[CIG-SHORT] elapsed time concerns

alberto cominelli alberto.cominelli at gmail.com
Wed Nov 23 12:38:57 PST 2016


Brad,
In my table I was also comparing elapsed times for models where I do not
use initial condition at all.
The section on inital conditions is commented:
# ----------------------------------------------------------------------
# initial stresses
# ----------------------------------------------------------------------
# We must specify initial stresses for each material.
# We provide a filename for the spatial database that gives the stresses,
# and we change the query_type from the default 'nearest' to 'linear'.
# alberto
#[pylithapp.timedependent.materials.material]
#db_initial_stress = spatialdata.spatialdb.SimpleDB
#db_initial_stress.label = Initial stress
#db_initial_stress.iohandler.filename = initial_stress.spatialdb
#db_initial_stress.query_type = nearest
#
## ----------------------------------------------------------------------
# boundary conditions
# ----------------------------------------------------------------------

Still also in this case set-up takes from 87% to 94% of the elapsed time.
I am attaching my cfg cases. I am puzzled: these cases should be eeven
better than  SinpleGridDB initilisation.
What do you think? Am I doing anything wrong?
Regards,
 Alberto.


2016-11-23 21:17 GMT+01:00 Brad Aagaard <baagaard at usgs.gov>:

> Alberto,
>
> If n is the number of cells, the setting the material parameters scales as
> O(n).
>
> If you are using a SimpleDB with one or more points per cell, then each
> SimpleDB query scales as O(n), and setting the material parameters scales
> as O(n)*O(n). This is why we usually only use SimpleDB for simple 1-D or
> 2-D spatial variations with a small number of points.
>
> If you are using a SimpleGridDB, then each query scales with O(log(p))
> where p is the number of points in that dimension, so setting the material
> parameters scales as O(n)*O(log(p)). With p << n, setting the material
> parameters should scale close to O(n).
>
> Regards,
> Brad
>
>
> On 11/23/2016 11:46 AM, alberto cominelli wrote:
>
>> Brad,
>> I made some tests with and w/o initial stress conditions.
>> My exctation was that set-up phase would dectrease realtive to the rest
>> of the computations, Counterintuitively, this did not happen, as the
>> table below shows.
>> Model   # cells         # nodes                 Total Time      Main
>> Stage      Meshing         Setup
>> Reform Jacobian         Reform Residual         Solve   Prestep
>>  Step    Poststep        Finalize
>> 2000x2000x100   4800    5733    No In. Cond.    22.28   2.70%   1.10%
>>  80.30%
>> 1.30%   0.50%   2.80%   0.70%   0.70%   9.00%   1.00%
>>                         In. Cond.       34.03   0.80%   0.90%   89.00%
>> 0.90%   0.30%   1.80%
>> 0.20%   0.40%   5.30%   0.40%
>> 1000x1000x100   7280    8505    No In. Cond.    48.73   0.50%   0.50%
>>  88.60%
>> 1.10%   0.40%   2.30%   0.30%   0.60%   5.40%   0.40%
>>                         In. Cond.       86.55   0.30%   0.30%   91.80%
>> 0.60%   0.20%   1.50%
>> 0.30%   1.20%   3.50%   0.20%
>> 500x500x50      20520   22971   No In. Cond.    317.1   0.10%   0.10%
>>  94.00%
>> 0.40%   0.30%   190.00%         0.00%   0.10%   3.00%   0.10%
>>                         In. Cond.       662.1   0.10%   0.30%   97.40%
>> 0.20%   0.10%   0.90%
>> 0.00%   0.00%   1.00%   0.00%
>>
>> The time saving w/o initial conditions is negligible, and it does not
>> decrease (relative to..) when I increase the number of nodes, Wat am I
>> doing wrong? Is it what you expect? Consoilidation type problems are
>> set-up dominated in pylith?
>>
>> Regards,
>>  Alberto.
>>
>> P.S: these numbers are for a case w/o explicit fault.
>>
>>
>> 2016-11-22 21:37 GMT+01:00 alberto cominelli
>> <alberto.cominelli at gmail.com <mailto:alberto.cominelli at gmail.com>>:
>>
>>     Brad,
>>     I definitely agree with you on the issue we have the coarsest mesh.
>>     The error in any norm will be gigantic. The point is to run a model
>>     fine enough that i can assume it is the "truth". My fault is 20
>>     degree far form vertical - my grid should be fairly smooth. Now I am
>>     running a very fine case 25x25x25 m^3, which should be the best I
>>     can probably run, the most accurate solution possible. This means
>>      4199000 elements and  4316895 nodes. Unfortunately the case is
>>     running using SimpleDB to initiate stress  with fluid pressure
>>     included and it is still running:
>>
>>     54172 cominelli   20   0 7393m 6.7g  11m R 94.4 10.7   5989:47
>>     mpinemesis
>>
>>     Not sure it will survive for long. If I linearly scale with respect
>>     to node number from a previous case where I run with 52000 nodes in
>>     3000 sec, this should take 64 hours serial, but it seems to be scale
>>     worse than linearly.
>>
>>     I will check if I can use SimpleGridDB. Please, apologize if I
>>     bother you again on this, but could you confirm that a grid as in
>>     the pictures below can be filled with cellwise constant initial
>>     stresses using SimpleGridDB.
>>
>>     regards,
>>
>>      Alberto,
>>
>>
>>     Il 22/Nov/2016 19:19, "Brad Aagaard" <baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov>> ha scritto:
>>     >
>>     > Alberto,
>>     >
>>     > Cells with dimensions 2km x 2km x 0.1km have a very poor aspect
>>     ratio. They will certainly degrade the rate of convergence and
>>     affect the accuracy of the results. Skewing cells so they conform to
>>     the fault should be okay as long as the sides have about equal
>>     dimension and the angles are greater than 45 degrees. Aspect ratio
>>     and/or condition number mesh quality metrics can be used in both
>>     cases to assess the quality of you mesh.
>>     >
>>     > Regards,
>>     > Brad
>>     >
>>     >
>>     >
>>     > On 11/21/2016 02:44 PM, alberto cominelli wrote:
>>     >>
>>     >> Dear Brad,
>>     >>
>>     >> my convergence studies begins with very coarse cells - say 2000 x
>>     2000 x
>>     >> 100 m^3  cells and then I am further refining the grid by a 2x2x2
>>     ratio
>>     >> at each stage. The fines possible grid I could run should provide
>> the
>>     >> reference solution, "the truth". Actually simulation time is
>> becoming
>>     >> prohibitive for 100x100x25 m^3 cells.
>>     >>
>>     >> This should reflect the logic of subsurface models where usually
>>     cells
>>     >> are thin (e.g. 100m x 100m x 5m). Do you think I should use
>> "regular"
>>     >> cubic cells? As regards elapsed time spent  in the set-up phase,
>> does
>>     >> your suggestion apply also in the case I am working with skewed
>> cells
>>     >> like the ones in my pdf, which ideally should mimic those in the
>>     picture?
>>     >>
>>     >> Regards,
>>     >>
>>     >>  Alberto.
>>     >>
>>     >> Immagine incorporata 1
>>     >>
>>     >> 2016-11-21 23:28 GMT+01:00 Brad Aagaard <baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov>
>>     >> <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>>:
>>     >>
>>     >>
>>     >>     Alberto,
>>     >>
>>     >>     If your cells have aspect ratios as shown in the figure, then
>>     this
>>     >>     will certainly degrade the convergence. The aspect ratios and
>>     >>     condition number metrics should be close to 1.0. In
>>     CUBIT/Trelis we
>>     >>     try to get condition numbers down to less than 2.0.
>>     >>
>>     >>     Brad
>>     >>
>>     >>
>>     >>     On 11/21/2016 02:20 PM, alberto cominelli wrote:
>>     >>
>>     >>         Thank you so much Brad.
>>     >>         i will try tomorrow.
>>     >>         I wonder if you suggestions do apply aslo for a skewed
>>     cartesian
>>     >>         grid..
>>     >>         Acualy my grid is skwed to follow a sloping fault, hence
>>     cell cross
>>     >>         section paralle to y is not a square. I am attaching a
>>     pdf to show a
>>     >>         (poor) view of the grid and some vtlk files to explain
>>     better my
>>     >>         geometry.
>>     >>         regards,
>>     >>         Alberto.
>>     >>
>>     >>
>>     >>         2016-11-21 21:58 GMT+01:00 Brad Aagaard
>>     <baagaard at usgs.gov <mailto:baagaard at usgs.gov>
>>     >>         <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>
>>     >>         <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>
>>     <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>>>:
>>     >>
>>     >>             Alberto,
>>     >>
>>     >>             The log shows that the Setup Stage is mostly spent in
>>     "ElIm
>>     >>         init",
>>     >>             which is ElasticityImplicit.initialize(). This is
>>     most likely
>>     >>             associated with setting the initial stresses using a
>>     >>         SimpleDB object.
>>     >>
>>     >>             The SimpleGridDB provides much faster interpolation
>> than
>>     >>             SimpleDB for a logically Cartesian grid because it
>>     can find the
>>     >>             relevant points without a global search. The points
>>     need to
>>     >>         conform
>>     >>             to a grid, but the x, y, and z coordinates do not
>>     have to be
>>     >>         spaced
>>     >>             uniformly.
>>     >>
>>     >>             See Appendix C.3 of the manual for an example of the
>>     >>         SimpleGridDB.
>>     >>
>>     >>             Regards,
>>     >>             Brad
>>     >>
>>     >>
>>     >>             On 11/21/2016 12:34 PM, alberto cominelli wrote:
>>     >>
>>     >>                 Brad,
>>     >>                 I have included also my cfg files..
>>     >>                 regards,
>>     >>                 Alberto.
>>     >>
>>     >>                 2016-11-21 19:49 GMT+01:00 Brad Aagaard
>>     >>         <baagaard at usgs.gov <mailto:baagaard at usgs.gov>
>>     <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>
>>     >>                 <mailto:baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov> <mailto:baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov>>>
>>     >>                 <mailto:baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov> <mailto:baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov>>
>>     >>         <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>
>>     <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>>>>:
>>     >>
>>     >>                     Alberto,
>>     >>
>>     >>                     Please send the entire output of the PETSc log
>>     >>         (everything after
>>     >>                     "PETSc Performance Summary") for a
>> representative
>>     >>                 simulation. It is
>>     >>                     usually easiest to simply send the entire
>>     output of
>>     >>         stdout
>>     >>                 (gzip it
>>     >>                     if necessary to reduce size). The individual
>>     event
>>     >>         logging
>>     >>                 provides
>>     >>                     more specifics than the summary of stages. We
>>     add custom
>>     >>                 events in
>>     >>                     the PETSc logging for many of the PyLith
>>     routines.
>>     >>
>>     >>                     If you need help understanding the format of
>> the
>>     >>         summary,
>>     >>                 then see
>>     >>                     the Profiling chapter of the PETSc manual:
>>     >>
>>     >>
>>     http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf>
>>     >>
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf>>
>>     >>
>>     >>
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf>
>>     >>
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf>>>
>>     >>
>>     >>
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf>
>>     >>
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf>>
>>     >>
>>     >>
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf>
>>     >>
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
>>     <http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf>>>>.
>>     >>
>>     >>
>>     >>                     Regards,
>>     >>                     Brad
>>     >>
>>     >>
>>     >>
>>     >>
>>     >>
>>     >>                     On 11/19/2016 08:09 AM, alberto cominelli
>> wrote:
>>     >>
>>     >>                         Brad,
>>     >>                         I followed you suggestion and I also
>>     modified a
>>     >>         bit the
>>     >>                 code to
>>     >>                         track
>>     >>                         the time spent in integrator:
>>     >>
>>     >>                               start_time = time.time()
>>     >>                               integrator.initialize(totalTime,
>>     numTimeSteps,
>>     >>                 normalizer)
>>     >>                               str = "--- %s seconds in
>>     >>         integrator.initialize ---" %
>>     >>                         (time.time()
>>     >>                         - start_time)
>>     >>                               self._info.log(str)
>>     >>                          (import time at the beginning
>>     >>                         of
>>     >>
>>     >>
>>     lib64/python2.7/site-packages/pylith/problems/Formulation.py )
>>     >>                         The I run a simple case with 5733 nodes/
>> 4800
>>     >>         elements
>>     >>                 and  pylith
>>     >>                         spent  37 seconds to run with 26.5418641567
>>     >>         seconds in
>>     >>                         integrator.initialize.
>>     >>                         If I look at Petsc  log at the end I get
>>     this:
>>     >>                         Summary of Stages:   ----- Time ------
>>     ----- Flops
>>     >>                 -----  ---
>>     >>                         Messages
>>     >>                         ---  -- Message Lengths --  -- Reductions
>> --
>>     >>                                                 Avg     %Total
>>      Avg
>>     >>                  %Total   counts
>>     >>                         %Total     Avg         %Total   counts
>>      %Total
>>     >>                          0:      Main Stage: 1.3829e-01   0.4%
>>     0.0000e+00
>>     >>                  0.0%  0.000e+00
>>     >>                         0.0%  0.000e+00        0.0%  0.000e+00
>>  0.0%
>>     >>                          1:         Meshing: 1.5950e-01   0.4%
>>     1.7262e+04
>>     >>                  0.0%  0.000e+00
>>     >>                         0.0%  3.874e-02        0.0%  8.000e+00
>> 100.0%
>>     >>                          2:           Setup: 2.7486e+01  77.3%
>>     2.7133e+07
>>     >>                  0.2%  8.000e+00
>>     >>                         1.9%  2.181e+01        0.0%  0.000e+00
>>  0.0%
>>     >>                          3: Reform Jacobian: 2.8208e-01   0.8%
>>     4.1906e+08
>>     >>                  3.5%  0.000e+00
>>     >>                         0.0%  0.000e+00        0.0%  0.000e+00
>>  0.0%
>>     >>                          4: Reform Residual: 9.8572e-02   0.3%
>>     6.1111e+07
>>     >>                  0.5%  8.000e+00
>>     >>                         1.9%  1.967e+03        3.1%  0.000e+00
>>  0.0%
>>     >>                          5:           Solve: 5.5077e+00  15.5%
>>     1.1537e+10
>>     >>                 95.1%  3.970e+02
>>     >>                          96.1%  6.197e+04       96.9%  0.000e+00
>>      0.0%
>>     >>                          6:         Prestep: 5.7586e-02   0.2%
>>     0.0000e+00
>>     >>                  0.0%  0.000e+00
>>     >>                         0.0%  0.000e+00        0.0%  0.000e+00
>>  0.0%
>>     >>                          7:            Step: 8.9577e-02   0.3%
>>     0.0000e+00
>>     >>                  0.0%  0.000e+00
>>     >>                         0.0%  0.000e+00        0.0%  0.000e+00
>>  0.0%
>>     >>                          8:        Poststep: 1.6417e+00   4.6%
>>     8.2252e+07
>>     >>                  0.7%  0.000e+00
>>     >>                         0.0%  0.000e+00        0.0%  0.000e+00
>>  0.0%
>>     >>                          9:        Finalize: 7.7139e-02   0.2%
>>     0.0000e+00
>>     >>                  0.0%  0.000e+00
>>     >>                         0.0%  0.000e+00        0.0%  0.000e+00
>>  0.0%
>>     >>
>>     >>                         As far as I understand 27 seconds are
>>     spent in
>>     >>         setup,
>>     >>                 which I
>>     >>                         suppose
>>     >>                         includes integrators.
>>     >>                         I simplified the problem using a linear
>>     >>         interpolation
>>     >>                 between
>>     >>                         two points
>>     >>                         to define the initial stress state but
>> still
>>     >>         setup phase
>>     >>                 takes
>>     >>                         80% of
>>     >>                         the time.
>>     >>                         Is it fine this timing?
>>     >>                         I may send you my cfg files if you like,
>>     >>                         Regards,
>>     >>                           Alberto.
>>     >>
>>     >>                         P.S: I noticed that Petsc log makes my
>> little
>>     >>                 modification into
>>     >>                         python
>>     >>                         scripts useless..I will remove.
>>     >>
>>     >>
>>     >>                         2016-11-19 0:04 GMT+01:00 Brad Aagaard
>>     >>                 <baagaard at usgs.gov <mailto:baagaard at usgs.gov>
>>     <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>
>>     >>         <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>
>>     <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>>
>>     >>                         <mailto:baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov>
>>     >>         <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>
>>     <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>
>>     >>         <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>>>
>>     >>                         <mailto:baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov>
>>     >>         <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>
>>     <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>
>>     >>         <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>>
>>     >>                 <mailto:baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov> <mailto:baagaard at usgs.gov
>>     <mailto:baagaard at usgs.gov>>
>>     >>         <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>
>>     <mailto:baagaard at usgs.gov <mailto:baagaard at usgs.gov>>>>>>:
>>     >>
>>     >>
>>     >>
>>     >>                             Alberto,
>>     >>
>>     >>                             The PETSc log summary provides
>> important
>>     >>         performance
>>     >>                         information.
>>     >>
>>     >>                             Use these settings to see what is
>>     happening
>>     >>         in the
>>     >>                 solver
>>     >>                         and the
>>     >>                             performance (as used in
>>     >>         examples/3d/hex8/pylithapp.cfg):
>>     >>
>>     >>
>>     >>                             [pylithapp.petsc]
>>     >>                             ksp_monitor = true
>>     >>                             ksp_view = true
>>     >>                             snes_monitor = true
>>     >>                             snes_view = true
>>     >>                             log_view = true
>>     >>
>>     >>                             Regards,
>>     >>                             Brad
>>     >>
>>     >>
>>     >>
>>     >>                             On 11/18/16 2:24 PM, alberto
>>     cominelli wrote:
>>     >>
>>     >>                                 Dear All,
>>     >>
>>     >>                                 I am using pylith to make a
>>     convergence
>>     >>         study on
>>     >>                 a 12
>>     >>                         core Xeon box,
>>     >>                                 with Intel(R) Xeon(R)  E5-2643 v2
>>     cpus
>>     >>         running at @
>>     >>                         3.50GHz and
>>     >>                                 64 gb of
>>     >>                                 memory.
>>     >>                                 The problem at hand is a 3D domain
>>     >>         consisting of two
>>     >>                         layers, the
>>     >>                                 upper
>>     >>                                 one dry, with 25000kg/m3 density
>>     and the
>>     >>         lower
>>     >>                 on water
>>     >>                                 saturated with a
>>     >>                                 20% porosity.  Besides differences
>> in
>>     >>         saturated
>>     >>                         condistions, rock is
>>     >>                                 characterised as an elastic,
>>     istropic and
>>     >>                 homogeneous
>>     >>                         material.
>>     >>                                 The domain is discretised  by
>>     means of
>>     >>         hexaedral
>>     >>                         elements using a
>>     >>                                 tartan type grid developed around a
>>     >>         fault, a 20%
>>     >>                 sloping
>>     >>                         fault.
>>     >>                                 Fault
>>     >>                                 rehology is very simple, a friction
>>     >>         model with
>>     >>                 0.6 friction
>>     >>                                 coefficient,
>>     >>
>>     >>                                 To simulate a consolidation
>>     problem, fluid
>>     >>                 pressure is
>>     >>                         included
>>     >>                                 in the
>>     >>                                 model using initial stress on a
>>     cell basis
>>     >>                 assuming that
>>     >>                         pressure is
>>     >>                                 constant inside each cell.
>>     >>                                 This means I input a
>>     >>         initial_stress.spatialdb file
>>     >>                         containg data for
>>     >>                                 ncells * 8 quadrature points.
>>     >>                                 I am a bit surprised by elapsed
>> time
>>     >>         values I
>>     >>                 get along my
>>     >>                                 convergence
>>     >>                                 study.
>>     >>                                 For instance, one case consists
>>     of 52731
>>     >>         nodes
>>     >>                 and 48630
>>     >>                                 elements. To
>>     >>                                 properly initialise the model I
>> give
>>     >>         initial stress
>>     >>                         values in
>>     >>                                 386880. I
>>     >>                                 make two steps in 48 minutes,
>>     with most
>>     >>         of the
>>     >>                 time spent in
>>     >>                                 integrators
>>     >>                                 - as far as I understand.
>>     >>
>>     >>                                 With "Integrators" I mean what is
>>     >>         labelled by
>>     >>                 these lines in
>>     >>                                 pylith output:
>>     >>                                 -- Initializing integrators.
>>     >>                                  >>
>>     >>
>>     >>
>>     >>
>>     >>
>>     /home/comi/Pylith2.1.3/lib64/python2.7/site-packages/pylith/
>> problems/Formulation.py
>>     >>                                 [0m:474 [0m:_initialize [0m
>>     >>                                 I guess this step means building
>>     >>         residuals and
>>     >>                 stiffness
>>     >>                                 matrices, but I
>>     >>                                 am not sure about. Notably, in the
>>     >>         second steo I
>>     >>                 do not
>>     >>                         change
>>     >>                                 anything
>>     >>                                 and then I get very few
>>     linear/non linear
>>     >>                 iteration in the
>>     >>                                 latter step.
>>     >>
>>     >>                                 I wonder if this time is fine
>>     according
>>     >>         to you
>>     >>                         experience and if
>>     >>                                 it is
>>     >>                                 worth going parallel to improve
>>     >>         computational
>>     >>                         efficiency. I am
>>     >>                                 willing
>>     >>                                 to make much more complx cases
>>     up to some
>>     >>                 millions of
>>     >>                         nodes and I
>>     >>                                 wonder how far I can go using
>>     only one core.
>>     >>                                 Regards,
>>     >>                                  Alberto.
>>     >>
>>     >>                                 I am attaching a snapshot of one
>>     >>         simulation log
>>     >>                 (not for
>>     >>                         the entire
>>     >>                                 case) in case it may help.
>>     >>                                 Regards,
>>     >>                                   Alberto.
>>     >>
>>     >>
>>     >>
>>     >>
>>     >>
>>     >>         _______________________________________________
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