217-231}
+ author = {P. F. Fischer and L. W. Ho and G. E. Karniadakis and E. M. R{\o}nquist
+ and A. T. Patera},
+ title = {Recent advances in parallel spectral element simulation of unsteady
+ incompressible flows},
+ journal = {Computers and Structures},
+ year = {1988},
+ volume = {30},
+ pages = {217-231}
}
@ARTICLE{FiRo94,
-author = {P. F. Fischer and E. M. R{\o}nquist},
-title = {{S}pectral-element Methods for Large Scale Parallel {N}avier-{S}tokes
-Calculations},
-journal = cmame,
-year = {1994},
-volume = {116},
-pages = {69-76}
+ author = {P. F. Fischer and E. M. R{\o}nquist},
+ title = {{S}pectral-element Methods for Large Scale Parallel {N}avier-{S}tokes
+ Calculations},
+ journal = cmame,
+ year = {1994},
+ volume = {116},
+ pages = {69-76}
}
@ARTICLE{Fish3,
-author = {L. Fishman},
-title = {Applications of {D}irectional {W}avefield {D}ecomposition, {P}hase
-{S}pace and {P}ath {I}ntegral {M}ethods to {S}eismic {W}ave {P}ropagation
-and {I}nversion},
-journal = {Pure and Applied Geophysics},
-year = {2002},
-volume = {159},
-pages = {1637-1679}
+ author = {L. Fishman},
+ title = {Applications of {D}irectional {W}avefield {D}ecomposition, {P}hase
+ {S}pace and {P}ath {I}ntegral {M}ethods to {S}eismic {W}ave {P}ropagation
+ and {I}nversion},
+ journal = {Pure and Applied Geophysics},
+ year = {2002},
+ volume = {159},
+ pages = {1637-1679}
}
@ARTICLE{Fish1,
-author = {L. Fishman},
-title = {Exact and {O}perator {R}ational {A}pproximate {S}olutions of the
-{H}elmholtz, {W}eyl {C}omposition {E}quation in {U}nderwater {A}coustics
-- the {Q}uadratic {P}rofile},
-journal = {J. Math. Phys.},
-year = {1992},
-volume = {33},
-pages = {1887-1914}
+ author = {L. Fishman},
+ title = {Exact and {O}perator {R}ational {A}pproximate {S}olutions of the
+ {H}elmholtz, {W}eyl {C}omposition {E}quation in {U}nderwater {A}coustics
+ - the {Q}uadratic {P}rofile},
+ journal = {J. Math. Phys.},
+ year = {1992},
+ volume = {33},
+ pages = {1887-1914}
}
@ARTICLE{Fish2,
-author = {L. Fishman and J. J. McCoy and S. C. Wales},
-title = {Factorization and Path Integration of the {H}elmholtz Equation :
-{N}umerical Algorithms},
-journal = {J. Acoust. Soc. Am.},
-year = {1987},
-volume = {81},
-pages = {1355-1376}
+ author = {L. Fishman and J. J. McCoy and S. C. Wales},
+ title = {Factorization and Path Integration of the {H}elmholtz Equation :
+ {N}umerical Algorithms},
+ journal = {J. Acoust. Soc. Am.},
+ year = {1987},
+ volume = {81},
+ pages = {1355-1376}
}
@BOOK{Fle91,
-title = {Computational Fluid Dynamics},
-publisher = {Springer-Verlag},
-year = {1991},
-author = {C. A. J. Fletcher},
-address = {New York}
+ title = {Computational Fluid Dynamics},
+ publisher = {Springer-Verlag},
+ year = {1991},
+ author = {C. A. J. Fletcher},
+ address = {New York}
}
@ARTICLE{taf,
-author = {T. A. Foley},
-title = {Weighted bicubic spline interpolation to rapidly varying data},
-journal = {ACM Trans. Graphics},
-year = {1987},
-volume = {6},
-pages = {1-18}
+ author = {T. A. Foley},
+ title = {Weighted bicubic spline interpolation to rapidly varying data},
+ journal = {ACM Trans. Graphics},
+ year = {1987},
+ volume = {6},
+ pages = {1-18}
}
@PHDTHESIS{Fon06,
-author = {Mathieu Fontes},
-title = {Propri\'et\'es math\'ematiques de mod\`eles g\'eophysiques pour l'absorption
-des ondes. {A}pplication aux conditions de bords absorbants. ({M}athematical
-properties of geophysical models for the absorption of waves. {A}pplication
-to absorbing boundary conditions)},
-school = {Universit\'e de Pau et des Pays de l'Adour},
-year = {2006},
-address = {Pau, France},
-month = {July}
+ author = {Mathieu Fontes},
+ title = {Propri\'et\'es math\'ematiques de mod\`eles g\'eophysiques pour l'absorption
+ des ondes. {A}pplication aux conditions de bords absorbants. ({M}athematical
+ properties of geophysical models for the absorption of waves. {A}pplication
+ to absorbing boundary conditions)},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {2006},
+ address = {Pau, France},
+ month = {July}
}
@ARTICLE{For88,
-author = {B. Fornberg},
-title = {The pseudospectral method: accurate representation of interfaces
-in elastic wave calculations},
-journal = geophysics,
-year = {1988},
-volume = {53},
-pages = {625-637}
+ author = {B. Fornberg},
+ title = {The pseudospectral method: accurate representation of interfaces
+ in elastic wave calculations},
+ journal = geophysics,
+ year = {1988},
+ volume = {53},
+ pages = {625-637}
}
@ARTICLE{For75,
-author = {D. W. Forsyth},
-title = {The early structural evolution and anisotropy of the oceanic upper
-mantle},
-journal = gjras,
-year = {1975},
-volume = {43},
-pages = {103-162}
+ author = {D. W. Forsyth},
+ title = {The early structural evolution and anisotropy of the oceanic upper
+ mantle},
+ journal = gjras,
+ year = {1975},
+ volume = {43},
+ pages = {103-162}
}
@ARTICLE{FoFiWy01,
-author = {M. J. Fouch and K. M. Fischer and M. E. Wysession},
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-source of the {H}awaiian plume},
-journal = epsl,
-year = {2001},
-volume = {190},
-pages = {167-180}
+ author = {M. J. Fouch and K. M. Fischer and M. E. Wysession},
+ title = {Lowermost mantle anisotropy beneath the {P}acific: {I}maging the
+ source of the {H}awaiian plume},
+ journal = epsl,
+ year = {2001},
+ volume = {190},
+ pages = {167-180}
}
@ARTICLE{rf,
-author = {R. Franke},
-title = {Thin plate spline with tension},
-journal = {Computer Aided Geometric Design},
-year = {1985},
-volume = {2},
-pages = {87-95}
+ author = {R. Franke},
+ title = {Thin plate spline with tension},
+ journal = {Computer Aided Geometric Design},
+ year = {1985},
+ volume = {2},
+ pages = {87-95}
}
@ARTICLE{Fra93,
-author = {A. Frankel},
-title = {Three-dimensional simulations of ground motions in the {S}an {B}ernardino
-valley, {C}alifornia, for hypothetical earthquakes on the {S}an {A}ndreas
-fault},
-journal = bssa,
-year = {1993},
-volume = {83},
-pages = {1020-1041}
+ author = {A. Frankel},
+ title = {Three-dimensional simulations of ground motions in the {S}an {B}ernardino
+ valley, {C}alifornia, for hypothetical earthquakes on the {S}an {A}ndreas
+ fault},
+ journal = bssa,
+ year = {1993},
+ volume = {83},
+ pages = {1020-1041}
}
@ARTICLE{FrLe92,
-author = {A. Frankel and W. Leith},
-title = {Evaluation of topographic effects on {{\it P}} and {{\it S}} waves
-of explosions at the northern {N}ovaya {Z}emlya test site using 3-{D}
-numerical simulations},
-journal = grl,
-year = {1992},
-volume = {19},
-pages = {1887-1890}
+ author = {A. Frankel and W. Leith},
+ title = {Evaluation of topographic effects on {{\it P}} and {{\it S}} waves
+ of explosions at the northern {N}ovaya {Z}emlya test site using 3-{D}
+ numerical simulations},
+ journal = grl,
+ year = {1992},
+ volume = {19},
+ pages = {1887-1890}
}
@ARTICLE{FrVi92,
-author = {A. Frankel and J. Vidale},
-title = {A three-dimensional simulation of seismic waves in the {S}anta {C}lara
-valley, {C}alifornia, from the {L}oma {P}rieta aftershock},
-journal = bssa,
-year = {1992},
-volume = {82},
-pages = {2045-2074}
+ author = {A. Frankel and J. Vidale},
+ title = {A three-dimensional simulation of seismic waves in the {S}anta {C}lara
+ valley, {C}alifornia, from the {L}oma {P}rieta aftershock},
+ journal = bssa,
+ year = {1992},
+ volume = {82},
+ pages = {2045-2074}
}
@ARTICLE{FrDa95,
-author = {Wolfgang Friederich and J\"org Dalkolmo},
-title = {Complete synthetic seismograms for a spherically-symmetric {E}arth
-by a numerical computation of the {G}reen's function in the frequency
-domain},
-journal = gji,
-year = {1995},
-volume = {122},
-pages = {537-550},
-number = {2},
-doi = {10.1111/j.1365-246X.1995.tb07012.x}
+ author = {Wolfgang Friederich and J\"org Dalkolmo},
+ title = {Complete synthetic seismograms for a spherically-symmetric {E}arth
+ by a numerical computation of the {G}reen's function in the frequency
+ domain},
+ journal = gji,
+ year = {1995},
+ volume = {122},
+ pages = {537-550},
+ number = {2},
+ doi = {10.1111/j.1365-246X.1995.tb07012.x}
}
@ARTICLE{fuchsmuller1971,
-author = {K. Fuchs and G. Muller},
-title = {Computation of synthetic seismograms with the reflectivity method
-and comparison of observations},
-journal = gjras,
-year = {1971},
-volume = {23},
-pages = {417-433}
+ author = {K. Fuchs and G. Muller},
+ title = {Computation of synthetic seismograms with the reflectivity method
+ and comparison of observations},
+ journal = gjras,
+ year = {1971},
+ volume = {23},
+ pages = {417-433}
}
@ARTICLE{Fuisetal2003,
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-Murphy and M. L. Benthien and S. A. Baher and M. D. Kohler and K.
-Thygesen and G. Simila and G. R. Keller},
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-images from {LARSE~II}},
-journal = {Geology},
-year = {2003},
-volume = {31},
-pages = {171-174}
+ author = {G. S. Fuis and R. W. Clayton and P. M. Davis and T. Ryberg and W.
+ J. Lutter and D. A. Okaya and E. Hauksson and C. Prodehl and J. M.
+ Murphy and M. L. Benthien and S. A. Baher and M. D. Kohler and K.
+ Thygesen and G. Simila and G. R. Keller},
+ title = {Fault systems of the 1971 {S}an {F}ernando and 1994 {N}orthridge
+ earthquakes, {S}outhern {C}alifornia: relocated aftershocks and seismic
+ images from {LARSE~II}},
+ journal = {Geology},
+ year = {2003},
+ volume = {31},
+ pages = {171-174}
}
@BOOK{Fun92,
-title = {Polynomial approximation of differential equations},
-publisher = {Springer Verlag},
-year = {1992},
-author = {D. Funaro},
-volume = {8},
-series = {Lecture Notes in Physics},
-address = {Heidelberg, Germany}
+ title = {Polynomial approximation of differential equations},
+ publisher = {Springer Verlag},
+ year = {1992},
+ author = {D. Funaro},
+ volume = {8},
+ series = {Lecture Notes in Physics},
+ address = {Heidelberg, Germany}
}
@ARTICLE{FuKeFu99,
-author = {M. Furumura and B. L. N. Kennett and T. Furumura},
-title = {Seismic wavefield calculation for laterally heterogeneous {E}arth
-models-{II}. The influence of upper mantle heterogeneity},
-journal = gji,
-year = {1999},
-volume = {139},
-pages = {623-644},
-number = {3},
-doi = {10.1046/j.1365-246x.1999.00962.x}
+ author = {M. Furumura and B. L. N. Kennett and T. Furumura},
+ title = {Seismic wavefield calculation for laterally heterogeneous {E}arth
+ models-{II}. The influence of upper mantle heterogeneity},
+ journal = gji,
+ year = {1999},
+ volume = {139},
+ pages = {623-644},
+ number = {3},
+ doi = {10.1046/j.1365-246x.1999.00962.x}
}
@ARTICLE{FuKeFu98,
-author = {T. Furumura and B. L. N. Kennett and M. Furumura},
-title = {Seismic wavefield calculation for laterally heterogeneous whole {E}arth
-models using the pseudospectral method},
-journal = gji,
-year = {1998},
-volume = {135},
-pages = {845-860},
-number = {3},
-doi = {10.1046/j.1365-246X.1998.00682.x}
+ author = {T. Furumura and B. L. N. Kennett and M. Furumura},
+ title = {Seismic wavefield calculation for laterally heterogeneous whole {E}arth
+ models using the pseudospectral method},
+ journal = gji,
+ year = {1998},
+ volume = {135},
+ pages = {845-860},
+ number = {3},
+ doi = {10.1046/j.1365-246X.1998.00682.x}
}
@ARTICLE{GoStMoMcBuGrTu07,
-author = {Dominik G\"oddeke and Robert Strzodka and Jamaludin Mohd-Yusof and
-Patrick McCormick and Sven H. M. Buijssen and Matthias Grajewski
-and Stefan Turek},
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-cluster},
-journal = {Parallel Computing},
-year = {2007},
-volume = {33},
-pages = {685-699},
-number = {10-11}
+ author = {Dominik G\"oddeke and Robert Strzodka and Jamaludin Mohd-Yusof and
+ Patrick McCormick and Sven H. M. Buijssen and Matthias Grajewski
+ and Stefan Turek},
+ title = {Exploring weak scalability for {FEM} calculations on a {GPU}-enhanced
+ cluster},
+ journal = {Parallel Computing},
+ year = {2007},
+ volume = {33},
+ pages = {685-699},
+ number = {10-11}
}
@ARTICLE{GoStTu07,
-author = {Dominik G\"oddeke and Robert Strzodka and Stefan Turek},
-title = {Performance and accuracy of hardware-oriented native-, emulated-
-and mixed-precision solvers in {FEM} simulations},
-journal = {International Journal of Parallel, Emergent and Distributed Systems},
-year = {2007},
-volume = {22},
-pages = {221-256},
-number = {4}
+ author = {Dominik G\"oddeke and Robert Strzodka and Stefan Turek},
+ title = {Performance and accuracy of hardware-oriented native-, emulated-
+ and mixed-precision solvers in {FEM} simulations},
+ journal = {International Journal of Parallel, Emergent and Distributed Systems},
+ year = {2007},
+ volume = {22},
+ pages = {221-256},
+ number = {4}
}
@ARTICLE{GeBaJu88,
-author = {L. G\'eli and P. Y. Bard and B. Julien},
-title = {The effect of topography on earthquake ground motion: a review and
-new results},
-journal = bssa,
-year = {1988},
-volume = {78},
-pages = {42-63}
+ author = {L. G\'eli and P. Y. Bard and B. Julien},
+ title = {The effect of topography on earthquake ground motion: a review and
+ new results},
+ journal = bssa,
+ year = {1988},
+ volume = {78},
+ pages = {42-63}
}
@ARTICLE{GaBo89,
-author = {S. Gaffet and M. Bouchon},
-title = {Effects of two-dimensional topographies using the discrete wavenumber-boundary
-integral equation method in {{\it P-SV}} cases},
-journal = jasa,
-year = {1989},
-volume = {85},
-pages = {2277-2283}
+ author = {S. Gaffet and M. Bouchon},
+ title = {Effects of two-dimensional topographies using the discrete wavenumber-boundary
+ integral equation method in {{\it P-SV}} cases},
+ journal = jasa,
+ year = {1989},
+ volume = {85},
+ pages = {2277-2283}
}
@TECHREPORT{GaMaNaHelene,
-author = {M. J. Gander and F. Magoul\`es and F. Nataf},
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-institution = {CMAP, UMR CNRS 67641},
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+ author = {M. J. Gander and F. Magoul\`es and F. Nataf},
+ title = {Optimized {S}chwarz method without overlap for the {H}elmholtz equation},
+ institution = {CMAP, UMR CNRS 67641},
+ year = {2001}
}
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+ title = {An attempt to seismic ray tracing with symplectic algorithm},
+ journal = {Chinese J. Geophys.},
+ year = {2000},
+ volume = {43},
+ pages = {433-440},
+ number = {3}
}
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+ author = {Kazuteru Garatani and Hisashi Nakamura and Hiroshi Okuda and Genki
+ Yagawa},
+ title = {Geo{FEM}: a High Performance Parallel finite element method for the
+ Solid {E}arth},
+ journal = {J. Future Generation Computer Systems},
+ year = {2001},
+ volume = {18},
+ pages = {107-114}
}
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+ author = {Kazuteru Garatani and Hisashi Nakamura and Hiroshi Okuda and Genki
+ Yagawa},
+ title = {Large-Scale Parallel Wave Propagation Analysis by {G}eo{FEM}},
+ journal = {Lecture Notes in Computer Science},
+ year = {2000},
+ volume = {1823},
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+ year = {2002},
+ volume = {150},
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+ title = {Non-linear waveform and delay time analysis of triplicated core phases},
+ journal = jgr,
+ year = {2004},
+ volume = {109},
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}
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+ year = {2000},
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}
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+ title = {A new global {PKP} dataset to study {E}arth's core and deep mantle},
+ journal = pepi,
+ year = {2006},
+ volume = {159},
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+ author = {Michael Garland and Scott Le Grand and John Nickolls and Joshua A.
+ Anderson and Jim Hardwick and Scott Morton and Everett H. Phillips
+ and Yao Zhang and Vasily Volkov},
+ title = {Parallel Computing Experiences with {CUDA}},
+ journal = {IEEE Micro},
+ year = {2008},
+ volume = {28},
+ pages = {13--27},
+ number = {4},
+ month = jul,
+ doi = {10.1109/MM.2008.57}
}
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+ title = {Heterogeneity of the lowermost mantle},
+ journal = {Annual Review of Earth and Planetary Sciences},
+ year = {2000},
+ volume = {33},
+ pages = {1-66}
}
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}
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+ author = {S. D. Gedney},
+ title = {The {P}erfectly {M}atched {L}ayer absorbing medium},
+ booktitle = {Advances in Computational Electrodynamics: the Finite-Difference
+ Time-Domain method},
+ publisher = {Artech House},
+ year = {1998},
+ editor = {Allen Taflove},
+ chapter = {5},
+ pages = {263-343},
+ address = {Boston, USA}
}
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+ author = {S. D. Gedney},
+ title = {An anisotropic perfectly matched layer-absorbing medium for the truncation
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+ journal = {IEEE Transactions on Antennas and Propagation},
+ year = {1996},
+ volume = {44},
+ pages = {1630-1639},
+ number = {12},
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}
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+ author = {S. D. Gedney and B. Zhao},
+ title = {An Auxiliary Differential Equation Formulation for the Complex-Frequency
+ Shifted {PML}},
+ journal = {IEEE Transactions on Antennas and Propagation},
+ year = {2010},
+ volume = {58},
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+ number = {3},
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}
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}
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+ journal = ijnme,
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+ owner = {komatits},
+ timestamp = {2011.01.23}
}
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+ year = {1960},
+ volume = {65},
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}
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}
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+ title = {Computational Absorbing Boundaries},
+ booktitle = {Computational acoustics noise propagation in fluids},
+ publisher = {Springer-Verlag},
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+ address = {Berlin, Germany}
}
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-hyperbolic problems in one space dimension},
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-in Applied Sciences and Engineering},
-year = {1990},
-address = {SIAM, Philadelphia}
+ author = {R. Glowinski and W. Lawton and M. Ravachol and E. Tenebaum},
+ title = {Wavelet solution of linear and nonlinear elliptic, parabolic and
+ hyperbolic problems in one space dimension},
+ booktitle = {Proceedings of the 9th International Conference on Numerical Methods
+ in Applied Sciences and Engineering},
+ year = {1990},
+ address = {SIAM, Philadelphia}
}
@ARTICLE{GoAmTaCaSmSaMaKo09,
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-C. Smerzini and F. J. S\'anchez-Sesma and R. Madec and Dimitri Komatitsch},
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-journal = bssa,
-year = {2009},
-volume = {99},
-pages = {1147-1161},
-number = {2B},
-doi = {10.1785/0120080096}
+ author = {L. Godinho and P. Amado Mendes and A. Tadeu and A. Cadena-Isaza and
+ C. Smerzini and F. J. S\'anchez-Sesma and R. Madec and Dimitri Komatitsch},
+ title = {Numerical simulation of ground rotations along {2D} topographical
+ profiles under the incidence of elastic plane waves},
+ journal = bssa,
+ year = {2009},
+ volume = {99},
+ pages = {1147-1161},
+ number = {2B},
+ doi = {10.1785/0120080096}
}
@ARTICLE{Gol56,
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-journal = {Physical Review},
-year = {1956},
-volume = {104},
-pages = {1532-1536},
-number = {6}
+ author = {L. Gold},
+ title = {Rayleigh wave propagation on anisotropic (cubic) media},
+ journal = {Physical Review},
+ year = {1956},
+ volume = {104},
+ pages = {1532-1536},
+ number = {6}
}
@INPROCEEDINGS{Goodnight:2003:AMS,
-author = {Nolan Goodnight and Cliff Woolley and Gregory Lewin and David P.
-Luebke and Greg Humphreys},
-title = {A Multigrid Solver for Boundary Value Problems Using Programmable
-Graphics Hardware},
-booktitle = {Graphics Hardware 2003},
-year = {2003},
-editor = {Michael Doggett and Wolfgang Heidrich and William R. Mark and Andreas
-Schilling},
-pages = {102--111},
-month = jul
+ author = {Nolan Goodnight and Cliff Woolley and Gregory Lewin and David P.
+ Luebke and Greg Humphreys},
+ title = {A Multigrid Solver for Boundary Value Problems Using Programmable
+ Graphics Hardware},
+ booktitle = {Graphics Hardware 2003},
+ year = {2003},
+ editor = {Michael Doggett and Wolfgang Heidrich and William R. Mark and Andreas
+ Schilling},
+ pages = {102--111},
+ month = jul
}
@INPROCEEDINGS{GoHa72,
-author = {W. J. Gordon and C. A. Hall},
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-booktitle = {Mathematical Foundations of the Finite Element Method with Applications
-to Partial Differential Equations},
-year = {1972},
-editor = {A. K. Aziz},
-pages = {769-784},
-address = {New York, USA},
-publisher = {Academic Press}
+ author = {W. J. Gordon and C. A. Hall},
+ title = {Geometric aspects of the finite element method},
+ booktitle = {Mathematical Foundations of the Finite Element Method with Applications
+ to Partial Differential Equations},
+ year = {1972},
+ editor = {A. K. Aziz},
+ pages = {769-784},
+ address = {New York, USA},
+ publisher = {Academic Press}
}
@ARTICLE{Got81,
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-title = {The stability of pseudospectral {C}hebyshev methods},
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-year = {1981},
-volume = {36},
-pages = {107-118}
+ author = {D. Gottlieb},
+ title = {The stability of pseudospectral {C}hebyshev methods},
+ journal = {Math. Comp.},
+ year = {1981},
+ volume = {36},
+ pages = {107-118}
}
@INCOLLECTION{cgnash,
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-year = {1999},
-editor = {C. K. Chui and L. L. Schumaker},
-volume = {1},
-pages = {151-158},
-address = {Nashville}
+ author = {C. Gout},
+ title = {Approximation using scale transformations},
+ booktitle = {Approximation Theory {IX}},
+ publisher = {Vanderbilt University Press},
+ year = {1999},
+ editor = {C. K. Chui and L. L. Schumaker},
+ volume = {1},
+ pages = {151-158},
+ address = {Nashville}
}
@TECHREPORT{cg1001,
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-institution = {Center for Pure and Applied Mathematics},
-year = {1998},
-number = {1001},
-address = {University of California at Berkeley, USA},
-note = {36 p.}
+ author = {C. Gout},
+ title = {Approximation of curves and surfaces from rapidly varying data},
+ institution = {Center for Pure and Applied Mathematics},
+ year = {1998},
+ number = {1001},
+ address = {University of California at Berkeley, USA},
+ note = {36 p.}
}
@PHDTHESIS{cgthesis,
-author = {C. Gout},
-title = {Etude de changements d'\'echelle en approximation - ajustement spline
-sur des morceaux de surfaces},
-school = {Universit\'e de Pau et des Pays de l'Adour},
-year = {1997},
-address = {Pau, France},
-note = {203 p.}
+ author = {C. Gout},
+ title = {Etude de changements d'\'echelle en approximation - ajustement spline
+ sur des morceaux de surfaces},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {1997},
+ address = {Pau, France},
+ note = {203 p.}
}
@TECHREPORT{GoLeGuVe05,
-author = {C. Gout and C. Le Guyader and L. Vese},
-title = {Image segmentation under interpolation conditions},
-institution = {Univ. of California, Los Angeles},
-year = {2005},
-note = {CAM 03-44}
+ author = {C. Gout and C. Le Guyader and L. Vese},
+ title = {Image segmentation under interpolation conditions},
+ institution = {Univ. of California, Los Angeles},
+ year = {2005},
+ note = {CAM 03-44}
}
@ARTICLE{GoKo00,
-author = {C. Gout and D. Komatitsch},
-title = {Surface fitting of rapidly varying data using rank coding: application
-to geophysical surfaces},
-journal = {Math. Geol.},
-year = {2000},
-volume = {32},
-pages = {873-888},
-number = {7},
-doi = {10.1023/A:1007500624487}
+ author = {C. Gout and D. Komatitsch},
+ title = {Surface fitting of rapidly varying data using rank coding: application
+ to geophysical surfaces},
+ journal = {Math. Geol.},
+ year = {2000},
+ volume = {32},
+ pages = {873-888},
+ number = {7},
+ doi = {10.1023/A:1007500624487}
}
@ARTICLE{GoVi03,
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-deformable models},
-journal = {Int. J. Comput. Math.},
-year = {2003},
-volume = {80},
-pages = {47-54},
-number = {1}
+ author = {C. Gout and S. Vieira-Test\'e},
+ title = {An algorithm for segmentation under interpolation conditions using
+ deformable models},
+ journal = {Int. J. Comput. Math.},
+ year = {2003},
+ volume = {80},
+ pages = {47-54},
+ number = {1}
}
@ARTICLE{GoMa07,
-author = {Naga K. Govindaraju and Dinesh Manocha},
-title = {Cache-Efficient Numerical Algorithms using Graphics Hardware},
-journal = {Parallel Computing},
-year = {2007},
-volume = {33},
-pages = {663-684}
+ author = {Naga K. Govindaraju and Dinesh Manocha},
+ title = {Cache-Efficient Numerical Algorithms using Graphics Hardware},
+ journal = {Parallel Computing},
+ year = {2007},
+ volume = {33},
+ pages = {663-684}
}
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-editor = {K. Irikura and K. Kudo and H. Okada and T. Sasatani},
-volume = {1},
-pages = {103-120},
-address = {Rotterdam, The Netherlands}
+ author = {R. W. Graves},
+ title = {Three-dimensional computer simulations of realistic earthquake ground
+ motions in regions of deep sedimentary basin},
+ booktitle = {The Effects of Surface Geology on Seismic Motion},
+ publisher = {Balkema},
+ year = {1999},
+ editor = {K. Irikura and K. Kudo and H. Okada and T. Sasatani},
+ volume = {1},
+ pages = {103-120},
+ address = {Rotterdam, The Netherlands}
}
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-year = {1996},
-volume = {86},
-pages = {1091-1106},
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+ author = {R. W. Graves},
+ title = {Simulating seismic wave propagation in 3{D} elastic media using staggered-grid
+ finite differences},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1091-1106},
+ number = {4}
}
@INPROCEEDINGS{Gra96b,
-author = {R. W. Graves},
-title = {Simulating realistic earthquake ground motions in regions of deep
-sedimentary basins},
-booktitle = {Proceedings of the 11th World Conference on Earthquake Engineering},
-year = {1996},
-address = {Acapulco, Mexico}
+ author = {R. W. Graves},
+ title = {Simulating realistic earthquake ground motions in regions of deep
+ sedimentary basins},
+ booktitle = {Proceedings of the 11th World Conference on Earthquake Engineering},
+ year = {1996},
+ address = {Acapulco, Mexico}
}
@ARTICLE{GrDa03,
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-journal = bssa,
-year = {2003},
-volume = {93},
-pages = {283-300}
+ author = {R. W. Graves and S. M. Day},
+ title = {Stability and accuracy of coarse-grain viscoelastic simulations},
+ journal = bssa,
+ year = {2003},
+ volume = {93},
+ pages = {283-300}
}
@ARTICLE{GrZa10,
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-year = {2010},
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-pages = {65-73},
-number = {1-2},
-doi = {10.1007/s00450-010-0111-7}
+ author = {Michael Griebel and Peter Zaspel},
+ title = {A multi-{GPU} accelerated solver for the three-dimensional two-phase
+ incompressible {N}avier-{S}tokes equations},
+ journal = {Computer Science Research and Development},
+ year = {2010},
+ volume = {25},
+ pages = {65-73},
+ number = {1-2},
+ doi = {10.1007/s00450-010-0111-7}
}
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+ author = {D. W. Griffiths and G. A. Bollinger},
+ title = {The effect of {A}ppalachian mountain topography on seismic waves},
+ journal = bssa,
+ year = {1979},
+ volume = {69},
+ pages = {1081-1105}
}
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+ author = {W. Gropp and E. Lusk and N. Doss and A. Skjellum},
+ title = {A high-performance, portable implementation of the {MPI} message
+ passing interface standard},
+ journal = {Parallel Computing},
+ year = {1996},
+ volume = {22},
+ pages = {789-828},
+ number = {6}
}
@BOOK{GrLuSk94,
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-{I}nterface},
-publisher = {MIT Press},
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-author = {W. Gropp and E. Lusk and A. Skjellum},
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+ title = {Using {MPI}, portable parallel programming with the {M}essage-{P}assing
+ {I}nterface},
+ publisher = {MIT Press},
+ year = {1994},
+ author = {W. Gropp and E. Lusk and A. Skjellum},
+ address = {Cambridge, USA}
}
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-journal = jcp,
-year = {2000},
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+ author = {M. J. Grote},
+ title = {Nonreflecting boundary conditions for elastodynamics scattering},
+ journal = jcp,
+ year = {2000},
+ volume = {161},
+ pages = {331-353}
}
@ARTICLE{GrScSc06,
-author = {Marcus J. Grote and Anna Schneebeli and Dominik Sch\"{o}tzau},
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-year = {2006},
-volume = {44},
-pages = {2408-2431},
-number = {6},
-doi = {10.1137/05063194X}
+ author = {Marcus J. Grote and Anna Schneebeli and Dominik Sch\"{o}tzau},
+ title = {Discontinuous {G}alerkin Finite Element Method for the Wave Equation},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {2006},
+ volume = {44},
+ pages = {2408-2431},
+ number = {6},
+ doi = {10.1137/05063194X}
}
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-year = {2006},
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-pages = {949-977},
-number = {6},
-doi = {10.1002/nme.1574}
+ author = {Murthy N. Guddati and Keng Wit Lim},
+ title = {Continued fraction absorbing boundary conditions for convex polygonal
+ domains},
+ journal = ijnme,
+ year = {2006},
+ volume = {66},
+ pages = {949-977},
+ number = {6},
+ doi = {10.1002/nme.1574}
}
@ARTICLE{GuBa86b,
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+ author = {W. Gui and I. Babu\u{s}ka},
+ title = {The {\it h}, {\it p} and {\it h-p} versions of the finite element
+ method in one dimension},
+ journal = {Numer. Math.},
+ year = {1986},
+ volume = {49},
+ pages = {577-683}
}
@ARTICLE{GuDu08,
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-journal = jcp,
-year = {2008},
-volume = {227},
-pages = {8290-8313},
-doi = {10.1016/j.jcp.2008.05.023}
+ author = {Nail A. Gumerov and Ramani Duraiswami},
+ title = {Fast multipole methods on graphics processors},
+ journal = jcp,
+ year = {2008},
+ volume = {227},
+ pages = {8290-8313},
+ doi = {10.1016/j.jcp.2008.05.023}
}
@ARTICLE{GunWanLot91,
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-year = {1991},
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+ author = {S. A. Gundersen and L. Wang and J. Lothe},
+ title = {Secluded supersonic elastic surface waves},
+ journal = {Wave Motion},
+ year = {1991},
+ volume = {14},
+ pages = {129-143}
}
@ARTICLE{GuBa86a,
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-journal = {Comput. Mech.},
-year = {1986},
-volume = {1},
-pages = {21-41}
+ author = {B. Guo and I. Babu\u{s}ka},
+ title = {The {\it h-p} version of the finite element method},
+ journal = {Comput. Mech.},
+ year = {1986},
+ volume = {1},
+ pages = {21-41}
}
@ARTICLE{LeGuApGo05,
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-title = {Using a level set approach for image segmentation under interpolation
-conditions},
-journal = {Numer. Algorithms},
-year = {2005},
-volume = {39},
-pages = {221-235}
+ author = {C. Le Guyader and D. Apprato and C. Gout},
+ title = {Using a level set approach for image segmentation under interpolation
+ conditions},
+ journal = {Numer. Algorithms},
+ year = {2005},
+ volume = {39},
+ pages = {221-235}
}
@PHDTHESIS{Goeddeke:2010:FAA,
-author = {Dominik G{\"o}ddeke},
-title = {Fast and Accurate Finite-Element Multigrid Solvers for {PDE} Simulations
-on {GPU} Clusters},
-school = {{T}echnische {U}niversit{\"a}t Dortmund, {F}akult{\"a}t f{\"u}r {M}athematik},
-year = {2010},
-month = may,
-note = {\url{http://hdl.handle.net/2003/27243}}
+ author = {Dominik G{\"o}ddeke},
+ title = {Fast and Accurate Finite-Element Multigrid Solvers for {PDE} Simulations
+ on {GPU} Clusters},
+ school = {{T}echnische {U}niversit{\"a}t Dortmund, {F}akult{\"a}t f{\"u}r {M}athematik},
+ year = {2010},
+ month = may,
+ note = {\url{http://hdl.handle.net/2003/27243}}
}
@INPROCEEDINGS{Goeddeke:2009:GAO,
-author = {Dominik G{\"o}ddeke and Sven H.M. Buijssen and Hilmar Wobker and
-Stefan Turek},
-title = {{GPU} Acceleration of an Unmodified Parallel Finite Element {N}avier-{S}tokes
-Solver},
-booktitle = {High Performance Computing \& Simulation 2009},
-year = {2009},
-editor = {Waleed W. Smari and John P. McIntire},
-pages = {12-21},
-address = {Leipzig, Germany},
-month = jun
+ author = {Dominik G{\"o}ddeke and Sven H.M. Buijssen and Hilmar Wobker and
+ Stefan Turek},
+ title = {{GPU} Acceleration of an Unmodified Parallel Finite Element {N}avier-{S}tokes
+ Solver},
+ booktitle = {High Performance Computing \& Simulation 2009},
+ year = {2009},
+ editor = {Waleed W. Smari and John P. McIntire},
+ pages = {12-21},
+ address = {Leipzig, Germany},
+ month = jun
}
@ARTICLE{Goeddeke:2009:CPA,
-author = {Dominik G{\"o}ddeke and Hilmar Wobker and Robert Strzodka and Jamaludin
-Mohd-Yusof and Patrick S. McCormick and Stefan Turek},
-title = {Co-Processor Acceleration of an Unmodified Parallel Solid Mechanics
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-journal = {International Journal of Computational Science and Engineering},
-year = {2009},
-volume = {4},
-pages = {254--269},
-number = {4},
-month = oct,
-editor = {Hans Petter Langtangen and Michael Thun{\'e}}
+ author = {Dominik G{\"o}ddeke and Hilmar Wobker and Robert Strzodka and Jamaludin
+ Mohd-Yusof and Patrick S. McCormick and Stefan Turek},
+ title = {Co-Processor Acceleration of an Unmodified Parallel Solid Mechanics
+ Code with {FEASTGPU}},
+ journal = {International Journal of Computational Science and Engineering},
+ year = {2009},
+ volume = {4},
+ pages = {254--269},
+ number = {4},
+ month = oct,
+ editor = {Hans Petter Langtangen and Michael Thun{\'e}}
}
@ARTICLE{barucqduquetprat2006,
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-note = {Submitted, available at lma.univ-pau.fr/publis/publis\_pre.php}
+ author = {H. Barucq, B. Duquet and F. Prat},
+ title = {True-amplitude one way propagation in heterogeneous media},
+ journal = {J. of Scientific Computing},
+ year = {2006},
+ note = {Submitted, available at lma.univ-pau.fr/publis/publis\_pre.php}
}
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+ author = {L. H\o{}rmander},
+ title = {Pseudo-differential Operators and Non Elliptic Boundary Problems},
+ journal = {Ann. of Math.},
+ year = {1966},
+ volume = {83},
+ pages = {129-209}
}
@ARTICLE{Hor1,
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+ author = {L. H\o{}rmander},
+ title = {Pseudo-differential Operators},
+ journal = {Comm. Pure Appl. Math.},
+ year = {1965},
+ volume = {18},
+ pages = {501-517}
}
@BOOKLET{Haa09,
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+ title = {Zur Theorie der orthogonalen Funktionensysteme},
+ author = {A. Haar},
+ address = {G\"ottingen},
+ year = {1909}
}
@ARTICLE{HaKa77,
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+ author = {D. Hadley and H. Kanamori},
+ title = {Seismic structure of the {T}ransverse {R}anges, {C}alifornia},
+ journal = {Geol. Soc. Am. Bull.},
+ year = {1977},
+ volume = {88},
+ pages = {1469-1478}
}
@ARTICLE{Hager85,
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-year = {1985},
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+ author = {Hager, B. H. and R. W. Clayton and M. A. Richards and R. P. Comer
+ and A. M. Dziewo\'nski},
+ title = {Lower mantle heterogeneity, dynamic topography and the geoid},
+ journal = {Nature},
+ year = {1985},
+ volume = {313},
+ pages = {541--546}
}
@INPROCEEDINGS{Hag03,
-author = {T. Hagstrom},
-title = {Perfectly matched layers for hyperbolic systems with applications
-to the linearized {E}uler equations},
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-year = {2003},
-editor = {Gary Cohen and Erkki Heikkola and Patrick Joly and Pekka Neittaanm\"aki},
-series = {Proceedings of the Sixth International Conference on Mathematical
-and Numerical Aspects of Wave Propagation},
-pages = {125-129},
-address = {Jyv\"askyl\"a, Finland},
-publisher = {Springer-Verlag}
+ author = {T. Hagstrom},
+ title = {Perfectly matched layers for hyperbolic systems with applications
+ to the linearized {E}uler equations},
+ booktitle = {Mathematical and Numerical Aspects of Wave Propagation: Waves 2003},
+ year = {2003},
+ editor = {Gary Cohen and Erkki Heikkola and Patrick Joly and Pekka Neittaanm\"aki},
+ series = {Proceedings of the Sixth International Conference on Mathematical
+ and Numerical Aspects of Wave Propagation},
+ pages = {125-129},
+ address = {Jyv\"askyl\"a, Finland},
+ publisher = {Springer-Verlag}
}
@ARTICLE{Ha99,
-author = {T. Hagstrom},
-title = {Radiation boundary conditions for the numerical simulation of waves},
-journal = {Acta Numerica},
-year = {1999},
-volume = {8},
-pages = {47-106}
+ author = {T. Hagstrom},
+ title = {Radiation boundary conditions for the numerical simulation of waves},
+ journal = {Acta Numerica},
+ year = {1999},
+ volume = {8},
+ pages = {47-106}
}
@ARTICLE{HaHa98,
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-title = {A formulation of asymptotic and exact boundary conditions using local
-operators},
-journal = {Appl. Num. Math.},
-year = {1998},
-volume = {27},
-pages = {403-416}
+ author = {T. Hagstrom and S. I. Hariharan},
+ title = {A formulation of asymptotic and exact boundary conditions using local
+ operators},
+ journal = {Appl. Num. Math.},
+ year = {1998},
+ volume = {27},
+ pages = {403-416}
}
@BOOK{HaLuWa06,
-title = {Geometric numerical integration},
-publisher = {Springer-Verlag},
-year = {2006},
-author = {Hairer, Ernst and Lubich, Christian and Wanner, Gerhard},
-volume = {31},
-series = {Springer Series in Computational Mathematics},
-address = {Berlin, Germany},
-edition = {Second}
+ title = {Geometric numerical integration},
+ publisher = {Springer-Verlag},
+ year = {2006},
+ author = {Hairer, Ernst and Lubich, Christian and Wanner, Gerhard},
+ volume = {31},
+ series = {Springer Series in Computational Mathematics},
+ address = {Berlin, Germany},
+ edition = {Second}
}
@ARTICLE{HalHelene,
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-of hyperbolic systems},
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-year = {1991},
-volume = {22},
-pages = {1256-1283},
-number = {5}
+ author = {L. Halpern},
+ title = {Artificial boundary conditions for incompletely parabolic perturbations
+ of hyperbolic systems},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1991},
+ volume = {22},
+ pages = {1256-1283},
+ number = {5}
}
@ARTICLE{HaOuVe78,
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-systems},
-journal = ijnme,
-year = {1978},
-volume = {13},
-pages = {139-150}
+ author = {M. A. Hamdi and Y. Ousset and G. Verchery},
+ title = {A displacement method for the analysis of vibrations of coupled fluid-structure
+ systems},
+ journal = ijnme,
+ year = {1978},
+ volume = {13},
+ pages = {139-150}
}
@ARTICLE{HaKoGi10,
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-ideal {MHD} equations based on an unsplit, convolutional perfectly
-matched layer},
-journal = {Astronomy and Astrophysics},
-year = {2010},
-volume = {522},
-pages = {1-8},
-number = {A87},
-doi = {10.1051/0004-6361/201014345}
+ author = {Shravan M. Hanasoge and Dimitri Komatitsch and Laurent Gizon},
+ title = {An absorbing boundary formulation for the stratified, linearized,
+ ideal {MHD} equations based on an unsplit, convolutional perfectly
+ matched layer},
+ journal = {Astronomy and Astrophysics},
+ year = {2010},
+ volume = {522},
+ pages = {1-8},
+ number = {A87},
+ doi = {10.1051/0004-6361/201014345}
}
@ARTICLE{HaSe93,
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-title = {Absorbing boundary conditions for {M}axwell's equations},
-journal = {Notes on Numerical Fluid Dynamics},
-year = {1993},
-volume = {43},
-pages = {315-322}
+ author = {B. Hanouzet and M. Sesques},
+ title = {Absorbing boundary conditions for {M}axwell's equations},
+ journal = {Notes on Numerical Fluid Dynamics},
+ year = {1993},
+ volume = {43},
+ pages = {315-322}
}
@ARTICLE{Haetal91,
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-heterogeneous starting model: preliminary results},
-journal = gji,
-year = {1991},
-volume = {104},
-pages = {523-540}
+ author = {T. Hara and S. Tsuboi and R.J. Geller},
+ title = {Inversion for laterally heterogeneous {E}arth structure using a laterally
+ heterogeneous starting model: preliminary results},
+ journal = gji,
+ year = {1991},
+ volume = {104},
+ pages = {523-540}
}
@ARTICLE{harari2006,
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-journal = cmame,
-year = {2006},
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-pages = {1594-1607}
+ author = {I. Harari},
+ title = {A survey of finite element methods for time-harmonic acoustics},
+ journal = cmame,
+ year = {2006},
+ volume = {195},
+ pages = {1594-1607}
}
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-{H}elmholtz equation},
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-year = {2000},
-volume = {8},
-pages = {121-137},
-number = {1}
+ author = {I. Harari and M. Slavutin and E. Turkel},
+ title = {Analytical and numerical studies of a finite element {PML} for the
+ {H}elmholtz equation},
+ journal = jca,
+ year = {2000},
+ volume = {8},
+ pages = {121-137},
+ number = {1}
}
@BOOK{Har88,
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-of pipelines},
-publisher = {British Gas Editions},
-year = {1988},
-author = {A. H. Harker},
-address = {Bristol}
+ title = {Elastic waves in solids, with application to non destructive testing
+ of pipelines},
+ publisher = {British Gas Editions},
+ year = {1988},
+ author = {A. H. Harker},
+ address = {Bristol}
}
@PHDTHESIS{Harris:2003:RTC,
-author = {Mark J. Harris},
-title = {Real-Time Cloud Simulation and Rendering},
-school = {University of North Carolina at Chapel Hill, USA},
-year = {2003},
-month = sep
+ author = {Mark J. Harris},
+ title = {Real-Time Cloud Simulation and Rendering},
+ school = {University of North Carolina at Chapel Hill, USA},
+ year = {2003},
+ month = sep
}
@ARTICLE{HaDa99,
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-title = {Dynamic 3{D} simulations of earthquakes on en-echelon faults},
-journal = grl,
-year = {1999},
-volume = {26},
-pages = {2089-2092}
+ author = {R. A. Harris and S. M. Day},
+ title = {Dynamic 3{D} simulations of earthquakes on en-echelon faults},
+ journal = grl,
+ year = {1999},
+ volume = {26},
+ pages = {2089-2092}
}
@ARTICLE{HaHaFrCaCrMeMi98,
-author = {S. Hartzell and S. Harmsen and A. Frankel and D. Carver and E. Cranswick
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-based on earthquake ground motions},
-journal = bssa,
-year = {1998},
-volume = {88},
-pages = {463-472}
+ author = {S. Hartzell and S. Harmsen and A. Frankel and D. Carver and E. Cranswick
+ and M. Meremonte and J. Michael},
+ title = {First-generation site-response maps for the {L}os {A}ngeles region
+ based on earthquake ground motions},
+ journal = bssa,
+ year = {1998},
+ volume = {88},
+ pages = {463-472}
}
@ARTICLE{HaCaKi94,
-author = {S. H. Hartzell and D. L. Carver and K. W. King},
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-ridge, {C}alifornia},
-journal = bssa,
-year = {1994},
-volume = {84},
-pages = {1336-1349}
+ author = {S. H. Hartzell and D. L. Carver and K. W. King},
+ title = {Initial investigation of site and topographic effects at {R}obinwood
+ ridge, {C}alifornia},
+ journal = bssa,
+ year = {1994},
+ volume = {84},
+ pages = {1336-1349}
}
@ARTICLE{HaLeFrMi96,
-author = {S. H. Hartzell and A. Leeds and A. Frankel and J. Michael},
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-{N}orthridge earthquake},
-journal = bssa,
-year = {1996},
-volume = {86},
-pages = {S168-S192},
-number = {1B}
+ author = {S. H. Hartzell and A. Leeds and A. Frankel and J. Michael},
+ title = {Site response for urban {L}os {A}ngeles using aftershocks of the
+ {N}orthridge earthquake},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {S168-S192},
+ number = {1B}
}
@ARTICLE{HaScBr96,
-author = {F. D. Hastings and J. B. Schneider and S. L. Broschat},
-title = {Application of the {P}erfectly {M}atched {L}ayer {(PML)} absorbing
-boundary condition to elastic wave propagation},
-journal = jasa,
-year = {1996},
-volume = {100},
-pages = {3061-3069},
-number = {5}
+ author = {F. D. Hastings and J. B. Schneider and S. L. Broschat},
+ title = {Application of the {P}erfectly {M}atched {L}ayer {(PML)} absorbing
+ boundary condition to elastic wave propagation},
+ journal = jasa,
+ year = {1996},
+ volume = {100},
+ pages = {3061-3069},
+ number = {5}
}
@ARTICLE{hauksson2000,
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-and {N}orth {A}merica plate boundary in {S}outhern {C}alifornia},
-journal = jgr,
-year = {2000},
-volume = {105},
-pages = {13875-13903}
+ author = {E. Hauksson},
+ title = {Crustal structure and seismicity distribution adjacent to the {P}acific
+ and {N}orth {A}merica plate boundary in {S}outhern {C}alifornia},
+ journal = jgr,
+ year = {2000},
+ volume = {105},
+ pages = {13875-13903}
}
@ARTICLE{Hau90,
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-journal = jgr,
-year = {1990},
-volume = {95},
-pages = {15365-15394}
+ author = {E. Hauksson},
+ title = {Earthquakes, faulting, and stress in the {L}os {A}ngeles basin},
+ journal = jgr,
+ year = {1990},
+ volume = {95},
+ pages = {15365-15394}
}
@ARTICLE{HaHa97,
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-title = {Three-dimensional {$V_p$} and {$V_p/V_s$} velocity models of the
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-journal = jgr,
-year = {1997},
-volume = {102},
-pages = {5423-5453}
+ author = {E. Hauksson and J. S. Haase},
+ title = {Three-dimensional {$V_p$} and {$V_p/V_s$} velocity models of the
+ {L}os {A}ngeles basin and central {T}ransverse {R}anges, {C}alifornia},
+ journal = jgr,
+ year = {1997},
+ volume = {102},
+ pages = {5423-5453}
}
@ARTICLE{HaTeHe87,
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-site response, low {$Q$} values, and $f_{max}$},
-journal = bssa,
-year = {1987},
-volume = {77},
-pages = {1883-1904}
+ author = {E. Hauksson and T. L. Teng and T. L. Henyey},
+ title = {Results from a 1500~m deep, three-level downhole seismometer array:
+ site response, low {$Q$} values, and $f_{max}$},
+ journal = bssa,
+ year = {1987},
+ volume = {77},
+ pages = {1883-1904}
}
@TECHREPORT{HaKeLe02,
-author = {P. Hav\'e and M. Kern and Ch. Lemuet},
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-d'\'el\'ements finis d'ordre \'elev\'e sur calculateur parall\`ele},
-institution = {INRIA},
-year = {2002},
-number = {RR 4381},
-address = {France},
-month = {February}
+ author = {P. Hav\'e and M. Kern and Ch. Lemuet},
+ title = {R\'esolution num\'erique de l'\'equation des ondes par une m\'ethode
+ d'\'el\'ements finis d'ordre \'elev\'e sur calculateur parall\`ele},
+ institution = {INRIA},
+ year = {2002},
+ number = {RR 4381},
+ address = {France},
+ month = {February}
}
@BOOK{Hea00,
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-publisher = {Farrar, Straus and Giroux Publishers},
-year = {2000},
-author = {S. Heaney},
-address = {New York}
+ title = {Beowulf, a new verse translation, bilingual edition},
+ publisher = {Farrar, Straus and Giroux Publishers},
+ year = {2000},
+ author = {S. Heaney},
+ address = {New York}
}
@INCOLLECTION{Hel94,
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-editor = {K. Helbig and S. Treitel},
-volume = {22},
-address = {Oxford, England}
+ author = {K. Helbig},
+ title = {Foundations of anisotropy for exploration seismics},
+ booktitle = {Handbook of Geophysical exploration, section I: Seismic exploration},
+ publisher = {Pergamon},
+ year = {1994},
+ editor = {K. Helbig and S. Treitel},
+ volume = {22},
+ address = {Oxford, England}
}
@ARTICLE{helmbergerburdick1979,
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-year = {1979},
-volume = {7},
-pages = {417-442}
+ author = {D. V. Helmberger and L. J. Burdick},
+ title = {Synthetics seismograms},
+ journal = {Annual Review of Earth and Planetary Sciences},
+ year = {1979},
+ volume = {7},
+ pages = {417-442}
}
@ARTICLE{helmbergeretal1996,
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-journal = jgr,
-year = {1996},
-volume = {101},
-pages = {13,963-13,972}
+ author = {D. V. Helmberger and E. J. Garnero and X. Ding},
+ title = {Modeling two-dimensional structure at the core-mantle boundary},
+ journal = jgr,
+ year = {1996},
+ volume = {101},
+ pages = {13,963-13,972}
}
@ARTICLE{hemon78,
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+ author = {C. Hemon},
+ title = {Equations d'onde et mod\`{e}les},
+ journal = {Geophys. Prosp.},
+ year = {1978},
+ volume = {26},
+ pages = {790-821}
}
@INCOLLECTION{HeKa93,
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-publisher = {Pineridge Press},
-year = {1993},
-editor = {K. Morgan and E. Onate and J. Periaux and J. Peraire and O. C. Zienkiewicz},
-address = {Swansea}
+ author = {R. D. Henderson and G. E. Karniadakis},
+ title = {Unstructured spectral element methods for the incompressible {N}avier-{S}tokes
+ equations},
+ booktitle = {Finite elements in fluids},
+ publisher = {Pineridge Press},
+ year = {1993},
+ editor = {K. Morgan and E. Onate and J. Periaux and J. Peraire and O. C. Zienkiewicz},
+ address = {Swansea}
}
@ARTICLE{Hest98,
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-in a simplex},
-journal = {SIAM Journal on Numerical Analysis},
-year = {1998},
-volume = {35},
-pages = {655-676}
+ author = {J. S. Hesthaven},
+ title = {From electrostatics to almost optimal nodal sets for polynomial interpolation
+ in a simplex},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1998},
+ volume = {35},
+ pages = {655-676}
}
@ARTICLE{Hest98b,
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-the linearized {E}uler equations},
-journal = jcp,
-year = {1998},
-volume = {142},
-pages = {129-147},
-number = {1}
+ author = {J. S. Hesthaven},
+ title = {On the analysis and construction of perfectly matched layers for
+ the linearized {E}uler equations},
+ journal = jcp,
+ year = {1998},
+ volume = {142},
+ pages = {129-147},
+ number = {1}
}
@ARTICLE{Hest99,
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-year = {2000},
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+ author = {J. S. Hesthaven and C. H. Teng},
+ title = {Stable spectral methods on tetrahedral elements},
+ journal = {SIAM J. Sci. Comput.},
+ year = {2000},
+ volume = {21},
+ pages = {2352-2380}
}
@ARTICLE{HeRu94,
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-journal = gp,
-year = {1994},
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+ author = {S. Hestholm and B. Ruud},
+ title = {2{D} finite-difference elastic wave modelling including surface topography},
+ journal = gp,
+ year = {1994},
+ volume = {42},
+ pages = {371-390}
}
@ARTICLE{Hickey97,
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-year = {1997},
-volume = {102},
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+ author = {C. J. Hickey and J. M. Sabatier},
+ title = {Choosing {B}iot parameters for modeling water-saturated sand},
+ journal = jasa,
+ year = {1997},
+ volume = {102},
+ pages = {1480-1484}
}
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-journal = geophysics,
-year = {1991},
-volume = {56},
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+ author = {R. L. Higdon},
+ title = {Absorbing boundary conditions for elastic waves},
+ journal = geophysics,
+ year = {1991},
+ volume = {56},
+ pages = {231-241}
}
@ARTICLE{Hig90,
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+ author = {R. L. Higdon},
+ title = {Radiation boundary conditions for elastic wave propagation},
+ journal = {SIAM Journal on Numerical Analysis},
+ year = {1990},
+ volume = {27},
+ pages = {831-870}
}
@BOOK{Hij87,
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+ title = {Propagation of transient elastic waves in stratified anisotropic
+ media},
+ publisher = {North-Holland, Amsterdam, The Netherlands},
+ year = {1987},
+ author = {van der Hijden, J. H. M. T.}
}
@ARTICLE{hilletal1993,
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-journal = {Science},
-year = {1993},
-volume = {260},
-pages = {1617-1623}
+ author = {D. P. Hill and {et al.}},
+ title = {Seismicity remotely triggered by the magnitude~7.3 {L}anders, {C}alifornia
+ earthquake},
+ journal = {Science},
+ year = {1993},
+ volume = {260},
+ pages = {1617-1623}
}
@ARTICLE{HoRo94,
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+ author = {L. W. Ho and E. M. R{\o}nquist},
+ title = {Spectral-Element Solution of Steady Incompressible Viscous Free-Surface
+ Flows},
+ journal = {Finite Elements in Analysis and Design},
+ year = {1994},
+ volume = {16},
+ pages = {207-227}
}
@ARTICLE{Hol87,
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-for numerical differentiation in large-scale simulation of wave phenomena},
-journal = gp,
-year = {1987},
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+ author = {O. Holberg},
+ title = {Computational aspects of the choice of operator and sampling interval
+ for numerical differentiation in large-scale simulation of wave phenomena},
+ journal = gp,
+ year = {1987},
+ volume = {35},
+ pages = {629-655}
}
@ARTICLE{Hoo60,
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+ author = {A. T. de Hoop},
+ title = {A modification of {C}agniard's method for solving seismic pulse problems},
+ journal = {Applied Science Research},
+ year = {1960},
+ volume = {B8},
+ pages = {349-356}
}
@ARTICLE{dehoop96,
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+ author = {M. V. de Hoop},
+ title = {Generalization of the {B}remmer coupling series},
+ journal = {J. Math. Phys.},
+ year = {1996},
+ volume = {37},
+ pages = {3246-3282}
}
@ARTICLE{dehoop3,
-author = {M. V. De Hoop and J. H. Le Rousseau},
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-with a Vertical Symmetry Axis},
-journal = {Geophysics},
-year = {2001},
-volume = {66},
-pages = {1538-1550},
-number = {5}
+ author = {M. V. De Hoop and J. H. Le Rousseau},
+ title = {Scalar Generalized-Screen Algorithms in Transversely Isotropic Media
+ with a Vertical Symmetry Axis},
+ journal = {Geophysics},
+ year = {2001},
+ volume = {66},
+ pages = {1538-1550},
+ number = {5}
}
@ARTICLE{dehoop2000,
-author = {M. V. De Hoop and J. H. Le Rousseau and R. S. Wu},
-title = {Generalization of the phase-screen approximation for the scattering
-of acoustic waves},
-journal = {Wave Motion},
-year = {2000},
-volume = {31},
-pages = {43-70}
+ author = {M. V. De Hoop and J. H. Le Rousseau and R. S. Wu},
+ title = {Generalization of the phase-screen approximation for the scattering
+ of acoustic waves},
+ journal = {Wave Motion},
+ year = {2000},
+ volume = {31},
+ pages = {43-70}
}
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-year = {1999},
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+ author = {M. V. De Hoop and C. Spencer and R. Burridge},
+ title = {The Resolving Power of Seismic Amplitude Data: An Isotropic Inversion/Migration
+ Approach},
+ journal = geophysics,
+ year = {1999},
+ volume = {64},
+ pages = {852-873}
}
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+ author = {M. Horike and H. Uebayashi and T. Takeuchi},
+ title = {Seismic response in three dimensional sedimentary basin due to plane
+ {{\it S}} wave incidence},
+ journal = {J. Phys. Earth},
+ year = {1990},
+ volume = {38},
+ pages = {261-284}
}
@BOOK{HoJo85,
-title = {Matrix analysis},
-publisher = {Cambridge University Press},
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-author = {R. A. Horn and C. R. Johnson},
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+ title = {Matrix analysis},
+ publisher = {Cambridge University Press},
+ year = {1985},
+ author = {R. A. Horn and C. R. Johnson},
+ address = {Cambridge}
}
@ARTICLE{hch,
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+ author = {H. C. Hsieh and W. T. Chang},
+ title = {Virtual knot technique for curve fitting of rapidly varying data},
+ journal = {Computer Aided Geometric Design},
+ year = {1994},
+ volume = {11},
+ pages = {71-95}
}
@ARTICLE{Hu01,
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-journal = jcp,
-year = {2001},
-volume = {173},
-pages = {455-480},
-number = {2},
-doi = {10.1006/jcph.2001.6887}
+ author = {Fang Q. Hu},
+ title = {A Stable Perfectly Matched Layer for Linearized {E}uler Equations
+ in Unsplit Physical Variables},
+ journal = jcp,
+ year = {2001},
+ volume = {173},
+ pages = {455-480},
+ number = {2},
+ doi = {10.1006/jcph.2001.6887}
}
@ARTICLE{HuHuRa99,
-author = {Hu, Fang Q. and Hussaini, M. Y. and Rasetarinera, Patrick},
-title = {An analysis of the discontinuous {G}alerkin method for wave propagation
-problems},
-journal = jcp,
-year = {1999},
-volume = {151},
-pages = {921-946},
-number = {2},
-doi = {10.1006/jcph.1999.6227}
+ author = {Hu, Fang Q. and Hussaini, M. Y. and Rasetarinera, Patrick},
+ title = {An analysis of the discontinuous {G}alerkin method for wave propagation
+ problems},
+ journal = jcp,
+ year = {1999},
+ volume = {151},
+ pages = {921-946},
+ number = {2},
+ doi = {10.1006/jcph.1999.6227}
}
@ARTICLE{Huang95,
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-journal = {Eng. Frac. Mech.},
-year = {1995},
-volume = {51},
-pages = {217-224}
+ author = {J. Y. Huang},
+ title = {Interaction of {$SH$} waves with a finite crack in half space},
+ journal = {Eng. Frac. Mech.},
+ year = {1995},
+ volume = {51},
+ pages = {217-224}
}
@ARTICLE{Hud67,
-author = {J. A. Hudson},
-title = {Scattered surface waves from a surface obstacle},
-journal = gjras,
-year = {1967},
-volume = {13},
-pages = {441-458}
+ author = {J. A. Hudson},
+ title = {Scattered surface waves from a surface obstacle},
+ journal = gjras,
+ year = {1967},
+ volume = {13},
+ pages = {441-458}
}
@ARTICLE{Hubo80,
-author = {J. A. Hudson and D. M. Boore},
-title = {Comments on ``Scattered surface waves from a surface obstacle''},
-journal = gjras,
-year = {1980},
-volume = {60},
-pages = {123-127}
+ author = {J. A. Hudson and D. M. Boore},
+ title = {Comments on ``Scattered surface waves from a surface obstacle''},
+ journal = gjras,
+ year = {1980},
+ volume = {60},
+ pages = {123-127}
}
@ARTICLE{HuKn64a,
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-title = {Transmission and reflection of surface waves at a corner, part 1:
-{L}ove waves},
-journal = jgr,
-year = {1964},
-volume = {69},
-pages = {275-280}
+ author = {J. A. Hudson and L. Knopoff},
+ title = {Transmission and reflection of surface waves at a corner, part 1:
+ {L}ove waves},
+ journal = jgr,
+ year = {1964},
+ volume = {69},
+ pages = {275-280}
}
@ARTICLE{HuKn64b,
-author = {J. A. Hudson and L. Knopoff},
-title = {Transmission and reflection of surface waves at a corner, part 2:
-{R}ayleigh waves (theoretical)},
-journal = jgr,
-year = {1964},
-volume = {69},
-pages = {281-289}
+ author = {J. A. Hudson and L. Knopoff},
+ title = {Transmission and reflection of surface waves at a corner, part 2:
+ {R}ayleigh waves (theoretical)},
+ journal = jgr,
+ year = {1964},
+ volume = {69},
+ pages = {281-289}
}
@ARTICLE{Hud96,
-author = {J. A. Hudson and E. Liu and S. Crampin},
-title = {The mechanical properties of materials with interconnected cracks
-and pores},
-journal = gji,
-year = {1996},
-volume = {124},
-pages = {105-112}
+ author = {J. A. Hudson and E. Liu and S. Crampin},
+ title = {The mechanical properties of materials with interconnected cracks
+ and pores},
+ journal = gji,
+ year = {1996},
+ volume = {124},
+ pages = {105-112}
}
@ARTICLE{HuYe95,
-author = {G. J. Huftile and R. S. Yeats},
-title = {Convergence rates across a displacement transfer zone in the western
-{T}ransverse {R}anges, {V}entura Basin, {C}alifornia},
-journal = jgr,
-year = {1995},
-volume = {100},
-pages = {2043-2067},
-number = {2}
+ author = {G. J. Huftile and R. S. Yeats},
+ title = {Convergence rates across a displacement transfer zone in the western
+ {T}ransverse {R}anges, {V}entura Basin, {C}alifornia},
+ journal = jgr,
+ year = {1995},
+ volume = {100},
+ pages = {2043-2067},
+ number = {2}
}
@BOOK{Hug87,
-title = {The finite element method, linear static and dynamic finite element
-analysis},
-publisher = {Prentice-Hall International},
-year = {1987},
-author = {Thomas J. R. Hughes},
-address = {Englewood Cliffs, New Jersey, USA}
+ title = {The finite element method, linear static and dynamic finite element
+ analysis},
+ publisher = {Prentice-Hall International},
+ year = {1987},
+ author = {Thomas J. R. Hughes},
+ address = {Englewood Cliffs, New Jersey, USA}
}
@ARTICLE{HuFeHa87,
-author = {T. J. R. Hughes and R. M. Ferencz and J. O. Hallquist},
-title = {Large-scale vectorized implicit calculations in solid mechanics on
-a {Cray X-MP/48} utilizing {EBE} preconditioned conjugate gradients},
-journal = cmame,
-year = {1987},
-volume = {61},
-pages = {215-248},
-number = {2}
+ author = {T. J. R. Hughes and R. M. Ferencz and J. O. Hallquist},
+ title = {Large-scale vectorized implicit calculations in solid mechanics on
+ a {Cray X-MP/48} utilizing {EBE} preconditioned conjugate gradients},
+ journal = cmame,
+ year = {1987},
+ volume = {61},
+ pages = {215-248},
+ number = {2}
}
@ARTICLE{HuHu88,
-author = {T. J. R. Hughes and G. M. Hulbert},
-title = {Space-time finite element methods for elastodynamics, formulation
-and error estimates},
-journal = cmame,
-year = {1988},
-volume = {66},
-pages = {339-363}
+ author = {T. J. R. Hughes and G. M. Hulbert},
+ title = {Space-time finite element methods for elastodynamics, formulation
+ and error estimates},
+ journal = cmame,
+ year = {1988},
+ volume = {66},
+ pages = {339-363}
}
@ARTICLE{HuMa78,
-author = {T. J. R. Hughes and J. E. Marsden},
-title = {Classical elastodynamics as a linear symmetric hyperbolic system},
-journal = {Journal of Elasticity},
-year = {1978},
-volume = {8},
-pages = {97-110},
-number = {1}
+ author = {T. J. R. Hughes and J. E. Marsden},
+ title = {Classical elastodynamics as a linear symmetric hyperbolic system},
+ journal = {Journal of Elasticity},
+ year = {1978},
+ volume = {8},
+ pages = {97-110},
+ number = {1}
}
@PHDTHESIS{Hul89,
-author = {G. M. Hulbert},
-title = {Space-time finite element methods for second-order hyperbolic equations},
-school = {Stanford University},
-year = {1989},
-address = {Stanford}
+ author = {G. M. Hulbert},
+ title = {Space-time finite element methods for second-order hyperbolic equations},
+ school = {Stanford University},
+ year = {1989},
+ address = {Stanford}
}
@ARTICLE{HuCh92,
-author = {G. M. Hulbert and J. Chung},
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-explicit generalized $\alpha$-method},
-journal = {New Methods in Transient Analysis},
-year = {1992},
-volume = {143},
-pages = {73-78}
+ author = {G. M. Hulbert and J. Chung},
+ title = {A new explicit time integration method for structural dynamics: the
+ explicit generalized $\alpha$-method},
+ journal = {New Methods in Transient Analysis},
+ year = {1992},
+ volume = {143},
+ pages = {73-78}
}
@ARTICLE{HuHu90,
-author = {G. M. Hulbert and T. J. R. Hughes},
-title = {Space-time finite element methods for second-order hyperbolic equations},
-journal = cmame,
-year = {1990},
-volume = {84},
-pages = {327-348}
+ author = {G. M. Hulbert and T. J. R. Hughes},
+ title = {Space-time finite element methods for second-order hyperbolic equations},
+ journal = cmame,
+ year = {1990},
+ volume = {84},
+ pages = {327-348}
}
@INCOLLECTION{HuPrDuKeMa06,
-author = {John R. Humphrey and Daniel K. Price and James P. Durbano and Eric
-J. Kelmelis and Richard D. Martin},
-title = {High performance {2D} and {3D FDTD} solvers on {GPU}s},
-booktitle = {Proceedings of the 10th WSEAS International Conference on Applied
-Mathematics},
-publisher = {World Scientific and Engineering Academy and Society (WSEAS)},
-year = {2006},
-pages = {547-550},
-address = {Dallas, Texas, USA}
+ author = {John R. Humphrey and Daniel K. Price and James P. Durbano and Eric
+ J. Kelmelis and Richard D. Martin},
+ title = {High performance {2D} and {3D FDTD} solvers on {GPU}s},
+ booktitle = {Proceedings of the 10th WSEAS International Conference on Applied
+ Mathematics},
+ publisher = {World Scientific and Engineering Academy and Society (WSEAS)},
+ year = {2006},
+ pages = {547-550},
+ address = {Dallas, Texas, USA}
}
@ARTICLE{HuFo98,
-author = {S. H. Hung and D. Forsyth},
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-using the parallel multidomain pseudo-spectral method},
-journal = gji,
-year = {1998},
-volume = {133},
-pages = {726-740},
-number = {3}
+ author = {S. H. Hung and D. Forsyth},
+ title = {Modelling anisotropic wave propagation in oceanic inhomogeneous structures
+ using the parallel multidomain pseudo-spectral method},
+ journal = gji,
+ year = {1998},
+ volume = {133},
+ pages = {726-740},
+ number = {3}
}
@ARTICLE{HurTewRic01,
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-title = {Surface acoustic wave methods to determine the anisotropic elastic
-properties of thin films},
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-year = {2001},
-volume = {12},
-pages = {1486-1494}
+ author = {D. C. Hurley and V. K. Tewary and A. J. Richards},
+ title = {Surface acoustic wave methods to determine the anisotropic elastic
+ properties of thin films},
+ journal = {Measurement Science Technology},
+ year = {2001},
+ volume = {12},
+ pages = {1486-1494}
}
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-year = {1985},
-volume = {32},
-pages = {2568-2587},
-number = {4}
+ author = {D. C. Hurley and J. P. Wolfe},
+ title = {Phonon focusing in cubic crystals},
+ journal = {Physical Review B},
+ year = {1985},
+ volume = {32},
+ pages = {2568-2587},
+ number = {4}
}
@ARTICLE{HeSa06,
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-Graph Decomposition},
-journal = {SIAM Journal of Scientific Computing},
-year = {2006},
-volume = {28},
-pages = {2266-2293},
-number = {6}
+ author = {Pascal H{\'e}non and Yousef Saad},
+ title = {A Parallel Multistage {ILU} Factorization Based on a Hierarchical
+ Graph Decomposition},
+ journal = {SIAM Journal of Scientific Computing},
+ year = {2006},
+ volume = {28},
+ pages = {2266-2293},
+ number = {6}
}
@ARTICLE{ianculescuthompson2006,
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-non-reflecting boundary conditions},
-journal = cmame,
-year = {2006},
-volume = {195},
-pages = {3709-3741}
+ author = {C. Ianculescu and L. L. Thompson},
+ title = {Parallel iterative solution for the {H}elmholtz equation with exact
+ non-reflecting boundary conditions},
+ journal = cmame,
+ year = {2006},
+ volume = {195},
+ pages = {3709-3741}
}
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-journal = grl,
-year = {1996},
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-pages = {3095-3098}
+ author = {G. A. Ichinose and S. M. Day and H. Magistrale and T. Prush and F.
+ Vernon and A. Edelman},
+ title = {Crustal thickness variations beneath the {P}eninsular {R}anges, southern
+ {C}alifornia},
+ journal = grl,
+ year = {1996},
+ volume = {23},
+ pages = {3095-3098}
}
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-spectral method},
-journal = gji,
-year = {1999},
-volume = {136},
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+ author = {H. Igel},
+ title = {Wave propagation in three-dimensional spherical sections by the {C}hebyshev
+ spectral method},
+ journal = gji,
+ year = {1999},
+ volume = {136},
+ pages = {559-566}
}
@PHDTHESIS{Ige93,
-author = {Heiner Igel},
-title = {Seismic modeling and inversion},
-school = {Universit\'e Paris {\sc VII} Jussieu},
-year = {1993},
-address = {Paris}
+ author = {Heiner Igel},
+ title = {Seismic modeling and inversion},
+ school = {Universit\'e Paris {\sc VII} Jussieu},
+ year = {1993},
+ address = {Paris}
}
@ARTICLE{IgGe00,
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-accuracy, verification},
-journal = pepi,
-year = {2000},
-volume = {119},
-pages = {1-2}
+ author = {H. Igel and R. J. Geller},
+ title = {Numerical modeling of global seismic wave propagation: algorithms,
+ accuracy, verification},
+ journal = pepi,
+ year = {2000},
+ volume = {119},
+ pages = {1-2}
}
@ARTICLE{IgMoRi95,
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-title = {Anisotropic wave propagation through finite-difference grids},
-journal = geophysics,
-year = {1995},
-volume = {60},
-pages = {1203-1216},
-number = {4}
+ author = {H. Igel and P. Mora and B. Riollet},
+ title = {Anisotropic wave propagation through finite-difference grids},
+ journal = geophysics,
+ year = {1995},
+ volume = {60},
+ pages = {1203-1216},
+ number = {4}
}
@ARTICLE{IgWe96,
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-differences: application to lowermost mantle structure},
-journal = grl,
-year = {1996},
-volume = {23},
-pages = {415-418}
+ author = {H. Igel and M. Weber},
+ title = {{P-SV} wave propagation in the whole mantle using high-order finite
+ differences: application to lowermost mantle structure},
+ journal = grl,
+ year = {1996},
+ volume = {23},
+ pages = {415-418}
}
@ARTICLE{IgWe95,
-author = {H. Igel and M. Weber},
-title = {{SH}-wave propagation in the whole mantle using high-order finite
-differences},
-journal = grl,
-year = {1995},
-volume = {22},
-pages = {731-734}
+ author = {H. Igel and M. Weber},
+ title = {{SH}-wave propagation in the whole mantle using high-order finite
+ differences},
+ journal = grl,
+ year = {1995},
+ volume = {22},
+ pages = {731-734}
}
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-journal = {Physical Review},
-year = {1969},
-volume = {184},
-pages = {942-951},
-number = {3}
+ author = {K. A. Ingebrigtsen and A. Tonning},
+ title = {Elastic surface waves in crystals},
+ journal = {Physical Review},
+ year = {1969},
+ volume = {184},
+ pages = {942-951},
+ number = {3}
}
@INPROCEEDINGS{InEl08,
-author = {Inman, M. J. and Elsherbeni, A. Z.},
-title = {Optimization and parameter exploration using {GPU} based {FDTD} solvers},
-booktitle = {Proceedings of the 2008 IEEE MTT-S International Microwave Symposium},
-year = {2008},
-pages = {149-152},
-address = {Atlanta, Georgia, USA},
-month = {June},
-doi = {10.1109/MWSYM.2008.4633125}
+ author = {Inman, M. J. and Elsherbeni, A. Z.},
+ title = {Optimization and parameter exploration using {GPU} based {FDTD} solvers},
+ booktitle = {Proceedings of the 2008 IEEE MTT-S International Microwave Symposium},
+ year = {2008},
+ pages = {149-152},
+ address = {Atlanta, Georgia, USA},
+ month = {June},
+ doi = {10.1109/MWSYM.2008.4633125}
}
@INPROCEEDINGS{InElMaBa07,
-author = {Inman, M. J. and Elsherbeni, A. Z. and Maloney, J. G. and Baker,
-B. N.},
-title = {{GPU} based {FDTD} solver with {CPML} boundaries},
-booktitle = {Proceedings of the 2007 IEEE Antennas and Propagation Society International
-Symposium},
-year = {2007},
-pages = {5255-5258},
-address = {Honolulu, Hawaii, USA},
-month = {June},
-doi = {10.1109/APS.2007.4396732}
+ author = {Inman, M. J. and Elsherbeni, A. Z. and Maloney, J. G. and Baker,
+ B. N.},
+ title = {{GPU} based {FDTD} solver with {CPML} boundaries},
+ booktitle = {Proceedings of the 2007 IEEE Antennas and Propagation Society International
+ Symposium},
+ year = {2007},
+ pages = {5255-5258},
+ address = {Honolulu, Hawaii, USA},
+ month = {June},
+ doi = {10.1109/APS.2007.4396732}
}
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-publisher = {Springer-Verlag},
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-editor = {J. H. Fink},
-pages = {174-207},
-address = {Berlin}
+ author = {K. Ishihara and M. Iguchi and K. Kamo},
+ title = {Numerical simulation of lava flows on some volcanoes in {J}apan},
+ booktitle = {Lava flows and domes},
+ publisher = {Springer-Verlag},
+ year = {1990},
+ editor = {J. H. Fink},
+ pages = {174-207},
+ address = {Berlin}
}
@BOOK{Iss89,
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-publisher = {Oxford University Press},
-year = {1989},
-author = {E. H. Issaks and R. M. Srivastava},
-address = {Oxford},
-note = {560 p.}
+ title = {An Introduction to Applied Geostatistics},
+ publisher = {Oxford University Press},
+ year = {1989},
+ author = {E. H. Issaks and R. M. Srivastava},
+ address = {Oxford},
+ note = {560 p.}
}
@ARTICLE{IwHaKaIr96,
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-title = {Site Amplification of Ground motions during aftershocks of the 1995
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-{J}apan},
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-year = {1996},
-volume = {44},
-pages = {553-561}
+ author = {T. Iwata and K. Hatayama and H. Kawase and K. Irikura},
+ title = {Site Amplification of Ground motions during aftershocks of the 1995
+ {H}yogo-ken {N}anbu earthquake in severely damaged zone - {A}rray
+ observation of ground motions at {H}igashinada {W}ard, {K}obe city,
+ {J}apan},
+ journal = {J. Phys. Earth},
+ year = {1996},
+ volume = {44},
+ pages = {553-561}
}
@PHDTHESIS{Jon02,
-author = {S. J\'onsson},
-title = {Modeling volcano and earthquake deformation from satellite {R}adar
-interferometric observations},
-school = {Stanford University},
-year = {2002},
-address = {California}
+ author = {S. J\'onsson},
+ title = {Modeling volcano and earthquake deformation from satellite {R}adar
+ interferometric observations},
+ school = {Stanford University},
+ year = {2002},
+ address = {California}
}
@ARTICLE{JaJiGeLo06,
-author = {R. K. Jaiman and X. Jiao and P. H. Geubelle and E. Loth},
-title = {Conservative load transfer along curved fluid-solid interface with
-non-matching meshes},
-journal = jcp,
-year = {2006},
-volume = {218},
-pages = {372-397},
-number = {1},
-doi = {10.1016/j.jcp.2006.02.016}
+ author = {R. K. Jaiman and X. Jiao and P. H. Geubelle and E. Loth},
+ title = {Conservative load transfer along curved fluid-solid interface with
+ non-matching meshes},
+ journal = jcp,
+ year = {2006},
+ volume = {218},
+ pages = {372-397},
+ number = {1},
+ doi = {10.1016/j.jcp.2006.02.016}
}
@OTHER{JaReNeGue2008,
-author = {A. Jarvis and H.I. Reuter and A. Nelson and E. Guevara},
-lastchecked = {2008},
-title = {Hole-filled seamless SRTM data V4},
-url = {http://srtm.csi.cgiar.org},
-urldate = {http://srtm.csi.cgiar.org},
-year = {2008}
+ author = {A. Jarvis and H.I. Reuter and A. Nelson and E. Guevara},
+ lastchecked = {2008},
+ title = {Hole-filled seamless SRTM data V4},
+ url = {http://srtm.csi.cgiar.org},
+ urldate = {http://srtm.csi.cgiar.org},
+ year = {2008}
}
@ARTICLE{JaBe92,
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-title = {Acoustic modeling on a grid of vertically varying spacing},
-journal = gp,
-year = {1992},
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+ author = {C. Jastram and A. Behle},
+ title = {Acoustic modeling on a grid of vertically varying spacing},
+ journal = gp,
+ year = {1992},
+ volume = {40},
+ pages = {157-169}
}
@ARTICLE{JaTe92,
-author = {C. Jastram and E. Tessmer},
-title = {Elastic modelling on a grid with vertically varying spacing},
-journal = gp,
-year = {1992},
-volume = {42},
-pages = {357-370}
+ author = {C. Jastram and E. Tessmer},
+ title = {Elastic modelling on a grid with vertically varying spacing},
+ journal = gp,
+ year = {1992},
+ volume = {42},
+ pages = {357-370}
}
@BOOK{Jeffreys3,
-title = {The {E}arth},
-publisher = {Cambridge University Press},
-year = {1959},
-author = {Harold Jeffreys},
-address = {New York, USA}
+ title = {The {E}arth},
+ publisher = {Cambridge University Press},
+ year = {1959},
+ author = {Harold Jeffreys},
+ address = {New York, USA}
}
@INCOLLECTION{Jen75,
-author = {P. Jennings},
-title = {Fault map of {C}alifornia with volcanoes, thermal springs and thermal
-wells at 1:750,000 scale},
-booktitle = {Geological Data Map 1},
-publisher = {California Division of Mines and Geology},
-year = {1975},
-address = {Sacramento, California}
+ author = {P. Jennings},
+ title = {Fault map of {C}alifornia with volcanoes, thermal springs and thermal
+ wells at 1:750,000 scale},
+ booktitle = {Geological Data Map 1},
+ publisher = {California Division of Mines and Geology},
+ year = {1975},
+ address = {Sacramento, California}
}
+ at BOOK{COA2011,
+ title = {Computational Ocean Acoustics},
+ publisher = {Springer},
+ year = {2011},
+ author = {F. B. Jensen and W. Kuperman and M. Porter and H. Schmidt},
+ edition = {2nd}
+}
+
+ at INPROCEEDINGS{Jensen2008,
+ author = {F. B. Jensen and P. L. Nielsen and M. Zampolli and M. D. Collins
+ and W. L. Siegmann},
+ title = {Benchmark scenarios for range-dependent seismo-acoustic models},
+ booktitle = {Proceedings of the 8th International Conference on Theoretical and
+ Computational Acoustics (ICTCA)},
+ year = {2007},
+ editor = {M. Taroudakis and P. Papadakis}
+}
+
@ARTICLE{JiHeWa04,
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-and Implications for Rapid Strong-Motion Estimation},
-journal = {Earthquake Spectra},
-year = {2004},
-volume = {20},
-pages = {617-637},
-number = {3}
+ author = {Chen Ji and Don V. Helmberger and David J. Wald},
+ title = {A Teleseismic Study of the 2002 {D}enali Fault, {A}laska, Earthquake
+ and Implications for Rapid Strong-Motion Estimation},
+ journal = {Earthquake Spectra},
+ year = {2004},
+ volume = {20},
+ pages = {617-637},
+ number = {3}
}
@ARTICLE{JiHeWa2000,
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-title = {Basin structure estimation by waveform modeling: forward and inverse
-methods},
-journal = bssa,
-year = {2000},
-volume = {90},
-pages = {964-976}
+ author = {C. Ji and D. V. Helmberger and D. J. Wald},
+ title = {Basin structure estimation by waveform modeling: forward and inverse
+ methods},
+ journal = bssa,
+ year = {2000},
+ volume = {90},
+ pages = {964-976}
}
@ARTICLE{JiTsKoTr05,
-author = {Chen Ji and Seiji Tsuboi and Dimitri Komatitsch and Jeroen Tromp},
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-journal = bssa,
-year = {2005},
-volume = {95},
-pages = {2115-2124},
-number = {6},
-doi = {10.1785/0120040180}
+ author = {Chen Ji and Seiji Tsuboi and Dimitri Komatitsch and Jeroen Tromp},
+ title = {Rayleigh-Wave Multipathing along the West Coast of North America},
+ journal = bssa,
+ year = {2005},
+ volume = {95},
+ pages = {2115-2124},
+ number = {6},
+ doi = {10.1785/0120040180}
}
@ARTICLE{Ji2002a,
-author = {C. Ji and D. J. Wald and D. V. Helmberger},
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-{Part I: Wavelet} Domain Inversion Theory and Resolution Analysis},
-journal = bssa,
-year = {2002},
-volume = {92},
-pages = {1192-1207}
+ author = {C. Ji and D. J. Wald and D. V. Helmberger},
+ title = {Source description of the 1999 {Hector Mine, California} earthquake;
+ {Part I: Wavelet} Domain Inversion Theory and Resolution Analysis},
+ journal = bssa,
+ year = {2002},
+ volume = {92},
+ pages = {1192-1207}
}
@ARTICLE{Jia99,
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-title = {Quadrangle-grid velocity-stress finite difference method for poroelastic
-wave equations},
-journal = gji,
-year = {1999},
-volume = {139},
-pages = {171-182}
+ author = {Zhang Jianfeng},
+ title = {Quadrangle-grid velocity-stress finite difference method for poroelastic
+ wave equations},
+ journal = gji,
+ year = {1999},
+ volume = {139},
+ pages = {171-182}
}
@ARTICLE{JiWaBe95,
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-earthquake},
-journal = grl,
-year = {1995},
-volume = {22},
-pages = {2285-2288},
-number = {16}
+ author = {W. Jiao and T. C. Wallace and S. L. Beck},
+ title = {Evidence for static displacements from the {J}une 9, 1994 deep {B}olivian
+ earthquake},
+ journal = grl,
+ year = {1995},
+ volume = {22},
+ pages = {2285-2288},
+ number = {16}
}
@ARTICLE{JiMcDe88,
-author = {R. S. Jih and K. L. McLaughlin and Z. A Der},
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-explicit elastic finite-difference scheme},
-journal = geophysics,
-year = {1988},
-volume = {53},
-pages = {1045-1055}
+ author = {R. S. Jih and K. L. McLaughlin and Z. A Der},
+ title = {Free-boundary conditions of arbitrary polygonal topography in a two-dimensional
+ explicit elastic finite-difference scheme},
+ journal = geophysics,
+ year = {1988},
+ volume = {53},
+ pages = {1045-1055}
}
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-title = {Two dimensional asymptotic iterative elastic inversion},
-journal = gji,
-year = {1992},
-volume = {108},
-pages = {575-588}
+ author = {S. Jin and R. Madariaga and J. Virieux and G. Lambar\'e},
+ title = {Two dimensional asymptotic iterative elastic inversion},
+ journal = gji,
+ year = {1992},
+ volume = {108},
+ pages = {575-588}
}
@ARTICLE{JoGaDiRo77,
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-sup\'erieur},
-journal = {Comptes rendus Acad. Sci. Paris},
-year = {1977},
-volume = {S\'erie B, 285},
-pages = {49-51}
+ author = {N. Jobert and R. Gaulon and A. Dieulin and G. Roult},
+ title = {Sur les ondes de tr\`es longue p\'eriode, caract\'eristiques du manteau
+ sup\'erieur},
+ journal = {Comptes rendus Acad. Sci. Paris},
+ year = {1977},
+ volume = {S\'erie B, 285},
+ pages = {49-51}
}
@ARTICLE{JoHuMaJo92,
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-on the {C}onnection {M}achine system},
-journal = cmame,
-year = {1992},
-volume = {99},
-pages = {113-134}
+ author = {Z. Johan and T. J. R. Hughes and K. K. Mathur and S. L. Johnsson},
+ title = {A data parallel finite element method for computational fluid dynamics
+ on the {C}onnection {M}achine system},
+ journal = cmame,
+ year = {1992},
+ volume = {99},
+ pages = {113-134}
}
@ARTICLE{JoMaJoHu94,
-author = {Z. Johan and K. K. Mathur and S. L. Johnsson and T. J. R. Hughes},
-title = {An efficient communications strategy for finite element methods on
-the {C}onnection {Machine} {CM-5} system},
-journal = cmame,
-year = {1994},
-volume = {113},
-pages = {363-387}
+ author = {Z. Johan and K. K. Mathur and S. L. Johnsson and T. J. R. Hughes},
+ title = {An efficient communications strategy for finite element methods on
+ the {C}onnection {Machine} {CM-5} system},
+ journal = cmame,
+ year = {1994},
+ volume = {113},
+ pages = {363-387}
}
@TECHREPORT{Jol95,
-author = {P. Joly},
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-institution = {Laboratoire d'Analyse Num\'erique},
-year = {1995},
-address = {Universit\'e Pierre et Marie Curie, Paris}
+ author = {P. Joly},
+ title = {R\'esolution de l'\'equation de {B}urgers par paquets d'ondelettes},
+ institution = {Laboratoire d'Analyse Num\'erique},
+ year = {1995},
+ address = {Universit\'e Pierre et Marie Curie, Paris}
}
@INPROCEEDINGS{JoKoVi95,
-author = {P. Joly and D. Komatitsch and J. P. Vilotte},
-title = {Solution of the wave equation by a wavelet basis approximation},
-booktitle = {Proceedings of the Enumath'1995 conference},
-year = {1995},
-pages = {12-24},
-address = {Paris, France}
+ author = {P. Joly and D. Komatitsch and J. P. Vilotte},
+ title = {Solution of the wave equation by a wavelet basis approximation},
+ booktitle = {Proceedings of the Enumath'1995 conference},
+ year = {1995},
+ pages = {12-24},
+ address = {Paris, France}
}
@ARTICLE{JoMaPe94,
-author = {P. Joly and Y. Maday and V. Perrier},
-title = {Towards a method for solving partial differential equations by using
-wavelet packet bases},
-journal = cmame,
-year = {1994},
-volume = {116},
-pages = {9999998-9999999}
+ author = {P. Joly and Y. Maday and V. Perrier},
+ title = {Towards a method for solving partial differential equations by using
+ wavelet packet bases},
+ journal = cmame,
+ year = {1994},
+ volume = {116},
+ pages = {9999998-9999999}
}
@ARTICLE{Jordan2,
-author = {P. M. Jordan},
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-Operator Symbols: The Focusing Quadratic Profile}},
-journal = {J. Math. Phys.},
-year = {2000},
-volume = {42},
-pages = {4618-4623}
+ author = {P. M. Jordan},
+ title = {{C}omment on \textit{{E}xact Constructions of Square-root {H}elmholtz
+ Operator Symbols: The Focusing Quadratic Profile}},
+ journal = {J. Math. Phys.},
+ year = {2000},
+ volume = {42},
+ pages = {4618-4623}
}
@INPROCEEDINGS{JoJiLaGiCa03,
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-and Jordi Caubet},
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-Processing Symposium},
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-pages = {80.2},
-address = {Nice, France},
-month = apr,
-bdsk-url-2 = {http://dx.doi.org/10.1109/IPDPS.2003.1213183},
-doi = {10.1109/IPDPS.2003.1213183},
-url = {www.cepba.upc.es/paraver}
+ author = {Gabriele Jost and Haoquian Jin and Jesus Labarta and Judit Gim\'enez
+ and Jordi Caubet},
+ title = {Performance Analysis of Multilevel Parallel Applications on Shared
+ Memory Architectures},
+ booktitle = {Proceedings of the IPDPS'2003 International Parallel and Distributed
+ Processing Symposium},
+ year = {2003},
+ pages = {80.2},
+ address = {Nice, France},
+ month = apr,
+ bdsk-url-2 = {http://dx.doi.org/10.1109/IPDPS.2003.1213183},
+ doi = {10.1109/IPDPS.2003.1213183},
+ url = {www.cepba.upc.es/paraver}
}
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-title = {Calculation of nonlinear ground response on earthquakes},
-journal = bssa,
-year = {1975},
-volume = {65},
-pages = {1315-1336}
+ author = {W. B. Joyner and T. F. Chen},
+ title = {Calculation of nonlinear ground response on earthquakes},
+ journal = bssa,
+ year = {1975},
+ volume = {65},
+ pages = {1315-1336}
}
@ARTICLE{KaDu08,
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-Between Solids and Moving Fluids},
-journal = geophysics,
-year = {2008},
-volume = {73},
-pages = {T23-T35},
-number = {3},
-doi = {10.1190/1.2870081}
+ author = {Martin K\"aser and Michael Dumbser},
+ title = {A Highly Accurate Discontinuous {G}alerkin Method for Complex Interfaces
+ Between Solids and Moving Fluids},
+ journal = geophysics,
+ year = {2008},
+ volume = {73},
+ pages = {T23-T35},
+ number = {3},
+ doi = {10.1190/1.2870081}
}
@ARTICLE{KaDu06,
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-waves on unstructured meshes-{I}. {T}he two-dimensional isotropic
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-year = {2006},
-volume = {166},
-pages = {855-877},
-number = {2},
-doi = {10.1111/j.1365-246X.2006.03051.x}
+ author = {M. K\"aser and M. Dumbser},
+ title = {An arbitrary high-order discontinuous {G}alerkin method for elastic
+ waves on unstructured meshes-{I}. {T}he two-dimensional isotropic
+ case with external source terms},
+ journal = gji,
+ year = {2006},
+ volume = {166},
+ pages = {855-877},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2006.03051.x}
}
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-year = {1993},
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-pages = {3480-3492},
-number = {6}
+ author = {L. F. Kallivokas and J. Bielak},
+ title = {Time-domain analysis of transient structural acoustics problems based
+ on the finite element method and a novel boundary element},
+ journal = jasa,
+ year = {1993},
+ volume = {94},
+ pages = {3480-3492},
+ number = {6}
}
@ARTICLE{KaSgKi95,
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-wave propagation},
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-year = {1995},
-volume = {38},
-pages = {755-773}
+ author = {A. Kamel and P. Sguazzero and M. Kindelan},
+ title = {Cost-effective staggered schemes for the numerical simulation of
+ wave propagation},
+ journal = ijnme,
+ year = {1995},
+ volume = {38},
+ pages = {755-773}
}
@ARTICLE{KaMaOrWe03,
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-year = {2003},
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+ author = {C. Kane and J. E. Marsden and M. Ortiz and M. West},
+ title = {Variational integrators and the {N}ewmark algorithm for conservative
+ and dissipative mechanical systems},
+ journal = ijnme,
+ year = {2003},
+ volume = {49},
+ pages = {1295-1325},
+ number = {10}
}
@ARTICLE{KaBa04,
-author = {Tae-Seob Kang and Chang-Eob Baag},
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-journal = bssa,
-year = {2004},
-volume = {94},
-pages = {207-219},
-number = {1},
-doi = {10.1785/0120030080}
+ author = {Tae-Seob Kang and Chang-Eob Baag},
+ title = {Finite-Difference Seismic Simulation Combining Discontinuous Grids
+ with Locally Variable Timesteps},
+ journal = bssa,
+ year = {2004},
+ volume = {94},
+ pages = {207-219},
+ number = {1},
+ doi = {10.1785/0120030080}
}
@ARTICLE{KapKuz99,
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-year = {1999},
-volume = {327},
-pages = {1123-1128},
-number = {IIb}
+ author = {A. V. Kaptsov and S. V. Kuznetsov},
+ title = {Spectral properties of {C}hristoffel equation for {R}ayleigh waves},
+ journal = {Compte Rendu de l'Academie des Sciences de Paris},
+ year = {1999},
+ volume = {327},
+ pages = {1123-1128},
+ number = {IIb}
}
@ARTICLE{karato1993,
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-journal = grl,
-year = {1993},
-volume = {20},
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+ author = {S. Karato},
+ title = {Importance of anelasticity in the interpretation of seismic tomography},
+ journal = grl,
+ year = {1993},
+ volume = {20},
+ pages = {1623-1626}
}
@ARTICLE{KaKu98a,
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-year = {1998},
-volume = {20},
-pages = {359-392},
-number = {1}
+ author = {George Karypis and Vipin Kumar},
+ title = {A Fast and High-Quality Multilevel Scheme for Partitioning Irregular
+ Graphs},
+ journal = {SIAM Journal on Scientific Computing},
+ year = {1998},
+ volume = {20},
+ pages = {359-392},
+ number = {1}
}
@ARTICLE{KaKu98b,
-author = {George Karypis and Vipin Kumar},
-title = {Multilevel {$k$}-way Partitioning Scheme for Irregular Graphs},
-journal = {Journal of Parallel and Distributed Computing},
-year = {1998},
-volume = {48},
-pages = {96-129},
-number = {1}
+ author = {George Karypis and Vipin Kumar},
+ title = {Multilevel {$k$}-way Partitioning Scheme for Irregular Graphs},
+ journal = {Journal of Parallel and Distributed Computing},
+ year = {1998},
+ volume = {48},
+ pages = {96-129},
+ number = {1}
}
@ARTICLE{KaKu98c,
-author = {George Karypis and Vipin Kumar},
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-Matrix Ordering},
-journal = {Journal of Parallel and Distributed Computing},
-year = {1998},
-volume = {48},
-pages = {71-85}
+ author = {George Karypis and Vipin Kumar},
+ title = {A Parallel Algorithm for Multilevel Graph Partitioning and Sparse
+ Matrix Ordering},
+ journal = {Journal of Parallel and Distributed Computing},
+ year = {1998},
+ volume = {48},
+ pages = {71-85}
}
@ARTICLE{KaWiTeSn87,
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-title = {Active contour models},
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-year = {1987},
-volume = {1},
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+ author = {Kass, M. and Witkin, A.P. and Terzopoulos, D. and Snakes},
+ title = {Active contour models},
+ journal = {Int. J. Comput. Vis.},
+ year = {1987},
+ volume = {1},
+ pages = {133-144},
+ number = {4}
}
@INPROCEEDINGS{KaAn02,
-author = {Theodoros K. Katsibas and Christos S. Antonopoulos},
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-year = {2002},
-volume = {1},
-pages = {551-554},
-address = {Munich, Germany},
-month = {October},
-organization = {IEEE}
+ author = {Theodoros K. Katsibas and Christos S. Antonopoulos},
+ title = {An efficient {PML} absorbing medium in {FDTD} simulations of acoustic
+ scattering in lossy media},
+ booktitle = {Proceedings of the 2002 IEEE ultrasonics symposium},
+ year = {2002},
+ volume = {1},
+ pages = {551-554},
+ address = {Munich, Germany},
+ month = {October},
+ organization = {IEEE}
}
@ARTICLE{Kau92,
-author = {E. Kausel},
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-journal = bssa,
-year = {1992},
-volume = {82},
-pages = {898-913}
+ author = {E. Kausel},
+ title = {Physical interpretation and stability of paraxial boundary conditions},
+ journal = bssa,
+ year = {1992},
+ volume = {82},
+ pages = {898-913}
}
@ARTICLE{KaTaGe06,
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-year = {2006},
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-number = {2},
-doi = {10.1111/j.1365-246X.2005.02829.x}
+ author = {K. Kawai and N. Takeuchi and R. J. Geller},
+ title = {Complete synthetic seismograms up to 2~{H}z for transversely-isotropic
+ spherically-symmetric media},
+ journal = gji,
+ year = {2006},
+ volume = {164},
+ pages = {411-424},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2005.02829.x}
}
@ARTICLE{Kaw88,
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+ author = {H. Kawase},
+ title = {Time-domain response of a semi-circular canyon for incident {{\it
+ SV}}, {{\it P}} and {R}ayleigh waves calculated by the discrete wavenumber
+ boundary element method},
+ journal = bssa,
+ year = {1988},
+ volume = {78},
+ pages = {1415-1437}
}
@ARTICLE{KaAk90,
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-journal = bssa,
-year = {1990},
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-pages = {1-22}
+ author = {H. Kawase and K. Aki},
+ title = {Topography effect at the critical {{\it SV}} wave incidence: possible
+ explanation of damage pattern by the {W}hittier {N}arrows, {C}alifornia,
+ earthquake of 1 {O}ctober 1987},
+ journal = bssa,
+ year = {1990},
+ volume = {80},
+ pages = {1-22}
}
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-year = {1989},
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+ author = {H. Kawase and K. Aki},
+ title = {A study on the response of a soft sedimentary basin for incident
+ {{\it S}}, {{\it P}} and {R}ayleigh waves, with special reference
+ to the long duration observed in {M}exico {C}ity},
+ journal = bssa,
+ year = {1989},
+ volume = {79},
+ pages = {1361-1382}
}
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+ author = {I. Kay and E. S. Krebes},
+ title = {Applying finite element analysis to the memory variable formulation
+ of wave propagation in anelastic media},
+ journal = geophysics,
+ year = {1999},
+ volume = {64},
+ pages = {300-307}
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+ journal = geophysics,
+ year = {1976},
+ volume = {41},
+ pages = {2-27}
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+ author = {J. M. Kendall and P. G. Silver},
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+ mantle},
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+ year = {1996},
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+ pages = {409}
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+ journal = gji,
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+ volume = {122},
+ pages = {108-124}
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@UNPUBLISHED{Khronos:2008:TOS,
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+ author = {{Khronos OpenCL Working Group}},
+ title = {The {OpenCL} {S}pecification, Version 1.0},
+ note = {\url{http://www.khronos.org/opencl}},
+ month = dec,
+ year = {2008},
+ editor = {Aaftab Munshi}
}
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-year = {2002},
-note = {ERI, University of Tokyo, Japan, wwweic.eri.u-tokyo.ac.jp/EIC/EIC\_News/021103AL-e.html}
+ author = {M. Kikuchi and Y. Yamanaka},
+ title = {Source rupture process of the central {A}laska earthquake of {N}ovember
+ 3, 2002, inferred from teleseismic body waves},
+ year = {2002},
+ note = {ERI, University of Tokyo, Japan, wwweic.eri.u-tokyo.ac.jp/EIC/EIC\_News/021103AL-e.html}
}
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+ journal = {J. Eng. Mech. ASCE},
+ year = {1993},
+ volume = {119},
+ pages = {603-624}
}
@INPROCEEDINGS{Kim08,
-author = {Theodore Kim},
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-booktitle = {I3D '08: Proceedings of the 2008 symposium on Interactive 3D graphics
-and games},
-year = {2008},
-pages = {99--106},
-doi = {10.1145/1342250.1342265}
+ author = {Theodore Kim},
+ title = {Hardware-Aware Analysis and Optimization of `{S}table {F}luids'},
+ booktitle = {I3D '08: Proceedings of the 2008 symposium on Interactive 3D graphics
+ and games},
+ year = {2008},
+ pages = {99--106},
+ doi = {10.1145/1342250.1342265}
}
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+ title = {Elastic modeling and its application to amplitude versus angle interpretation},
+ journal = gp,
+ year = {1989},
+ volume = {37},
+ pages = {3-30}
}
@INPROCEEDINGS{KiEnShShArStPhHw09,
-author = {Volodymyr V. Kindratenko and Jeremy J. Enos and Guochun Shi and Michael
-T. Showerman and Galen W. Arnold and John E. Stone and James C. Phillips
-and Wen{-}mei Hwu},
-title = {{GPU} Clusters for High-Performance Computing},
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-on Accelerator Clusters (PPAC'09)},
-year = {2009},
-pages = {1-8},
-address = {New Orleans, Louisiana, USA},
-month = aug
+ author = {Volodymyr V. Kindratenko and Jeremy J. Enos and Guochun Shi and Michael
+ T. Showerman and Galen W. Arnold and John E. Stone and James C. Phillips
+ and Wen{-}mei Hwu},
+ title = {{GPU} Clusters for High-Performance Computing},
+ booktitle = {Proceedings on the IEEE Cluster'2009 Workshop on Parallel Programming
+ on Accelerator Clusters (PPAC'09)},
+ year = {2009},
+ pages = {1-8},
+ address = {New Orleans, Louisiana, USA},
+ month = aug
}
@BOOK{KiHw10,
-title = {Programming Massively Parallel Processors: A Hands-on Approach},
-publisher = {Morgan Kaufmann},
-year = {2010},
-author = {Kirk, David B. and Hwu, Wen-mei W.},
-address = {Boston, Massachusetts, USA}
+ title = {Programming Massively Parallel Processors: A Hands-on Approach},
+ publisher = {Morgan Kaufmann},
+ year = {2010},
+ author = {Kirk, David B. and Hwu, Wen-mei W.},
+ address = {Boston, Massachusetts, USA}
}
@INPROCEEDINGS{kiyashchenkoplessix2005,
-author = {D. A. Kiyashchenko and R. E. Plessix},
-title = {True amplitude multi-one-way migration: comparison of different imaging
-principles},
-booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
-year = {2005},
-note = {75th international meeting of the SEG}
+ author = {D. A. Kiyashchenko and R. E. Plessix},
+ title = {True amplitude multi-one-way migration: comparison of different imaging
+ principles},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {2005},
+ note = {75th international meeting of the SEG}
}
@ARTICLE{KlWaBrHe09,
-author = {A. Kl\"ockner and T. Warburton and J. Bridge and J. S. Hesthaven},
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-journal = jcp,
-year = {2009},
-volume = {228},
-pages = {7863-7882},
-doi = {10.1016/j.jcp.2009.06.041}
+ author = {A. Kl\"ockner and T. Warburton and J. Bridge and J. S. Hesthaven},
+ title = {Nodal discontinuous {G}alerkin methods on graphics processors},
+ journal = jcp,
+ year = {2009},
+ volume = {228},
+ pages = {7863-7882},
+ doi = {10.1016/j.jcp.2009.06.041}
}
@TECHREPORT{KlVi02,
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-title = {Perfectly matched layers in the spectral element method},
-institution = {Lithos Scientific Report},
-year = {2002},
-number = {4},
-note = {Unpublished}
+ author = {E. M. C. Klien and J. P. Vilotte},
+ title = {Perfectly matched layers in the spectral element method},
+ institution = {Lithos Scientific Report},
+ year = {2002},
+ number = {4},
+ note = {Unpublished}
}
@ARTICLE{Kli96,
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-journal = pageoph,
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+ author = {L. Klimes},
+ title = {Accuracy of elastic finite differences in smooth media},
+ journal = pageoph,
+ year = {1996},
+ volume = {148},
+ pages = {39-76},
+ number = {1}
}
@ARTICLE{Kno52,
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-title = {On {R}ayleigh wave velocities},
-journal = {Bulletin of the Seismological Society of America},
-year = {1952},
-volume = {42},
-pages = {307-308}
+ author = {L. Knopoff},
+ title = {On {R}ayleigh wave velocities},
+ journal = {Bulletin of the Seismological Society of America},
+ year = {1952},
+ volume = {42},
+ pages = {307-308}
}
@ARTICLE{Knu99,
-author = {Patrick M. Knupp},
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-quadrilateral meshes},
-journal = ijnme,
-year = {1999},
-volume = {45},
-pages = {37-45},
-number = {1}
+ author = {Patrick M. Knupp},
+ title = {Applications of mesh smoothing: copy, morph, and sweep on unstructured
+ quadrilateral meshes},
+ journal = ijnme,
+ year = {1999},
+ volume = {45},
+ pages = {37-45},
+ number = {1}
}
@INCOLLECTION{Kob84,
-author = {S. Kobayashi},
-title = {Fundamentals of boundary integral equations methods in elastodynamics},
-booktitle = {Boundary element research},
-publisher = {Springer-Verlag},
-year = {1984},
-editor = {C. A. Brebbia},
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-address = {New York}
+ author = {S. Kobayashi},
+ title = {Fundamentals of boundary integral equations methods in elastodynamics},
+ booktitle = {Boundary element research},
+ publisher = {Springer-Verlag},
+ year = {1984},
+ editor = {C. A. Brebbia},
+ volume = {2},
+ address = {New York}
}
@BOOK{Kob87,
-title = {Elastodynamics in boundary element methods in mechanics},
-publisher = {North-Holland},
-year = {1987},
-author = {S. Kobayashi},
-address = {Amsterdam, The Netherlands}
+ title = {Elastodynamics in boundary element methods in mechanics},
+ publisher = {North-Holland},
+ year = {1987},
+ author = {S. Kobayashi},
+ address = {Amsterdam, The Netherlands}
}
@ARTICLE{KohnNir,
-author = {J. J. Kohn and L. Nirenberg},
-title = {On the Algebra of Pseudo-Differential Operators},
-journal = {Comm. Pure Appl. Math.},
-year = {1965},
-volume = {18},
-pages = {269-305}
+ author = {J. J. Kohn and L. Nirenberg},
+ title = {On the Algebra of Pseudo-Differential Operators},
+ journal = {Comm. Pure Appl. Math.},
+ year = {1965},
+ volume = {18},
+ pages = {269-305}
}
@ARTICLE{KolMaz93,
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-title = {Phonon-focusing effect with laser-generated ultrasonic surface waves},
-journal = {Physical Review B},
-year = {1993},
-volume = {48},
-pages = {14502-14512},
-number = {19}
+ author = {Al. A. Kolomenskii and A. A. Maznev},
+ title = {Phonon-focusing effect with laser-generated ultrasonic surface waves},
+ journal = {Physical Review B},
+ year = {1993},
+ volume = {48},
+ pages = {14502-14512},
+ number = {19}
}
@ARTICLE{Kom11,
-author = {Dimitri Komatitsch},
-title = {Fluid-solid coupling on a cluster of {GPU} graphics cards for seismic
-wave propagation},
-journal = {Comptes Rendus de l'Acad\'emie des Sciences - M\'ecanique},
-year = {2011},
-doi = {10.1016/j.crme.2010.11.007},
-volume = {339},
-pages = {125-135}
+ author = {Dimitri Komatitsch},
+ title = {Fluid-solid coupling on a cluster of {GPU} graphics cards for seismic
+ wave propagation},
+ journal = {Comptes Rendus de l'Acad\'emie des Sciences - M\'ecanique},
+ year = {2011},
+ volume = {339},
+ pages = {125-135},
+ doi = {10.1016/j.crme.2010.11.007}
}
@ARTICLE{Kom08,
-author = {Dimitri Komatitsch},
-title = {Comment on ``{M}ultidomain {P}seudospectral {T}ime-{D}omain ({PSTD})
-method for acoustic waves in lossy media'' by {Y. Q. Zeng, Q. H.
-Liu and G. Zhao, Journal of Computational Acoustics, vol. 12, no.
-3, pp 277-299 (2004)}},
-journal = jca,
-year = {2008},
-volume = {16},
-pages = {465-467},
-number = {3}
+ author = {Dimitri Komatitsch},
+ title = {Comment on ``{M}ultidomain {P}seudospectral {T}ime-{D}omain ({PSTD})
+ method for acoustic waves in lossy media'' by {Y. Q. Zeng, Q. H.
+ Liu and G. Zhao, Journal of Computational Acoustics, vol. 12, no.
+ 3, pp 277-299 (2004)}},
+ journal = jca,
+ year = {2008},
+ volume = {16},
+ pages = {465-467},
+ number = {3}
}
@PHDTHESIS{Kom03,
-author = {Dimitri Komatitsch},
-title = {Advanced numerical modeling in geophysics ({M}od\'elisation num\'erique
-avanc\'ee pour la g\'eophysique)},
-school = {Universit\'e de Pau et des Pays de l'Adour},
-year = {2003},
-address = {Pau, France},
-month = {September},
-note = {Habilitation Thesis (Habilitation \`a {D}iriger des {R}echerches,
-{H.D.R.}), 114 pages}
+ author = {Dimitri Komatitsch},
+ title = {Advanced numerical modeling in geophysics ({M}od\'elisation num\'erique
+ avanc\'ee pour la g\'eophysique)},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {2003},
+ address = {Pau, France},
+ month = {September},
+ note = {Habilitation Thesis (Habilitation \`a {D}iriger des {R}echerches,
+ {H.D.R.}), 114 pages}
}
@PHDTHESIS{Kom97,
-author = {Dimitri Komatitsch},
-title = {M\'ethodes spectrales et \'el\'ements spectraux pour l'\'equation
-de l'\'elastodynamique 2{D} et 3{D} en milieu h\'et\'erog\`ene ({S}pectral
-and spectral-element methods for the 2{D} and 3{D} elastodynamics
-equations in heterogeneous media)},
-school = {Institut de Physique du Globe},
-year = {1997},
-address = {Paris, France},
-month = {May},
-note = {187 pages}
+ author = {Dimitri Komatitsch},
+ title = {M\'ethodes spectrales et \'el\'ements spectraux pour l'\'equation
+ de l'\'elastodynamique 2{D} et 3{D} en milieu h\'et\'erog\`ene ({S}pectral
+ and spectral-element methods for the 2{D} and 3{D} elastodynamics
+ equations in heterogeneous media)},
+ school = {Institut de Physique du Globe},
+ year = {1997},
+ address = {Paris, France},
+ month = {May},
+ note = {187 pages}
}
- at PHDTHESIS{Mad09,
-author = {Ronan Madec},
-title = {M\'ethode des \'el\'ements spectraux pour la propagation d'ondes sismiques en milieu g\'eologique fluide-solide avec pas de temps locaux et couches absorbantes parfaitement adapt\'ees C-PML},
-school = {Universit\'e de Pau et des Pays de l'Adour},
-year = {2009},
-address = {Pau, France},
-month = {December}
-}
-
@ARTICLE{KoBaTr00,
-author = {D. Komatitsch and C. Barnes and J. Tromp},
-title = {Wave propagation near a fluid-solid interface: a spectral element
-approach},
-journal = geophysics,
-year = {2000},
-volume = {65},
-pages = {623-631},
-number = {2},
-doi = {10.1190/1.1444758}
+ author = {D. Komatitsch and C. Barnes and J. Tromp},
+ title = {Wave propagation near a fluid-solid interface: a spectral element
+ approach},
+ journal = geophysics,
+ year = {2000},
+ volume = {65},
+ pages = {623-631},
+ number = {2},
+ doi = {10.1190/1.1444758}
}
@ARTICLE{KoBaTr00b,
-author = {D. Komatitsch and C. Barnes and J. Tromp},
-title = {Simulation of anisotropic wave propagation based upon a spectral
-element method},
-journal = geophysics,
-year = {2000},
-volume = {65},
-pages = {1251-1260},
-number = {4},
-doi = {10.1190/1.1444816}
+ author = {D. Komatitsch and C. Barnes and J. Tromp},
+ title = {Simulation of anisotropic wave propagation based upon a spectral
+ element method},
+ journal = geophysics,
+ year = {2000},
+ volume = {65},
+ pages = {1251-1260},
+ number = {4},
+ doi = {10.1190/1.1444816}
}
+ at ARTICLE{KoCaCaFa11,
+ author = {Dimitri Komatitsch and Jos\'e Carcione and Fabio Cavallini and Nathalie
+ Favretto-Cristini},
+ title = {Elastic surface waves in crystals: {P}art {II} : Cross-check of two
+ full-wave numerical modeling methods},
+ journal = {Ultrasonics},
+ year = {2011},
+ volume = {51},
+ pages = {878-889},
+ number = {8},
+ doi = {10.1016/j.ultras.2011.05.001}
+}
+
@ARTICLE{KoCoMo96,
-author = {D. Komatitsch and F. Coutel and P. Mora},
-title = {Tensorial formulation of the wave equation for modelling curved interfaces},
-journal = gji,
-year = {1996},
-volume = {127},
-pages = {156-168},
-number = {1},
-doi = {10.1111/j.1365-246X.1996.tb01541.x}
+ author = {D. Komatitsch and F. Coutel and P. Mora},
+ title = {Tensorial formulation of the wave equation for modelling curved interfaces},
+ journal = gji,
+ year = {1996},
+ volume = {127},
+ pages = {156-168},
+ number = {1},
+ doi = {10.1111/j.1365-246X.1996.tb01541.x}
}
@ARTICLE{KoErGoMi10,
-author = {Dimitri Komatitsch and Gordon Erlebacher and Dominik G\"oddeke and
-David Mich\'ea},
-title = {High-order finite-element seismic wave propagation modeling with
-{MPI} on a large {GPU} cluster},
-journal = jcp,
-year = {2010},
-volume = {229},
-pages = {7692-7714},
-number = {20},
-doi = {10.1016/j.jcp.2010.06.024}
+ author = {Dimitri Komatitsch and Gordon Erlebacher and Dominik G\"oddeke and
+ David Mich\'ea},
+ title = {High-order finite-element seismic wave propagation modeling with
+ {MPI} on a large {GPU} cluster},
+ journal = jcp,
+ year = {2010},
+ volume = {229},
+ pages = {7692-7714},
+ number = {20},
+ doi = {10.1016/j.jcp.2010.06.024}
}
@ARTICLE{KoGoErMi10,
-author = {Dimitri Komatitsch and Dominik G\"oddeke and Gordon Erlebacher and
-David Mich\'ea},
-title = {Modeling the propagation of elastic waves using spectral elements
-on a cluster of 192 {GPU}s},
-journal = {Computer Science Research and Development},
-year = {2010},
-volume = {25},
-pages = {75-82},
-number = {1-2},
-doi = {10.1007/s00450-010-0109-1}
+ author = {Dimitri Komatitsch and Dominik G\"oddeke and Gordon Erlebacher and
+ David Mich\'ea},
+ title = {Modeling the propagation of elastic waves using spectral elements
+ on a cluster of 192 {GPU}s},
+ journal = {Computer Science Research and Development},
+ year = {2010},
+ volume = {25},
+ pages = {75-82},
+ number = {1-2},
+ doi = {10.1007/s00450-010-0109-1}
}
@ARTICLE{KoLaMi08a,
-author = {Dimitri Komatitsch and Jes\'us Labarta and David Mich\'ea},
-title = {A simulation of seismic wave propagation at high resolution in the
-inner core of the {E}arth on 2166 processors of {M}are{N}ostrum},
-journal = lncs,
-year = {2008},
-volume = {5336},
-pages = {364-377}
+ author = {Dimitri Komatitsch and Jes\'us Labarta and David Mich\'ea},
+ title = {A simulation of seismic wave propagation at high resolution in the
+ inner core of the {E}arth on 2166 processors of {M}are{N}ostrum},
+ journal = lncs,
+ year = {2008},
+ volume = {5336},
+ pages = {364-377}
}
@INPROCEEDINGS{KoLaMi08b,
-author = {Dimitri Komatitsch and Jes\'us Labarta and David Mich\'ea},
-title = {A 21 billion degrees of freedom, 2.5 terabyte simulation of seismic
-wave propagation in the inner core of the {E}arth on {M}are{N}ostrum},
-booktitle = {Proceedings of the 8th. World Congress on Computational Mechanics
-(WCCM8) and the 5th. European Congress on Computational Methods in
-Applied Sciences and Engineering (ECCOMAS 2008)},
-year = {2008},
-address = {Venice, Italy},
-note = {30 June - 4 July 2008}
+ author = {Dimitri Komatitsch and Jes\'us Labarta and David Mich\'ea},
+ title = {A 21 billion degrees of freedom, 2.5 terabyte simulation of seismic
+ wave propagation in the inner core of the {E}arth on {M}are{N}ostrum},
+ booktitle = {Proceedings of the 8th. World Congress on Computational Mechanics
+ (WCCM8) and the 5th. European Congress on Computational Methods in
+ Applied Sciences and Engineering (ECCOMAS 2008)},
+ year = {2008},
+ address = {Venice, Italy},
+ note = {30 June - 4 July 2008}
}
@ARTICLE{KoLiTrSuStSh04,
-author = {Dimitri Komatitsch and Qinya Liu and Jeroen Tromp and Peter S\"{u}ss
-and Christiane Stidham and John H. Shaw},
-title = {Simulations of Ground Motion in the {L}os {A}ngeles Basin based upon
-the Spectral-Element Method},
-journal = bssa,
-year = {2004},
-volume = {94},
-pages = {187-206},
-number = {1},
-doi = {10.1785/0120030077}
+ author = {Dimitri Komatitsch and Qinya Liu and Jeroen Tromp and Peter S\"{u}ss
+ and Christiane Stidham and John H. Shaw},
+ title = {Simulations of Ground Motion in the {L}os {A}ngeles Basin based upon
+ the Spectral-Element Method},
+ journal = bssa,
+ year = {2004},
+ volume = {94},
+ pages = {187-206},
+ number = {1},
+ doi = {10.1785/0120030077}
}
@ARTICLE{KoMa07,
-author = {Dimitri Komatitsch and Roland Martin},
-title = {An unsplit convolutional {P}erfectly {M}atched {L}ayer improved at
-grazing incidence for the seismic wave equation},
-journal = geophysics,
-year = {2007},
-volume = {72},
-pages = {SM155-SM167},
-number = {5},
-doi = {10.1190/1.2757586}
+ author = {Dimitri Komatitsch and Roland Martin},
+ title = {An unsplit convolutional {P}erfectly {M}atched {L}ayer improved at
+ grazing incidence for the seismic wave equation},
+ journal = geophysics,
+ year = {2007},
+ volume = {72},
+ pages = {SM155-SM167},
+ number = {5},
+ doi = {10.1190/1.2757586}
}
@ARTICLE{KoMaTrTaWi01,
-author = {D. Komatitsch and R. Martin and J. Tromp and M. A. Taylor and B.
-A. Wingate},
-title = {Wave propagation in 2-{D} elastic media using a spectral element
-method with triangles and quadrangles},
-journal = jca,
-year = {2001},
-volume = {9},
-pages = {703-718},
-number = {2},
-doi = {10.1142/S0218396X01000796}
+ author = {D. Komatitsch and R. Martin and J. Tromp and M. A. Taylor and B.
+ A. Wingate},
+ title = {Wave propagation in 2-{D} elastic media using a spectral element
+ method with triangles and quadrangles},
+ journal = jca,
+ year = {2001},
+ volume = {9},
+ pages = {703-718},
+ number = {2},
+ doi = {10.1142/S0218396X01000796}
}
@ARTICLE{KoMiEr09,
-author = {Dimitri Komatitsch and David Mich\'ea and Gordon Erlebacher},
-title = {Porting a high-order finite-element earthquake modeling application
-to {NVIDIA} graphics cards using {CUDA}},
-journal = jpdc,
-year = {2009},
-volume = {69},
-pages = {451-460},
-number = {5},
-doi = {10.1016/j.jpdc.2009.01.006}
+ author = {Dimitri Komatitsch and David Mich\'ea and Gordon Erlebacher},
+ title = {Porting a high-order finite-element earthquake modeling application
+ to {NVIDIA} graphics cards using {CUDA}},
+ journal = jpdc,
+ year = {2009},
+ volume = {69},
+ pages = {451-460},
+ number = {5},
+ doi = {10.1016/j.jpdc.2009.01.006}
}
@ARTICLE{KoRiTr02,
-author = {D. Komatitsch and J. Ritsema and J. Tromp},
-title = {The Spectral-Element Method, {B}eowulf Computing, and Global Seismology},
-journal = {Science},
-year = {2002},
-volume = {298},
-pages = {1737-1742},
-number = {5599},
-doi = {10.1126/science.1076024}
+ author = {D. Komatitsch and J. Ritsema and J. Tromp},
+ title = {The Spectral-Element Method, {B}eowulf Computing, and Global Seismology},
+ journal = {Science},
+ year = {2002},
+ volume = {298},
+ pages = {1737-1742},
+ number = {5599},
+ doi = {10.1126/science.1076024}
}
@INCOLLECTION{KoTr02c,
-author = {D. Komatitsch and J. Tromp},
-title = {Propagaci{\'o}n de ondas s{\'\i}smicas en modelos de tierra global
-3-{D} usando elementos espectrales},
-booktitle = {M\'etodos num\'ericos en ingenieria y ciencias aplicadas},
-publisher = {CIMNE},
-year = {2002},
-editor = {{E. O{\~{n}}ate et al.}},
-pages = {676-686},
-address = {Barcelona, Espa{\~{n}}a}
+ author = {D. Komatitsch and J. Tromp},
+ title = {Propagaci{\'o}n de ondas s{\'\i}smicas en modelos de tierra global
+ 3-{D} usando elementos espectrales},
+ booktitle = {M\'etodos num\'ericos en ingenieria y ciencias aplicadas},
+ publisher = {CIMNE},
+ year = {2002},
+ editor = {{E. O{\~{n}}ate et al.}},
+ pages = {676-686},
+ address = {Barcelona, Espa{\~{n}}a}
}
@ARTICLE{KoTr03,
-author = {D. Komatitsch and J. Tromp},
-title = {A {P}erfectly {M}atched {L}ayer absorbing boundary condition for
-the second-order seismic wave equation},
-journal = gji,
-year = {2003},
-volume = {154},
-pages = {146-153},
-number = {1},
-doi = {10.1046/j.1365-246X.2003.01950.x}
+ author = {D. Komatitsch and J. Tromp},
+ title = {A {P}erfectly {M}atched {L}ayer absorbing boundary condition for
+ the second-order seismic wave equation},
+ journal = gji,
+ year = {2003},
+ volume = {154},
+ pages = {146-153},
+ number = {1},
+ doi = {10.1046/j.1365-246X.2003.01950.x}
}
@ARTICLE{KoTr02a,
-author = {D. Komatitsch and J. Tromp},
-title = {Spectral-Element Simulations of Global Seismic Wave Propagation{-I.
-V}alidation},
-journal = gji,
-year = {2002},
-volume = {149},
-pages = {390-412},
-number = {2},
-doi = {10.1046/j.1365-246X.2002.01653.x}
+ author = {D. Komatitsch and J. Tromp},
+ title = {Spectral-Element Simulations of Global Seismic Wave Propagation{-I.
+ V}alidation},
+ journal = gji,
+ year = {2002},
+ volume = {149},
+ pages = {390-412},
+ number = {2},
+ doi = {10.1046/j.1365-246X.2002.01653.x}
}
@ARTICLE{KoTr02b,
-author = {D. Komatitsch and J. Tromp},
-title = {Spectral-Element Simulations of Global Seismic Wave Propagation{-II.
-3-D} Models, Oceans, Rotation, and Self-Gravitation},
-journal = gji,
-year = {2002},
-volume = {150},
-pages = {303-318},
-number = {1},
-doi = {10.1046/j.1365-246X.2002.01716.x}
+ author = {D. Komatitsch and J. Tromp},
+ title = {Spectral-Element Simulations of Global Seismic Wave Propagation{-II.
+ 3-D} Models, Oceans, Rotation, and Self-Gravitation},
+ journal = gji,
+ year = {2002},
+ volume = {150},
+ pages = {303-318},
+ number = {1},
+ doi = {10.1046/j.1365-246X.2002.01716.x}
}
@ARTICLE{KoTr01c,
-author = {D. Komatitsch and J. Tromp},
-title = {Modeling of seismic wave propagation at the scale of the {E}arth
-on a large {B}eowulf},
-journal = {Proceedings of the ACM/IEEE Supercomputing SC'2001 conference},
-year = {2001},
-pages = {33-41},
-doi = {10.1109/SC.2001.10003}
+ author = {D. Komatitsch and J. Tromp},
+ title = {Modeling of seismic wave propagation at the scale of the {E}arth
+ on a large {B}eowulf},
+ journal = {Proceedings of the ACM/IEEE Supercomputing SC'2001 conference},
+ year = {2001},
+ pages = {33-41},
+ doi = {10.1109/SC.2001.10003}
}
@ARTICLE{KoTr01d,
-author = {D. Komatitsch and J. Tromp},
-title = {Modeling Seismic Wave Propagation on a 156~{GB PC} Cluster},
-journal = {Linux Journal},
-year = {2001},
-volume = {90},
-pages = {38-45}
+ author = {D. Komatitsch and J. Tromp},
+ title = {Modeling Seismic Wave Propagation on a 156~{GB PC} Cluster},
+ journal = {Linux Journal},
+ year = {2001},
+ volume = {90},
+ pages = {38-45}
}
@ARTICLE{KoTr99,
-author = {D. Komatitsch and J. Tromp},
-title = {Introduction to the spectral-element method for 3-{D} seismic wave
-propagation},
-journal = gji,
-year = {1999},
-volume = {139},
-pages = {806-822},
-number = {3},
-doi = {10.1046/j.1365-246x.1999.00967.x}
+ author = {D. Komatitsch and J. Tromp},
+ title = {Introduction to the spectral-element method for 3-{D} seismic wave
+ propagation},
+ journal = gji,
+ year = {1999},
+ volume = {139},
+ pages = {806-822},
+ number = {3},
+ doi = {10.1046/j.1365-246x.1999.00967.x}
}
@ARTICLE{KoTsChTr03,
-author = {Dimitri Komatitsch and Seiji Tsuboi and Chen Ji and Jeroen Tromp},
-title = {A 14.6~billion degrees of freedom, 5~teraflops, 2.5~terabyte earthquake
-simulation on the {E}arth~{S}imulator},
-journal = {Proceedings of the ACM/IEEE Supercomputing SC'2003 conference},
-year = {2003},
-pages = {4-11},
-note = {{G}ordon {B}ell {P}rize winner article},
-doi = {10.1109/SC.2003.10023}
+ author = {Dimitri Komatitsch and Seiji Tsuboi and Chen Ji and Jeroen Tromp},
+ title = {A 14.6~billion degrees of freedom, 5~teraflops, 2.5~terabyte earthquake
+ simulation on the {E}arth~{S}imulator},
+ journal = {Proceedings of the ACM/IEEE Supercomputing SC'2003 conference},
+ year = {2003},
+ pages = {4-11},
+ note = {{G}ordon {B}ell {P}rize winner article},
+ doi = {10.1109/SC.2003.10023}
}
@INCOLLECTION{KoTsTr05,
-author = {D. Komatitsch and S. Tsuboi and J. Tromp},
-title = {The Spectral-Element Method in Seismology},
-booktitle = {Seismic Earth: Array Analysis of Broadband Seismograms},
-publisher = {American Geophysical Union},
-year = {2005},
-editor = {Alan Levander and Guust Nolet},
-volume = {157},
-series = {Geophysical Monograph},
-pages = {205-228},
-address = {Washington DC, USA}
+ author = {D. Komatitsch and S. Tsuboi and J. Tromp},
+ title = {The Spectral-Element Method in Seismology},
+ booktitle = {Seismic Earth: Array Analysis of Broadband Seismograms},
+ publisher = {American Geophysical Union},
+ year = {2005},
+ editor = {Alan Levander and Guust Nolet},
+ volume = {157},
+ series = {Geophysical Monograph},
+ pages = {205-228},
+ address = {Washington DC, USA}
}
@ARTICLE{KoVi98,
-author = {D. Komatitsch and J. P. Vilotte},
-title = {The spectral-element method: an efficient tool to simulate the seismic
-response of 2{D} and 3{D} geological structures},
-journal = bssa,
-year = {1998},
-volume = {88},
-pages = {368-392},
-number = {2}
+ author = {D. Komatitsch and J. P. Vilotte},
+ title = {The spectral-element method: an efficient tool to simulate the seismic
+ response of 2{D} and 3{D} geological structures},
+ journal = bssa,
+ year = {1998},
+ volume = {88},
+ pages = {368-392},
+ number = {2}
}
@ARTICLE{KoViVaCaSa99,
-author = {D. Komatitsch and J. P. Vilotte and R. Vai and J. M. Castillo-Covarrubias
-and F. J. S\'anchez-Sesma},
-title = {The spectral-element method for elastic wave equations: application
-to 2{D} and 3{D} seismic problems},
-journal = ijnme,
-year = {1999},
-volume = {45},
-pages = {1139-1164},
-number = {9},
-doi = {10.1002/(SICI)1097-0207(19990730)45:9<1139::AID-NME617>3.0.CO;2-T}
+ author = {D. Komatitsch and J. P. Vilotte and R. Vai and J. M. Castillo-Covarrubias
+ and F. J. S\'anchez-Sesma},
+ title = {The spectral-element method for elastic wave equations: application
+ to 2{D} and 3{D} seismic problems},
+ journal = ijnme,
+ year = {1999},
+ volume = {45},
+ pages = {1139-1164},
+ number = {9},
+ doi = {10.1002/(SICI)1097-0207(19990730)45:9<1139::AID-NME617>3.0.CO;2-T}
}
@ARTICLE{KoViCh10,
-author = {D. Komatitsch and L. P. Vinnik and S. Chevrot},
-title = {{SH}diff/{SV}diff splitting in an isotropic {E}arth},
-journal = jgr,
-year = {2010},
-volume = {115},
-pages = {B07312},
-number = {B7},
-doi = {10.1029/2009JB006795}
+ author = {D. Komatitsch and L. P. Vinnik and S. Chevrot},
+ title = {{SH}diff/{SV}diff splitting in an isotropic {E}arth},
+ journal = jgr,
+ year = {2010},
+ volume = {115},
+ pages = {B07312},
+ number = {B7},
+ doi = {10.1029/2009JB006795}
}
@ARTICLE{Komornik,
-author = {V. Komornik},
-title = {Stabilisation fronti\`ere des \'equations de {M}axwell},
-journal = {C. R. Acad. Sci. Paris S\'er. I},
-year = {1994},
-volume = {318},
-pages = {535-540}
+ author = {V. Komornik},
+ title = {Stabilisation fronti\`ere des \'equations de {M}axwell},
+ journal = {C. R. Acad. Sci. Paris S\'er. I},
+ year = {1994},
+ volume = {318},
+ pages = {535-540}
}
@ARTICLE{Kop06,
-author = {D. A. Kopriva},
-title = {Metric identities and the discontinuous spectral element method on
-curvilinear meshes},
-journal = {Journal of Scientific Computing},
-year = {2006},
-volume = {26},
-pages = {301-327},
-number = {3},
-doi = {10.1007/s10915-005-9070-8}
+ author = {D. A. Kopriva},
+ title = {Metric identities and the discontinuous spectral element method on
+ curvilinear meshes},
+ journal = {Journal of Scientific Computing},
+ year = {2006},
+ volume = {26},
+ pages = {301-327},
+ number = {3},
+ doi = {10.1007/s10915-005-9070-8}
}
@ARTICLE{Kop96,
-author = {D. A. Kopriva},
-title = {A conservative staggered-grid {C}hebyshev multidomain method for
-compressible flows: {P}art {II}, a semi-structured method},
-journal = jcp,
-year = {1996},
-volume = {128},
-pages = {475-488}
+ author = {D. A. Kopriva},
+ title = {A conservative staggered-grid {C}hebyshev multidomain method for
+ compressible flows: {P}art {II}, a semi-structured method},
+ journal = jcp,
+ year = {1996},
+ volume = {128},
+ pages = {475-488}
}
@ARTICLE{Kop89,
-author = {David A. Kopriva},
-title = {Computation of Hyperbolic Equations on Complicated Domains with Patched
-and Overset {C}hebyshev Grids},
-journal = {SIAM Journal on Scientific and Statistical Computing},
-year = {1989},
-volume = {10},
-pages = {120-132},
-number = {1},
-doi = {10.1137/0910010}
+ author = {David A. Kopriva},
+ title = {Computation of Hyperbolic Equations on Complicated Domains with Patched
+ and Overset {C}hebyshev Grids},
+ journal = {SIAM Journal on Scientific and Statistical Computing},
+ year = {1989},
+ volume = {10},
+ pages = {120-132},
+ number = {1},
+ doi = {10.1137/0910010}
}
@ARTICLE{Kop86,
-author = {David A. Kopriva},
-title = {A spectral multidomain method for the solution of hyperbolic systems},
-journal = {Applied Numerical Mathematics},
-year = {1986},
-volume = {2},
-pages = {221-241},
-number = {3-5},
-doi = {10.1016/0168-9274(86)90030-9}
+ author = {David A. Kopriva},
+ title = {A spectral multidomain method for the solution of hyperbolic systems},
+ journal = {Applied Numerical Mathematics},
+ year = {1986},
+ volume = {2},
+ pages = {221-241},
+ number = {3-5},
+ doi = {10.1016/0168-9274(86)90030-9}
}
@ARTICLE{KoWoHu02,
-author = {D. A. Kopriva and S. L. Woodruff and M. Y. Hussaini},
-title = {Computation of electromagnetic scattering with a non-conforming discontinuous
-spectral element method},
-journal = ijnme,
-year = {2002},
-volume = {53},
-pages = {105-122},
-number = {1},
-doi = {10.1002/nme.394}
+ author = {D. A. Kopriva and S. L. Woodruff and M. Y. Hussaini},
+ title = {Computation of electromagnetic scattering with a non-conforming discontinuous
+ spectral element method},
+ journal = ijnme,
+ year = {2002},
+ volume = {53},
+ pages = {105-122},
+ number = {1},
+ doi = {10.1002/nme.394}
}
@ARTICLE{KosKosSyr85,
-author = {A. M. Kosevich and Yu. A. Kosevich and E. S. Syrkin},
-title = {Generalized {R}ayleigh waves and the geometry of isofrequency surfaces
-of sound oscillation waves in crystals},
-journal = {Soviet Physics - Journal of Experimental and Theoretical Physics},
-year = {1985},
-volume = {61},
-pages = {639-644}
+ author = {A. M. Kosevich and Yu. A. Kosevich and E. S. Syrkin},
+ title = {Generalized {R}ayleigh waves and the geometry of isofrequency surfaces
+ of sound oscillation waves in crystals},
+ journal = {Soviet Physics - Journal of Experimental and Theoretical Physics},
+ year = {1985},
+ volume = {61},
+ pages = {639-644}
}
@ARTICLE{KosSyr85,
-author = {Yu. A. Kosevich and E. S. Syrkin},
-title = {Existence criterion and properties of deeply penetrating {R}ayleigh
-waves in crystals},
-journal = {Soviet Physics - Journal of Experimental and Theoretical Physics},
-year = {1985},
-volume = {62},
-pages = {1282-1286},
-number = {6}
+ author = {Yu. A. Kosevich and E. S. Syrkin},
+ title = {Existence criterion and properties of deeply penetrating {R}ayleigh
+ waves in crystals},
+ journal = {Soviet Physics - Journal of Experimental and Theoretical Physics},
+ year = {1985},
+ volume = {62},
+ pages = {1282-1286},
+ number = {6}
}
@ARTICLE{KosSyrKos97,
-author = {Yu. A. Kosevich and E. S. Syrkin and A. M. Kosevich},
-title = {Vibrations localized near surfaces and interfaces in non-traditional
-crystals},
-journal = {Progress in Surface Science},
-year = {1997},
-volume = {55},
-pages = {59-111},
-number = {1}
+ author = {Yu. A. Kosevich and E. S. Syrkin and A. M. Kosevich},
+ title = {Vibrations localized near surfaces and interfaces in non-traditional
+ crystals},
+ journal = {Progress in Surface Science},
+ year = {1997},
+ volume = {55},
+ pages = {59-111},
+ number = {1}
}
@ARTICLE{KoBa82,
-author = {D. Kosloff and E. Baysal},
-title = {Forward modeling by the {F}ourier method},
-journal = geophysics,
-year = {1982},
-volume = {47},
-pages = {1402-1412}
+ author = {D. Kosloff and E. Baysal},
+ title = {Forward modeling by the {F}ourier method},
+ journal = geophysics,
+ year = {1982},
+ volume = {47},
+ pages = {1402-1412}
}
@ARTICLE{KoKeFiTeBeSt90,
-author = {D. Kosloff and D. Kessler and A. Q. Filho and E. Tessmer and A. Behle
-and R. Strahilevitz},
-title = {Solution of the equations of dynamic elasticity by a {C}hebychev
-spectral method},
-journal = geophysics,
-year = {1990},
-volume = {55},
-pages = {734-748},
-doi = {10.1190/1.1442885}
+ author = {D. Kosloff and D. Kessler and A. Q. Filho and E. Tessmer and A. Behle
+ and R. Strahilevitz},
+ title = {Solution of the equations of dynamic elasticity by a {C}hebychev
+ spectral method},
+ journal = geophysics,
+ year = {1990},
+ volume = {55},
+ pages = {734-748},
+ doi = {10.1190/1.1442885}
}
@ARTICLE{KoReLo84,
-author = {D. Kosloff and M. Reshef and D. Loewenthal},
-title = {Elastic wave calculations by the {F}ourier method},
-journal = bssa,
-year = {1984},
-volume = {74},
-pages = {875-891}
+ author = {D. Kosloff and M. Reshef and D. Loewenthal},
+ title = {Elastic wave calculations by the {F}ourier method},
+ journal = bssa,
+ year = {1984},
+ volume = {74},
+ pages = {875-891}
}
@ARTICLE{KoTa93,
-author = {D. Kosloff and H. Tal-Ezer},
-title = {A modified {C}hebyshev pseudospectral method with an {{$O(N^{-1})$}}
-time step restriction},
-journal = jcp,
-year = {1993},
-volume = {104},
-pages = {457-469}
+ author = {D. Kosloff and H. Tal-Ezer},
+ title = {A modified {C}hebyshev pseudospectral method with an {{$O(N^{-1})$}}
+ time step restriction},
+ journal = jcp,
+ year = {1993},
+ volume = {104},
+ pages = {457-469}
}
@ARTICLE{KoYiTs99,
-author = {T. I. Kosmanis and T. V. Yioultsis and T. D. Tsiboukis},
-title = {Perfectly matched anisotropic layer for the numerical analysis of
-unbounded eddy-current problems},
-journal = {IEEE transactions on Magnetics},
-year = {1999},
-volume = {35},
-pages = {4452-4458},
-number = {6}
+ author = {T. I. Kosmanis and T. V. Yioultsis and T. D. Tsiboukis},
+ title = {Perfectly matched anisotropic layer for the numerical analysis of
+ unbounded eddy-current problems},
+ journal = {IEEE transactions on Magnetics},
+ year = {1999},
+ volume = {35},
+ pages = {4452-4458},
+ number = {6}
}
@ARTICLE{KrTuOk04a,
-author = {Sean E. Krakiwsky and Laurence E. Turner and Michal M. Okoniewski},
-title = {Graphics processor unit ({GPU}) acceleration of a finite-difference
-time-domain ({FDTD}) algorithm},
-journal = {Proceedings of the 2004 IEEE International Symposium on Circuits
-and Systems},
-year = {2004},
-pages = {265-268},
-address = {Vancouver, British Columbia, Canada}
+ author = {Sean E. Krakiwsky and Laurence E. Turner and Michal M. Okoniewski},
+ title = {Graphics processor unit ({GPU}) acceleration of a finite-difference
+ time-domain ({FDTD}) algorithm},
+ journal = {Proceedings of the 2004 IEEE International Symposium on Circuits
+ and Systems},
+ year = {2004},
+ pages = {265-268},
+ address = {Vancouver, British Columbia, Canada}
}
@ARTICLE{KrTuOk04b,
-author = {S. E. Krakiwsky and L. E. Turner and M. M. Okoniewski},
-title = {Acceleration of finite-difference time-domain ({FDTD}) using graphics
-processor units ({GPU})},
-journal = {IEEE 2004 MTT-S International Microwave Symposium Digest},
-year = {2004},
-volume = {2},
-pages = {1033-1036},
-doi = {10.1109/MWSYM.2004.1339160}
+ author = {S. E. Krakiwsky and L. E. Turner and M. M. Okoniewski},
+ title = {Acceleration of finite-difference time-domain ({FDTD}) using graphics
+ processor units ({GPU})},
+ journal = {IEEE 2004 MTT-S International Microwave Symposium Digest},
+ year = {2004},
+ volume = {2},
+ pages = {1033-1036},
+ doi = {10.1109/MWSYM.2004.1339160}
}
@ARTICLE{Kra76,
-author = {E. Kraut},
-title = {Review of theories of scattering of elastic waves by cracks},
-journal = {IEEE Trans. S. U.},
-year = {1976},
-volume = {3},
-pages = {162-167}
+ author = {E. Kraut},
+ title = {Review of theories of scattering of elastic waves by cracks},
+ journal = {IEEE Trans. S. U.},
+ year = {1976},
+ volume = {3},
+ pages = {162-167}
}
@ARTICLE{Kra63,
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-journal = {Reviews of Geophysics},
-year = {1963},
-volume = {1},
-pages = {401-448},
-number = {3}
+ author = {E. A. Kraut},
+ title = {Advances in the theory of anisotropic elastic wave propagation},
+ journal = {Reviews of Geophysics},
+ year = {1963},
+ volume = {1},
+ pages = {401-448},
+ number = {3}
}
@ARTICLE{Kre06,
-author = {Steen Krenk},
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-journal = cmame,
-year = {2006},
-pages = {6110-6124},
-doi = {10.1016/j.cma.2005.12.001}
+ author = {Steen Krenk},
+ title = {Energy conservation in {N}ewmark based time integration algorithms},
+ journal = cmame,
+ year = {2006},
+ pages = {6110-6124},
+ doi = {10.1016/j.cma.2005.12.001}
}
@ARTICLE{KrJiKoTr06a,
-author = {Swaminathan Krishnan and Chen Ji and Dimitri Komatitsch and Jeroen
-Tromp},
-title = {Case Studies of Damage to Tall Steel Moment-Frame Buildings in {S}outhern
-{C}alifornia during Large {S}an {A}ndreas Earthquakes},
-journal = bssa,
-year = {2006},
-volume = {96},
-pages = {1523-1537},
-number = {4A},
-doi = {10.1785/0120050145}
+ author = {Swaminathan Krishnan and Chen Ji and Dimitri Komatitsch and Jeroen
+ Tromp},
+ title = {Case Studies of Damage to Tall Steel Moment-Frame Buildings in {S}outhern
+ {C}alifornia during Large {S}an {A}ndreas Earthquakes},
+ journal = bssa,
+ year = {2006},
+ volume = {96},
+ pages = {1523-1537},
+ number = {4A},
+ doi = {10.1785/0120050145}
}
@ARTICLE{KrJiKoTr06b,
-author = {Swaminathan Krishnan and Chen Ji and Dimitri Komatitsch and Jeroen
-Tromp},
-title = {Performance of two 18-story steel moment-frame buildings in {S}outhern
-{C}alifornia during two large simulated {S}an {A}ndreas Earthquakes},
-journal = {Earthquake Spectra},
-year = {2006},
-volume = {22},
-pages = {1035-1061},
-number = {4},
-doi = {10.1193/1.2360698}
+ author = {Swaminathan Krishnan and Chen Ji and Dimitri Komatitsch and Jeroen
+ Tromp},
+ title = {Performance of two 18-story steel moment-frame buildings in {S}outhern
+ {C}alifornia during two large simulated {S}an {A}ndreas Earthquakes},
+ journal = {Earthquake Spectra},
+ year = {2006},
+ volume = {22},
+ pages = {1035-1061},
+ number = {4},
+ doi = {10.1193/1.2360698}
}
@INPROCEEDINGS{KrJiKoTr06c,
-author = {Swaminathan Krishnan and Chen Ji and Dimitri Komatitsch and Jeroen
-Tromp},
-title = {Impact of a large {S}an {A}ndreas fault earthquake on tall buildings
-in {S}outhern {C}alifornia},
-booktitle = {Proceedings of the 8th U.S. National Conference on Earthquake Engineering},
-year = {2006},
-pages = {1-12},
-month = {April 18-22},
-note = {Paper No. 154, available on CD-ROM.}
+ author = {Swaminathan Krishnan and Chen Ji and Dimitri Komatitsch and Jeroen
+ Tromp},
+ title = {Impact of a large {S}an {A}ndreas fault earthquake on tall buildings
+ in {S}outhern {C}alifornia},
+ booktitle = {Proceedings of the 8th U.S. National Conference on Earthquake Engineering},
+ year = {2006},
+ pages = {1-12},
+ month = {April 18-22},
+ note = {Paper No. 154, available on CD-ROM.}
}
@ARTICLE{KrMo03,
-author = {J. Kristek and P. Moczo},
-title = {Seismic-Wave Propagation in Viscoelastic Media with Material Discontinuities:
-{A 3D} Fourth-Order Staggered-Grid Finite-Difference Modeling},
-journal = bssa,
-year = {2003},
-volume = {93},
-pages = {2273-2280},
-number = {5}
+ author = {J. Kristek and P. Moczo},
+ title = {Seismic-Wave Propagation in Viscoelastic Media with Material Discontinuities:
+ {A 3D} Fourth-Order Staggered-Grid Finite-Difference Modeling},
+ journal = bssa,
+ year = {2003},
+ volume = {93},
+ pages = {2273-2280},
+ number = {5}
}
@ARTICLE{KrMoGa09,
-author = {Jozef Kristek and Peter Moczo and Martin Galis},
-title = {A brief summary of some {PML} formulations and discretizations for
-the velocity-stress equation of seismic motion},
-journal = {Studia Geophysica et Geodaetica},
-year = {2009},
-volume = {53},
-pages = {459-474},
-number = {4},
-doi = {10.1007/s11200-009-0034-6}
+ author = {Jozef Kristek and Peter Moczo and Martin Galis},
+ title = {A brief summary of some {PML} formulations and discretizations for
+ the velocity-stress equation of seismic motion},
+ journal = {Studia Geophysica et Geodaetica},
+ year = {2009},
+ volume = {53},
+ pages = {459-474},
+ number = {4},
+ doi = {10.1007/s11200-009-0034-6}
}
@INCOLLECTION{KrMoIrIwSe99,
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-editor = {K. Irikura and K. Kudo and H. Okada and T. Sasatani},
-volume = {3},
-pages = {1361-1368},
-address = {Rotterdam, The Netherlands}
+ author = {J. Kristek and P. Moczo and K. Irikura and T. Iwata and H. Sekiguchi},
+ title = {The 1995 {K}obe mainshock simulated by {3D} finite differences},
+ booktitle = {The Effects of Surface Geology on Seismic Motion},
+ publisher = {Balkema},
+ year = {1999},
+ editor = {K. Irikura and K. Kudo and H. Okada and T. Sasatani},
+ volume = {3},
+ pages = {1361-1368},
+ address = {Rotterdam, The Netherlands}
}
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+ author = {F. Krueger and M. Weber and F. Scherbaum and J. Schlittenhardt},
+ title = {Evidence for normal and inhomogeneous lowermost mantle and core-mantle
+ boundary structure under the {A}rctic and northern {C}anada},
+ journal = gji,
+ year = {1995},
+ volume = {122},
+ pages = {637-657},
+ number = {2}
}
@PHDTHESIS{Krueger:2006:AGF,
-author = {Jens Kr{\"u}ger},
-title = {A {GPU} Framework for Interactive Simulation and Rendering of Fluid
-Effects},
-school = {Technische Universit{\"a}t M{\"u}nchen, Germany},
-year = {2006},
-month = dec
+ author = {Jens Kr{\"u}ger},
+ title = {A {GPU} Framework for Interactive Simulation and Rendering of Fluid
+ Effects},
+ school = {Technische Universit{\"a}t M{\"u}nchen, Germany},
+ year = {2006},
+ month = dec
}
@ARTICLE{Krueger:2003:LAO,
-author = {Jens Kr{\"u}ger and R{\"u}diger Westermann},
-title = {Linear algebra operators for {GPU} implementation of numerical algorithms},
-journal = {ACM Transactions on Graphics},
-year = {2003},
-volume = {22},
-pages = {908--916},
-number = {3},
-month = jul,
-doi = {10.1145/882262.882363}
+ author = {Jens Kr{\"u}ger and R{\"u}diger Westermann},
+ title = {Linear algebra operators for {GPU} implementation of numerical algorithms},
+ journal = {ACM Transactions on Graphics},
+ year = {2003},
+ volume = {22},
+ pages = {908--916},
+ number = {3},
+ month = jul,
+ doi = {10.1145/882262.882363}
}
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-Olivine and Single-Crystal Forstite},
-journal = jgr,
-year = {1969},
-volume = {74},
-pages = {5961-5972}
+ author = {M. Kumazawa and O. L. Anderson},
+ title = {Elastic Moduli, Pressure Derivates and Temperature Derivates of Single-Crystal
+ Olivine and Single-Crystal Forstite},
+ journal = jgr,
+ year = {1969},
+ volume = {74},
+ pages = {5961-5972}
}
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-booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
-year = {1988},
-pages = {1175-1177},
-note = {58th international meeting of the SEG}
+ author = {B. Kummer and A. Behle},
+ title = {Fast modeling of seismic waves in laterally inhomogeneous media},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1988},
+ pages = {1175-1177},
+ note = {58th international meeting of the SEG}
}
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-journal = {EOS},
-year = {2006},
-volume = {87},
-pages = {Abstract S41E-02},
-number = {52},
-note = {Fall Meet. Suppl.}
+ author = {B. Kustowski and A. M. Dziewo\'nski and G. Ekstrom},
+ title = {Modeling the anisotropic shear-wave velocity structure in the {E}arth's
+ mantle on global and regional scales},
+ journal = {EOS},
+ year = {2006},
+ volume = {87},
+ pages = {Abstract S41E-02},
+ number = {52},
+ note = {Fall Meet. Suppl.}
}
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+ author = {S. V. Kuznetsov},
+ title = {"Forbidden" planes for {R}ayleigh waves},
+ journal = {Quarterly of Applied Mathematics},
+ year = {2002},
+ volume = {60},
+ pages = {87-97}
}
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+ author = {M. Kuzuoglu and R. Mittra},
+ title = {Frequency dependence of the constitutive parameters of causal perfectly
+ matched anisotropic absorbers},
+ journal = {IEEE Microwave and Guided Wave Letters},
+ year = {1996},
+ volume = {6},
+ pages = {447-449},
+ number = {12}
}
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+ author = {D. J. P. Lahaye and F. Maggio and A. Quarteroni},
+ title = {Hybrid finite element-spectral element approximation of wave propagation
+ problems},
+ journal = {East-West J. Numer. Math.},
+ year = {1997},
+ volume = {5},
+ pages = {265-289},
+ number = {4}
}
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+ author = {R. Lakes},
+ title = {Foam structures with a negative {P}oisson's ratio},
+ journal = {Science},
+ year = {1987},
+ volume = {235},
+ pages = {1038-1040}
}
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+ title = {Le\c cons sur la th\'eorie math\'ematique de l'\'elasticit\'e des
+ corps solides},
+ publisher = {Gauthier-Villars},
+ year = {1852},
+ author = {Gabriel Lam\'e},
+ address = {Paris}
}
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+ author = {H. Lamb},
+ title = {On the propagation of tremors over the surface of an elastic solid},
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+ author = {Gilles Lambar\'e and Jean Virieux and Raul Madariaga and Side Jin},
+ title = {Iterative asymptotic inversion in the acoustic approximation},
+ journal = geophysics,
+ year = {1992},
+ volume = {57},
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}
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+ title = {Th\'eorie de l'\'elasticit\'e ({T}heory of {E}lasticity)},
+ publisher = {Mir},
+ year = {1953},
+ author = {L. Landau and E. Lifchitz},
+ address = {Moscow, Russia},
+ edition = {2nd}
}
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+ title = {Fluid mechanics},
+ publisher = {Pergamon Press},
+ year = {1959},
+ author = {L. D. Landau and E. M. Lifshitz},
+ address = {New York}
}
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+ author = {E. R. Lapwood},
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+ volume = {4},
+ pages = {174-196}
}
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+ author = {S. Larsen and M. Antolik and D. Dreger and C. Stidham and C. Schultz
+ and A. Lomax and B. Romanowicz},
+ title = {3-{D} Models of Seismic Wave Propagation: Simulating Scenario Earthquakes
+ Along the {H}ayward Fault},
+ journal = {Seis. Res. Lett.},
+ year = {1997},
+ volume = {68},
+ pages = {328}
}
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+ author = {Konstantin Latychev and Jerry X. Mitrovica and Jeroen Tromp and Mark
+ E. Tamisiea and Dimitri Komatitsch and Christina C. Christara},
+ title = {Glacial isostatic adjustment on 3-{D} {E}arth models: a finite-volume
+ formulation},
+ journal = gji,
+ year = {2005},
+ volume = {161},
+ pages = {421-444},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2005.02536.x}
}
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+ author = {T. Lay and H. Kanamori and C.J. Ammon and M. Nettles and S. N. Ward
+ and R. C. Aster and S. L. Beck and S. L. Bilek and M. R. Brudzinski
+ and R. Butler and H. R. DeShon and G. Ekstrom and K. Satake and S.
+ Sipkin},
+ title = {The great {S}umatra-{A}ndaman earthquake of 26 {D}ecember 2004},
+ journal = {Science},
+ year = {2005},
+ volume = {3},
+ pages = {1127-1133},
+ number = {5725}
}
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+ author = {T. Lay and C. Young},
+ title = {Analysis of seismic {SV} waves in the core's penumbra},
+ journal = grl,
+ year = {1991},
+ volume = {18},
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@PHDTHESIS{LeRousseau2001,
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-propagators},
-school = {Center for Wave Phenomena, Colorado School of Mines},
-year = {2001}
+ author = {J. H. {Le Rousseau}},
+ title = {Microlocal analysis of wave-equation imaging and generalized-screen
+ propagators},
+ school = {Center for Wave Phenomena, Colorado School of Mines},
+ year = {2001}
}
@ARTICLE{LeLi07,
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-journal = {IEEE Transactions on Microwave Theory and Techniques},
-year = {2007},
-volume = {55},
-pages = {983-991},
-number = {5},
-doi = {10.1109/TMTT.2007.895398}
+ author = {Joon Ho Lee and Qing Huo Liu},
+ title = {A {3-D} Spectral-Element Time-Domain Method for Electromagnetic Simulation},
+ journal = {IEEE Transactions on Microwave Theory and Techniques},
+ year = {2007},
+ volume = {55},
+ pages = {983-991},
+ number = {5},
+ doi = {10.1109/TMTT.2007.895398}
}
@ARTICLE{LeLi05,
-author = {Joon Ho Lee and Qing Huo Liu},
-title = {An efficient {3-D} spectral element method for {S}chr\"odinger equation
-in nanodevice simulation},
-journal = {IEEE Transactions on Computer-Aided Design of Integrated Circuits
-and Systems},
-year = {2005},
-volume = {24},
-pages = {1848-1858},
-number = {12}
+ author = {Joon Ho Lee and Qing Huo Liu},
+ title = {An efficient {3-D} spectral element method for {S}chr\"odinger equation
+ in nanodevice simulation},
+ journal = {IEEE Transactions on Computer-Aided Design of Integrated Circuits
+ and Systems},
+ year = {2005},
+ volume = {24},
+ pages = {1848-1858},
+ number = {12}
}
@ARTICLE{LeChKoHuTr09,
-author = {Shiann Jong Lee and Yu Chang Chan and Dimitri Komatitsch and Bor
-Shouh Huang and Jeroen Tromp},
-title = {Effects of realistic surface topography on seismic ground motion
-in the {Y}angminshan region of {T}aiwan based upon the spectral-element
-method and {LiDAR DTM}},
-journal = bssa,
-year = {2009},
-volume = {99},
-pages = {681-693},
-number = {2A},
-doi = {10.1785/0120080264}
+ author = {Shiann Jong Lee and Yu Chang Chan and Dimitri Komatitsch and Bor
+ Shouh Huang and Jeroen Tromp},
+ title = {Effects of realistic surface topography on seismic ground motion
+ in the {Y}angminshan region of {T}aiwan based upon the spectral-element
+ method and {LiDAR DTM}},
+ journal = bssa,
+ year = {2009},
+ volume = {99},
+ pages = {681-693},
+ number = {2A},
+ doi = {10.1785/0120080264}
}
@ARTICLE{LeChLiKoHuTr08,
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-and Bor Shouh Huang and Jeroen Tromp},
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-{T}aipei Basin with Realistic Topography Based upon the Spectral-Element
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+ author = {Shiann Jong Lee and How Wei Chen and Qinya Liu and Dimitri Komatitsch
+ and Bor Shouh Huang and Jeroen Tromp},
+ title = {Three-Dimensional Simulations of Seismic Wave Propagation in the
+ {T}aipei Basin with Realistic Topography Based upon the Spectral-Element
+ Method},
+ journal = bssa,
+ year = {2008},
+ volume = {98},
+ pages = {253-264},
+ number = {1},
+ doi = {10.1785/0120070033}
}
@ARTICLE{LeKoHuTr09,
-author = {S. J. Lee and Dimitri Komatitsch and B. S. Huang and J. Tromp},
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-journal = bssa,
-year = {2009},
-volume = {99},
-pages = {314-325},
-number = {1},
-doi = {10.1785/0120080020}
+ author = {S. J. Lee and Dimitri Komatitsch and B. S. Huang and J. Tromp},
+ title = {Effects of topography on seismic wave propagation: An example from
+ northern {T}aiwan},
+ journal = bssa,
+ year = {2009},
+ volume = {99},
+ pages = {314-325},
+ number = {1},
+ doi = {10.1785/0120080020}
}
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+ author = {A. Legay and H. W. Wang and T. Belytschko},
+ title = {Strong and weak arbitrary discontinuities in spectral finite elements},
+ journal = ijnme,
+ year = {2005},
+ volume = {64},
+ pages = {991-1008},
+ number = {8},
+ doi = {10.1002/nme.1388}
}
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+ title = {M\'ecanique des mat\'eriaux solides},
+ publisher = {Dunod},
+ year = {1985},
+ author = {J. Lemaitre and J. L. Chaboche},
+ address = {Paris}
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+ title = {Imag(in)ing the continental lithosphere},
+ journal = {Tectonophysics},
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+ author = {A. Levander and F. Niu and W. W. Symes},
+ title = {Imaging teleseismic {P} to {S} scattered waves using the {K}irchhoff
+ integral},
+ booktitle = {Seismic Earth: Array Analysis of Broadband Seismograms},
+ publisher = {American Geophysical Union},
+ year = {2005},
+ editor = {Alan Levander and Guust Nolet},
+ volume = {157},
+ series = {Geophysical Monograph},
+ pages = {149-170},
+ address = {Washington DC, USA}
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+ Vernon},
+ title = {Crustal thickness of the {P}eninsular {R}anges, southern {C}alifornia,
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+ journal = {Geology},
+ year = {2000},
+ volume = {28},
+ pages = {303-306}
}
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+ booktitle = {Proc. 10th World Conf. Earthquake Eng.},
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+ journal = {IEEE Micro},
+ year = {2008},
+ volume = {28},
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+ number = {2},
+ month = mar # {\slash } # apr,
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+ author = {K. Liu and Xiao Bing Wang and Yang Zhang and Cheng Liao},
+ title = {Acceleration of Time-Domain Finite Element Method ({TD-FEM}) Using
+ {Graphics Processor Units (GPU)}},
+ booktitle = {Proceedings of the 7th International Symposium on Antennas, Propagation
+ \& EM Theory (ISAPE '06)},
+ year = {2006},
+ pages = {1-4},
+ address = {Guilin, China},
+ month = {October},
+ doi = {10.1109/ISAPE.2006.353223},
+ journal = {Antennas, Propagation and EM Theory}
}
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+ author = {Qinya Liu and Jascha Polet and Dimitri Komatitsch and Jeroen Tromp},
+ title = {Spectral-element moment tensor inversions for earthquakes in {S}outhern
+ {C}alifornia},
+ journal = bssa,
+ year = {2004},
+ volume = {94},
+ pages = {1748-1761},
+ number = {5},
+ doi = {10.1785/012004038}
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+ author = {Q. Liu and J. Tromp},
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+ based upon adjoint methods},
+ journal = gji,
+ year = {2008},
+ volume = {174},
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+ number = {1},
+ doi = {10.1111/j.1365-246X.2008.03798.x}
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+ author = {Qinya Liu and Jeroen Tromp},
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+ journal = bssa,
+ year = {2006},
+ volume = {96},
+ pages = {2383-2397},
+ number = {6},
+ doi = {10.1785/0120060041}
}
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+ author = {B. Lombard and J. Piraux},
+ title = {Numerical treatment of two-dimensional interfaces for acoustic and
+ elastic waves},
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+ year = {2008},
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-year = {1987},
-editor = {R. V. Ingersoll and W. G. Ernst},
-pages = {259-283},
-address = {Old Tappan, New Jersey}
+ author = {B. P. Luyendyk and J. S. Hornafius},
+ title = {Neogene crustal rotations, fault slip and basin development in southern
+ {C}alifornia},
+ booktitle = {Cenozoic basin development of coastal {C}alifornia},
+ publisher = {Prentice-Hall},
+ year = {1987},
+ editor = {R. V. Ingersoll and W. G. Ernst},
+ pages = {259-283},
+ address = {Old Tappan, New Jersey}
}
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-basin (southern {S}pain) up to 1.335~{H}z under incident plane waves},
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-pages = {584-594}
+ author = {F. Luz\'on and S. A. Gil-Zepeda and F. J. S\'anchez-Sesma and C.
+ Ortiz-Alem\'an},
+ title = {Three-dimensional simulation of ground motion in the {Z}afarraya
+ basin (southern {S}pain) up to 1.335~{H}z under incident plane waves},
+ journal = gji,
+ year = {2004},
+ volume = {156},
+ pages = {584-594}
}
@ARTICLE{LuSaRoPoGaMaRoNa97,
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-topographies},
-journal = gji,
-year = {1997},
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-pages = {571-578}
+ author = {F. Luz\'on and F. J. S\'anchez-Sesma and J. L. Rodr{\'\i}guez-Z\'u{\~{n}}iga
+ and A. M. Posadas and J. M. Garc{\'\i}a and J. Mart{\'\i}n and M.
+ D. Romacho and M. Navarro},
+ title = {Diffraction of {{\it P}}, {{\it S}} and {R}ayleigh waves by three-dimensional
+ topographies},
+ journal = gji,
+ year = {1997},
+ volume = {129},
+ pages = {571-578}
}
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-year = {1994},
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-pages = {127-150}
+ author = {J. Lyness and R. Cools},
+ title = {A survey of numerical cubature over triangles},
+ journal = {Proceedings of Symposia in Applied Mathematics},
+ year = {1994},
+ volume = {48},
+ pages = {127-150}
}
@INCOLLECTION{LyDr72,
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-editor = {B. Alder and S. Fernbach and B. A. Bolt},
-volume = {11},
-chapter = {6},
-pages = {181-216},
-address = {New York, USA}
+ author = {J. Lysmer and L. A. Drake},
+ title = {A finite element method for seismology},
+ booktitle = {Methods in Computational Physics},
+ publisher = {Academic Press},
+ year = {1972},
+ editor = {B. Alder and S. Fernbach and B. A. Bolt},
+ volume = {11},
+ chapter = {6},
+ pages = {181-216},
+ address = {New York, USA}
}
@ARTICLE{LyKu69,
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-journal = {J. Eng. Mech. Div. ASCE 95 EM},
-year = {1969},
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+ author = {J. Lysmer and R. L. Kuhlemeyer},
+ title = {Finite dynamic model for infinite media},
+ journal = {J. Eng. Mech. Div. ASCE 95 EM},
+ year = {1969},
+ volume = {4},
+ pages = {859-877}
}
@ARTICLE{LyuSan75,
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-and surfaces in crystals},
-journal = {Soviet Solid State Physics},
-year = {1975},
-volume = {17},
-pages = {478-483},
-number = {2}
+ author = {V. N. Lyubimov and D. G. Sannikov},
+ title = {Surface quasi-bulk waves in the neighbourhood of exceptional directions
+ and surfaces in crystals},
+ journal = {Soviet Solid State Physics},
+ year = {1975},
+ volume = {17},
+ pages = {478-483},
+ number = {2}
}
@ARTICLE{Mul85,
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-title = {The reflectivity method: a tutorial},
-journal = {Journal of Geophysics},
-year = {1985},
-volume = {58},
-pages = {153-174}
+ author = {G. M\"{u}ller},
+ title = {The reflectivity method: a tutorial},
+ journal = {Journal of Geophysics},
+ year = {1985},
+ volume = {58},
+ pages = {153-174}
}
@ARTICLE{MeRo00,
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-of body, surface and higher modes wave forms},
-journal = gji,
-year = {2000},
-volume = {143},
-pages = {709-728}
+ author = {Charles M\'{e}gnin and Barabara Romanowicz},
+ title = {The 3{D} shear velocity structure of the mantle from the inversion
+ of body, surface and higher modes wave forms},
+ journal = gji,
+ year = {2000},
+ volume = {143},
+ pages = {709-728}
}
@ARTICLE{MaLi06,
-author = {Shuo Ma and Pengcheng Liu},
-title = {Modeling of the Perfectly Matched Layer Absorbing Boundaries and
-Intrinsic Attenuation in Explicit Finite-Element Methods},
-journal = bssa,
-year = {2006},
-volume = {96},
-pages = {1779-1794},
-number = {5},
-doi = {10.1785/0120050219}
+ author = {Shuo Ma and Pengcheng Liu},
+ title = {Modeling of the Perfectly Matched Layer Absorbing Boundaries and
+ Intrinsic Attenuation in Explicit Finite-Element Methods},
+ journal = bssa,
+ year = {2006},
+ volume = {96},
+ pages = {1779-1794},
+ number = {5},
+ doi = {10.1785/0120050219}
}
@INCOLLECTION{Mad83,
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-year = {1983},
-editor = {H. Kanamori and E. Boschi},
-address = {Amsterdam},
-note = {The Enrico Fermi Summer School of Physics, 55th course}
+ author = {R. Madariaga},
+ title = {Earthquake source theory: a review},
+ booktitle = {Earthquakes, Observation Theory and Interpretation},
+ publisher = {North-Holland},
+ year = {1983},
+ editor = {H. Kanamori and E. Boschi},
+ address = {Amsterdam},
+ note = {The Enrico Fermi Summer School of Physics, 55th course}
}
@ARTICLE{Mad87,
-author = {R. Madariaga},
-title = {Seismology, theoretical},
-journal = {Encyclopedia of Physical Science and Technology},
-year = {1987},
-volume = {12},
-pages = {519-533}
+ author = {R. Madariaga},
+ title = {Seismology, theoretical},
+ journal = {Encyclopedia of Physical Science and Technology},
+ year = {1987},
+ volume = {12},
+ pages = {519-533}
}
@ARTICLE{Mad76,
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-title = {Dynamics of an expanding circular fault},
-journal = bssa,
-year = {1976},
-volume = {66},
-pages = {639-666},
-number = {3}
+ author = {R. Madariaga},
+ title = {Dynamics of an expanding circular fault},
+ journal = bssa,
+ year = {1976},
+ volume = {66},
+ pages = {639-666},
+ number = {3}
}
@ARTICLE{MaMePaRo93,
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-title = {Analysis of Iterative Methods for the Steady and Unsteady {S}tokes
-Problem: Application to {S}pectral {E}lement Discretizations},
-journal = {SIAM J. Sci. Stat. Comput.},
-year = {1993},
-volume = {14},
-pages = {310-337}
+ author = {Y. Maday and D. Meiron and A. T. Patera and E. M. R{\o}nquist},
+ title = {Analysis of Iterative Methods for the Steady and Unsteady {S}tokes
+ Problem: Application to {S}pectral {E}lement Discretizations},
+ journal = {SIAM J. Sci. Stat. Comput.},
+ year = {1993},
+ volume = {14},
+ pages = {310-337}
}
@INPROCEEDINGS{MaPa89,
-author = {Y. Maday and A. T. Patera},
-title = {Spectral-element methods for the incompressible {N}avier-{S}tokes
-equations},
-booktitle = {State of the art survey in computational mechanics},
-year = {1989},
-pages = {71-143},
-note = {{A}. K. Noor and J. T. Oden editors}
+ author = {Y. Maday and A. T. Patera},
+ title = {Spectral-element methods for the incompressible {N}avier-{S}tokes
+ equations},
+ booktitle = {State of the art survey in computational mechanics},
+ year = {1989},
+ pages = {71-143},
+ note = {{A}. K. Noor and J. T. Oden editors}
}
@ARTICLE{MaQu82,
-author = {Y. Maday and A. Quarteroni},
-title = {Approximation of {B}urgers equation by pseudospectral methods},
-journal = {RAIRO Anal. Numer.},
-year = {1982},
-volume = {16},
-pages = {375-404}
+ author = {Y. Maday and A. Quarteroni},
+ title = {Approximation of {B}urgers equation by pseudospectral methods},
+ journal = {RAIRO Anal. Numer.},
+ year = {1982},
+ volume = {16},
+ pages = {375-404}
}
@ARTICLE{MaRo90,
-author = {Y. Maday and E. M. R{\o}nquist},
-title = {Optimal error analysis of spectral methods with emphasis on non-constant
-coefficients and deformed geometries},
-journal = cmame,
-year = {1990},
-volume = {80},
-pages = {91-115}
+ author = {Y. Maday and E. M. R{\o}nquist},
+ title = {Optimal error analysis of spectral methods with emphasis on non-constant
+ coefficients and deformed geometries},
+ journal = cmame,
+ year = {1990},
+ volume = {80},
+ pages = {91-115}
}
+ at PHDTHESIS{Mad09,
+ author = {Ronan Madec},
+ title = {M\'ethode des \'el\'ements spectraux pour la propagation d'ondes
+ sismiques en milieu g\'eologique fluide-solide avec pas de temps
+ locaux et couches absorbantes parfaitement adapt\'ees C-PML},
+ school = {Universit\'e de Pau et des Pays de l'Adour},
+ year = {2009},
+ address = {Pau, France},
+ month = {December}
+}
+
@ARTICLE{MaKoDi09,
-author = {Ronan Madec and Dimitri Komatitsch and Julien Diaz},
-title = {Energy-conserving local time stepping based on high-order finite
-elements for seismic wave propagation across a fluid-solid interface},
-journal = cmes,
-year = {2009},
-volume = {49},
-pages = {163-189},
-number = {2}
+ author = {Ronan Madec and Dimitri Komatitsch and Julien Diaz},
+ title = {Energy-conserving local time stepping based on high-order finite
+ elements for seismic wave propagation across a fluid-solid interface},
+ journal = cmes,
+ year = {2009},
+ volume = {49},
+ pages = {163-189},
+ number = {2}
}
@ARTICLE{MaDaClGr2000,
-author = {H. Magistrale and S. Day and R. W. Clayton and R. Graves},
-title = {The {SCEC} {S}outhern {C}alifornia reference three-dimensional seismic
-velocity model version~2},
-journal = bssa,
-year = {2000},
-volume = {90},
-pages = {S65-S76}
+ author = {H. Magistrale and S. Day and R. W. Clayton and R. Graves},
+ title = {The {SCEC} {S}outhern {C}alifornia reference three-dimensional seismic
+ velocity model version~2},
+ journal = bssa,
+ year = {2000},
+ volume = {90},
+ pages = {S65-S76}
}
@ARTICLE{MaMcDa96,
-author = {H. Magistrale and K. McLaughlin and S. Day},
-title = {A geology based 3-{D} velocity model of the {L}os {A}ngeles basin
-sediments},
-journal = bssa,
-year = {1996},
-volume = {86},
-pages = {1161-1166}
+ author = {H. Magistrale and K. McLaughlin and S. Day},
+ title = {A geology based 3-{D} velocity model of the {L}os {A}ngeles basin
+ sediments},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {1161-1166}
}
@ARTICLE{MaMoTa94,
-author = {S. A. Magnier and P. Mora and A. Tarantola},
-title = {Finite differences on minimal grids},
-journal = geophysics,
-year = {1994},
-volume = {59},
-pages = {1435-1443}
+ author = {S. A. Magnier and P. Mora and A. Tarantola},
+ title = {Finite differences on minimal grids},
+ journal = geophysics,
+ year = {1994},
+ volume = {59},
+ pages = {1435-1443}
}
@ARTICLE{Mah90,
-author = {K. D. Mahrer},
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-absorbing boundary conditions},
-journal = bssa,
-year = {1990},
-volume = {80},
-pages = {213-217}
+ author = {K. D. Mahrer},
+ title = {Numerical time step instability and {S}tacey's and {C}layton-{E}ngquist's
+ absorbing boundary conditions},
+ journal = bssa,
+ year = {1990},
+ volume = {80},
+ pages = {213-217}
}
@ARTICLE{Mainprice08,
-author = {Mainprice, D. and A. Tommasi and D. Ferre and P. Carrez and P. Cordier},
-title = {Predicted glide systems and crystal preferred orientations of polycrystalline
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-seismic anisotropy in the lower mantle},
-journal = epsl,
-year = {2008},
-volume = {271},
-pages = {135--144}
+ author = {Mainprice, D. and A. Tommasi and D. Ferre and P. Carrez and P. Cordier},
+ title = {Predicted glide systems and crystal preferred orientations of polycrystalline
+ silicate {M}g-Perovskite at high pressure: {I}mplications for the
+ seismic anisotropy in the lower mantle},
+ journal = epsl,
+ year = {2008},
+ volume = {271},
+ pages = {135--144}
}
@ARTICLE{MaKn66,
-author = {A. K. Mal and L. Knopoff},
-title = {Transmission of {R}ayleigh waves at a corner},
-journal = bssa,
-year = {1966},
-volume = {56},
-pages = {455-466}
+ author = {A. K. Mal and L. Knopoff},
+ title = {Transmission of {R}ayleigh waves at a corner},
+ journal = bssa,
+ year = {1966},
+ volume = {56},
+ pages = {455-466}
}
@ARTICLE{Mal89,
-author = {S. G. Mallat},
-title = {Multiresolution approximation and wavelet orthonormal bases of ${L}^2({R})$},
-journal = {Transactions of the AMS},
-year = {1989},
-volume = {135},
-pages = {9999998-9999999}
+ author = {S. G. Mallat},
+ title = {Multiresolution approximation and wavelet orthonormal bases of ${L}^2({R})$},
+ journal = {Transactions of the AMS},
+ year = {1989},
+ volume = {135},
+ pages = {9999998-9999999}
}
@ARTICLE{Mal88,
-author = {S. G. Mallat},
-title = {A theory for multiresolution signal decomposition: the wavelet representation},
-journal = {Communications in Pure and Applied Mathematics},
-year = {1988},
-volume = {41},
-pages = {9999998-9999999}
+ author = {S. G. Mallat},
+ title = {A theory for multiresolution signal decomposition: the wavelet representation},
+ journal = {Communications in Pure and Applied Mathematics},
+ year = {1988},
+ volume = {41},
+ pages = {9999998-9999999}
}
@ARTICLE{Mal97,
-author = {J. L. Mallet},
-title = {Discrete modeling for natural objects},
-journal = {Math. Geol.},
-year = {1997},
-volume = {29},
-pages = {199-219}
+ author = {J. L. Mallet},
+ title = {Discrete modeling for natural objects},
+ journal = {Math. Geol.},
+ year = {1997},
+ volume = {29},
+ pages = {199-219}
}
@ARTICLE{Mal92,
-author = {J. L. Mallet},
-title = {Discrete smooth interpolation in geometric modeling},
-journal = {Computer-Aided Design},
-year = {1992},
-volume = {24},
-pages = {178-191}
+ author = {J. L. Mallet},
+ title = {Discrete smooth interpolation in geometric modeling},
+ journal = {Computer-Aided Design},
+ year = {1992},
+ volume = {24},
+ pages = {178-191}
}
@BOOK{MaBe88,
-title = {Boundary element methods in elastodynamics},
-publisher = {Umwin Hyman},
-year = {1988},
-author = {G. Manolis and D. E. Beskos},
-address = {London}
+ title = {Boundary element methods in elastodynamics},
+ publisher = {Umwin Hyman},
+ year = {1988},
+ author = {G. Manolis and D. E. Beskos},
+ address = {London}
}
@ARTICLE{MaOl03,
-author = {Carey Marcinkovich and Kim Bak Olsen},
-title = {On the implementation of perfectly matched layers in a three-dimensional
-fourth-order velocity-stress finite-difference scheme},
-journal = jgr,
-year = {2003},
-volume = {108},
-pages = {2276},
-number = {B5},
-doi = {10.1029/2002JB002235}
+ author = {Carey Marcinkovich and Kim Bak Olsen},
+ title = {On the implementation of perfectly matched layers in a three-dimensional
+ fourth-order velocity-stress finite-difference scheme},
+ journal = jgr,
+ year = {2003},
+ volume = {108},
+ pages = {2276},
+ number = {B5},
+ doi = {10.1029/2002JB002235}
}
@ARTICLE{Mar84,
-author = {K. J. Marfurt},
-title = {Accuracy of finite-difference and finite-element modeling of the
-scalar and elastic wave equation},
-journal = geophysics,
-year = {1984},
-volume = {49},
-pages = {533-549},
-number = {5}
+ author = {K. J. Marfurt},
+ title = {Accuracy of finite-difference and finite-element modeling of the
+ scalar and elastic wave equation},
+ journal = geophysics,
+ year = {1984},
+ volume = {49},
+ pages = {533-549},
+ number = {5}
}
@ARTICLE{MaGu69,
-author = {L. Martel and S. K. Gupta},
-title = {{\`A} propos des ondes de {R}ayleigh sur une surface courbe},
-journal = {Ann. G\'eophys.},
-year = {1969},
-volume = {25},
-pages = {973-979},
-number = {4}
+ author = {L. Martel and S. K. Gupta},
+ title = {{\`A} propos des ondes de {R}ayleigh sur une surface courbe},
+ journal = {Ann. G\'eophys.},
+ year = {1969},
+ volume = {25},
+ pages = {973-979},
+ number = {4}
}
@ARTICLE{MaKo09,
-author = {Roland Martin and Dimitri Komatitsch},
-title = {An unsplit convolutional perfectly matched layer technique improved
-at grazing incidence for the viscoelastic wave equation},
-journal = gji,
-year = {2009},
-volume = {179},
-pages = {333-344},
-number = {1},
-doi = {10.1111/j.1365-246X.2009.04278.x}
+ author = {Roland Martin and Dimitri Komatitsch},
+ title = {An unsplit convolutional perfectly matched layer technique improved
+ at grazing incidence for the viscoelastic wave equation},
+ journal = gji,
+ year = {2009},
+ volume = {179},
+ pages = {333-344},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2009.04278.x}
}
@ARTICLE{MaKo06,
-author = {Roland Martin and Dimitri Komatitsch},
-title = {An optimized Convolution-Perfectly Matched Layer {(C-PML)} absorbing
-technique for {3D} seismic wave simulation based on a finite-difference
-method},
-journal = {Geophysical Research Abstracts},
-year = {2006},
-volume = {8},
-pages = {03988},
-month = {April},
-note = {Abstract EGU06-A-03988, www.cosis.net/abstracts/EGU06/03988/EGU06-J-03988-1.pdf}
+ author = {Roland Martin and Dimitri Komatitsch},
+ title = {An optimized Convolution-Perfectly Matched Layer {(C-PML)} absorbing
+ technique for {3D} seismic wave simulation based on a finite-difference
+ method},
+ journal = {Geophysical Research Abstracts},
+ year = {2006},
+ volume = {8},
+ pages = {03988},
+ month = {April},
+ note = {Abstract EGU06-A-03988, www.cosis.net/abstracts/EGU06/03988/EGU06-J-03988-1.pdf}
}
@ARTICLE{MaKoBa05,
-author = {Roland Martin and Dimitri Komatitsch and H\'el\`ene Barucq},
-title = {An optimized Convolution-Perfectly Matched Layer {(C-PML)} absorbing
-technique for {3D} seismic wave simulation based on a finite-difference
-method},
-journal = {Eos Trans. AGU},
-year = {2005},
-volume = {86},
-pages = {Fall Meet. Suppl., Abstract NG43B-0574},
-number = {52},
-month = {December},
-note = {www.agu.org/meetings/fm05/waisfm05.html}
+ author = {Roland Martin and Dimitri Komatitsch and H\'el\`ene Barucq},
+ title = {An optimized Convolution-Perfectly Matched Layer {(C-PML)} absorbing
+ technique for {3D} seismic wave simulation based on a finite-difference
+ method},
+ journal = {Eos Trans. AGU},
+ year = {2005},
+ volume = {86},
+ pages = {Fall Meet. Suppl., Abstract NG43B-0574},
+ number = {52},
+ month = {December},
+ note = {www.agu.org/meetings/fm05/waisfm05.html}
}
@ARTICLE{MaKoBlLe08,
-author = {Roland Martin and Dimitri Komatitsch and C\'eline Blitz and Nicolas
-{Le Goff}},
-title = {Simulation of seismic wave propagation in an asteroid based upon
-an unstructured {MPI} spectral-element method: blocking and non-blocking
-communication strategies},
-journal = lncs,
-year = {2008},
-volume = {5336},
-pages = {350-363}
+ author = {Roland Martin and Dimitri Komatitsch and C\'eline Blitz and Nicolas
+ {Le Goff}},
+ title = {Simulation of seismic wave propagation in an asteroid based upon
+ an unstructured {MPI} spectral-element method: blocking and non-blocking
+ communication strategies},
+ journal = lncs,
+ year = {2008},
+ volume = {5336},
+ pages = {350-363}
}
@ARTICLE{MaKoEz08,
-author = {Roland Martin and Dimitri Komatitsch and Abdela\^aziz Ezziani},
-title = {An unsplit convolutional perfectly matched layer improved at grazing
-incidence for seismic wave equation in poroelastic media},
-journal = geophysics,
-year = {2008},
-volume = {73},
-pages = {T51-T61},
-number = {4},
-doi = {10.1190/1.2939484}
+ author = {Roland Martin and Dimitri Komatitsch and Abdela\^aziz Ezziani},
+ title = {An unsplit convolutional perfectly matched layer improved at grazing
+ incidence for seismic wave equation in poroelastic media},
+ journal = geophysics,
+ year = {2008},
+ volume = {73},
+ pages = {T51-T61},
+ number = {4},
+ doi = {10.1190/1.2939484}
}
@ARTICLE{MaKoGe08,
-author = {Roland Martin and Dimitri Komatitsch and Stephen D. Gedney},
-title = {A variational formulation of a stabilized unsplit convolutional perfectly
-matched layer for the isotropic or anisotropic seismic wave equation},
-journal = cmes,
-year = {2008},
-volume = {37},
-pages = {274-304},
-number = {3}
+ author = {Roland Martin and Dimitri Komatitsch and Stephen D. Gedney},
+ title = {A variational formulation of a stabilized unsplit convolutional perfectly
+ matched layer for the isotropic or anisotropic seismic wave equation},
+ journal = cmes,
+ year = {2008},
+ volume = {37},
+ pages = {274-304},
+ number = {3}
}
@ARTICLE{MaKoGeBr10,
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-Bruthiaux},
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-Equations (ADE-PML)}},
-journal = cmes,
-year = {2010},
-volume = {56},
-pages = {17-42},
-number = {1}
+ author = {Roland Martin and Dimitri Komatitsch and Stephen D. Gedney and Emilien
+ Bruthiaux},
+ title = {A high-order time and space formulation of the unsplit perfectly
+ matched layer for the seismic wave equation using {Auxiliary Differential
+ Equations (ADE-PML)}},
+ journal = cmes,
+ year = {2010},
+ volume = {56},
+ pages = {17-42},
+ number = {1}
}
@ARTICLE{MaKoMa11,
-author = {Roland Martin and Dimitri Komatitsch and Ronan Madec},
-title = {An improved perfectly matched layer for high-order finite element
-fluid-viscoelastic wave propagation and sensitivity kernel construction},
-journal = grl,
-year = {2011},
-note = {Submitted in October 2010.}
+ author = {Roland Martin and Dimitri Komatitsch and Ronan Madec},
+ title = {An improved perfectly matched layer for high-order finite element
+ fluid-viscoelastic wave propagation and sensitivity kernel construction},
+ journal = grl,
+ year = {2011},
+ note = {Submitted in October 2010.}
}
@ARTICLE{MaPr07,
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-journal = jgr,
-year = {2007},
-volume = {112},
-pages = {B03204},
-number = {B3},
-doi = {10.1029/2006JB004592}
+ author = {Y. J. Masson and S. R. Pride},
+ title = {Poroelastic finite-difference modeling of seismic attenuation and
+ dispersion due to mesoscopic-scale heterogeneity},
+ journal = jgr,
+ year = {2007},
+ volume = {112},
+ pages = {B03204},
+ number = {B3},
+ doi = {10.1029/2006JB004592}
}
@ARTICLE{Masson2006,
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-volume = {111},
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-doi = {10.1029/2006JB004366}
+ author = {Y. J. Masson and S. R. Pride and K. T. Nihei},
+ title = {Finite-difference modelling of {B}iot's poroelastic equations at
+ seismic frequencies},
+ journal = jgr,
+ year = {2006},
+ volume = {111},
+ pages = {B10305},
+ doi = {10.1029/2006JB004366}
}
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+ surface},
+ journal = {Reviews of Geophysics},
+ year = {1998},
+ volume = {36},
+ pages = {441-500}
}
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+ author = {E. Matzel and M. K. Sen and S. P. Grand},
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+ journal = grl,
+ year = {1996},
+ volume = {23},
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+ number = {18}
}
+ at ARTICLE{Mat11,
+ author = {Ren\'e Matzen},
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+ journal = ijnme,
+ year = {2011},
+pages = {951-973},
+volume = {88},
+number = {10},
+doi = {10.1002/nme.3205}
+}
+
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+ author = {V. Maupin},
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+ journal = pepi,
+ year = {1994},
+ volume = {87},
+ pages = {1-32}
}
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+ author = {A. A. Maznev and A. G. Every},
+ title = {Time-domain dynamic surface response of an anisotropic elastic solid
+ to an impulsive line force},
+ journal = {International Journal of Engineering Science},
+ year = {1997},
+ volume = {35},
+ pages = {321-327},
+ number = {4}
}
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+ year = {1995},
+ volume = {A197},
+ pages = {423-427}
}
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+ title = {Ray surface and focusing of surface acoustic waves on the basal plane
+ of cubic crystals},
+ journal = {Acta Acustica},
+ year = {1994},
+ volume = {1},
+ pages = {137-143}
}
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+ author = {A. A. Maznev and Al. A. Kolomenskii and P. Hess},
+ title = {Time-resolved cuspidal structure in the wavefront of surface acoustic
+ pulses on (111) {G}allium {A}rsenide},
+ journal = {Physics Review Letters},
+ year = {1995},
+ volume = {75},
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+ number = {18}
}
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+ author = {A.A. Maznev and A. M. Lomonosov and P. Hess and Al. A. Kolomenskii},
+ title = {Anisotropic effects in surface acoustic wave propagation from a point
+ source in a crystal},
+ journal = {The European Physical Journal B},
+ year = {2003},
+ volume = {35},
+ pages = {429-439}
}
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+ title = {Applications of tensor analysis},
+ publisher = {Dover Publications},
+ year = {1957},
+ author = {A. J. McConnell},
+ address = {New York}
}
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+ author = {Michael McCool and Stefanus {Du Toit} and Tiberiu S. Popa and Bryan
+ Chan and Kevin Moule},
+ title = {Shader Algebra},
+ journal = {ACM Transactions on Graphics},
+ year = {2004},
+ volume = {23},
+ pages = {787--795},
+ number = {3},
+ month = aug,
+ doi = {10.1145/1015706.1015801}
}
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+ author = {Patrick McCormick and Jeff Inman and James Ahrens and Jamaludin Mohd-Yusof
+ and Greg Roth and Sharen Cummins},
+ title = {Scout: a data-parallel programming language for graphics processors},
+ journal = {Parallel Computing},
+ year = {2007},
+ volume = {33},
+ pages = {648-662}
}
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+ author = {T. H. McCulloh},
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+ {C}alifornia},
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+ year = {1960},
+ volume = {400-B},
+ pages = {320-325}
}
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+ J. L. Stevens},
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+ waves: 3{D} numerical simulations},
+ journal = gji,
+ year = {1992},
+ volume = {111},
+ pages = {291-308}
}
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}
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+ year = {1988},
+ volume = {78},
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}
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+ author = {E. D. Mercerat and J. P. Vilotte and F. J. S\'anchez-Sesma},
+ title = {Triangular spectral-element simulation of two-dimensional elastic
+ wave propagation using unstructured triangular grids},
+ journal = gji,
+ year = {2006},
+ volume = {166},
+ pages = {679-698},
+ number = {2}
}
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+ author = {Merkel, S. and A. K. McNamara and A. Kubo and S. Speziale and L.
+ Miyagi and Y. Meng and T. S. Duffy and H. R. Wenk},
+ title = {Deformation of ({M}g,{F}e){S}i{O}3 post-perovskite and {D}'' anisotropy},
+ journal = {Science},
+ year = {2007},
+ volume = {316},
+ pages = {1729--1732}
}
@ARTICLE{MeMuGr08,
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-pages = {70-73},
-number = {5},
-doi = {10.1109/MCSE.2008.135}
+ author = {Peter Messmer and Paul J. Mullowney and Brian E. Granger},
+ title = {{GPULib: GPU} Computing in High-Level Languages},
+ journal = {Computing in Science and Engineering},
+ year = {2008},
+ volume = {10},
+ pages = {70-73},
+ number = {5},
+ doi = {10.1109/MCSE.2008.135}
}
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-address = {Mannheim, Germany},
-note = {{{\tt www.top500.org}}}
+ author = {H. W. Meuer and E. Strohmaier and J. J. Dongarra and H. D. Simon},
+ title = {Top500 list of Supercomputer Sites},
+ institution = {University of Mannheim},
+ year = {2002},
+ address = {Mannheim, Germany},
+ note = {{{\tt www.top500.org}}}
}
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+ year = {1992},
+ volume = {7},
+ pages = {9999998-9999999}
}
@BOOK{Mey90,
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+ title = {Ondelettes et op\'erateurs},
+ publisher = {Hermann},
+ year = {1990},
+ author = {Y. Meyer},
+ address = {Paris}
}
@TECHREPORT{Mey87,
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-year = {1987},
-address = {Universit\'e Paris Dauphine}
+ author = {Y. Meyer},
+ title = {Ondelettes, fonctions splines et analyses gradu\'ees},
+ institution = {Ceremade 8703},
+ year = {1987},
+ address = {Universit\'e Paris Dauphine}
}
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-journal = bssa,
-year = {2008},
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-number = {4},
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+ author = {Kristel C. Meza-Fajardo and Apostolos S. Papageorgiou},
+ title = {A nonconvolutional, split-field, perfectly matched layer for wave
+ propagation in isotropic and anisotropic elastic media: Stability
+ analysis},
+ journal = bssa,
+ year = {2008},
+ volume = {98},
+ pages = {1811-1836},
+ number = {4},
+ doi = {10.1785/0120070223}
}
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+ author = {David Mich\'{e}a and Dimitri Komatitsch},
+ title = {Accelerating a 3{D} finite-difference wave propagation code using
+ {GPU} graphics cards},
+ journal = gji,
+ year = {2010},
+ volume = {182},
+ pages = {389-402},
+ number = {1},
+ doi = {10.1111/j.1365-246X.2010.04616.x}
}
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-year = {2009},
-pages = {79-84},
-address = {Washington, DC, USA},
-month = mar,
-doi = {10.1145/1513895.1513905}
+ author = {Paulius Micikevicius},
+ title = {{3D} finite-difference computation on {GPUs} using {CUDA}},
+ booktitle = {GPGPU-2: Proceedings of the 2nd Workshop on General Purpose Processing
+ on Graphics Processing Units},
+ year = {2009},
+ pages = {79-84},
+ address = {Washington, DC, USA},
+ month = mar,
+ doi = {10.1145/1513895.1513905}
}
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+ author = {A. Mielke and Y. B. Fu},
+ title = {Uniqueness of the surface-wave speed: a proof that is independent
+ of the {S}troh formalism},
+ journal = {Mathematics and Mechanics of Solids},
+ year = {2004},
+ volume = {9},
+ pages = {5-15}
}
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}
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+ Wave Propagation Code},
+ journal = {SIAM Journal on Scientific Computing},
+ year = {2002},
+ volume = {24},
+ pages = {1-19},
+ number = {1},
+ doi = {10.1137/S1064827501390960},
+ publisher = {SIAM}
}
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+ author = {S. Mitchell},
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+ booktitle = {STACS 96},
+ publisher = {Springer Berlin / Heidelberg},
+ year = {1996},
+ editor = {Puech, Claude and Reischuk, R{\"u}diger},
+ volume = {1046},
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}
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+ year = {1991},
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+ M. Bouchon},
+ title = {Hybrid modeling of {{\it P-SV}} seismic motion at inhomogeneous viscoelastic
+ topographic structures},
+ journal = bssa,
+ year = {1997},
+ volume = {87},
+ pages = {1305-1323}
}
@ARTICLE{MoKr05,
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+ author = {P. Moczo and J. Kristek},
+ title = {On the rheological models used for time-domain methods of seismic
+ wave propagation},
+ journal = grl,
+ year = {2005},
+ volume = {32},
+ pages = {L01306},
+ doi = {10.1029/2004GL021598}
}
@ARTICLE{MoKrBy01,
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+ author = {P. Moczo and J. Kristek and E. Bystrick{\'y}},
+ title = {Efficiency and optimization of the {3-D} finite-difference modeling
+ of seismic ground motion},
+ journal = jca,
+ year = {2001},
+ volume = {9},
+ pages = {593-609},
+ number = {2}
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+ author = {P. Moczo and J. Robertsson and L. Eisner},
+ title = {The Finite-difference Time-domain method for Modeling of Seismic
+ Wave Propagation},
+ booktitle = {Advances in wave propagation in heterogeneous media},
+ publisher = {Elsevier - Academic Press, London, UK},
+ year = {2007},
+ editor = {Ru-Shan Wu and Val\'erie Maupin},
+ volume = {48},
+ series = {Advances in Geophysics},
+ chapter = {8},
+ pages = {421-516}
}
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+ school = {\'Ecole Centrale de Paris},
+ year = {1986},
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+ Systems in Inhomogeneous Media},
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+ author = {C. Morency and J. Tromp},
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+ journal = gji,
+ year = {2008},
+ volume = {175},
+ pages = {301-345}
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+ author = {A. Moura},
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+ author = {A. Mourad and M. Deschamps and B. Castagn\`ede},
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+ year = {1982},
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+ author = {M. K. Murakami and K. Hirose and N. Sata and Y. Ohishi and K. Kawamura},
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+ year = {2002},
+ volume = {4},
+ pages = {39-49}
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+ volume = {168},
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+ title = {A 2-{D} spectral-element method for computing spherical-earth seismograms
+ - {II. W}aves in solid-fluid media},
+ journal = gji,
+ year = {2008},
+ volume = {174},
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+ doi = {10.1111/j.1365-246X.2008.03813.x}
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+ title = {A two-dimensional spectral-element method for computing spherical-earth
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+ journal = gji,
+ year = {2007},
+ volume = {168},
+ pages = {1067-1092},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2006.03121.x}
}
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+ title = {National {O}ceanic and {A}tmospheric {A}dministration {(NOAA)} Product
+ Information Catalog - {ETOPO5} {E}arth {T}opography 5-minute digital
+ model},
+ institution = {U.S. Department of Commerce},
+ year = {1988},
+ address = {Washington D.C., USA},
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+ journal = jgr,
+ year = {2000},
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@MANUAL{CUDAmanual,
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+ title = {{NVIDIA CUDA} Programming Guide version 2.3},
+ author = {{NVIDIA Corporation}},
+ address = {Santa Clara, California, USA},
+ month = jul,
+ year = {2009},
+ note = {139 pages},
+ url = {http://www.nvidia.com/cuda}
}
@TECHREPORT{NVIDIA:2009:FERMI,
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+ author = {{NVIDIA Corporation}},
+ title = {{NVIDIA's} Next Generation {CUDA} Compute Architecture: {FERMI}},
+ institution = {NVIDIA},
+ year = {2009},
+ address = {Santa Clara, California, USA},
+ month = sep,
+ note = {22 pages},
+ url = {http://www.nvidia.com/object/fermi\_architecture.html}
}
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+ author = {{NVIDIA Corporation}},
+ title = {{NVIDIA} {G}e{F}orce {GTX} 200 {GPU} Architectural Overview, Second-Generation
+ Unified {GPU} Architecture for Visual Computing},
+ institution = {NVIDIA},
+ year = {2008},
+ pages = {1-23},
+ url = {www.nvidia.com/docs/IO/55506/GeForce\_GTX\_200\_GPU\_Technical\_Brief.pdf}
}
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-month = aug
+ author = {Lars Nyland and Mark Harris and Jan Prins},
+ title = {Fast {N}-body simulation with {CUDA}},
+ booktitle = {GPU Gems 3},
+ publisher = {Addison-Wesley Professional, Boston, MA, USA},
+ year = {2007},
+ chapter = {31},
+ pages = {677--695},
+ month = aug
}
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+ author = {A. R. Oganov and S. Ono},
+ title = {Theoretical and experimental evidence for a post-perovskite phase
+ of {MgSiO3} in {E}arth's {D}'' layer},
+ journal = {Nature},
+ year = {2004},
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+ author = {K. B. Olsen and S. M. Day and C. R. Bradley},
+ title = {Estimation of {$Q$} for long-period (>2 sec) waves in the {L}os {A}ngeles
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+ title = {Strong shaking in {L}os {A}ngeles expected from southern {S}an {A}ndreas
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+ author = {John D. Owens and David P. Luebke and Naga K. Govindaraju and Mark
+ J. Harris and Jens Kr{\"{u}}ger and Aaron E. Lefohn and Timothy J.
+ Purcell},
+ title = {A Survey of General-Purpose Computation on Graphics Hardware},
+ booktitle = {Eurographics 2005, State of the Art Reports},
+ year = {2005},
+ pages = {21--51},
+ month = sep
}
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-th\'eorique et applications},
-school = {Universit\'e Joseph Fourier},
-year = {1994},
-address = {Grenoble}
+ author = {H. A. Pedersen},
+ title = {{\'E}tude de la diffraction tridimensionnelle des ondes sismiques
+ dans des structures \`a g\'eom\'etrie bidimensionnelle, d\'eveloppement
+ th\'eorique et applications},
+ school = {Universit\'e Joseph Fourier},
+ year = {1994},
+ address = {Grenoble}
}
@ARTICLE{PeLeHaCaBa94,
-author = {H. A. Pedersen and B. LeBrun and D. Hatzfeld and M. Campillo and
-P.Y. Bard},
-title = {Ground motion amplitude across ridges},
-journal = bssa,
-year = {1994},
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-pages = {1786-1800}
+ author = {H. A. Pedersen and B. LeBrun and D. Hatzfeld and M. Campillo and
+ P.Y. Bard},
+ title = {Ground motion amplitude across ridges},
+ journal = bssa,
+ year = {1994},
+ volume = {84},
+ pages = {1786-1800}
}
@ARTICLE{PeSaCa94,
-author = {H. A. Pedersen and F. J. S\'anchez-Sesma and M. Campillo},
-title = {Three-dimensional scattering by two-dimensional topographies},
-journal = bssa,
-year = {1994},
-volume = {84},
-pages = {1169-1183}
+ author = {H. A. Pedersen and F. J. S\'anchez-Sesma and M. Campillo},
+ title = {Three-dimensional scattering by two-dimensional topographies},
+ journal = bssa,
+ year = {1994},
+ volume = {84},
+ pages = {1169-1183}
}
@ARTICLE{PeJoArSiFe03,
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-and K. L. Feigl},
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-journal = {Earth and Planetary Science Letters},
-year = {2003},
-volume = {9999999},
-pages = {999998-999999},
-note = {submitted}
+ author = {R. Pedersen and S. J\'onsson and T. \'Arnad\'ottir and F. Sigmundsson
+ and K. L. Feigl},
+ title = {Fault slip distribution estimated from joint inversion of {InSAR}
+ and {GPS} measurements of two {J}une 2000 {M$_w$}=6.5 earthquakes
+ in {S}outh {I}celand},
+ journal = {Earth and Planetary Science Letters},
+ year = {2003},
+ volume = {9999999},
+ pages = {999998-999999},
+ note = {submitted}
}
@ARTICLE{pedersenetal2001,
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-{I}celand {S}eismic {Z}one, {J}une 2000},
-journal = grl,
-year = {2001},
-volume = {28},
-pages = {3341-3344}
+ author = {R. Pedersen and F. Sigmundsson and K. L. Feigl and T. \'Arnad\'ottir},
+ title = {Coseismic interferograms of two {M}s=6.6 earthquakes in the {S}outh
+ {I}celand {S}eismic {Z}one, {J}une 2000},
+ journal = grl,
+ year = {2001},
+ volume = {28},
+ pages = {3341-3344}
}
@ARTICLE{PeRo96,
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-year = {1996},
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+ author = {F. Pellegrini and J. Roman},
+ title = {{SCOTCH}: A Software Package for Static Mapping by Dual Recursive
+ Bipartitioning of Process and Architecture Graphs},
+ journal = lncs,
+ year = {1996},
+ volume = {1067},
+ pages = {493-498}
}
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+ author = {W. R. Peltier},
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+ journal = gjras,
+ year = {1976},
+ volume = {46},
+ pages = {669-706}
}
@ARTICLE{PeKaHeCrCa10,
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-title = {Regular versus irregular meshing for complicated models and their
-effect on synthetic seismograms},
-journal = {Geophys. J. Int.},
-year = {2010},
-volume = {183},
-pages = {1031-1051}
+ author = {Ch. Pelties and M. K\"aser and V. Hermann and C. E. Castro},
+ title = {Regular versus irregular meshing for complicated models and their
+ effect on synthetic seismograms},
+ journal = {Geophys. J. Int.},
+ year = {2010},
+ volume = {183},
+ pages = {1031-1051}
}
@ARTICLE{Pel90,
-author = {R. B. Pelz},
-title = {Pseudospectral methods on massively parallel computers},
-journal = cmame,
-year = {1990},
-volume = {80},
-pages = {493-503}
+ author = {R. B. Pelz},
+ title = {Pseudospectral methods on massively parallel computers},
+ journal = cmame,
+ year = {1990},
+ volume = {80},
+ pages = {493-503}
}
@ARTICLE{PeTo95,
-author = {C. B. Peng and M. Nafi T\"oksoz},
-title = {An optimal absorbing boundary condition for elastic wave modeling},
-journal = geophysics,
-year = {1995},
-volume = {60},
-pages = {296-301}
+ author = {C. B. Peng and M. Nafi T\"oksoz},
+ title = {An optimal absorbing boundary condition for elastic wave modeling},
+ journal = geophysics,
+ year = {1995},
+ volume = {60},
+ pages = {296-301}
}
@ARTICLE{PeBa89,
-author = {V. Perrier and C. Basdevant},
-title = {La d\'ecomposition en ondelettes p\'eriodiques, un outil pour l'analyse
-de champs inhomog\`enes},
-journal = {La Recherche A\'erospatiale},
-year = {1989},
-volume = {3},
-pages = {99999998-99999999}
+ author = {V. Perrier and C. Basdevant},
+ title = {La d\'ecomposition en ondelettes p\'eriodiques, un outil pour l'analyse
+ de champs inhomog\`enes},
+ journal = {La Recherche A\'erospatiale},
+ year = {1989},
+ volume = {3},
+ pages = {99999998-99999999}
}
+ at ARTICLE{PeKoLuMaLeCaLeMaLiBlNiBaTr11,
+ author = {Daniel Peter and Dimitri Komatitsch and Yang Luo and Roland Martin
+ and Nicolas {Le Goff} and Emanuele Casarotti and Pieyre {Le Loher}
+ and Federica Magnoni and Qinya Liu and C\'eline Blitz and Tarje Nissen-Meyer
+ and Piero Basini and Jeroen Tromp},
+ title = {Forward and adjoint simulations of seismic wave propagation on fully
+ unstructured hexahedral meshes},
+ journal = gji,
+ year = {2011},
+ volume = {186},
+ pages = {721-739},
+ number = {2},
+ doi = {10.1111/j.1365-246X.2011.05044.x}
+}
+
@INPROCEEDINGS{PeBo06,
-author = {E. Petit and F. Bodin},
-title = {Extracting Threads Using Traces for System on a Chip},
-booktitle = {Proceedings of the Compilers for Parallel Computers (CPC'2006)},
-year = {2006},
-address = {La Coru{\~{n}}a, Spain},
-month = {January}
+ author = {E. Petit and F. Bodin},
+ title = {Extracting Threads Using Traces for System on a Chip},
+ booktitle = {Proceedings of the Compilers for Parallel Computers (CPC'2006)},
+ year = {2006},
+ address = {La Coru{\~{n}}a, Spain},
+ month = {January}
}
@ARTICLE{PeOlMa2001,
-author = {S. Peyrat and K. B. Olsen and R. Madariaga},
-title = {Dynamic modeling of the 1992 {L}anders earthquake},
-journal = jgr,
-year = {2001},
-volume = {106},
-pages = {26467-26482}
+ author = {S. Peyrat and K. B. Olsen and R. Madariaga},
+ title = {Dynamic modeling of the 1992 {L}anders earthquake},
+ journal = jgr,
+ year = {2001},
+ volume = {106},
+ pages = {26467-26482}
}
@INPROCEEDINGS{Phillips:2009:RAP,
-author = {Everett H. Phillips and Yao Zhang and Roger L. Davis and John D.
-Owens},
-title = {Rapid Aerodynamic Performance Prediction on a Cluster of Graphics
-Processing Units},
-booktitle = {Proceedings of the 47th {AIAA} Aerospace Sciences Meeting},
-year = {2009},
-pages = {1-11},
-month = jan
+ author = {Everett H. Phillips and Yao Zhang and Roger L. Davis and John D.
+ Owens},
+ title = {Rapid Aerodynamic Performance Prediction on a Cluster of Graphics
+ Processing Units},
+ booktitle = {Proceedings of the 47th {AIAA} Aerospace Sciences Meeting},
+ year = {2009},
+ pages = {1-11},
+ month = jan
}
@INPROCEEDINGS{PhStSc08,
-author = {James C. Phillips and John E. Stone and Klaus Schulten},
-title = {Adapting a message-driven parallel application to {GPU}-accelerated
-clusters},
-booktitle = {SC '08: Proceedings of the 2008 ACM/IEEE conference on Supercomputing},
-year = {2008},
-pages = {1--9},
-month = nov,
-doi = {10.1145/1413370.1413379}
+ author = {James C. Phillips and John E. Stone and Klaus Schulten},
+ title = {Adapting a message-driven parallel application to {GPU}-accelerated
+ clusters},
+ booktitle = {SC '08: Proceedings of the 2008 ACM/IEEE conference on Supercomputing},
+ year = {2008},
+ pages = {1--9},
+ month = nov,
+ doi = {10.1145/1413370.1413379}
}
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+ author = {Phinney, R. A and Alexander, S. S.},
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+ journal = jgr,
+ year = {1966},
+ volume = {71},
+ pages = {5959-5975}
}
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+ author = {R. A. Phinney and R. Burridge},
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+ {E}arth Model by Generalized Spherical Harmonics},
+ journal = gjras,
+ year = {1973},
+ volume = {34},
+ pages = {451-487}
}
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+ author = {K. D. Phung},
+ title = {Controllability and stabilization of electromagnetic waves},
+ journal = {ESAIM Control Optim. Calc. Var.},
+ year = {2000},
+ volume = {5},
+ pages = {87-137}
}
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-address = {Amsterdam, The Netherlands}
+ title = {Elastic waves in the {E}arth},
+ publisher = {Elsevier Scientific Publishing Company},
+ year = {1979},
+ author = {Walter L. Pilant},
+ volume = {11 of "Developments in Solid Earth Geophysics" Series},
+ address = {Amsterdam, The Netherlands}
}
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-{R}ayleigh waves (experimental)},
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+ author = {W. L. Pilant and L. Knopoff and F. Schwab},
+ title = {Transmission and reflection of surface waves at a corner, part 3:
+ {R}ayleigh waves (experimental)},
+ journal = jgr,
+ year = {1964},
+ volume = {69},
+ pages = {291-297}
}
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-station site, {J}apan, case study},
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-pages = {2729-2732}
+ author = {A. Pitarka and K. Irikura},
+ title = {Modeling 3{D} surface topography by a finite-difference method: {K}obe-{JMA}
+ station site, {J}apan, case study},
+ journal = grl,
+ year = {1996},
+ volume = {23},
+ pages = {2729-2732}
}
@ARTICLE{PiIr96b,
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-earthquake and aftershocks},
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-year = {1996},
-volume = {86},
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+ author = {A. Pitarka and K. Irikura},
+ title = {Basin structure effects on long period strong motions in the {S}an
+ {F}ernando valley and the {L}os {A}ngeles basin from the 1994 {N}orthridge
+ earthquake and aftershocks},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {S126-S137},
+ number = {1B}
}
@ARTICLE{PiIrIwKa96,
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-year = {1996},
-volume = {44},
-pages = {563-576}
+ author = {A. Pitarka and K. Irikura and T. Iwata and T. Kagawa},
+ title = {Basin structure effects in the {K}obe area inferred from modelling
+ of ground motions from two aftershocks of the {J}anuary 17, 1995,
+ {H}yogo-ken {N}anbu earthquake},
+ journal = {J. Phys. Earth},
+ year = {1996},
+ volume = {44},
+ pages = {563-576}
}
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-journal = bssa,
-year = {1998},
-volume = {88},
-pages = {428-440}
+ author = {A. Pitarka and K. Irikura and T. Iwata and H. Sekiguchi},
+ title = {Three-dimensional simulation of the near-fault ground motion for
+ the 1995 {H}yogo-ken {N}anbu ({K}obe), {J}apan, earthquake},
+ journal = bssa,
+ year = {1998},
+ volume = {88},
+ pages = {428-440}
}
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-year = {2009},
-volume = {23},
-pages = {284-299},
-number = {3},
-doi = {10.1177/1094342009106195}
+ author = {Judit Planas and Rosa M. Badia and Eduard Ayguad\'{e} and Jesus Labarta},
+ title = {Hierarchical Task-Based Programming With {StarSs}},
+ journal = {International Journal of High Performance Computing Applications},
+ year = {2009},
+ volume = {23},
+ pages = {284-299},
+ number = {3},
+ doi = {10.1177/1094342009106195}
}
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-year = {1988},
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+ author = {B. J. Plohr and D. H. Sharp},
+ title = {A conservative {E}ulerian formulation of the equations for elastic
+ flow},
+ journal = {Advances in Applied Mathematics},
+ year = {1988},
+ volume = {9},
+ pages = {481-499}
}
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+ author = {T. Pointer and E. Liu and J. A. Hudson},
+ title = {Seismic wave propagation in cracked porous media},
+ journal = gji,
+ year = {2000},
+ volume = {141},
+ pages = {199-231}
}
@ARTICLE{Poin98,
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-application of the indirect boundary method},
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+ author = {T. Pointer and E. Liu and J. A. Hudson},
+ title = {Numerical modelling of seismic waves scattered by hydrofractures:
+ application of the indirect boundary method},
+ journal = gji,
+ year = {1998},
+ volume = {135},
+ pages = {289-303}
}
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-treatment of near cusp behavior},
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-year = {2001},
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+ author = {O. Poncelet and M. Deschamps and A.G. Every and B. Audoin},
+ title = {Extension to cuspidal edges of wave surfaces of anisotropic solids:
+ treatment of near cusp behavior},
+ journal = {Review of Progress in Quantitative Nondestructive Evaluation},
+ year = {2001},
+ volume = {20},
+ pages = {51-58}
}
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+ author = {D. J. Ponti and R. E. Wells},
+ title = {Off-fault ground ruptures in the {S}anta-{C}ruz mountains, {C}alifornia:
+ ridge-top spreading versus tectonic extension during the 1989 {L}oma
+ {P}rieta earthquake},
+ journal = bssa,
+ year = {1991},
+ volume = {81},
+ pages = {1480-1510}
}
@ARTICLE{Poupinet83,
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-travel times},
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+ author = {G. Poupinet and R. Pillet and A. Souriau},
+ title = {Possible heterogeneity of the {E}arth's core deduced from {PKIKP}
+ travel times},
+ journal = {Nature},
+ year = {1983},
+ volume = {305},
+ pages = {204-206}
}
@PHDTHESIS{prat2005,
-author = {F. Prat},
-title = {Analyse du Generalized Screen Propagator},
-school = {Universit\'{e} de Pau et des Pays de l'Adour},
-year = {2005}
+ author = {F. Prat},
+ title = {Analyse du Generalized Screen Propagator},
+ school = {Universit\'{e} de Pau et des Pays de l'Adour},
+ year = {2005}
}
@ARTICLE{Pra99,
-author = {R. Gerhard Pratt},
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-and verification in a physical scale model},
-journal = geophysics,
-year = {1999},
-volume = {64},
-pages = {888-901},
-number = {3}
+ author = {R. Gerhard Pratt},
+ title = {Seismic waveform inversion in the frequency domain, {P}art 1: Theory
+ and verification in a physical scale model},
+ journal = geophysics,
+ year = {1999},
+ volume = {64},
+ pages = {888-901},
+ number = {3}
}
@ARTICLE{PrCh92,
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-year = {1992},
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+ author = {R. G. Pratt and C. Chapman},
+ title = {Traveltime tomography in anisotropic media -{II}: Application},
+ journal = gji,
+ year = {1992},
+ volume = {109},
+ pages = {20-37}
}
@ARTICLE{PrShHi98,
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-year = {1998},
-volume = {133},
-pages = {341-362},
-number = {2},
-doi = {10.1046/j.1365-246X.1998.00498.x}
+ author = {R. Gerhard Pratt and Changsoo Shin and G. J. Hicks},
+ title = {Gauss-{N}ewton and full {N}ewton methods in frequency-space seismic
+ waveform inversion},
+ journal = geophysics,
+ year = {1998},
+ volume = {133},
+ pages = {341-362},
+ number = {2},
+ doi = {10.1046/j.1365-246X.1998.00498.x}
}
@ARTICLE{PrSh99,
-author = {R. Gerhard Pratt and Richard M. Shipp},
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-delineation in sediments using crosshole data},
-journal = geophysics,
-year = {1999},
-volume = {64},
-pages = {902-914},
-number = {3}
+ author = {R. Gerhard Pratt and Richard M. Shipp},
+ title = {Seismic waveform inversion in the frequency domain, {P}art 2: Fault
+ delineation in sediments using crosshole data},
+ journal = geophysics,
+ year = {1999},
+ volume = {64},
+ pages = {902-914},
+ number = {3}
}
@ARTICLE{PrViPaSc09,
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-journal = jcp,
-year = {2009},
-volume = {228},
-pages = {4468-4477},
-doi = {10.1016/j.jcp.2009.03.018}
+ author = {Tobias Preis and Peter Virnau and Wolfgang Paul and Johannes J. Schneider},
+ title = {{GPU} accelerated {M}onte {C}arlo simulation of the {2D} and {3D}
+ {I}sing model},
+ journal = jcp,
+ year = {2009},
+ volume = {228},
+ pages = {4468-4477},
+ doi = {10.1016/j.jcp.2009.03.018}
}
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+ publisher = {Cambridge University Press},
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+ author = {W. H. Press and S. A. Teukolsky and W. T. Vetterling and B. P. Flannery},
+ address = {Cambridge, USA}
}
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+ author = {Daniel K. Price and John R. Humphrey and Eric J. Kelmelis},
+ title = {{GPU}-based accelerated {2D} and {3D FDTD} solvers},
+ booktitle = {Proceedings of the SPIE Physics and Simulation of Optoelectronic
+ Devices XV Conference},
+ publisher = {SPIE and the International Society for Optical Engineering},
+ year = {2007},
+ volume = {6468},
+ address = {San Jose, California, USA},
+ doi = {10.1117/12.715044}
}
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+ author = {S. R. Pride and J. G. Berryman and J. M. Harris},
+ title = {Seismic attenuation due to wave-induced flow},
+ journal = jgr,
+ year = {2004},
+ volume = {109},
+ pages = {681-693}
}
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+ journal = jgr,
+ year = {2009},
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+ pages = {B10302},
+ doi = {10.1029/2008JB006271}
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+ title = {Seismic anisotropy in the core-mantle transition zone},
+ journal = gji,
+ year = {1998},
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+ pages = {113-128},
+ number = {1}
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+ acoustics},
+ journal = jcp,
+ year = {1998},
+ volume = {139},
+ pages = {166-183},
+ number = {1}
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+ journal = cmame,
+ year = {1998},
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+ pages = {323-341}
}
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+ author = {G. Quiroga-Goode and S. Jim\'enez-Hern\'andez and M. A. P\'erez-Flores
+ and R. Padilla-Hern\'andez},
+ title = {Computational study of seismic waves in homogeneous dynamic-porosity
+ media with thermal and fluid relaxation: {G}auging {B}iot theory},
+ journal = jgr,
+ year = {2005},
+ volume = {110},
+ pages = {B07303},
+ doi = {10.1029/2004JB003347}
}
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+ author = {G. R\"umpker and T. Ryberg},
+ title = {New "Fresnel-zone" estimates for shear-wave splitting observations
+ from finite-difference modeling},
+ journal = grl,
+ year = {2000},
+ volume = {27},
+ pages = {2005-2008}
}
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+ author = {Nikunj Raghuvanshi and Rahul Narain and Ming C. Lin},
+ title = {Efficient and Accurate Sound Propagation Using Adaptive Rectangular
+ Decomposition},
+ journal = {IEEE Transactions on Visualization and Computer Graphics},
+ year = {2009},
+ volume = {15},
+ pages = {789-801},
+ number = {5},
+ doi = {10.1109/TVCG.2009.28}
}
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+ ({A} well-posed {PML} model for anisotropic elastodynamics)},
+ journal = {C. R. Acad. Sci. Paris, Ser. I},
+ year = {2004},
+ volume = {338},
+ pages = {963-968}
}
@PHDTHESIS{Rah00,
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-({S}ome well-posed {PML} models for several hyperbolic problems)},
-school = {University of Paris XIII, France},
-year = {2000}
+ author = {A. N. Rahmouni},
+ title = {Des mod\`eles {PML} bien pos\'es pour divers probl\`emes hyperboliques
+ ({S}ome well-posed {PML} models for several hyperbolic problems)},
+ school = {University of Paris XIII, France},
+ year = {2000}
}
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+ publisher = {Dover Publications},
+ year = {1945},
+ author = {L. J. W. S. Rayleigh},
+ address = {New York},
+ edition = {2nd}
}
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+ year = {1910},
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+ volume = {17},
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}
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+ author = {F. J. L. Reid and J. H. Woodhouse and H. J. van Heijst},
+ title = {Upper mantle attenuation and velocity structure from measurements
+ of differential S phases},
+ journal = gji,
+ year = {2001},
+ volume = {145},
+ pages = {615-630}
}
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+ year = {1996},
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+ author = {J. Ritsema},
+ title = {Global seismic structure maps},
+ booktitle = {Plates, Plumes, and Paradigms},
+ publisher = {Geological Soc. Amer. special paper},
+ year = {2005},
+ editor = {G. R. Foulger and J. H. Natland and D. C. Presnall and D. L. Anderson},
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}
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+ title = {{S40RTS}: a degree-40 shear-velocity model for the mantle from new
+ Rayleigh wave dispersion, teleseismic traveltime and normal-mode
+ splitting function measurements},
+ journal = gji,
+ year = {2010},
+ doi = {10.1111/j.1365-246X.2010.04884.x}
}
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+ author = {J. Ritsema and H. J. van Heijst},
+ title = {Constraints on the correlation of P- and S-wave velocity heterogeneity
+ in the mantle from P, PP, PPP, and PKPab traveltimes},
+ journal = gji,
+ year = {2002},
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+ J. van Heijst},
+ title = {The effects of crust and mantle heterogeneity on {PP/P} and {SS/S}
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+ year = {2002},
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+ number = {10},
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}
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+ Evidence for large-scale mantle flow},
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+ year = {2000},
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+ year = {1999},
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+ year = {2000},
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+ author = {Jer\'onimo Rodr\'{\i}guez},
+ title = {Raffinement de maillage spatio-temporel pour les \'equations de l'\'elastodynamique},
+ school = {Universit\'e Paris IX-Dauphine},
+ year = {2004},
+ address = {Paris, France}
}
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+ author = {A. Rodr\'{\i}guez-Castellanos and F.J. S\'anchez-Sesma and F. Luz\'on
+ and R. Martin},
+ title = {Multiple scattering of elastic waves by subsurface fractures and
+ cavities},
+ journal = bssa,
+ year = {2006},
+ volume = {96},
+ pages = {1359-1374},
+ number = {4A}
}
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-year = {2008},
-pages = {273--282},
-address = {New York, USA},
-publisher = {ACM}
+ author = {Christopher I. Rodrigues and David J. Hardy and John E. Stone and
+ Klaus Schulten and Wen{-}mei W. Hwu},
+ title = {{GPU} acceleration of cutoff pair potentials for molecular modeling
+ applications},
+ booktitle = {Proceedings of the 2008 conference on Computing Frontiers},
+ year = {2008},
+ pages = {273--282},
+ address = {New York, USA},
+ publisher = {ACM}
}
@PHDTHESIS{Rod93,
-author = {Dominique Rodrigues},
-title = {Simulation de la propagation d'ondes sismiques sur machine massivement
-parall\`ele},
-school = {\'Ecole Centrale de Paris},
-year = {1993},
-address = {Paris, France}
+ author = {Dominique Rodrigues},
+ title = {Simulation de la propagation d'ondes sismiques sur machine massivement
+ parall\`ele},
+ school = {\'Ecole Centrale de Paris},
+ year = {1993},
+ address = {Paris, France}
}
@INPROCEEDINGS{RoMo93,
-author = {D. Rodrigues and P. Mora},
-title = {Implementation of the free surface boundary condition in 2-{D} and
-3-{D} elastic cases},
-booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
-year = {1993},
-pages = {215-217},
-note = {63rd international meeting of the SEG}
+ author = {D. Rodrigues and P. Mora},
+ title = {Implementation of the free surface boundary condition in 2-{D} and
+ 3-{D} elastic cases},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1993},
+ pages = {215-217},
+ note = {63rd international meeting of the SEG}
}
@INPROCEEDINGS{RoMo92,
-author = {D. Rodrigues and P. Mora},
-title = {Analysis of a finite difference solution to 3-{D} elastic wave propagation},
-booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
-year = {1992},
-pages = {1247-1250},
-note = {62nd international meeting of the SEG}
+ author = {D. Rodrigues and P. Mora},
+ title = {Analysis of a finite difference solution to 3-{D} elastic wave propagation},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1992},
+ pages = {1247-1250},
+ note = {62nd international meeting of the SEG}
}
@ARTICLE{RoVaHelene,
-author = {A. A. Rodriguez and A. Valli},
-title = {Domain Decomposition Algorithms for Time-harmonic {M}axwell Equations
-with Damping},
-journal = {Mathematical Modelling and Numerical Analysis},
-year = {2001},
-volume = {35},
-pages = {825-848},
-number = {4}
+ author = {A. A. Rodriguez and A. Valli},
+ title = {Domain Decomposition Algorithms for Time-harmonic {M}axwell Equations
+ with Damping},
+ journal = {Mathematical Modelling and Numerical Analysis},
+ year = {2001},
+ volume = {35},
+ pages = {825-848},
+ number = {4}
}
@ARTICLE{RoLaGaRu04,
-author = {J. M. Rokosky and T. Lay and E. J. Garnero and S. A. Russel},
-title = {High-resolution investigation of shear wave anisotropy in {D}'' beneath
-the {C}ocos plate},
-journal = grl,
-year = {2004},
-volume = {31},
-pages = {L07605},
-doi = {10.1029/2003GL018902}
+ author = {J. M. Rokosky and T. Lay and E. J. Garnero and S. A. Russel},
+ title = {High-resolution investigation of shear wave anisotropy in {D}'' beneath
+ the {C}ocos plate},
+ journal = grl,
+ year = {2004},
+ volume = {31},
+ pages = {L07605},
+ doi = {10.1029/2003GL018902}
}
@ARTICLE{Rol68,
-author = {F. R. {Rollins Jr}},
-title = {Ultrasonic examination of liquid-solid boundaries using a right-angle
-reflector technique},
-journal = jasa,
-year = {1968},
-volume = {44},
-pages = {431-434},
-number = {2}
+ author = {F. R. {Rollins Jr}},
+ title = {Ultrasonic examination of liquid-solid boundaries using a right-angle
+ reflector technique},
+ journal = jasa,
+ year = {1968},
+ volume = {44},
+ pages = {431-434},
+ number = {2}
}
@ARTICLE{RolLimFar68,
-author = {F. R. {Rollins Jr} and T. C. Lim and G. W. Farnell},
-title = {Ultrasonic reflectivity and surface wave phenomena on surfaces of
-copper single crystals},
-journal = {Applied Physics Letters},
-year = {1968},
-volume = {12},
-pages = {236-238},
-number = {7}
+ author = {F. R. {Rollins Jr} and T. C. Lim and G. W. Farnell},
+ title = {Ultrasonic reflectivity and surface wave phenomena on surfaces of
+ copper single crystals},
+ journal = {Applied Physics Letters},
+ year = {1968},
+ volume = {12},
+ pages = {236-238},
+ number = {7}
}
@ARTICLE{Romanowicz08,
-author = {B. Romanowicz},
-title = {Using seismic waves to image {E}arth's internal structure},
-journal = {Nature},
-year = {2008},
-volume = {451},
-pages = {266-268}
+ author = {B. Romanowicz},
+ title = {Using seismic waves to image {E}arth's internal structure},
+ journal = {Nature},
+ year = {2008},
+ volume = {451},
+ pages = {266-268}
}
@ARTICLE{romanowicz1998,
-author = {B. Romanowicz},
-title = {Attenuation tomography of the {E}arth's mantle: a review of current
-status},
-journal = pageoph,
-year = {1998},
-volume = {153},
-pages = {257-272}
+ author = {B. Romanowicz},
+ title = {Attenuation tomography of the {E}arth's mantle: a review of current
+ status},
+ journal = pageoph,
+ year = {1998},
+ volume = {153},
+ pages = {257-272}
}
@ARTICLE{romanowiczgung2002,
-author = {B. Romanowicz and Y. C. Gung},
-title = {Superplumes from the core-mantle boundary to the lithosphere: implications
-for heat flux},
-journal = {Science},
-year = {2002},
-volume = {296},
-pages = {513-516}
+ author = {B. Romanowicz and Y. C. Gung},
+ title = {Superplumes from the core-mantle boundary to the lithosphere: implications
+ for heat flux},
+ journal = {Science},
+ year = {2002},
+ volume = {296},
+ pages = {513-516}
}
@ARTICLE{RoIaPa96,
-author = {C. Ronchi and R. Ianoco and P. S. Paolucci},
-title = {The ``{C}ubed {S}phere'': a new method for the solution of partial
-differential equations in spherical geometry},
-journal = jcp,
-year = {1996},
-volume = {124},
-pages = {93-114}
+ author = {C. Ronchi and R. Ianoco and P. S. Paolucci},
+ title = {The ``{C}ubed {S}phere'': a new method for the solution of partial
+ differential equations in spherical geometry},
+ journal = jcp,
+ year = {1996},
+ volume = {124},
+ pages = {93-114}
}
@INCOLLECTION{RoBoFi05,
-author = {S. Rondenay and M. G. Bostock and K. M. Fischer},
-title = {Multichannel inversion of scattered teleseismic body waves: practical
-considerations},
-booktitle = {Seismic Earth: Array Analysis of Broadband Seismograms},
-publisher = {American Geophysical Union},
-year = {2005},
-editor = {Alan Levander and Guust Nolet},
-volume = {157},
-series = {Geophysical Monograph},
-pages = {187-204},
-address = {Washington DC, USA}
+ author = {S. Rondenay and M. G. Bostock and K. M. Fischer},
+ title = {Multichannel inversion of scattered teleseismic body waves: practical
+ considerations},
+ booktitle = {Seismic Earth: Array Analysis of Broadband Seismograms},
+ publisher = {American Geophysical Union},
+ year = {2005},
+ editor = {Alan Levander and Guust Nolet},
+ volume = {157},
+ series = {Geophysical Monograph},
+ pages = {187-204},
+ address = {Washington DC, USA}
}
@ARTICLE{RoHiRi03,
-author = {S\'everine Rosat and Jacques Hinderer and Luis Rivera},
-title = {First observation of ${}_2{S}_1$ and study of the splitting of the
-football mode ${}_0{S}_2$ after the {J}une 2001 {P}eru earthquake
-of magnitude 8.4},
-journal = grl,
-year = {2003},
-volume = {30},
-pages = {2111},
-number = {21},
-doi = {10.1029/2003GL018304}
+ author = {S\'everine Rosat and Jacques Hinderer and Luis Rivera},
+ title = {First observation of ${}_2{S}_1$ and study of the splitting of the
+ football mode ${}_0{S}_2$ after the {J}une 2001 {P}eru earthquake
+ of magnitude 8.4},
+ journal = grl,
+ year = {2003},
+ volume = {30},
+ pages = {2111},
+ number = {21},
+ doi = {10.1029/2003GL018304}
}
@ARTICLE{RoBeCoKo10,
-author = {Diego Rossinelli and Michael Bergdorf and Georges-Henri Cottet and
-Petros Koumoutsakos},
-title = {{GPU} accelerated simulations of bluff body flows using vortex particle
-methods},
-journal = jcp,
-year = {2010},
-volume = {229},
-pages = {3316-3333},
-number = {9},
-doi = {10.1016/j.jcp.2010.01.004}
+ author = {Diego Rossinelli and Michael Bergdorf and Georges-Henri Cottet and
+ Petros Koumoutsakos},
+ title = {{GPU} accelerated simulations of bluff body flows using vortex particle
+ methods},
+ journal = jcp,
+ year = {2010},
+ volume = {229},
+ pages = {3316-3333},
+ number = {9},
+ doi = {10.1016/j.jcp.2010.01.004}
}
@ARTICLE{Roy08,
-author = {D. Royer},
-title = {Stresses and displacements for some Rayleigh-type surface acoustic
-waves propagating on an anisotropic half space (L)},
-journal = jasa,
-year = {2008},
-volume = {123},
-pages = {599-601},
-number = {2}
+ author = {D. Royer},
+ title = {Stresses and displacements for some Rayleigh-type surface acoustic
+ waves propagating on an anisotropic half space (L)},
+ journal = jasa,
+ year = {2008},
+ volume = {123},
+ pages = {599-601},
+ number = {2}
}
@BOOK{RoyDie96,
-title = {Ondes elastiques dans les solides},
-publisher = {Masson (Paris)},
-year = {1996},
-author = {D. Royer and E. Dieulesaint},
-volume = {1. Propagation libre et guid\'ee}
+ title = {Ondes elastiques dans les solides},
+ publisher = {Masson (Paris)},
+ year = {1996},
+ author = {D. Royer and E. Dieulesaint},
+ volume = {1. Propagation libre et guid\'ee}
}
@ARTICLE{RoyDie84,
-author = {D. Royer and E. Dieulesaint},
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-hexagonal, and cubic crystals},
-journal = jasa,
-year = {1984},
-volume = {76},
-pages = {1438-1444},
-number = {5}
+ author = {D. Royer and E. Dieulesaint},
+ title = {Rayleigh wave velocity and displacement in orthorhombic, tetragonal,
+ hexagonal, and cubic crystals},
+ journal = jasa,
+ year = {1984},
+ volume = {76},
+ pages = {1438-1444},
+ number = {5}
}
@ARTICLE{Rul69,
-author = {B. Rulf},
-title = {Rayleigh waves on curved surfaces},
-journal = jasa,
-year = {1969},
-volume = {45},
-pages = {493-499}
+ author = {B. Rulf},
+ title = {Rayleigh waves on curved surfaces},
+ journal = jasa,
+ year = {1969},
+ volume = {45},
+ pages = {493-499}
}
@INPROCEEDINGS{rumpf_strzodka_2006,
-author = {M. Rumpf and R. Strzodka},
-title = {Graphics {P}rocessor {U}nits: {N}ew prospects for parallel computing},
-booktitle = {Numerical Solution to Partial Differential Equations on Parallel
-Computers},
-year = {2006},
-volume = {51},
-series = {Lecture Notes in Computational Science and Engineering},
-pages = {89-134},
-address = {Germany},
-publisher = {Springer-Verlag}
+ author = {M. Rumpf and R. Strzodka},
+ title = {Graphics {P}rocessor {U}nits: {N}ew prospects for parallel computing},
+ booktitle = {Numerical Solution to Partial Differential Equations on Parallel
+ Computers},
+ year = {2006},
+ volume = {51},
+ series = {Lecture Notes in Computational Science and Engineering},
+ pages = {89-134},
+ address = {Germany},
+ publisher = {Springer-Verlag}
}
@INPROCEEDINGS{Rumpf:2001:NLD,
-author = {Martin Rumpf and Robert Strzodka},
-title = {Nonlinear Diffusion in Graphics Hardware},
-booktitle = {{Proceedings of EG/IEEE TCVG Symposium on Visualization (VisSym '01)}},
-year = {2001},
-pages = {75--84},
-month = may
+ author = {Martin Rumpf and Robert Strzodka},
+ title = {Nonlinear Diffusion in Graphics Hardware},
+ booktitle = {{Proceedings of EG/IEEE TCVG Symposium on Visualization (VisSym '01)}},
+ year = {2001},
+ pages = {75--84},
+ month = may
}
@ARTICLE{RuLaGa99,
-author = {S. A. Russell and T. Lay and E. J. Garnero},
-title = {Small-scale lateral shear velocity and anisotropy heterogeneity near
-the core-mantle boundary beneath the central {P}acific imaged using
-broadband {ScS} waves},
-journal = jgr,
-year = {1999},
-volume = {104},
-pages = {13,183-13,199},
-number = {B6}
+ author = {S. A. Russell and T. Lay and E. J. Garnero},
+ title = {Small-scale lateral shear velocity and anisotropy heterogeneity near
+ the core-mantle boundary beneath the central {P}acific imaged using
+ broadband {ScS} waves},
+ journal = jgr,
+ year = {1999},
+ volume = {104},
+ pages = {13,183-13,199},
+ number = {B6}
}
@ARTICLE{Rya71,
-author = {R. L. Ryan},
-title = {Pulse propagation in a transversely isotropic half-space},
-journal = {Journal of Sound and Vibration},
-year = {1971},
-volume = {14},
-pages = {511-524},
-number = {4}
+ author = {R. L. Ryan},
+ title = {Pulse propagation in a transversely isotropic half-space},
+ journal = {Journal of Sound and Vibration},
+ year = {1971},
+ volume = {14},
+ pages = {511-524},
+ number = {4}
}
@ARTICLE{RyLe83,
-author = {G. Ryskin and L. G. Leal},
-title = {Orthogonal mapping},
-journal = jcp,
-year = {1983},
-volume = {50},
-pages = {71-100}
+ author = {G. Ryskin and L. G. Leal},
+ title = {Orthogonal mapping},
+ journal = jcp,
+ year = {1983},
+ volume = {50},
+ pages = {71-100}
}
@ARTICLE{Ron96,
-author = {E. M. R{\o}nquist},
-title = {Convection treatment using spectral elements of different order},
-journal = {Int. J. Num. Meth. Fluids},
-year = {1996},
-volume = {22},
-pages = {241-264}
+ author = {E. M. R{\o}nquist},
+ title = {Convection treatment using spectral elements of different order},
+ journal = {Int. J. Num. Meth. Fluids},
+ year = {1996},
+ volume = {22},
+ pages = {241-264}
}
@PHDTHESIS{Ron88,
-author = {E. M. R{\o}nquist},
-title = {Optimal spectral element methods for the unsteady three-dimensional
-incompressible {N}avier-{S}tokes equations},
-school = {Massachussets Institute of Technology},
-year = {1988},
-address = {Massachussets}
+ author = {E. M. R{\o}nquist},
+ title = {Optimal spectral element methods for the unsteady three-dimensional
+ incompressible {N}avier-{S}tokes equations},
+ school = {Massachussets Institute of Technology},
+ year = {1988},
+ address = {Massachussets}
}
@INPROCEEDINGS{RoPa88,
-author = {E. M. R{\o}nquist and A. T. Patera},
-title = {A {L}egendre Spectral-Element Method for the Incompressible {N}avier-{S}tokes
-Equations},
-booktitle = {Proc. of the Seventh GAMM Conference on Numerical Methods in Fluid
-Mechanics},
-year = {1988},
-editor = {M. Deville},
-pages = {318-326},
-address = {Louvain-la-Neuve, Belgium}
+ author = {E. M. R{\o}nquist and A. T. Patera},
+ title = {A {L}egendre Spectral-Element Method for the Incompressible {N}avier-{S}tokes
+ Equations},
+ booktitle = {Proc. of the Seventh GAMM Conference on Numerical Methods in Fluid
+ Mechanics},
+ year = {1988},
+ editor = {M. Deville},
+ pages = {318-326},
+ address = {Louvain-la-Neuve, Belgium}
}
@ARTICLE{RoPa87,
-author = {E. M. R{\o}nquist and A. T. Patera},
-title = {A {L}egendre {S}pectral {E}lement Method for the {S}tefan Problem},
-journal = ijnme,
-year = {1987},
-volume = {24},
-pages = {2273-2299}
+ author = {E. M. R{\o}nquist and A. T. Patera},
+ title = {A {L}egendre {S}pectral {E}lement Method for the {S}tefan Problem},
+ journal = ijnme,
+ year = {1987},
+ volume = {24},
+ pages = {2273-2299}
}
@ARTICLE{SuSh03,
-author = {M. P. S\"uss and J. H. Shaw},
-title = {P wave seismic velocity structure derived from sonic logs and industry
-reflection data in the {L}os {A}ngeles basin, {C}alifornia},
-journal = jgr,
-year = {2003},
-volume = {108},
-pages = {2170},
-number = {B3},
-doi = {10.1029/2001JB001628}
+ author = {M. P. S\"uss and J. H. Shaw},
+ title = {P wave seismic velocity structure derived from sonic logs and industry
+ reflection data in the {L}os {A}ngeles basin, {C}alifornia},
+ journal = jgr,
+ year = {2003},
+ volume = {108},
+ pages = {2170},
+ number = {B3},
+ doi = {10.1029/2001JB001628}
}
@INCOLLECTION{San97,
-author = {F. J. S\'anchez-Sesma},
-title = {Strong ground motion and site effects},
-booktitle = {Computer Analysis and Design of Earthquake resistant structures},
-publisher = {Comp. Mech. Publications},
-year = {1997},
-editor = {D.E. Beskos and S.A. Angnostopoulos},
-pages = {201-239},
-address = {Southampton}
+ author = {F. J. S\'anchez-Sesma},
+ title = {Strong ground motion and site effects},
+ booktitle = {Computer Analysis and Design of Earthquake resistant structures},
+ publisher = {Comp. Mech. Publications},
+ year = {1997},
+ editor = {D.E. Beskos and S.A. Angnostopoulos},
+ pages = {201-239},
+ address = {Southampton}
}
@ARTICLE{San83,
-author = {F. J. S\'anchez-Sesma},
-title = {Diffraction of elastic waves by three-dimensional surface irregularities},
-journal = bssa,
-year = {1983},
-volume = {73},
-pages = {1621-1636},
-number = {6}
+ author = {F. J. S\'anchez-Sesma},
+ title = {Diffraction of elastic waves by three-dimensional surface irregularities},
+ journal = bssa,
+ year = {1983},
+ volume = {73},
+ pages = {1621-1636},
+ number = {6}
}
@INPROCEEDINGS{SaBeBi96,
-author = {F. J. S\'anchez-Sesma and R. Benites and J. Bielak},
-title = {The assessment of strong ground motion: what lies ahead?},
-booktitle = {Proceedings of the 11th World Conference on Earthquake Engineering},
-year = {1996},
-pages = {1-19},
-note = {Acapulco, Mexico, June 1996}
+ author = {F. J. S\'anchez-Sesma and R. Benites and J. Bielak},
+ title = {The assessment of strong ground motion: what lies ahead?},
+ booktitle = {Proceedings of the 11th World Conference on Earthquake Engineering},
+ year = {1996},
+ pages = {1-19},
+ note = {Acapulco, Mexico, June 1996}
}
@ARTICLE{SaCa93,
-author = {F. J. S\'anchez-Sesma and M. Campillo},
-title = {Topographic effects for incident {{\it P, SV}} and {R}ayleigh waves},
-journal = {Tectonophysics},
-year = {1993},
-volume = {218},
-pages = {113-125}
+ author = {F. J. S\'anchez-Sesma and M. Campillo},
+ title = {Topographic effects for incident {{\it P, SV}} and {R}ayleigh waves},
+ journal = {Tectonophysics},
+ year = {1993},
+ volume = {218},
+ pages = {113-125}
}
@ARTICLE{SaCa91,
-author = {F. J. S\'anchez-Sesma and M. Campillo},
-title = {Diffraction of {{\it P}}, {{\it SV}} and {R}ayleigh waves by topographic
-features: a boundary integral formulation},
-journal = bssa,
-year = {1991},
-volume = {81},
-pages = {2234-2253}
+ author = {F. J. S\'anchez-Sesma and M. Campillo},
+ title = {Diffraction of {{\it P}}, {{\it SV}} and {R}ayleigh waves by topographic
+ features: a boundary integral formulation},
+ journal = bssa,
+ year = {1991},
+ volume = {81},
+ pages = {2234-2253}
}
@ARTICLE{SaLu96,
-author = {F. J. S\'anchez-Sesma and F. Luz\'on},
-title = {Can horizontal {{\it P}} waves be trapped and resonate in a shallow
-sedimentary basin?},
-journal = gji,
-year = {1996},
-volume = {124},
-pages = {209-214}
+ author = {F. J. S\'anchez-Sesma and F. Luz\'on},
+ title = {Can horizontal {{\it P}} waves be trapped and resonate in a shallow
+ sedimentary basin?},
+ journal = gji,
+ year = {1996},
+ volume = {124},
+ pages = {209-214}
}
@ARTICLE{SaRaCa93,
-author = {F. J. S\'anchez-Sesma and J. Ramos-Martinez and M. Campillo},
-title = {An indirect boundary element method applied to simulate the seismic
-response of alluvial valleys for incident {{\it P, SV}} and {R}ayleigh
-waves},
-journal = eesd,
-year = {1993},
-volume = {22},
-pages = {279-295}
+ author = {F. J. S\'anchez-Sesma and J. Ramos-Martinez and M. Campillo},
+ title = {An indirect boundary element method applied to simulate the seismic
+ response of alluvial valleys for incident {{\it P, SV}} and {R}ayleigh
+ waves},
+ journal = eesd,
+ year = {1993},
+ volume = {22},
+ pages = {279-295}
}
@ARTICLE{SaRo79,
-author = {F. J. S\'anchez-Sesma and E. Rosenblueth},
-title = {Ground motion at canyons of arbitrary shape under incident {{\it
-SH}} waves},
-journal = eesd,
-year = {1979},
-volume = {7},
-pages = {441-450}
+ author = {F. J. S\'anchez-Sesma and E. Rosenblueth},
+ title = {Ground motion at canyons of arbitrary shape under incident {{\it
+ SH}} waves},
+ journal = eesd,
+ year = {1979},
+ volume = {7},
+ pages = {441-450}
}
@ARTICLE{SaKiLeLe95,
-author = {Z. S. Sacks and D. M. Kingsland and R. Lee and J. F. Lee},
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-boundary condition},
-journal = {IEEE transactions on Antennas and Propagation},
-year = {1995},
-volume = {43},
-pages = {1460-1463},
-number = {12}
+ author = {Z. S. Sacks and D. M. Kingsland and R. Lee and J. F. Lee},
+ title = {A {P}erfectly {M}atched anisotropic absorber for use as an absorbing
+ boundary condition},
+ journal = {IEEE transactions on Antennas and Propagation},
+ year = {1995},
+ volume = {43},
+ pages = {1460-1463},
+ number = {12}
}
@ARTICLE{Sad72,
-author = {R. Sadourny},
-title = {Conservative finite-difference approximations of the primitive equations
-on quasi-uniform spherical grids},
-journal = {Monthly Weather Review},
-year = {1972},
-volume = {100},
-pages = {136-144}
+ author = {R. Sadourny},
+ title = {Conservative finite-difference approximations of the primitive equations
+ on quasi-uniform spherical grids},
+ journal = {Monthly Weather Review},
+ year = {1972},
+ volume = {100},
+ pages = {136-144}
}
@ARTICLE{SaBo04,
-author = {Erik H. Saenger and Thomas Bohlen},
-title = {Finite-difference modeling of viscoelastic and anisotropic wave propagation
-using the rotated staggered grid},
-journal = geophysics,
-year = {2004},
-volume = {69},
-pages = {583-591},
-number = {2},
-doi = {10.1190/1.1707078}
+ author = {Erik H. Saenger and Thomas Bohlen},
+ title = {Finite-difference modeling of viscoelastic and anisotropic wave propagation
+ using the rotated staggered grid},
+ journal = geophysics,
+ year = {2004},
+ volume = {69},
+ pages = {583-591},
+ number = {2},
+ doi = {10.1190/1.1707078}
}
@ARTICLE{SaGoSh00,
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-grid},
-journal = {Wave Motion},
-year = {2000},
-volume = {31},
-pages = {77-92(16)},
-number = {1}
+ author = {E. H. Saenger and N. Gold and S. A. Shapiro},
+ title = {Modeling the propagation of elastic waves using a modified finite-difference
+ grid},
+ journal = {Wave Motion},
+ year = {2000},
+ volume = {31},
+ pages = {77-92(16)},
+ number = {1}
}
@ARTICLE{SaSh02,
-author = {E. H. Saenger and S. A. Shapiro},
-title = {Effective velocities in fractured media: a numerical study using
-the rotated staggered finite-difference grid},
-journal = {Geophysical Prospecting},
-year = {2002},
-volume = {50},
-pages = {183-194}
+ author = {E. H. Saenger and S. A. Shapiro},
+ title = {Effective velocities in fractured media: a numerical study using
+ the rotated staggered finite-difference grid},
+ journal = {Geophysical Prospecting},
+ year = {2002},
+ volume = {50},
+ pages = {183-194}
}
@ARTICLE{SaOd93,
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-second-order hyperbolic systems: application to elastodynamics},
-journal = cmame,
-year = {1993},
-volume = {103},
-pages = {187-230}
+ author = {A. Safjan and J. T. Oden},
+ title = {High-order {T}aylor-{G}alerkin and adaptative {\it h-p} methods for
+ second-order hyperbolic systems: application to elastodynamics},
+ journal = cmame,
+ year = {1993},
+ volume = {103},
+ pages = {187-230}
}
@ARTICLE{ks,
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-title = {{$C^1$} splines for interpolation of rapidly varying data},
-journal = {Rocky Mountain J. Math.},
-year = {1974},
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-pages = {239-250}
+ author = {K. Salkauskas},
+ title = {{$C^1$} splines for interpolation of rapidly varying data},
+ journal = {Rocky Mountain J. Math.},
+ year = {1974},
+ volume = {14},
+ pages = {239-250}
}
@ARTICLE{SaKaSaPi01,
-author = {Toshimi Satoh and Hiroshi Kawase and Toshiaki Sato and Arben Pitarka},
-title = {Three-Dimensional Finite-Difference Waveform Modeling of Strong Motions
-Observed in the {S}endai Basin, {J}apan},
-journal = bssa,
-year = {2001},
-volume = {91},
-pages = {365-380}
+ author = {Toshimi Satoh and Hiroshi Kawase and Toshiaki Sato and Arben Pitarka},
+ title = {Three-Dimensional Finite-Difference Waveform Modeling of Strong Motions
+ Observed in the {S}endai Basin, {J}apan},
+ journal = bssa,
+ year = {2001},
+ volume = {91},
+ pages = {365-380}
}
@ARTICLE{SaKoTr10,
-author = {Brian Savage and Dimitri Komatitsch and Jeroen Tromp},
-title = {Effects of {3D} attenuation on seismic wave amplitude and phase measurements},
-journal = bssa,
-year = {2010},
-volume = {100},
-pages = {1241-1251},
-number = {3},
-doi = {10.1785/0120090263}
+ author = {Brian Savage and Dimitri Komatitsch and Jeroen Tromp},
+ title = {Effects of {3D} attenuation on seismic wave amplitude and phase measurements},
+ journal = bssa,
+ year = {2010},
+ volume = {100},
+ pages = {1241-1251},
+ number = {3},
+ doi = {10.1785/0120090263}
}
@INPROCEEDINGS{SavWiTr05,
-author = {Savage, B. and D. A. Wiens and J. Tromp},
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-Zone},
-booktitle = {Expanded abstracts of the American Geophysical Union},
-year = {Fall Meeting 2005},
-note = {abstract T31D-04}
+ author = {Savage, B. and D. A. Wiens and J. Tromp},
+ title = {Effects of 3{D} Velocity and Attenuation in the {T}onga-{F}iji Subduction
+ Zone},
+ booktitle = {Expanded abstracts of the American Geophysical Union},
+ year = {Fall Meeting 2005},
+ note = {abstract T31D-04}
}
@ARTICLE{ScHuYeHu96,
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-based on growth strata},
-journal = {Tectonics},
-year = {1996},
-volume = {15},
-pages = {341-355}
+ author = {C. L. Schneider and C. Hummon and R. S. Yeats and G. J. Huftile},
+ title = {Structural evolution of the northern {L}os {A}ngeles basin, {C}alifornia,
+ based on growth strata},
+ journal = {Tectonics},
+ year = {1996},
+ volume = {15},
+ pages = {341-355}
}
@ARTICLE{ScMu89,
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-journal = geophysics,
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-number = {5}
+ author = {M. Schoenberg and F. Muir},
+ title = {A calculus for finely layered anisotropic media},
+ journal = geophysics,
+ year = {1989},
+ volume = {54},
+ pages = {581-589},
+ number = {5}
}
@INPROCEEDINGS{Schroeder:2009:DEI,
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-title = {{DRAM} errors in the wild: {A} large-scale field study},
-booktitle = {SIGMETRICS/Performance '09: Proceedings of the 2009 Joint International
-Conference on Measurement \& Modeling of Computer Systems},
-year = {2009},
-pages = {193--204},
-month = jun,
-doi = {10.1145/1555349.1555372}
+ author = {Bianca Schroeder and Eduardo Pinheiro and Wolf-Dietrich Weber},
+ title = {{DRAM} errors in the wild: {A} large-scale field study},
+ booktitle = {SIGMETRICS/Performance '09: Proceedings of the 2009 Joint International
+ Conference on Measurement \& Modeling of Computer Systems},
+ year = {2009},
+ pages = {193--204},
+ month = jun,
+ doi = {10.1145/1555349.1555372}
}
@TECHREPORT{Sch03,
-author = {B. Schubert},
-title = {The spectral-element method for seismic wave propagation: theory,
-implementation and comparison to finite-difference methods},
-institution = {University of Munich},
-year = {2003},
-address = {Germany},
-note = {unpublished report, 165 p.}
+ author = {B. Schubert},
+ title = {The spectral-element method for seismic wave propagation: theory,
+ implementation and comparison to finite-difference methods},
+ institution = {University of Munich},
+ year = {2003},
+ address = {Germany},
+ note = {unpublished report, 165 p.}
}
@ARTICLE{Ser04,
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-title = {Double-grid {C}hebyshev spectral elements for acoustic wave modeling},
-journal = {Wave Motion},
-year = {2004},
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+ author = {G. Seriani},
+ title = {Double-grid {C}hebyshev spectral elements for acoustic wave modeling},
+ journal = {Wave Motion},
+ year = {2004},
+ volume = {39},
+ pages = {351-360}
}
@ARTICLE{Ser98,
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-method on a {C}ray {T3E} multiprocessor},
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+ author = {G\'eza Seriani},
+ title = {3-{D} large-scale wave propagation modeling by a spectral element
+ method on a {C}ray {T3E} multiprocessor},
+ journal = cmame,
+ year = {1998},
+ volume = {164},
+ pages = {235-247}
}
@ARTICLE{Ser97,
-author = {G\'eza Seriani},
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-year = {1997},
-volume = {5},
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+ author = {G\'eza Seriani},
+ title = {A parallel spectral element method for acoustic wave modeling},
+ journal = jca,
+ year = {1997},
+ volume = {5},
+ pages = {53-69}
}
@ARTICLE{SeOl08,
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-propagation},
-journal = {Wave Motion},
-year = {2008},
-volume = {45},
-pages = {729-744},
-doi = {10.1016/j.wavemoti.2007.11.007}
+ author = {G. Seriani and S. P. Oliveira},
+ title = {Dispersion analysis of spectral-element methods for elastic wave
+ propagation},
+ journal = {Wave Motion},
+ year = {2008},
+ volume = {45},
+ pages = {729-744},
+ doi = {10.1016/j.wavemoti.2007.11.007}
}
@ARTICLE{SePr94,
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+ author = {G. Seriani and E. Priolo},
+ title = {A spectral element method for acoustic wave simulation in heterogeneous
+ media},
+ journal = {Finite Elements in Analysis and Design},
+ year = {1994},
+ volume = {16},
+ pages = {337-348}
}
@INPROCEEDINGS{SePr91,
-author = {G. Seriani and E. Priolo},
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-year = {1991},
-series = {61st international meeting of the SEG},
-pages = {1561-1564},
-address = {Houston, Texas, USA}
+ author = {G. Seriani and E. Priolo},
+ title = {High-order spectral element method for acoustic wave modeling},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1991},
+ series = {61st international meeting of the SEG},
+ pages = {1561-1564},
+ address = {Houston, Texas, USA}
}
@INPROCEEDINGS{SePrCaPa92,
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-title = {High-order spectral element method for elastic wave modeling},
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-year = {1992},
-series = {62nd international meeting of the SEG},
-pages = {1285-1288},
-address = {New-Orleans, Louisiana, USA}
+ author = {G. Seriani and E. Priolo and J. M. Carcione and E. Padovani},
+ title = {High-order spectral element method for elastic wave modeling},
+ booktitle = {Expanded abstracts of the Soc. Expl. Geophys.},
+ year = {1992},
+ series = {62nd international meeting of the SEG},
+ pages = {1285-1288},
+ address = {New-Orleans, Louisiana, USA}
}
@INPROCEEDINGS{SePrPr95,
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-and numerical aspects of wave propagation},
-year = {1995},
-editor = {G. Cohen},
-pages = {289-298},
-publisher = {SIAM, Philadephia, PA}
+ author = {G. Seriani and E. Priolo and A. Pregarz},
+ title = {Modelling waves in anisotropic media by a spectral element method},
+ booktitle = {Proceedings of the third international conference on mathematical
+ and numerical aspects of wave propagation},
+ year = {1995},
+ editor = {G. Cohen},
+ pages = {289-298},
+ publisher = {SIAM, Philadephia, PA}
}
@ARTICLE{SeOl07,
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-title = {Optimal blended spectral-element operators for acoustic wave modeling},
-journal = geophysics,
-year = {2007},
-volume = {72},
-pages = {SM95-SM106},
-number = {5},
-doi = {10.1190/1.2750715}
+ author = {G{\'e}za Seriani and Saulo P. Oliveira},
+ title = {Optimal blended spectral-element operators for acoustic wave modeling},
+ journal = geophysics,
+ year = {2007},
+ volume = {72},
+ pages = {SM95-SM106},
+ number = {5},
+ doi = {10.1190/1.2750715}
}
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-for subduction zone earthquakes},
-journal = gji,
-year = {2002},
-volume = {151},
-pages = {501-510}
+ author = {Nikolai M. Shapiro and Kim B. Olsen and Shri K. Singh},
+ title = {On the duration of seismic motion incident onto the Valley of {M}exico
+ for subduction zone earthquakes},
+ journal = gji,
+ year = {2002},
+ volume = {151},
+ pages = {501-510}
}
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-anisotropic elastic medium},
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-year = {2007},
-volume = {11},
-pages = {187-197}
+ author = {M. D. Sharma},
+ title = {Spatial dispersion of surface waves at the free surface of a general
+ anisotropic elastic medium},
+ journal = {Journal of Seismology},
+ year = {2007},
+ volume = {11},
+ pages = {187-197}
}
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-sources in the {L}os {A}ngeles metropolitan area},
-booktitle = {SCEC Annual Meeting},
-year = {1999},
-address = {Palm Springs, California}
+ author = {J. H. Shaw and P. S\"uss and C. Rivero},
+ title = {Structural and seismologic investigations of concealed earthquake
+ sources in the {L}os {A}ngeles metropolitan area},
+ booktitle = {SCEC Annual Meeting},
+ year = {1999},
+ address = {Palm Springs, California}
}
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+ author = {J. H. Shaw and P. Shearer},
+ title = {An elusive blind-thrust fault beneath metropolitan {L}os {A}ngeles},
+ journal = {Science},
+ year = {1999},
+ volume = {283},
+ pages = {1516-1518}
}
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+ title = {Earthquake hazards of active blind-thrust faults under the central
+ {L}os {A}ngeles basin, {C}alifornia},
+ journal = jgr,
+ year = {1996},
+ volume = {101},
+ pages = {8623-8642}
}
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-Computation on Graphics Processors},
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-editor = {Timo Aila and Mark Segal},
-pages = {55--64},
-month = aug
+ author = {Jeremy W. Sheaffer and David P. Luebke and Kevin Skadron},
+ title = {A Hardware Redundancy and Recovery Mechanism for Reliable Scientific
+ Computation on Graphics Processors},
+ booktitle = {Graphics Hardware 2007},
+ year = {2007},
+ editor = {Timo Aila and Mark Segal},
+ pages = {55--64},
+ month = aug
}
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+ journal = jgr,
+ year = {1994},
+ volume = {99},
+ pages = {19647-19659}
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+ author = {Dong-Hoon Sheen and Kagan Tuncay and Chang-Eob Baag and Peter J.
+ Ortoleva},
+ title = {Parallel implementation of a velocity-stress staggered-grid finite-difference
+ method for 2-{D} poroelastic wave propagation},
+ journal = {Computers and Geosciences},
+ year = {2006},
+ volume = {32},
+ pages = {1182-1191},
+ doi = {10.1016/j.cageo.2005.11.001}
}
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+ author = {J. F. Shepherd and Ch. R. Johnson},
+ title = {Hexahedral mesh generation constraints},
+ journal = {Engineering with Computers},
+ year = {2008},
+ volume = {24},
+ pages = {195 - 213},
+ number = {3},
+ doi = {10.1007/s00366-008-0091-4}
}
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+ publisher = {Cambridge University Press},
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+ address = {Cambridge}
}
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+ author = {S. J. Sherwin and G. E. Karniadakis},
+ title = {A triangular spectral element method: applications to the incompressible
+ {N}avier-{S}tokes equations},
+ journal = cmame,
+ year = {1995},
+ volume = {123},
+ pages = {189-229}
}
@ARTICLE{Shinguetal2002,
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-year = {2002},
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+ author = {Satoru Shingu and Hiroshi Takahara and Hiromitsu Fuchigami and Masayuki
+ Yamada and Yoshinori Tsuda and Wataru Ohfuchi and Yuji Sasaki and
+ Kazuo Kobayashi and Takashi Hagiwara and Shin-Ichi Habata and Mitsuo
+ Yokokawa and Hiroyuki Itoh and Kiyoshi Otsuka},
+ title = {A 26.58 teraflops Global Atmospheric Simulation with the Spectral
+ Transform Method on the {E}arth {S}imulator},
+ journal = {Proceedings of the ACM/IEEE Supercomputing SC'2002 conference},
+ year = {2002},
+ note = {Published on CD-ROM and at www.sc-conference.org/sc2002}
}
@ARTICLE{Shu02,
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+ author = {A. L. Shuvalov},
+ title = {Erratum: {O}n the theory of plane inhomogeneous waves in anisotropic
+ elastic media},
+ journal = {Wave Motion},
+ year = {2002},
+ volume = {36},
+ pages = {305}
}
@ARTICLE{Shu01,
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-media},
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-year = {2001},
-volume = {34},
-pages = {401-429}
+ author = {A. L. Shuvalov},
+ title = {On the theory of plane inhomogeneous waves in anisotropic elastic
+ media},
+ journal = {Wave Motion},
+ year = {2001},
+ volume = {34},
+ pages = {401-429}
}
@ARTICLE{ShuEve00,
-author = {A. L. Shuvalov and A. G. Every},
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-year = {2000},
-volume = {108},
-pages = {2107-2113},
-number = {5}
+ author = {A. L. Shuvalov and A. G. Every},
+ title = {Transverse curvature of the acoustic slowness surface in crystal
+ symmetry planes and associated phonon focusing cusps},
+ journal = jasa,
+ year = {2000},
+ volume = {108},
+ pages = {2107-2113},
+ number = {5}
}
@ARTICLE{ShuEve97,
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-points of conical degeneracy},
-journal = jasa,
-year = {1997},
-volume = {101},
-pages = {2381-2383},
-number = {4}
+ author = {A. L. Shuvalov and A. G. Every},
+ title = {Shape of the acoustic slowness surface of anisotropic solids near
+ points of conical degeneracy},
+ journal = jasa,
+ year = {1997},
+ volume = {101},
+ pages = {2381-2383},
+ number = {4}
}
@ARTICLE{ShuPonDes05,
-author = {A. L. Shuvalov and O. Poncelet and M. Deschamps},
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-explicit analysis of different types of degeneracy},
-journal = {Mathematics and Mechanics of Solids},
-year = {2005},
-volume = {10},
-pages = {249-279}
+ author = {A. L. Shuvalov and O. Poncelet and M. Deschamps},
+ title = {Plane inhomogeneous elastic waves in transversely isotropic media:
+ explicit analysis of different types of degeneracy},
+ journal = {Mathematics and Mechanics of Solids},
+ year = {2005},
+ volume = {10},
+ pages = {249-279}
}
@ARTICLE{SiLiTrTr07a,
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-year = {2007},
-volume = {168},
-pages = {1153-1174},
-number = {3},
-doi = {10.1111/j.1365-246X.2006.03261.x}
+ author = {Anne Sieminski and Qinya Liu and Jeannot Trampert and Jeroen Tromp},
+ title = {Finite-frequency sensitivity of surface waves to anisotropy based
+ upon adjoint methods},
+ journal = gji,
+ year = {2007},
+ volume = {168},
+ pages = {1153-1174},
+ number = {3},
+ doi = {10.1111/j.1365-246X.2006.03261.x}
}
@ARTICLE{SiLiTrTr07b,
-author = {Anne Sieminski and Qinya Liu and Jeannot Trampert and Jeroen Tromp},
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-journal = gji,
-year = {2007},
-volume = {171},
-pages = {368-389},
-doi = {10.1111/j.1365-246X.2007.03528.x}
+ author = {Anne Sieminski and Qinya Liu and Jeannot Trampert and Jeroen Tromp},
+ title = {Finite-frequency sensitivity of body waves to anisotropy based upon
+ adjoint methods},
+ journal = gji,
+ year = {2007},
+ volume = {171},
+ pages = {368-389},
+ doi = {10.1111/j.1365-246X.2007.03528.x}
}
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}
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+ year = {1992},
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}
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+ author = {F. J. Simons and R. D. van der Hilst and J. P. Montagner and A. Zielhuis},
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+ year = {2002},
+ volume = {151},
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}
@ARTICLE{SiSa77,
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}
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}
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}
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-publisher = {SEG}
+ author = {Thomas M. Smith and S. Scott Collis and Curtis C. Ober and James
+ R. Overfelt and Hans F. Schwaiger},
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+ Galerkin Method},
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+ year = {2010},
+ volume = {29},
+ pages = {2982-2987},
+ number = {1},
+ doi = {10.1190/1.3513466},
+ publisher = {SEG}
}
@ARTICLE{Soa09,
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-journal = ijnme,
-year = {2009},
-volume = {78},
-pages = {1076-1093},
-number = {9},
-doi = {10.1002/nme.2522}
+ author = {Soares Jr., Delfim},
+ title = {Acoustic modelling by {BEM-FEM} coupling procedures taking into account
+ explicit and implicit multi-domain decomposition techniques},
+ journal = ijnme,
+ year = {2009},
+ volume = {78},
+ pages = {1076-1093},
+ number = {9},
+ doi = {10.1002/nme.2522}
}
@ARTICLE{SoMa05,
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-year = {2005},
-volume = {8},
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-number = {2}
+ author = {Soares Jr., D. and W. J. Mansur},
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+ Interaction Problems},
+ journal = cmes,
+ year = {2005},
+ volume = {8},
+ pages = {153-164},
+ number = {2}
}
@ARTICLE{SoMaLi07,
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+ Coupled Procedures},
+ journal = cmes,
+ year = {2007},
+ volume = {17},
+ pages = {19-34},
+ number = {1}
}
@ARTICLE{SoKuGeFlSm87,
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+ author = {J. Sochacki and R. Kubichek and J. George and W. R. Fletcher and
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+ title = {Absorbing boundary conditions and surface waves},
+ journal = geophysics,
+ year = {1987},
+ volume = {52},
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+ number = {1}
}
@ARTICLE{Song95,
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-title = {Depth dependence of anisotropy of {E}arth's inner core},
-journal = jgr,
-year = {1995},
-volume = {100},
-pages = {9805-9816}
+ author = {X. Song and D. V. Helmberger},
+ title = {Depth dependence of anisotropy of {E}arth's inner core},
+ journal = jgr,
+ year = {1995},
+ volume = {100},
+ pages = {9805-9816}
}
@ARTICLE{Song93b,
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-title = {Anisotropy of {E}arth's inner core},
-journal = grl,
-year = {1993},
-volume = {20},
-pages = {2591-2594}
+ author = {X. Song and D. V. Helmberger},
+ title = {Anisotropy of {E}arth's inner core},
+ journal = grl,
+ year = {1993},
+ volume = {20},
+ pages = {2591-2594}
}
@ARTICLE{SoHe96,
-author = {X. J. Song and D. V. Helmberger},
-title = {Source estimation of finite faults from broadband regional networks},
-journal = bssa,
-year = {1996},
-volume = {86},
-pages = {797-804}
+ author = {X. J. Song and D. V. Helmberger},
+ title = {Source estimation of finite faults from broadband regional networks},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {797-804}
}
@ARTICLE{SoRo97,
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-journal = grl,
-year = {1997},
-volume = {23},
-pages = {1-4}
+ author = {A. Souriau and B. Romanowicz},
+ title = {Anisotropy in inner core attenuation: a new type of data to constrain
+ the nature of the solid core},
+ journal = grl,
+ year = {1997},
+ volume = {23},
+ pages = {1-4}
}
@BOOK{Spa65,
-title = {Tensor Calculus},
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-author = {B. Spain},
-address = {New York}
+ title = {Tensor Calculus},
+ publisher = {John Wiley and sons},
+ year = {1965},
+ author = {B. Spain},
+ address = {New York}
}
@ARTICLE{spetzleretal2001,
-author = {J. Spetzler and J. Trampert and R. Snieder},
-title = {{Are we exceeding the limits of the great circle approximation in
-global surface wave tomography?}},
-journal = grl,
-year = {2001},
-volume = {28},
-pages = {2341-2344}
+ author = {J. Spetzler and J. Trampert and R. Snieder},
+ title = {{Are we exceeding the limits of the great circle approximation in
+ global surface wave tomography?}},
+ journal = grl,
+ year = {2001},
+ volume = {28},
+ pages = {2341-2344}
}
@ARTICLE{SpHeLe96,
-author = {P. Spudich and M. Hellweg and W. H. K. Lee},
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-for mainshock motions},
-journal = bssa,
-year = {1996},
-volume = {86},
-pages = {S193-S208},
-number = {1B}
+ author = {P. Spudich and M. Hellweg and W. H. K. Lee},
+ title = {Directional topographic site response at {T}arzana observed in aftershocks
+ of the 1994 {N}orthridge, {C}alifornia, earthquake: implications
+ for mainshock motions},
+ journal = bssa,
+ year = {1996},
+ volume = {86},
+ pages = {S193-S208},
+ number = {1B}
}
@BOOK{Sta92,
-title = {Physics of the Earth},
-publisher = {Brookfield Press},
-year = {1992},
-author = {Franck D. Stacey},
-address = {Brisbane},
-edition = {3rd}
+ title = {Physics of the Earth},
+ publisher = {Brookfield Press},
+ year = {1992},
+ author = {Franck D. Stacey},
+ address = {Brisbane},
+ edition = {3rd}
}
@ARTICLE{Sta88,
-author = {R. Stacey},
-title = {Improved transparent boundary formulations for the elastic wave equation},
-journal = bssa,
-year = {1988},
-volume = {78},
-pages = {2089-2097},
-number = {6}
+ author = {R. Stacey},
+ title = {Improved transparent boundary formulations for the elastic wave equation},
+ journal = bssa,
+ year = {1988},
+ volume = {78},
+ pages = {2089-2097},
+ number = {6}
}
@ARTICLE{StKeOwBlStSh10,
-author = {M. L. Staten and R. A. Kerr and S. J. Owen and T. D. Blacker and
-M. Stupazzini and K. Shimada},
-title = {Unconstrained plastering---Hexahedral mesh generation via advancing-front
-geometry decomposition},
-journal = {International Journal for Numerical Methods in Engineering},
-year = {2010},
-volume = {81},
-pages = {135-171}
+ author = {M. L. Staten and R. A. Kerr and S. J. Owen and T. D. Blacker and
+ M. Stupazzini and K. Shimada},
+ title = {Unconstrained plastering---Hexahedral mesh generation via advancing-front
+ geometry decomposition},
+ journal = {International Journal for Numerical Methods in Engineering},
+ year = {2010},
+ volume = {81},
+ pages = {135-171}
}
@ARTICLE{Ste76,
-author = {G.I. Stegeman},
-title = {Normal-mode surface waves in pseudo-branch on (001) plane of gallium
-arsenide},
-journal = {Journal of Applied Physics},
-year = {1976},
-volume = {47},
-pages = {1712-1713}
+ author = {G.I. Stegeman},
+ title = {Normal-mode surface waves in pseudo-branch on (001) plane of gallium
+ arsenide},
+ journal = {Journal of Applied Physics},
+ year = {1976},
+ volume = {47},
+ pages = {1712-1713}
}
@TECHREPORT{Ste00,
-author = {T. L. Sterling},
-title = {Petaflops Computing: looking Back at the Future},
-institution = {California Institute of Technology},
-year = {2000},
-address = {Pasadena, California},
-note = {presented at the Supercomputing'2000 conference, Dallas, Texas, Nov.
-2000}
+ author = {T. L. Sterling},
+ title = {Petaflops Computing: looking Back at the Future},
+ institution = {California Institute of Technology},
+ year = {2000},
+ address = {Pasadena, California},
+ note = {presented at the Supercomputing'2000 conference, Dallas, Texas, Nov.
+ 2000}
}
@BOOK{StMe95,
-title = {Enabling technologies for {P}etaflops computing},
-publisher = {MIT Press},
-year = {1995},
-author = {T. L. Sterling and P. C. Messina},
-address = {Cambridge}
+ title = {Enabling technologies for {P}etaflops computing},
+ publisher = {MIT Press},
+ year = {1995},
+ author = {T. L. Sterling and P. C. Messina},
+ address = {Cambridge}
}
@BOOK{StSaBeSa99,
-title = {How to build a {B}eowulf, a guide to the implementation and application
-of {PC} clusters},
-publisher = {MIT Press},
-year = {1999},
-author = {T. L. Sterling and J. Salmon and D. J. Becker and D. F. Savarese},
-address = {Cambridge}
+ title = {How to build a {B}eowulf, a guide to the implementation and application
+ of {PC} clusters},
+ publisher = {MIT Press},
+ year = {1999},
+ author = {T. L. Sterling and J. Salmon and D. J. Becker and D. F. Savarese},
+ address = {Cambridge}
}
@ARTICLE{StMcShDa93,
-author = {J. L. Stevens and K. L. McLaughlin and B. Shkoller and S. M. Day},
-title = {2-{D} axisymmetric calculations of surface waves generated by an
-explosion in an island, mountain and sedimentary basin},
-journal = gji,
-year = {1993},
-volume = {114},
-pages = {548-560}
+ author = {J. L. Stevens and K. L. McLaughlin and B. Shkoller and S. M. Day},
+ title = {2-{D} axisymmetric calculations of surface waves generated by an
+ explosion in an island, mountain and sedimentary basin},
+ journal = gji,
+ year = {1993},
+ volume = {114},
+ pages = {548-560}
}
@ARTICLE{StAnDrLaRo99,
-author = {C. Stidham and M. Antolik and D. Dreger and S. Larsen and B. Romanowicz},
-title = {Three-dimensional Structure Influences on the Strong Motion Wavefield
-of the 1989 {L}oma {P}rieta Earthquake},
-journal = bssa,
-year = {1999},
-volume = {89},
-pages = {1184-1202}
+ author = {C. Stidham and M. Antolik and D. Dreger and S. Larsen and B. Romanowicz},
+ title = {Three-dimensional Structure Influences on the Strong Motion Wavefield
+ of the 1989 {L}oma {P}rieta Earthquake},
+ journal = bssa,
+ year = {1999},
+ volume = {89},
+ pages = {1184-1202}
}
@INPROCEEDINGS{StSuSh01,
-author = {C. Stidham and M. P. S\"uss and J. H. Shaw},
-title = {3{D} density and velocity model of the {L}os {A}ngeles basin},
-booktitle = {Geological Society of America 2001 annual meeting abstracts},
-year = {2001},
-volume = {33},
-pages = {299},
-publisher = {Geological Society of America}
+ author = {C. Stidham and M. P. S\"uss and J. H. Shaw},
+ title = {3{D} density and velocity model of the {L}os {A}ngeles basin},
+ booktitle = {Geological Society of America 2001 annual meeting abstracts},
+ year = {2001},
+ volume = {33},
+ pages = {299},
+ publisher = {Geological Society of America}
}
@ARTICLE{Stone:2007:AMM,
-author = {John E. Stone and James C. Phillips and Peter L. Freddolino and David
+ author = {John E. Stone and James C. Phillips and Peter L. Freddolino and David
J. Hardy and Leonardo G. Trabuco and Klaus Schulten},
title = {Accelerating molecular modeling applications with graphics processors},
journal = {Journal of Computational Chemistry},
@@ -13851,16 +13913,6 @@
pages = {1-16}
}
- at ARTICLE{Mat11,
- author = {Ren\'e Matzen},
- title = {An efficient finite element time-domain formulation for the elastic second-order wave equation: {A} non-split complex frequency shifted convolutional {PML}},
- journal = ijnme,
- year = {2011},
- volume = {999999},
- pages = {999998-999999},
-doi = {10.1002/nme.3205}
-}
-
@BOOK{ZiTa89,
title = {The finite element method: v.2, solid and fluid mechanics},
publisher = {McGraw-Hill},
@@ -13945,14 +13997,13 @@
less than plus or minus one~second}
}
- at article{AuHoVaCe11,
-author = {Aubry, R. and Houzeaux, G. and V\'azquez, M. and Cela, J. M.},
-title = {Some useful strategies for unstructured edge-based solvers on shared memory machines},
-journal = ijnme,
-volume = {85},
-number = {5},
-doi = {10.1002/nme.2973},
-pages = {537-561},
-year = {2011},
+
+ at article{Maggi2009,
+ AUTHOR = {A. Maggi and C. Tape and M. Chen and D. Chao and J. Tromp},
+ TITLE = {{An automated time-window selection algorithm for seismic tomography}},
+ JOURNAL = gji,
+ VOLUME = {178},
+ PAGES = {257-281},
+ YEAR = {2009}
}
Modified: seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.pdf
===================================================================
--- seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.pdf 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.pdf 2012-01-13 17:53:28 UTC (rev 19356)
@@ -22678,13 +22678,12 @@
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trailer
<< /Size 2807
/Root 2805 0 R
/Info 2806 0 R
-/ID [<69CCCDE2E2DEBBB9B5F232E3AC5694C3> <69CCCDE2E2DEBBB9B5F232E3AC5694C3>] >>
+/ID [<E188706520E1E73D931CB6C6C62EE973> <E188706520E1E73D931CB6C6C62EE973>] >>
startxref
-2292073
+2292076
%%EOF
Modified: seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_energy.f90
===================================================================
--- seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_energy.f90 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_energy.f90 2012-01-13 17:53:28 UTC (rev 19356)
@@ -126,8 +126,8 @@
real(kind=CUSTOM_REAL) :: xixl,xizl,gammaxl,gammazl,jacobianl
real(kind=CUSTOM_REAL) :: kinetic_energy,potential_energy
- real(kind=CUSTOM_REAL) :: cpl,csl,rhol,mul_relaxed,lambdal_relaxed, &
- lambdalplus2mul_relaxed,kappal
+ real(kind=CUSTOM_REAL) :: cpl,csl,rhol,mul_unrelaxed_elastic,lambdal_unrelaxed_elastic, &
+ lambdaplus2mu_unrelaxed_elastic,kappal
real(kind=CUSTOM_REAL) :: mul_s,kappal_s,rhol_s
real(kind=CUSTOM_REAL) :: kappal_f,rhol_f
real(kind=CUSTOM_REAL) :: mul_fr,kappal_fr,phil,tortl
@@ -151,9 +151,9 @@
endif
! get relaxed elastic parameters of current spectral element
- lambdal_relaxed = poroelastcoef(1,1,kmato(ispec))
- mul_relaxed = poroelastcoef(2,1,kmato(ispec))
- lambdalplus2mul_relaxed = poroelastcoef(3,1,kmato(ispec))
+ lambdal_unrelaxed_elastic = poroelastcoef(1,1,kmato(ispec))
+ mul_unrelaxed_elastic = poroelastcoef(2,1,kmato(ispec))
+ lambdaplus2mu_unrelaxed_elastic = poroelastcoef(3,1,kmato(ispec))
rhol = density(1,kmato(ispec))
! double loop over GLL points
@@ -165,9 +165,9 @@
cpl = vpext(i,j,ispec)
csl = vsext(i,j,ispec)
rhol = rhoext(i,j,ispec)
- mul_relaxed = rhol*csl*csl
- lambdal_relaxed = rhol*cpl*cpl - TWO*mul_relaxed
- lambdalplus2mul_relaxed = lambdal_relaxed + TWO*mul_relaxed
+ mul_unrelaxed_elastic = rhol*csl*csl
+ lambdal_unrelaxed_elastic = rhol*cpl*cpl - TWO*mul_unrelaxed_elastic
+ lambdaplus2mu_unrelaxed_elastic = lambdal_unrelaxed_elastic + TWO*mul_unrelaxed_elastic
endif
! derivative along x and along z
@@ -206,10 +206,10 @@
! compute potential energy
potential_energy = potential_energy &
- + (lambdalplus2mul_relaxed*dux_dxl**2 &
- + lambdalplus2mul_relaxed*duz_dzl**2 &
- + two*lambdal_relaxed*dux_dxl*duz_dzl &
- + mul_relaxed*(dux_dzl + duz_dxl)**2)*wxgll(i)*wzgll(j)*jacobianl / TWO
+ + (lambdaplus2mu_unrelaxed_elastic*dux_dxl**2 &
+ + lambdaplus2mu_unrelaxed_elastic*duz_dzl**2 &
+ + two*lambdal_unrelaxed_elastic*dux_dxl*duz_dzl &
+ + mul_unrelaxed_elastic*(dux_dzl + duz_dxl)**2)*wxgll(i)*wzgll(j)*jacobianl / TWO
enddo
enddo
@@ -219,7 +219,7 @@
!---
elseif(poroelastic(ispec)) then
- ! get relaxed elastic parameters of current spectral element
+ ! get unrelaxed elastic parameters of current spectral element
!for now replaced by solid, fluid, and frame parameters of current spectral element
phil = porosity(kmato(ispec))
tortl = tortuosity(kmato(ispec))
@@ -361,11 +361,11 @@
ispec,numat,kmato,density,rhoext,assign_external_model)
! get density of current spectral element
- lambdal_relaxed = poroelastcoef(1,1,kmato(ispec))
- mul_relaxed = poroelastcoef(2,1,kmato(ispec))
+ lambdal_unrelaxed_elastic = poroelastcoef(1,1,kmato(ispec))
+ mul_unrelaxed_elastic = poroelastcoef(2,1,kmato(ispec))
rhol = density(1,kmato(ispec))
- kappal = lambdal_relaxed + TWO*mul_relaxed/3._CUSTOM_REAL
- cpl = sqrt((kappal + 4._CUSTOM_REAL*mul_relaxed/3._CUSTOM_REAL)/rhol)
+ kappal = lambdal_unrelaxed_elastic + TWO*mul_unrelaxed_elastic/3._CUSTOM_REAL
+ cpl = sqrt((kappal + 4._CUSTOM_REAL*mul_unrelaxed_elastic/3._CUSTOM_REAL)/rhol)
! double loop over GLL points
do j = 1,NGLLZ
Modified: seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_poro_fluid.f90
===================================================================
--- seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_poro_fluid.f90 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_poro_fluid.f90 2012-01-13 17:53:28 UTC (rev 19356)
@@ -124,7 +124,7 @@
double precision, dimension(NGLLX,NGLLZ,nspec) :: rz_viscous
double precision :: theta_e,theta_s
logical ATTENUATION_PORO_FLUID_PART
- double precision, dimension(3):: bl_unrelaxed,bl_relaxed
+ double precision, dimension(3):: bl_relaxed_viscoelastic,bl_unrelaxed_elastic
! derivatives of Lagrange polynomials
real(kind=CUSTOM_REAL), dimension(NGLLX,NGLLX) :: hprime_xx,hprimewgll_xx
@@ -169,7 +169,7 @@
real(kind=CUSTOM_REAL) :: xixl,xizl,gammaxl,gammazl,jacobianl
! material properties of the poroelastic medium
- real(kind=CUSTOM_REAL) :: mul_unrelaxed,lambdal_unrelaxed,lambdalplus2mul_unrelaxed
+ real(kind=CUSTOM_REAL) :: mul_relaxed_viscoelastic,lambdal_relaxed_viscoelastic,lambdalplus2mul_relaxed_viscoelastic
real(kind=CUSTOM_REAL) :: mul_s,kappal_s,rhol_s
real(kind=CUSTOM_REAL) :: etal_f,kappal_f,rhol_f
real(kind=CUSTOM_REAL) :: mul_fr,kappal_fr,phil,tortl,viscodampx,viscodampz
@@ -322,20 +322,30 @@
! J. M. Carcione, D. Kosloff and R. Kosloff, Wave propagation simulation in a linear
! viscoelastic medium, Geophysical Journal International, vol. 95, p. 597-611 (1988).
-! compute unrelaxed elastic coefficients from formulas in Carcione 1993 page 111
- lambdal_unrelaxed = (lambdal_G + mul_G) - mul_G * Mu_nu2(i,j,ispec)
- mul_unrelaxed = mul_G * Mu_nu2(i,j,ispec)
- lambdalplus2mul_unrelaxed = lambdal_unrelaxed + TWO*mul_unrelaxed
+! When implementing viscoelasticity according to Carcione 1993 paper, the attenuation is
+! non-causal rather than causal. We fixed the problem by using equations in Carcione's
+! 2004 paper and his 2007 book.
-! compute the stress using the unrelaxed Lame parameters (Carcione 1993, page 111)
- sigma_xx = lambdalplus2mul_unrelaxed*dux_dxl + lambdal_unrelaxed*duz_dzl + C_biot*(dwx_dxl + dwz_dzl)
- sigma_xz = mul_unrelaxed*(duz_dxl + dux_dzl)
- sigma_zz = lambdalplus2mul_unrelaxed*duz_dzl + lambdal_unrelaxed*dux_dxl + C_biot*(dwx_dxl + dwz_dzl)
+!J. M. Carcione, H B. Helle, The physics and simulation of wave propagation at the ocean
+! bottom, Geophysics, vol. 69(3), p. 825-839, 2004
+!J. M. Carcione, Wave fields in real media: wave propagation in anisotropic, anelastic
+! and porous media, Elsevier, p. 124-125, 2007
+
+! compute unrelaxed elastic coefficients from formulas in Carcione 2007 page 125
+ lambdal_relaxed_viscoelastic = (lambdal_G + mul_G) - mul_G / Mu_nu2(i,j,ispec)
+ mul_relaxed_viscoelastic = mul_G / Mu_nu2(i,j,ispec)
+ lambdalplus2mul_relaxed_viscoelastic = lambdal_relaxed_viscoelastic + TWO*mul_relaxed_viscoelastic
+
+! compute the stress using the unrelaxed Lame parameters (Carcione 2007 page 125)
+ sigma_xx = (lambdal_G + 2.0 * mul_G)*dux_dxl + mul_G*duz_dzl + C_biot*(dwx_dxl + dwz_dzl)
+ sigma_xz = mul_G*(duz_dxl + dux_dzl)
+ sigma_zz = (lambdal_G + 2.0 * mul_G)*duz_dzl + mul_G*dux_dxl + C_biot*(dwx_dxl + dwz_dzl)
+
sigmap = C_biot*(dux_dxl + duz_dzl) + M_biot*(dwx_dxl + dwz_dzl)
-! add the memory variables using the relaxed parameters (Carcione 1993, page 111)
-! beware: there is a bug in Carcione's equation (2c) for sigma_zz, we fixed it in the code below
+! add the memory variables using the relaxed parameters (Carcione 2007 page 125)
+! beware: there is a bug in Carcione's equation (2c) of his 1993 paper for sigma_zz, we fixed it in the code below
e11_sum = 0._CUSTOM_REAL
e13_sum = 0._CUSTOM_REAL
@@ -348,9 +358,9 @@
! frame modulus (in compute_forces_poro_solid.f90), which Christina Morency noted
! mul_fr, which is in her case equivalent to the solid phase shear
! modulus, and whose value is entered in Par_file for example
- sigma_xx = sigma_xx + TWO * mul_G * e11_sum
- sigma_xz = sigma_xz + mul_G * e13_sum
- sigma_zz = sigma_zz - TWO * mul_G * e11_sum
+ sigma_xx = sigma_xx + TWO * mul_relaxed_viscoelastic * e11_sum
+ sigma_xz = sigma_xz + mul_relaxed_viscoelastic * e13_sum
+ sigma_zz = sigma_zz - TWO * mul_relaxed_viscoelastic * e11_sum
else
@@ -475,14 +485,14 @@
endif
! relaxed viscous coef
- bl_relaxed(1) = etal_f*invpermlxx
- bl_relaxed(2) = etal_f*invpermlxz
- bl_relaxed(3) = etal_f*invpermlzz
+ bl_unrelaxed_elastic(1) = etal_f*invpermlxx
+ bl_unrelaxed_elastic(2) = etal_f*invpermlxz
+ bl_unrelaxed_elastic(3) = etal_f*invpermlzz
if(ATTENUATION_PORO_FLUID_PART) then
- bl_unrelaxed(1) = etal_f*invpermlxx*theta_e/theta_s
- bl_unrelaxed(2) = etal_f*invpermlxz*theta_e/theta_s
- bl_unrelaxed(3) = etal_f*invpermlzz*theta_e/theta_s
+ bl_relaxed_viscoelastic(1) = etal_f*invpermlxx*theta_e/theta_s
+ bl_relaxed_viscoelastic(2) = etal_f*invpermlxz*theta_e/theta_s
+ bl_relaxed_viscoelastic(3) = etal_f*invpermlzz*theta_e/theta_s
endif
do j = 1,NGLLZ
@@ -492,14 +502,14 @@
if(ATTENUATION_PORO_FLUID_PART) then
! compute the viscous damping term with the unrelaxed viscous coef and add memory variable
- viscodampx = velocw_poroelastic(1,iglob)*bl_unrelaxed(1) + velocw_poroelastic(2,iglob)*bl_unrelaxed(2)&
+ viscodampx = velocw_poroelastic(1,iglob)*bl_relaxed_viscoelastic(1) + velocw_poroelastic(2,iglob)*bl_relaxed_viscoelastic(2)&
- rx_viscous(i,j,ispec)
- viscodampz = velocw_poroelastic(1,iglob)*bl_unrelaxed(2) + velocw_poroelastic(2,iglob)*bl_unrelaxed(3)&
+ viscodampz = velocw_poroelastic(1,iglob)*bl_relaxed_viscoelastic(2) + velocw_poroelastic(2,iglob)*bl_relaxed_viscoelastic(3)&
- rz_viscous(i,j,ispec)
else
! no viscous attenuation
- viscodampx = velocw_poroelastic(1,iglob)*bl_relaxed(1) + velocw_poroelastic(2,iglob)*bl_relaxed(2)
- viscodampz = velocw_poroelastic(1,iglob)*bl_relaxed(2) + velocw_poroelastic(2,iglob)*bl_relaxed(3)
+ viscodampx = velocw_poroelastic(1,iglob)*bl_unrelaxed_elastic(1) + velocw_poroelastic(2,iglob)*bl_unrelaxed_elastic(2)
+ viscodampz = velocw_poroelastic(1,iglob)*bl_unrelaxed_elastic(2) + velocw_poroelastic(2,iglob)*bl_unrelaxed_elastic(3)
endif
accelw_poroelastic(1,iglob) = accelw_poroelastic(1,iglob) - wxgll(i)*wzgll(j)*jacobian(i,j,ispec)*&
Modified: seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_poro_solid.f90
===================================================================
--- seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_poro_solid.f90 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_poro_solid.f90 2012-01-13 17:53:28 UTC (rev 19356)
@@ -124,7 +124,7 @@
double precision, dimension(NGLLX,NGLLZ,nspec) :: rz_viscous
double precision :: theta_e,theta_s
logical ATTENUATION_PORO_FLUID_PART
- double precision, dimension(3):: bl_unrelaxed,bl_relaxed
+ double precision, dimension(3):: bl_relaxed_viscoelastic,bl_unrelaxed_elastic
! derivatives of Lagrange polynomials
real(kind=CUSTOM_REAL), dimension(NGLLX,NGLLX) :: hprime_xx,hprimewgll_xx
@@ -171,7 +171,7 @@
real(kind=CUSTOM_REAL) :: xixl,xizl,gammaxl,gammazl,jacobianl
! material properties of the poroelastic medium
- real(kind=CUSTOM_REAL) :: mul_unrelaxed,lambdal_unrelaxed,lambdalplus2mul_unrelaxed
+ real(kind=CUSTOM_REAL) :: mul_relaxed_viscoelastic,lambdal_relaxed_viscoelastic,lambdalplus2mul_relaxed_viscoelastic
real(kind=CUSTOM_REAL) :: mul_s,kappal_s,rhol_s
real(kind=CUSTOM_REAL) :: etal_f,kappal_f,rhol_f
real(kind=CUSTOM_REAL) :: mul_fr,kappal_fr,phil,tortl,viscodampx,viscodampz
@@ -323,20 +323,29 @@
! J. M. Carcione, D. Kosloff and R. Kosloff, Wave propagation simulation in a linear
! viscoelastic medium, Geophysical Journal International, vol. 95, p. 597-611 (1988).
-! compute unrelaxed elastic coefficients from formulas in Carcione 1993 page 111
- lambdal_unrelaxed = (lambdal_G + mul_G) - mul_G * Mu_nu2(i,j,ispec)
- mul_unrelaxed = mul_G * Mu_nu2(i,j,ispec)
- lambdalplus2mul_unrelaxed = lambdal_unrelaxed + TWO*mul_unrelaxed
+! When implementing viscoelasticity according to Carcione 1993 paper, the attenuation is
+! non-causal rather than causal. We fixed the problem by using equations in Carcione's
+! 2004 paper and his 2007 book.
-! compute the stress using the unrelaxed Lame parameters (Carcione 1993, page 111)
- sigma_xx = lambdalplus2mul_unrelaxed*dux_dxl + lambdal_unrelaxed*duz_dzl + C_biot*(dwx_dxl + dwz_dzl)
- sigma_xz = mul_unrelaxed*(duz_dxl + dux_dzl)
- sigma_zz = lambdalplus2mul_unrelaxed*duz_dzl + lambdal_unrelaxed*dux_dxl + C_biot*(dwx_dxl + dwz_dzl)
+!J. M. Carcione, H B. Helle, The physics and simulation of wave propagation at the ocean
+! bottom, Geophysics, vol. 69(3), p. 825-839, 2004
+!J. M. Carcione, Wave fields in real media: wave propagation in anisotropic, anelastic
+! and porous media, Elsevier, p. 124-125, 2007
+! compute unrelaxed elastic coefficients from formulas in Carcione 2007 page 125
+ lambdal_relaxed_viscoelastic = (lambdal_G + mul_G) - mul_G / Mu_nu2(i,j,ispec)
+ mul_relaxed_viscoelastic = mul_G / Mu_nu2(i,j,ispec)
+ lambdalplus2mul_relaxed_viscoelastic = lambdal_relaxed_viscoelastic + TWO*mul_relaxed_viscoelastic
+
+! compute the stress using the unrelaxed Lame parameters (Carcione 2007 page 125)
+ sigma_xx = (lambdal_G + 2.0*mul_G)*dux_dxl + lambdal_G*duz_dzl + C_biot*(dwx_dxl + dwz_dzl)
+ sigma_xz = mul_G*(duz_dxl + dux_dzl)
+ sigma_zz = (lambdal_G + 2.0*mul_G)*duz_dzl + lambdal_G*dux_dxl + C_biot*(dwx_dxl + dwz_dzl)
+
sigmap = C_biot*(dux_dxl + duz_dzl) + M_biot*(dwx_dxl + dwz_dzl)
-! add the memory variables using the relaxed parameters (Carcione 1993, page 111)
-! beware: there is a bug in Carcione's equation (2c) for sigma_zz, we fixed it in the code below
+! add the memory variables using the relaxed parameters (Carcione 2007 page 125)
+! beware: there is a bug in Carcione's equation (2c) of his 1993 paper for sigma_zz, we fixed it in the code below
e11_sum = 0._CUSTOM_REAL
e13_sum = 0._CUSTOM_REAL
@@ -349,9 +358,9 @@
! frame modulus (in compute_forces_poro_solid.f90), which Christina Morency noted
! mul_fr, which is in her case equivalent to the solid phase shear
! modulus, and whose value is entered in Par_file for example
- sigma_xx = sigma_xx + TWO * mul_G * e11_sum
- sigma_xz = sigma_xz + mul_G * e13_sum
- sigma_zz = sigma_zz - TWO * mul_G * e11_sum
+ sigma_xx = sigma_xx + TWO * mul_relaxed_viscoelastic * e11_sum
+ sigma_xz = sigma_xz + mul_relaxed_viscoelastic * e13_sum
+ sigma_zz = sigma_zz - TWO * mul_relaxed_viscoelastic * e11_sum
else
@@ -495,14 +504,14 @@
endif
! relaxed viscous coef
- bl_relaxed(1) = etal_f*invpermlxx
- bl_relaxed(2) = etal_f*invpermlxz
- bl_relaxed(3) = etal_f*invpermlzz
+ bl_unrelaxed_elastic(1) = etal_f*invpermlxx
+ bl_unrelaxed_elastic(2) = etal_f*invpermlxz
+ bl_unrelaxed_elastic(3) = etal_f*invpermlzz
if(ATTENUATION_PORO_FLUID_PART) then
- bl_unrelaxed(1) = etal_f*invpermlxx*theta_e/theta_s
- bl_unrelaxed(2) = etal_f*invpermlxz*theta_e/theta_s
- bl_unrelaxed(3) = etal_f*invpermlzz*theta_e/theta_s
+ bl_relaxed_viscoelastic(1) = etal_f*invpermlxx*theta_e/theta_s
+ bl_relaxed_viscoelastic(2) = etal_f*invpermlxz*theta_e/theta_s
+ bl_relaxed_viscoelastic(3) = etal_f*invpermlzz*theta_e/theta_s
endif
do j = 1,NGLLZ
@@ -512,14 +521,14 @@
if(ATTENUATION_PORO_FLUID_PART) then
! compute the viscous damping term with the unrelaxed viscous coef and add memory variable
- viscodampx = velocw_poroelastic(1,iglob)*bl_unrelaxed(1) + velocw_poroelastic(2,iglob)*bl_unrelaxed(2)&
+ viscodampx = velocw_poroelastic(1,iglob)*bl_relaxed_viscoelastic(1) + velocw_poroelastic(2,iglob)*bl_relaxed_viscoelastic(2)&
- rx_viscous(i,j,ispec)
- viscodampz = velocw_poroelastic(1,iglob)*bl_unrelaxed(2) + velocw_poroelastic(2,iglob)*bl_unrelaxed(3)&
+ viscodampz = velocw_poroelastic(1,iglob)*bl_relaxed_viscoelastic(2) + velocw_poroelastic(2,iglob)*bl_relaxed_viscoelastic(3)&
- rz_viscous(i,j,ispec)
else
! no viscous attenuation
- viscodampx = velocw_poroelastic(1,iglob)*bl_relaxed(1) + velocw_poroelastic(2,iglob)*bl_relaxed(2)
- viscodampz = velocw_poroelastic(1,iglob)*bl_relaxed(2) + velocw_poroelastic(2,iglob)*bl_relaxed(3)
+ viscodampx = velocw_poroelastic(1,iglob)*bl_unrelaxed_elastic(1) + velocw_poroelastic(2,iglob)*bl_unrelaxed_elastic(2)
+ viscodampz = velocw_poroelastic(1,iglob)*bl_unrelaxed_elastic(2) + velocw_poroelastic(2,iglob)*bl_unrelaxed_elastic(3)
endif
accels_poroelastic(1,iglob) = accels_poroelastic(1,iglob) + phil/tortl*wxgll(i)*wzgll(j)*jacobian(i,j,ispec)*&
Modified: seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_viscoelastic.f90
===================================================================
--- seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_viscoelastic.f90 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_forces_viscoelastic.f90 2012-01-13 17:53:28 UTC (rev 19356)
@@ -155,8 +155,8 @@
real(kind=CUSTOM_REAL) :: xixl,xizl,gammaxl,gammazl,jacobianl
! material properties of the elastic medium
- real(kind=CUSTOM_REAL) :: mul_relaxed,lambdal_relaxed,lambdalplus2mul_relaxed,kappal,cpl,csl,rhol, &
- lambdal_unrelaxed,mul_unrelaxed,lambdalplus2mul_unrelaxed
+ real(kind=CUSTOM_REAL) :: mul_unrelaxed_elastic,lambdal_unrelaxed_elastic,lambdaplus2mu_unrelaxed_elastic,kappal,cpl,csl,rhol, &
+ lambdal_relaxed_viscoelastic,mul_relaxed_viscoelastic,lambdalplus2mul_relaxed_viscoelastic
! for attenuation
real(kind=CUSTOM_REAL) :: Un,Unp1,tauinv,Sn,Snp1,theta_n,theta_np1,tauinvsquare,tauinvcube,tauinvUn
@@ -219,10 +219,10 @@
!---
if(elastic(ispec)) then
- ! get relaxed elastic parameters of current spectral element
- lambdal_relaxed = poroelastcoef(1,1,kmato(ispec))
- mul_relaxed = poroelastcoef(2,1,kmato(ispec))
- lambdalplus2mul_relaxed = poroelastcoef(3,1,kmato(ispec))
+ ! get unrelaxed elastic parameters of current spectral element
+ lambdal_unrelaxed_elastic = poroelastcoef(1,1,kmato(ispec))
+ mul_unrelaxed_elastic = poroelastcoef(2,1,kmato(ispec))
+ lambdaplus2mu_unrelaxed_elastic = poroelastcoef(3,1,kmato(ispec))
! first double loop over GLL points to compute and store gradients
do j = 1,NGLLZ
@@ -233,9 +233,9 @@
cpl = vpext(i,j,ispec)
csl = vsext(i,j,ispec)
rhol = rhoext(i,j,ispec)
- mul_relaxed = rhol*csl*csl
- lambdal_relaxed = rhol*cpl*cpl - TWO*mul_relaxed
- lambdalplus2mul_relaxed = lambdal_relaxed + TWO*mul_relaxed
+ mul_unrelaxed_elastic = rhol*csl*csl
+ lambdal_unrelaxed_elastic = rhol*cpl*cpl - TWO*mul_unrelaxed_elastic
+ lambdaplus2mu_unrelaxed_elastic = lambdal_unrelaxed_elastic + TWO*mul_unrelaxed_elastic
endif
! derivative along x and along z
@@ -313,18 +313,28 @@
! J. M. Carcione, D. Kosloff and R. Kosloff, Wave propagation simulation in a linear
! viscoelastic medium, Geophysical Journal International, vol. 95, p. 597-611 (1988).
- ! compute unrelaxed elastic coefficients from formulas in Carcione 1993 page 111
- lambdal_unrelaxed = (lambdal_relaxed + mul_relaxed) * Mu_nu1(i,j,ispec) - mul_relaxed * Mu_nu2(i,j,ispec)
- mul_unrelaxed = mul_relaxed * Mu_nu2(i,j,ispec)
- lambdalplus2mul_unrelaxed = lambdal_unrelaxed + TWO*mul_unrelaxed
+ ! When implementing viscoelasticity according to Carcione 1993 paper, the attenuation is
+ ! non-causal rather than causal. We fixed the problem by using equations in Carcione's
+ ! 2004 paper and his 2007 book.
- ! compute the stress using the unrelaxed Lame parameters (Carcione 1993, page 111)
- sigma_xx = lambdalplus2mul_unrelaxed*dux_dxl + lambdal_unrelaxed*duz_dzl
- sigma_xz = mul_unrelaxed*(duz_dxl + dux_dzl)
- sigma_zz = lambdalplus2mul_unrelaxed*duz_dzl + lambdal_unrelaxed*dux_dxl
+ !J. M. Carcione, H B. Helle, The physics and simulation of wave propagation at the ocean
+ ! bottom, Geophysics, vol. 69(3), p. 825-839, 2004
+ !J. M. Carcione, Wave fields in real media: wave propagation in anisotropic, anelastic
+ ! and porous media, Elsevier, p. 124-125, 2007
- ! add the memory variables using the relaxed parameters (Carcione 1993, page 111)
- ! beware: there is a bug in Carcione's equation (2c) for sigma_zz, we fixed it in the code below
+ ! compute unrelaxed elastic coefficients from formulas in Carcione 2007 page 125
+ lambdal_relaxed_viscoelastic = (lambdal_unrelaxed_elastic + mul_unrelaxed_elastic) / Mu_nu1(i,j,ispec) &
+ - mul_unrelaxed_elastic / Mu_nu2(i,j,ispec)
+ mul_relaxed_viscoelastic = mul_unrelaxed_elastic / Mu_nu2(i,j,ispec)
+ lambdalplus2mul_relaxed_viscoelastic = lambdal_relaxed_viscoelastic + TWO*mul_relaxed_viscoelastic
+
+ ! compute the stress using the unrelaxed Lame parameters (Carcione 2007 page 125)
+ sigma_xx = lambdaplus2mu_unrelaxed_elastic*dux_dxl + lambdal_unrelaxed_elastic*duz_dzl
+ sigma_xz = mul_unrelaxed_elastic*(duz_dxl + dux_dzl)
+ sigma_zz = lambdaplus2mu_unrelaxed_elastic*duz_dzl + lambdal_unrelaxed_elastic*dux_dxl
+
+ ! add the memory variables using the relaxed parameters (Carcione 2007 page 125)
+ ! beware: there is a bug in Carcione's equation (2c) of his 1993 paper for sigma_zz, we fixed it in the code below
e1_sum = 0._CUSTOM_REAL
e11_sum = 0._CUSTOM_REAL
e13_sum = 0._CUSTOM_REAL
@@ -335,25 +345,27 @@
e13_sum = e13_sum + e13(i,j,ispec,i_sls)
enddo
- sigma_xx = sigma_xx + (lambdal_relaxed + mul_relaxed) * e1_sum + TWO * mul_relaxed * e11_sum
- sigma_xz = sigma_xz + mul_relaxed * e13_sum
- sigma_zz = sigma_zz + (lambdal_relaxed + mul_relaxed) * e1_sum - TWO * mul_relaxed * e11_sum
+ sigma_xx = sigma_xx + (lambdal_relaxed_viscoelastic + mul_relaxed_viscoelastic) * e1_sum &
+ + TWO * mul_relaxed_viscoelastic * e11_sum
+ sigma_xz = sigma_xz + mul_relaxed_viscoelastic * e13_sum
+ sigma_zz = sigma_zz + (lambdal_relaxed_viscoelastic + mul_relaxed_viscoelastic) * e1_sum &
+ - TWO * mul_relaxed_viscoelastic * e11_sum
else
! no attenuation
- sigma_xx = lambdalplus2mul_relaxed*dux_dxl + lambdal_relaxed*duz_dzl
- sigma_xy = mul_relaxed*duy_dxl
- sigma_xz = mul_relaxed*(duz_dxl + dux_dzl)
- sigma_zy = mul_relaxed*duy_dzl
- sigma_zz = lambdalplus2mul_relaxed*duz_dzl + lambdal_relaxed*dux_dxl
+ sigma_xx = lambdaplus2mu_unrelaxed_elastic*dux_dxl + lambdal_unrelaxed_elastic*duz_dzl
+ sigma_xy = mul_unrelaxed_elastic*duy_dxl
+ sigma_xz = mul_unrelaxed_elastic*(duz_dxl + dux_dzl)
+ sigma_zy = mul_unrelaxed_elastic*duy_dzl
+ sigma_zz = lambdaplus2mu_unrelaxed_elastic*duz_dzl + lambdal_unrelaxed_elastic*dux_dxl
if(SIMULATION_TYPE == 2) then ! Adjoint calculation, backward wavefield
- b_sigma_xx = lambdalplus2mul_relaxed*b_dux_dxl + lambdal_relaxed*b_duz_dzl
- b_sigma_xy = mul_relaxed*b_duy_dxl
- b_sigma_xz = mul_relaxed*(b_duz_dxl + b_dux_dzl)
- b_sigma_zy = mul_relaxed*b_duy_dzl
- b_sigma_zz = lambdalplus2mul_relaxed*b_duz_dzl + lambdal_relaxed*b_dux_dxl
+ b_sigma_xx = lambdaplus2mu_unrelaxed_elastic*b_dux_dxl + lambdal_unrelaxed_elastic*b_duz_dzl
+ b_sigma_xy = mul_unrelaxed_elastic*b_duy_dxl
+ b_sigma_xz = mul_unrelaxed_elastic*(b_duz_dxl + b_dux_dzl)
+ b_sigma_zy = mul_unrelaxed_elastic*b_duy_dzl
+ b_sigma_zz = lambdaplus2mu_unrelaxed_elastic*b_duz_dzl + lambdal_unrelaxed_elastic*b_dux_dxl
endif
endif
@@ -475,12 +487,12 @@
ispec = numabs(ispecabs)
! get elastic parameters of current spectral element
- lambdal_relaxed = poroelastcoef(1,1,kmato(ispec))
- mul_relaxed = poroelastcoef(2,1,kmato(ispec))
+ lambdal_unrelaxed_elastic = poroelastcoef(1,1,kmato(ispec))
+ mul_unrelaxed_elastic = poroelastcoef(2,1,kmato(ispec))
rhol = density(1,kmato(ispec))
- kappal = lambdal_relaxed + TWO*mul_relaxed/3._CUSTOM_REAL
- cpl = sqrt((kappal + 4._CUSTOM_REAL*mul_relaxed/3._CUSTOM_REAL)/rhol)
- csl = sqrt(mul_relaxed/rhol)
+ kappal = lambdal_unrelaxed_elastic + TWO*mul_unrelaxed_elastic/3._CUSTOM_REAL
+ cpl = sqrt((kappal + 4._CUSTOM_REAL*mul_unrelaxed_elastic/3._CUSTOM_REAL)/rhol)
+ csl = sqrt(mul_unrelaxed_elastic/rhol)
!--- left absorbing boundary
if(codeabs(ILEFT,ispecabs)) then
@@ -498,8 +510,8 @@
call compute_Bielak_conditions(coord,iglob,nglob,it,deltat,dxUx,dxUz,dzUx,dzUz,veloc_horiz,veloc_vert, &
x0_source, z0_source, A_plane, B_plane, C_plane, angleforce(1), angleforce_refl, &
c_inc, c_refl, time_offset,f0)
- traction_x_t0 = (lambdal_relaxed+2*mul_relaxed)*dxUx + lambdal_relaxed*dzUz
- traction_z_t0 = mul_relaxed*(dxUz + dzUx)
+ traction_x_t0 = (lambdal_unrelaxed_elastic+2*mul_unrelaxed_elastic)*dxUx + lambdal_unrelaxed_elastic*dzUz
+ traction_z_t0 = mul_unrelaxed_elastic*(dxUz + dzUx)
else
veloc_horiz=v0x_left(count_left)
veloc_vert=v0z_left(count_left)
@@ -589,8 +601,8 @@
call compute_Bielak_conditions(coord,iglob,nglob,it,deltat,dxUx,dxUz,dzUx,dzUz,veloc_horiz,veloc_vert, &
x0_source, z0_source, A_plane, B_plane, C_plane, angleforce(1), angleforce_refl, &
c_inc, c_refl, time_offset,f0)
- traction_x_t0 = (lambdal_relaxed+2*mul_relaxed)*dxUx + lambdal_relaxed*dzUz
- traction_z_t0 = mul_relaxed*(dxUz + dzUx)
+ traction_x_t0 = (lambdal_unrelaxed_elastic+2*mul_unrelaxed_elastic)*dxUx + lambdal_unrelaxed_elastic*dzUz
+ traction_z_t0 = mul_unrelaxed_elastic*(dxUz + dzUx)
else
veloc_horiz=v0x_right(count_right)
veloc_vert=v0z_right(count_right)
@@ -686,8 +698,8 @@
call compute_Bielak_conditions(coord,iglob,nglob,it,deltat,dxUx,dxUz,dzUx,dzUz,veloc_horiz,veloc_vert, &
x0_source, z0_source, A_plane, B_plane, C_plane, angleforce(1), angleforce_refl, &
c_inc, c_refl, time_offset,f0)
- traction_x_t0 = mul_relaxed*(dxUz + dzUx)
- traction_z_t0 = lambdal_relaxed*dxUx + (lambdal_relaxed+2*mul_relaxed)*dzUz
+ traction_x_t0 = mul_unrelaxed_elastic*(dxUz + dzUx)
+ traction_z_t0 = lambdal_unrelaxed_elastic*dxUx + (lambdal_unrelaxed_elastic+2*mul_unrelaxed_elastic)*dzUz
else
veloc_horiz=v0x_bot(count_bottom)
veloc_vert=v0z_bot(count_bottom)
@@ -791,8 +803,8 @@
call compute_Bielak_conditions(coord,iglob,nglob,it,deltat,dxUx,dxUz,dzUx,dzUz,veloc_horiz,veloc_vert, &
x0_source, z0_source, A_plane, B_plane, C_plane, angleforce(1), angleforce_refl, &
c_inc, c_refl, time_offset,f0)
- traction_x_t0 = mul_relaxed*(dxUz + dzUx)
- traction_z_t0 = lambdal_relaxed*dxUx + (lambdal_relaxed+2*mul_relaxed)*dzUz
+ traction_x_t0 = mul_unrelaxed_elastic*(dxUz + dzUx)
+ traction_z_t0 = lambdal_unrelaxed_elastic*dxUx + (lambdal_unrelaxed_elastic+2*mul_unrelaxed_elastic)*dzUz
else
veloc_horiz = 0
veloc_vert = 0
Modified: seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_pressure.f90
===================================================================
--- seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_pressure.f90 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_pressure.f90 2012-01-13 17:53:28 UTC (rev 19356)
@@ -190,8 +190,8 @@
real(kind=CUSTOM_REAL) :: dwx_dxl,dwz_dzl
! material properties of the elastic medium
- real(kind=CUSTOM_REAL) :: mul_relaxed,lambdal_relaxed,lambdalplus2mul_relaxed,denst
- real(kind=CUSTOM_REAL) :: mul_unrelaxed,lambdal_unrelaxed,lambdalplus2mul_unrelaxed,cpl,csl
+ real(kind=CUSTOM_REAL) :: mul_unrelaxed_elastic,lambdal_unrelaxed_elastic,lambdaplus2mu_unrelaxed_elastic,denst
+ real(kind=CUSTOM_REAL) :: mul_relaxed_viscoelastic,lambdal_relaxed_viscoelastic,lambdalplus2mul_relaxed_viscoelastic,cpl,csl
real(kind=CUSTOM_REAL) :: mul_s,kappal_s,rhol_s
real(kind=CUSTOM_REAL) :: kappal_f,rhol_f
@@ -229,9 +229,9 @@
if(elastic(ispec)) then
! get relaxed elastic parameters of current spectral element
- lambdal_relaxed = poroelastcoef(1,1,kmato(ispec))
- mul_relaxed = poroelastcoef(2,1,kmato(ispec))
- lambdalplus2mul_relaxed = poroelastcoef(3,1,kmato(ispec))
+ lambdal_unrelaxed_elastic = poroelastcoef(1,1,kmato(ispec))
+ mul_unrelaxed_elastic = poroelastcoef(2,1,kmato(ispec))
+ lambdaplus2mu_unrelaxed_elastic = poroelastcoef(3,1,kmato(ispec))
do j = 1,NGLLZ
do i = 1,NGLLX
@@ -241,8 +241,8 @@
cpl = vpext(i,j,ispec)
csl = vsext(i,j,ispec)
denst = rhoext(i,j,ispec)
- mul_relaxed = denst*csl*csl
- lambdal_relaxed = denst*cpl*cpl - TWO*mul_relaxed
+ mul_unrelaxed_elastic = denst*csl*csl
+ lambdal_unrelaxed_elastic = denst*cpl*cpl - TWO*mul_unrelaxed_elastic
endif
! derivative along x and along z
@@ -280,18 +280,27 @@
! J. M. Carcione, D. Kosloff and R. Kosloff, Wave propagation simulation in a linear
! viscoelastic medium, Geophysical Journal International, vol. 95, p. 597-611 (1988).
- ! compute unrelaxed elastic coefficients from formulas in Carcione 1993 page 111
- lambdal_unrelaxed = (lambdal_relaxed + mul_relaxed) * Mu_nu1(i,j,ispec) &
- - mul_relaxed * Mu_nu2(i,j,ispec)
- mul_unrelaxed = mul_relaxed * Mu_nu2(i,j,ispec)
- lambdalplus2mul_unrelaxed = lambdal_unrelaxed + TWO*mul_unrelaxed
+! When implementing viscoelasticity according to Carcione 1993 paper, the attenuation is
+! non-causal rather than causal. We fixed the problem by using equations in Carcione's
+! 2004 paper and his 2007 book.
- ! compute the stress using the unrelaxed Lame parameters (Carcione 1993, page 111)
- sigma_xx = lambdalplus2mul_unrelaxed*dux_dxl + lambdal_unrelaxed*duz_dzl
- sigma_zz = lambdalplus2mul_unrelaxed*duz_dzl + lambdal_unrelaxed*dux_dxl
+!J. M. Carcione, H B. Helle, The physics and simulation of wave propagation at the ocean
+! bottom, Geophysics, vol. 69(3), p. 825-839, 2004
+!J. M. Carcione, Wave fields in real media: wave propagation in anisotropic, anelastic
+! and porous media, Elsevier, p. 124-125, 2007
- ! add the memory variables using the relaxed parameters (Carcione 1993, page 111)
- ! beware: there is a bug in Carcione's equation (2c) for sigma_zz, we fixed it in the code below
+ ! compute unrelaxed elastic coefficients from formulas in Carcione 2007 page 125
+ lambdal_relaxed_viscoelastic = (lambdal_unrelaxed_elastic + mul_unrelaxed_elastic) / Mu_nu1(i,j,ispec) &
+ - mul_unrelaxed_elastic / Mu_nu2(i,j,ispec)
+ mul_relaxed_viscoelastic = mul_unrelaxed_elastic / Mu_nu2(i,j,ispec)
+ lambdalplus2mul_relaxed_viscoelastic = lambdal_relaxed_viscoelastic + TWO*mul_relaxed_viscoelastic
+
+ ! compute the stress using the unrelaxed Lame parameters (Carcione 2007 page 125)
+ sigma_xx = lambdaplus2mu_unrelaxed_elastic*dux_dxl + lambdal_unrelaxed_elastic*duz_dzl
+ sigma_zz = lambdaplus2mu_unrelaxed_elastic*duz_dzl + lambdal_unrelaxed_elastic*dux_dxl
+
+ ! add the memory variables using the relaxed parameters (Carcione 2007 page 125)
+ ! beware: there is a bug in Carcione's equation (2c) of his 1993 paper for sigma_zz, we fixed it in the code below
e1_sum = 0._CUSTOM_REAL
e11_sum = 0._CUSTOM_REAL
@@ -300,16 +309,16 @@
e11_sum = e11_sum + e11(i,j,ispec,i_sls)
enddo
- sigma_xx = sigma_xx + (lambdal_relaxed + mul_relaxed) * e1_sum &
- + TWO * mul_relaxed * e11_sum
- sigma_zz = sigma_zz + (lambdal_relaxed + mul_relaxed) * e1_sum &
- - TWO * mul_relaxed * e11_sum
+ sigma_xx = sigma_xx + (lambdal_relaxed_viscoelastic + mul_relaxed_viscoelastic) * e1_sum &
+ + TWO * mul_unrelaxed_elastic * e11_sum
+ sigma_zz = sigma_zz + (lambdal_relaxed_viscoelastic + mul_relaxed_viscoelastic) * e1_sum &
+ - TWO * mul_relaxed_viscoelastic * e11_sum
else
! no attenuation
- sigma_xx = lambdalplus2mul_relaxed*dux_dxl + lambdal_relaxed*duz_dzl
- sigma_zz = lambdalplus2mul_relaxed*duz_dzl + lambdal_relaxed*dux_dxl
+ sigma_xx = lambdaplus2mu_unrelaxed_elastic*dux_dxl + lambdal_unrelaxed_elastic*duz_dzl
+ sigma_zz = lambdaplus2mu_unrelaxed_elastic*duz_dzl + lambdal_unrelaxed_elastic*dux_dxl
endif
@@ -348,8 +357,8 @@
elseif(poroelastic(ispec)) then
- lambdal_relaxed = poroelastcoef(1,1,kmato(ispec))
- mul_relaxed = poroelastcoef(2,1,kmato(ispec))
+ lambdal_unrelaxed_elastic = poroelastcoef(1,1,kmato(ispec))
+ mul_unrelaxed_elastic = poroelastcoef(2,1,kmato(ispec))
! get poroelastic parameters of current spectral element
phil = porosity(kmato(ispec))
@@ -432,18 +441,27 @@
! J. M. Carcione, D. Kosloff and R. Kosloff, Wave propagation simulation in a linear
! viscoelastic medium, Geophysical Journal International, vol. 95, p. 597-611 (1988).
- ! compute unrelaxed elastic coefficients from formulas in Carcione 1993 page 111
- lambdal_unrelaxed = (lambdal_relaxed + mul_relaxed) * Mu_nu1(i,j,ispec) &
- - mul_relaxed * Mu_nu2(i,j,ispec)
- mul_unrelaxed = mul_relaxed * Mu_nu2(i,j,ispec)
- lambdalplus2mul_unrelaxed = lambdal_unrelaxed + TWO*mul_unrelaxed
+! When implement viscoelasticity according to Carcione 1993 paper, the attenuation is
+! non-causal rather than causal. We fixed the problem by using equations in Carcione's
+! 2004 paper and his 2007 book.
- ! compute the stress using the unrelaxed Lame parameters (Carcione 1993, page 111)
- sigma_xx = lambdalplus2mul_unrelaxed*dux_dxl + lambdal_unrelaxed*duz_dzl
- sigma_zz = lambdalplus2mul_unrelaxed*duz_dzl + lambdal_unrelaxed*dux_dxl
+!J. M. Carcione, H B. Helle, The physics and simulation of wave propagation at the ocean
+! bottom, Geophysics, vol. 69(3), p. 825-839, 2004
+!J. M. Carcione, Wave fields in real media: wave propagation in anisotropic, anelastic
+! and porous media, Elsevier, p. 124-125, 2007
- ! add the memory variables using the relaxed parameters (Carcione 1993, page 111)
- ! beware: there is a bug in Carcione's equation (2c) for sigma_zz, we fixed it in the code below
+ ! compute relaxed elastic coefficients from formulas in Carcione 2007 page 125
+ lambdal_relaxed_viscoelastic = (lambdal_unrelaxed_elastic + mul_unrelaxed_elastic) / Mu_nu1(i,j,ispec) &
+ - mul_unrelaxed_elastic / Mu_nu2(i,j,ispec)
+ mul_relaxed_viscoelastic = mul_unrelaxed_elastic / Mu_nu2(i,j,ispec)
+ lambdalplus2mul_relaxed_viscoelastic = lambdal_relaxed_viscoelastic + TWO*mul_relaxed_viscoelastic
+
+ ! compute the stress using the unrelaxed Lame parameters (Carcione 2007 page 125)
+ sigma_xx = (lambdal_unrelaxed_elastic + 2.0 * mul_unrelaxed_elastic)*dux_dxl + lambdal_unrelaxed_elastic*duz_dzl
+ sigma_zz = (lambdal_unrelaxed_elastic + 2.0 * mul_unrelaxed_elastic)*duz_dzl + lambdal_unrelaxed_elastic*dux_dxl
+
+ ! add the memory variables using the relaxed parameters (Carcione 2007 page 125)
+ ! beware: there is a bug in Carcione's equation (2c) of his 1993 paper for sigma_zz, we fixed it in the code below
e1_sum = 0._CUSTOM_REAL
e11_sum = 0._CUSTOM_REAL
@@ -452,10 +470,10 @@
e11_sum = e11_sum + e11(i,j,ispec,i_sls)
enddo
- sigma_xx = sigma_xx + (lambdal_relaxed + mul_relaxed) * e1_sum &
- + TWO * mul_relaxed * e11_sum
- sigma_zz = sigma_zz + (lambdal_relaxed + mul_relaxed) * e1_sum &
- - TWO * mul_relaxed * e11_sum
+ sigma_xx = sigma_xx + (lambdal_relaxed_viscoelastic + mul_relaxed_viscoelastic) * e1_sum &
+ + TWO * mul_relaxed_viscoelastic * e11_sum
+ sigma_zz = sigma_zz + (lambdal_relaxed_viscoelastic + mul_relaxed_viscoelastic) * e1_sum &
+ - TWO * mul_relaxed_viscoelastic * e11_sum
else
Modified: seismo/2D/SPECFEM2D/trunk/src/specfem2D/specfem2D.F90
===================================================================
--- seismo/2D/SPECFEM2D/trunk/src/specfem2D/specfem2D.F90 2012-01-13 17:44:53 UTC (rev 19355)
+++ seismo/2D/SPECFEM2D/trunk/src/specfem2D/specfem2D.F90 2012-01-13 17:53:28 UTC (rev 19356)
@@ -427,7 +427,7 @@
double precision :: xixl,xizl,gammaxl,gammazl,jacobianl
! material properties of the elastic medium
- double precision :: mul_relaxed,lambdal_relaxed,lambdalplus2mul_relaxed,kappal
+ double precision :: mul_unrelaxed_elastic,lambdal_unrelaxed_elastic,lambdaplus2mu_unrelaxed_elastic,kappal
real(kind=CUSTOM_REAL), dimension(:,:), allocatable :: accel_elastic,veloc_elastic,displ_elastic
real(kind=CUSTOM_REAL), dimension(:,:), allocatable :: accel_elastic_adj_coupling
@@ -538,7 +538,7 @@
logical :: ATTENUATION_PORO_FLUID_PART
double precision, dimension(NGLLX,NGLLZ) :: viscox_loc,viscoz_loc
double precision :: Sn,Snp1,etal_f
- double precision, dimension(3):: bl_relaxed
+ double precision, dimension(3):: bl_unrelaxed_elastic
double precision :: permlxx,permlxz,permlzz,invpermlxx,invpermlxz,invpermlzz,detk
! adjoint
real(kind=CUSTOM_REAL), dimension(:), allocatable :: b_viscodampx,b_viscodampz
@@ -1635,9 +1635,9 @@
kappal = rhol * vpext(i,j,ispec)**2
else
rhol = density(1,kmato(ispec))
- lambdal_relaxed = poroelastcoef(1,1,kmato(ispec))
- mul_relaxed = poroelastcoef(2,1,kmato(ispec))
- kappal = lambdal_relaxed + 2.d0/3.d0*mul_relaxed
+ lambdal_unrelaxed_elastic = poroelastcoef(1,1,kmato(ispec))
+ mul_unrelaxed_elastic = poroelastcoef(2,1,kmato(ispec))
+ kappal = lambdal_unrelaxed_elastic + 2.d0/3.d0*mul_unrelaxed_elastic
endif
rmass_inverse_elastic(iglob) = rmass_inverse_elastic(iglob) &
@@ -4189,19 +4189,19 @@
endif
! relaxed viscous coef
- bl_relaxed(1) = etal_f*invpermlxx
- bl_relaxed(2) = etal_f*invpermlxz
- bl_relaxed(3) = etal_f*invpermlzz
+ bl_unrelaxed_elastic(1) = etal_f*invpermlxx
+ bl_unrelaxed_elastic(2) = etal_f*invpermlxz
+ bl_unrelaxed_elastic(3) = etal_f*invpermlzz
do j=1,NGLLZ
do i=1,NGLLX
iglob = ibool(i,j,ispec)
- viscox_loc(i,j) = velocw_poroelastic(1,iglob)*bl_relaxed(1) + &
- velocw_poroelastic(2,iglob)*bl_relaxed(2)
- viscoz_loc(i,j) = velocw_poroelastic(1,iglob)*bl_relaxed(2) + &
- velocw_poroelastic(2,iglob)*bl_relaxed(3)
+ viscox_loc(i,j) = velocw_poroelastic(1,iglob)*bl_unrelaxed_elastic(1) + &
+ velocw_poroelastic(2,iglob)*bl_unrelaxed_elastic(2)
+ viscoz_loc(i,j) = velocw_poroelastic(1,iglob)*bl_unrelaxed_elastic(2) + &
+ velocw_poroelastic(2,iglob)*bl_unrelaxed_elastic(3)
! evolution rx_viscous
Sn = - (1.d0 - theta_e/theta_s)/theta_s*viscox(i,j,ispec)
@@ -5018,9 +5018,9 @@
iglob = ibool(ii2,jj2,ispec_elastic)
! get elastic properties
- lambdal_relaxed = poroelastcoef(1,1,kmato(ispec_elastic))
- mul_relaxed = poroelastcoef(2,1,kmato(ispec_elastic))
- lambdalplus2mul_relaxed = poroelastcoef(3,1,kmato(ispec_elastic))
+ lambdal_unrelaxed_elastic = poroelastcoef(1,1,kmato(ispec_elastic))
+ mul_unrelaxed_elastic = poroelastcoef(2,1,kmato(ispec_elastic))
+ lambdaplus2mu_unrelaxed_elastic = poroelastcoef(3,1,kmato(ispec_elastic))
! derivative along x and along z for u_s and w
dux_dxi = ZERO
@@ -5097,15 +5097,15 @@
sigma_xz = sigma_xz + c15*dux_dxl + c55*(duz_dxl + dux_dzl) + c35*duz_dzl
else
! no attenuation
- sigma_xx = sigma_xx + lambdalplus2mul_relaxed*dux_dxl + lambdal_relaxed*duz_dzl
- sigma_xz = sigma_xz + mul_relaxed*(duz_dxl + dux_dzl)
- sigma_zz = sigma_zz + lambdalplus2mul_relaxed*duz_dzl + lambdal_relaxed*dux_dxl
+ sigma_xx = sigma_xx + lambdaplus2mu_unrelaxed_elastic*dux_dxl + lambdal_unrelaxed_elastic*duz_dzl
+ sigma_xz = sigma_xz + mul_unrelaxed_elastic*(duz_dxl + dux_dzl)
+ sigma_zz = sigma_zz + lambdaplus2mu_unrelaxed_elastic*duz_dzl + lambdal_unrelaxed_elastic*dux_dxl
endif
if(SIMULATION_TYPE == 2) then
- b_sigma_xx = b_sigma_xx + lambdalplus2mul_relaxed*b_dux_dxl + lambdal_relaxed*b_duz_dzl
- b_sigma_xz = b_sigma_xz + mul_relaxed*(b_duz_dxl + b_dux_dzl)
- b_sigma_zz = b_sigma_zz + lambdalplus2mul_relaxed*b_duz_dzl + lambdal_relaxed*b_dux_dxl
+ b_sigma_xx = b_sigma_xx + lambdaplus2mu_unrelaxed_elastic*b_dux_dxl + lambdal_unrelaxed_elastic*b_duz_dzl
+ b_sigma_xz = b_sigma_xz + mul_unrelaxed_elastic*(b_duz_dxl + b_dux_dzl)
+ b_sigma_zz = b_sigma_zz + lambdaplus2mu_unrelaxed_elastic*b_duz_dzl + lambdal_unrelaxed_elastic*b_dux_dxl
endif
! compute the 1D Jacobian and the normal to the edge: for their expression see for instance
@@ -5560,9 +5560,9 @@
iglob = ibool(i,j,ispec_elastic)
! get elastic properties
- lambdal_relaxed = poroelastcoef(1,1,kmato(ispec_elastic))
- mul_relaxed = poroelastcoef(2,1,kmato(ispec_elastic))
- lambdalplus2mul_relaxed = poroelastcoef(3,1,kmato(ispec_elastic))
+ lambdal_unrelaxed_elastic = poroelastcoef(1,1,kmato(ispec_elastic))
+ mul_unrelaxed_elastic = poroelastcoef(2,1,kmato(ispec_elastic))
+ lambdaplus2mu_unrelaxed_elastic = poroelastcoef(3,1,kmato(ispec_elastic))
! derivative along x and along z for u_s and w
dux_dxi = ZERO
@@ -5638,15 +5638,15 @@
sigma_xz = c15*dux_dxl + c55*(duz_dxl + dux_dzl) + c35*duz_dzl
else
! no attenuation
- sigma_xx = lambdalplus2mul_relaxed*dux_dxl + lambdal_relaxed*duz_dzl
- sigma_xz = mul_relaxed*(duz_dxl + dux_dzl)
- sigma_zz = lambdalplus2mul_relaxed*duz_dzl + lambdal_relaxed*dux_dxl
+ sigma_xx = lambdaplus2mu_unrelaxed_elastic*dux_dxl + lambdal_unrelaxed_elastic*duz_dzl
+ sigma_xz = mul_unrelaxed_elastic*(duz_dxl + dux_dzl)
+ sigma_zz = lambdaplus2mu_unrelaxed_elastic*duz_dzl + lambdal_unrelaxed_elastic*dux_dxl
endif
if(SIMULATION_TYPE == 2) then
- b_sigma_xx = lambdalplus2mul_relaxed*b_dux_dxl + lambdal_relaxed*b_duz_dzl
- b_sigma_xz = mul_relaxed*(b_duz_dxl + b_dux_dzl)
- b_sigma_zz = lambdalplus2mul_relaxed*b_duz_dzl + lambdal_relaxed*b_dux_dxl
+ b_sigma_xx = lambdaplus2mu_unrelaxed_elastic*b_dux_dxl + lambdal_unrelaxed_elastic*b_duz_dzl
+ b_sigma_xz = mul_unrelaxed_elastic*(b_duz_dxl + b_dux_dzl)
+ b_sigma_zz = lambdaplus2mu_unrelaxed_elastic*b_duz_dzl + lambdal_unrelaxed_elastic*b_dux_dxl
endif ! if(SIMULATION_TYPE == 2)
! get point values for the poroelastic side
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