[cig-commits] r19461 - in seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES: . attenuation
xie.zhinan at geodynamics.org
xie.zhinan at geodynamics.org
Tue Jan 24 11:07:50 PST 2012
Author: xie.zhinan
Date: 2012-01-24 11:07:50 -0800 (Tue, 24 Jan 2012)
New Revision: 19461
Added:
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Par_LDDRK
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Par_file_attenuation_2D
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/README
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/SOURCE
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/SOURCE_attenuation_2D
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution_viscoelastic.dat
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution_viscoelastic.dat
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_causality_problem_fixed_by_Xie_Zhinan.f
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_ori_with_causality_problem.f
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/copy.gnu
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/interfaces_attenuation_analytic.dat
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/plot_compare_to_analytical_solution.gnu
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/plot_points_per_wavelength_histogram.gnu
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/points_per_wavelength_histogram_S_in_solid.txt
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/process.sh
seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/ss.txt
Log:
add attenuation example
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Par_LDDRK
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Par_LDDRK (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Par_LDDRK 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,26 @@
+# parameter file for low dispersion and dissipation Runge-Kutta Scheme
+# here we following the parameter definition used in J Berland's paper
+# J. Berland, C. Bogey, C Bailly. Low-dissipation and low-dispersion
+# fourth-order Runge–Kutta algorithm,Computers & Fluids 2006,35:1459–1463
+# alpha_LDDRK(Stage)
+0.0d0
+-0.737101392796d0
+-1.634740794341d0
+-0.744739003780d0
+-1.469897351522d0
+-2.813971388035d0
+# beta_LDDRK(Stage)
+0.032918605146d0
+0.823256998200d0
+0.381530948900d0
+0.200092213184d0
+1.718581042715d0
+0.27d0
+# c_LDDRK(Stage)
+0.0d0
+0.032918605146d0
+0.249351723343d0
+0.466911705055d0
+0.582030414044d0
+0.847252983783d0
+
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Par_file_attenuation_2D
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Par_file_attenuation_2D (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Par_file_attenuation_2D 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,134 @@
+# title of job
+title = Test for 2D attenuation 1999 GJI paper
+
+# forward or adjoint simulation
+SIMULATION_TYPE = 1 # 1 = forward, 2 = adjoint + kernels
+NOISE_TOMOGRAPHY = 0 # 0 = earthquake simulation, 1/2/3 = noise simulation
+SAVE_FORWARD = .false. # save the last frame, needed for adjoint simulation
+
+# parameters concerning partitioning
+nproc = 1 # number of processes
+partitioning_method = 3 # SCOTCH = 3, ascending order (very bad idea) = 1
+PERFORM_CUTHILL_MCKEE = .true. # perform inverse Cuthill-McKee (1969) optimization/permutation for mesh numbering
+
+ngnod = 4 # number of control nodes per element (4 or 9)
+initialfield = .false. # use a plane wave as source or not
+add_Bielak_conditions = .false. # add Bielak conditions or not if initial plane wave
+assign_external_model = .false. # define external earth model or not
+READ_EXTERNAL_SEP_FILE = .false. # Read external SEP file from DATA/model_velocity.dat_input, or use routine
+ATTENUATION_VISCOELASTIC_SOLID = .false. # turn attenuation (viscoelasticity) on or off for non-poroelastic solid parts of the model
+ATTENUATION_PORO_FLUID_PART = .false. # turn viscous attenuation on or off for the fluid part of poroelastic parts of the model
+Q0 = 1 # quality factor for viscous attenuation
+freq0 = 10 # frequency for viscous attenuation
+p_sv = .true. # set the type of calculation (P-SV or SH/membrane waves)
+
+# time step parameters
+nt = 2000 # total number of time steps
+deltat = 0.75e-3 # duration of a time step
+USER_T0 = 0.0d0 # use this t0 as earliest starting time rather than the automatically calculated one
+time_stepping_scheme = 2 # 1 = Newmark (2nd order), 2 = LDDRK4-6 (4th-order 6-stage low storage Runge-Kutta), 3 = classical 4th-order 4-stage Runge-Kutta
+
+# source parameters
+NSOURCES = 1 # number of sources [source info read in CMTSOLUTION file]
+force_normal_to_surface = .false. # angleforce normal to surface (external mesh and curve file needed)
+
+# constants for attenuation
+N_SLS = 2 # number of standard linear solids for attenuation
+f0_attenuation = 5.196152422706633 # (Hz) relevant only if source is a Dirac or a Heaviside, else it is f0
+
+# receiver set parameters for seismograms
+seismotype = 1 # record 1=displ 2=veloc 3=accel 4=pressure
+generate_STATIONS = .true. # creates a STATION file in ./DATA
+nreceiversets = 1 # number of receiver sets
+anglerec = 0.d0 # angle to rotate components at receivers
+rec_normal_to_surface = .false. # base anglerec normal to surface (external mesh and curve file needed)
+SU_FORMAT = .false. # output seismograms in Seismic Unix format (adjoint traces will be read in the same format)
+
+# first receiver set
+nrec = 1 # number of receivers
+xdeb = 1500.d0
+zdeb = 1500.d0
+xfin = 99999.d0 # ignored because only one receiver
+zfin = 99999.d0 # ignored because only one receiver
+enreg_surf_same_vertical = .false. # receivers inside the medium or at the surface
+
+# display parameters
+NTSTEP_BETWEEN_OUTPUT_INFO = 100 # display frequency in time steps
+output_postscript_snapshot = .true. # output Postscript snapshot of the results
+output_color_image = .true. # output color image of the results
+imagetype = 1 # display 1=displ 2=veloc 3=accel 4=pressure
+cutsnaps = 1. # minimum amplitude in % for snapshots
+meshvect = .true. # display mesh on vector plots or not
+modelvect = .false. # display velocity model on vector plots
+boundvect = .true. # display boundary conditions on plots
+interpol = .true. # interpolation of the display or not
+pointsdisp = 6 # points for interpolation of display (set to 1 for lower-left corner only)
+subsamp_postscript = 1 # subsampling of color snapshots
+factor_subsample_image = 1 # factor to subsample color images output by the code (useful for very large models)
+POWER_DISPLAY_COLOR = 0.30d0 # non linear display to enhance small amplitudes in color images
+DRAW_WATER_CONSTANT_BLUE_IN_JPG = .true. # display acoustic layers as constant blue in JPEG images, because they likely correspond to water
+sizemax_arrows = 1.d0 # maximum size of arrows on vector plots in cm
+US_LETTER = .false. # US letter paper or European A4
+USE_SNAPSHOT_NUMBER_IN_FILENAME = .false. # use snapshot number in the file name of JPEG color snapshots instead of the time step
+gnuplot = .false. # generate a GNUPLOT file for the grid
+output_grid = .false. # save the grid in a text file or not
+output_energy = .false. # compute and output acoustic and elastic energy (slows down the code significantly)
+output_wavefield_snapshot = .false. # output Ux,Uy,Uz text file for each output time (big files)
+
+# velocity and density models
+nbmodels = 1 # nb of different models
+# define models as
+# I: (model_number 1 rho Vp Vs 0 0 QKappa Qmu 0 0 0 0 0 0) or
+# II: (model_number 2 rho c11 c13 c15 c33 c35 c55 0 0 0 0 0 0) or
+# III: (model_number 3 rhos rhof phi c kxx kxz kzz Ks Kf Kfr etaf mufr Qmu).
+# For istropic elastic/acoustic material use I and set Vs to zero to make a given model acoustic, for anisotropic elastic use II,
+# and for isotropic poroelastic material use III. The mesh can contain acoustic, elastic, and poroelastic models simultaneously.
+1 1 2000.d0 3000.d0 2000.d0 0 0 27. 20. 0 0 0 0 0 0
+
+# external mesh or not
+read_external_mesh = .false.
+
+# absorbing boundary active or not
+absorbing_conditions = .false.
+
+# for horizontal periodic conditions: detect common points between left and right edges
+ADD_PERIODIC_CONDITIONS = .false.
+
+# horizontal periodicity distance for periodic conditions
+PERIODIC_horiz_dist = 0.3597d0
+
+# grid point detection tolerance for periodic conditions
+PERIODIC_DETECT_TOL = 3.3334d-6
+
+#-----------------------------------------------------------------------------
+# PARAMETERS FOR EXTERNAL MESHING
+
+# data concerning mesh, when generated using third-party app (more info in README)
+# (see also absorbing_conditions above)
+mesh_file = ./DATA/Mesh_canyon/canyon_mesh_file # file containing the mesh
+nodes_coords_file = ./DATA/Mesh_canyon/canyon_nodes_coords_file # file containing the nodes coordinates
+materials_file = ./DATA/Mesh_canyon/canyon_materials_file # file containing the material number for each element
+free_surface_file = ./DATA/Mesh_canyon/canyon_free_surface_file # file containing the free surface
+absorbing_surface_file = ./DATA/Mesh_canyon/canyon_absorbing_surface_file # file containing the absorbing surface
+tangential_detection_curve_file = ./DATA/courbe_eros_nodes # file containing the curve delimiting the velocity model
+
+#-----------------------------------------------------------------------------
+# PARAMETERS FOR INTERNAL MESHING
+
+# file containing interfaces for internal mesh
+interfacesfile = interfaces_attenuation_analytic.dat
+
+# geometry of the model (origin lower-left corner = 0,0) and mesh description
+xmin = 0.d0 # abscissa of left side of the model
+xmax = 2000.d0 # abscissa of right side of the model
+nx = 44 # number of elements along X
+
+# absorbing boundary parameters (see absorbing_conditions above)
+absorbbottom = .false.
+absorbright = .false.
+absorbtop = .false.
+absorbleft = .false.
+
+# define the different regions of the model in the (nx,nz) spectral element mesh
+nbregions = 1 # nb of regions and model number for each
+1 44 1 44 1
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/README
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/README (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/README 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,52 @@
+----------------------------------------------------------------------
+README
+----------------------------------------------------------------------
+
+This example creates the 2D attenuation benchmark of Komatitsch and Tromp (1999, Figure 16), with an important modification:
+the two articles by Carcione et al. (1988, 1993) have non-causal attenuation, i.e., waves going faster rather than slower when attenuation
+is turned on. Xie Zhinan fixed that in January 2011. This example thus presents the example of our 1999 article but with that problem fixed;
+in 1999 we did not know that there was a problem in Carcione et al. (1988, 1993) and thus our 1999 article contains the problem as well.
+
+
+TO RUN:
+
+0. Read the user manual in SPECFEM2D/doc/manual_SPECFEM2D.pdf
+
+1. in the SPECFEM2D root directory, configure, e.g.,
+ ./configure FC=gfortran
+
+2. compile:
+ make all
+
+3. cd EXAMPLES/attenuation
+
+4. execute script to run mesher and solver for the PSV case:
+ ./process.sh
+
+5. check out the output files in the local directory OUTPUT_FILES; in particular, you can type "gnuplot plot_compare_to_analytical_solution.gnu" to compare the seismograms computed to the quasi-analytical solution of Carcione et al. (1988).
+
+Note that because our example has no absorbing conditions on the edges of the grid, there are extra (spurious) waves after the main P and S waves, reflected off the edges of the grid, which are not present in the quasi-analytical solution and which you can safely ignore.
+
+Beware that the reference solution is not exact, only quasi-exact (i.e., the formulation uses an approximation, and some integrals are computed numerically) therefore some small discrepancies can be noticed.
+
+More importantly, in the example provided, "tau" relaxation times for attenuation memory variables are recomputed using approximate quality factor targets of Qkappa approximately equal to 27 and Qmu / Qs approximately equal to 20, read (roughly) from Figure 1 page 604 of the article of Carcione et al. (1988). This will NOT lead to the exact same "tau" values as in Table 1 of Carcione et al. (1988). Thus, in order to perform a far more precise comparison to the analytical solution, which is computed using the "tau" values from Table 1 of Carcione et al. (1988), in file "src/specfem2D/attenuation_model.f90" you should impose this instead for this test (only) by uncommenting the following 8 lines:
+
+! tau_epsilon_nu1(1) = 0.0325305d0
+! tau_sigma_nu1(1) = 0.0311465d0
+! tau_epsilon_nu2(1) = 0.0332577d0
+! tau_sigma_nu2(1) = 0.0304655d0
+
+! tau_epsilon_nu1(2) = 0.0032530d0
+! tau_sigma_nu1(2) = 0.0031146d0
+! tau_epsilon_nu2(2) = 0.0033257d0
+! tau_sigma_nu2(2) = 0.0030465d0
+
+
+References:
+-----------
+
+Dimitri Komatitsch and Jeroen Tromp, Introduction to the spectral-element method for 3-D seismic wave propagation, Geophysical Journal International, vol. 139, p. 806-822 (1999).
+
+Jose M. Carcione, D. Kosloff and R. Kosloff, Wave propagation simulation in a linear viscoelastic medium, Geophysical Journal International, vol. 95, p. 597-611 (1988).
+
+----------------------------------------------------------------------
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/SOURCE
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/SOURCE (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/SOURCE 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,13 @@
+#source 1. The components of a moment tensor source must be given in N.m, not in dyne.cm as in the DATA/CMTSOLUTION source file of the 3D version of the code.
+source_surf = .false. # source inside the medium or at the surface
+xs = 1000. # source location x in meters
+zs = 1000. # source location z in meters
+source_type = 1 # elastic force or acoustic pressure = 1 or moment tensor = 2
+time_function_type = 1 # Ricker = 1, first derivative = 2, Gaussian = 3, Dirac = 4, Heaviside = 5
+f0 = 18.0 # dominant source frequency (Hz) if not Dirac or Heaviside
+tshift = 0.0 # time shift when multi sources (if one source, must be zero)
+angleforce = 0. # angle of the source (for a force only)
+Mxx = 1. # Mxx component (for a moment tensor source only)
+Mzz = 1. # Mzz component (for a moment tensor source only)
+Mxz = 0. # Mxz component (for a moment tensor source only)
+factor = 44371246.83d10 # amplification factor
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/SOURCE_attenuation_2D
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/SOURCE_attenuation_2D (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/SOURCE_attenuation_2D 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,13 @@
+#source 1. The components of a moment tensor source must be given in N.m, not in dyne.cm as in the DATA/CMTSOLUTION source file of the 3D version of the code.
+source_surf = .false. # source inside the medium or at the surface
+xs = 1000. # source location x in meters
+zs = 1000. # source location z in meters
+source_type = 1 # elastic force or acoustic pressure = 1 or moment tensor = 2
+time_function_type = 1 # Ricker = 1, first derivative = 2, Gaussian = 3, Dirac = 4, Heaviside = 5
+f0 = 18.0 # dominant source frequency (Hz) if not Dirac or Heaviside
+tshift = 0.0 # time shift when multi sources (if one source, must be zero)
+angleforce = 0. # angle of the source (for a force only)
+Mxx = 1. # Mxx component (for a moment tensor source only)
+Mzz = 1. # Mzz component (for a moment tensor source only)
+Mxz = 0. # Mxz component (for a moment tensor source only)
+factor = 44371246.83d10 # amplification factor
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution_viscoelastic.dat
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution_viscoelastic.dat (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Ux_time_analytical_solution_viscoelastic.dat 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,5290 @@
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Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution_viscoelastic.dat
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution_viscoelastic.dat (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/Uz_time_analytical_solution_viscoelastic.dat 2012-01-24 19:07:50 UTC (rev 19461)
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Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_causality_problem_fixed_by_Xie_Zhinan.f
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_causality_problem_fixed_by_Xie_Zhinan.f (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_causality_problem_fixed_by_Xie_Zhinan.f 2012-01-24 19:07:50 UTC (rev 19461)
@@ -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/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_ori_with_causality_problem.f
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_ori_with_causality_problem.f (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/analytical_solution_viscoelastic_Carcione_ori_with_causality_problem.f 2012-01-24 19:07:50 UTC (rev 19461)
@@ -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
+
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/copy.gnu
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/copy.gnu (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/copy.gnu 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,15 @@
+
+set term x11
+
+set xlabel "Time (s)"
+set ylabel "Amplitude of displacement component (m)"
+
+set xrange [0:1.4]
+
+plot "OUTPUT_FILES/S0001.AA.BXX.semd" t 'Numerical Ux' w l lc 1, "S0001.AA.BXX.semd.LDDRK" t 'LDDRK Ux' w l lc 3, "S0001.AA.BXX.semd.rk" t 'rkUx' w l lc 5
+pause -1 "Hit any key..."
+
+plot "OUTPUT_FILES/S0001.AA.BXZ.semd" t 'Numerical Uz' w l lc 1, "S0001.AA.BXZ.semd.LDDRK" t 'LDDRK Uz' w l lc 3, "S0001.AA.BXZ.semd.rk" t 'rkUw' w l lc 5
+pause -1 "Hit any key..."
+
+
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/interfaces_attenuation_analytic.dat
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/interfaces_attenuation_analytic.dat (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/interfaces_attenuation_analytic.dat 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,25 @@
+#
+# number of interfaces
+#
+ 2
+#
+# for each interface below, we give the number of points and then x,y for each point
+#
+#
+# interface number 1 (bottom of the mesh)
+#
+ 2
+ 0 0
+ 5000 0
+#
+# interface number 2
+#
+ 2
+ 0 2000
+ 5000 2000
+# for each layer, we give the number of spectral elements in the vertical direction
+#
+#
+# layer number 1 (bottom layer)
+#
+ 44
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/plot_compare_to_analytical_solution.gnu
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/plot_compare_to_analytical_solution.gnu (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/plot_compare_to_analytical_solution.gnu 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,14 @@
+
+set term x11
+
+set xlabel "Time (s)"
+set ylabel "Amplitude of displacement component (m)"
+
+set xrange [0:1.4]
+
+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_viscoelastic.dat" t 'Quasi-analytical Uz' w l lc 3
+pause -1 "Hit any key..."
+
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/plot_points_per_wavelength_histogram.gnu
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/plot_points_per_wavelength_histogram.gnu (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/plot_points_per_wavelength_histogram.gnu 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,9 @@
+ set term x11
+ #set term gif
+ #set output "points_per_wavelength_histogram_S_in_solid.gif"
+
+ set boxwidth 3.91111104E-03
+ set xlabel "Range of min number of points per S wavelength in solid"
+ set ylabel "Percentage of elements (%)"
+ plot "points_per_wavelength_histogram_S_in_solid.txt" with boxes
+ pause -1 "hit any key..."
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/points_per_wavelength_histogram_S_in_solid.txt
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/points_per_wavelength_histogram_S_in_solid.txt (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/points_per_wavelength_histogram_S_in_solid.txt 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,20 @@
+ 3.8739555 0.0000000
+ 3.8778667 0.0000000
+ 3.8817778 0.0000000
+ 3.8856888 0.0000000
+ 3.8896000 0.0000000
+ 3.8935111 0.0000000
+ 3.8974223 0.0000000
+ 3.9013333 0.0000000
+ 3.9052444 0.0000000
+ 3.9091556 14.721074
+ 3.9130666 85.278923
+ 3.9169779 0.0000000
+ 3.9208889 0.0000000
+ 3.9247999 0.0000000
+ 3.9287112 0.0000000
+ 3.9326222 0.0000000
+ 3.9365335 0.0000000
+ 3.9404445 0.0000000
+ 3.9443555 0.0000000
+ 3.9482665 0.0000000
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/process.sh
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/process.sh (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/process.sh 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,68 @@
+#!/bin/bash
+#
+# script runs mesher and solver (in serial)
+# using this example setup
+#
+
+echo "running example: `date`"
+currentdir=`pwd`
+
+echo
+echo "(will take a few minutes)"
+echo
+
+# sets up directory structure in current example directoy
+echo
+echo " setting up example..."
+echo
+
+mkdir -p OUTPUT_FILES
+mkdir -p DATA
+
+# sets up local DATA/ directory
+cd DATA/
+cp ../Par_file_attenuation_2D Par_file
+cp ../interfaces_attenuation_analytic.dat .
+cp ../SOURCE_attenuation_2D SOURCE
+cp ../Par_LDDRK LDDRK
+cd ../
+
+# cleans output files
+rm -rf OUTPUT_FILES/*
+
+# compiles executables in root directory
+cd ../../
+make > tmp.log
+cd $currentdir
+
+# links executables
+rm -f xmeshfem2D xspecfem2D
+ln -s ../../bin/xmeshfem2D
+ln -s ../../bin/xspecfem2D
+
+# stores setup
+cp DATA/Par_file OUTPUT_FILES/
+cp DATA/SOURCE OUTPUT_FILES/
+
+# runs database generation
+echo
+echo " running mesher..."
+echo
+./xmeshfem2D > OUTPUT_FILES/output_mesher.txt
+
+# runs simulation
+echo
+echo " running solver..."
+echo
+./xspecfem2D > OUTPUT_FILES/output_solver.txt #xiezhinan
+
+# stores output
+cp DATA/SOURCE_xz.dat OUTPUT_FILES/ #xiezhinan
+cp DATA/STATIONS OUTPUT_FILES/ #xiezhinan
+cp DATA/STATIONS_target OUTPUT_FILES/ #xiezhinan
+
+echo
+echo "see results in directory: OUTPUT_FILES/"
+echo
+echo "done"
+echo `date`
Property changes on: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/process.sh
___________________________________________________________________
Name: svn:executable
+ *
Added: seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/ss.txt
===================================================================
--- seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/ss.txt (rev 0)
+++ seismo/2D/SPECFEM2D/branches/new_branch_for_Xie_Zhinan/trunk/EXAMPLES/attenuation/ss.txt 2012-01-24 19:07:50 UTC (rev 19461)
@@ -0,0 +1,2 @@
+time_stepping_scheme = 1 # 1 = Newmark (2nd order), 2 = LDDRK4-6 (4th-order 6-stage low storage Runge-Kutta), 3 = classical 4th-order 4-stage Runge-Kutta
+
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