[petsc-users] Is it possible to keep track of original elements # after a call to DMPlexDistribute ?
Matthew Knepley
knepley at gmail.com
Mon Nov 1 14:25:43 CDT 2021
On Sun, Oct 31, 2021 at 10:07 AM Eric Chamberland <
Eric.Chamberland at giref.ulaval.ca> wrote:
> Hi Matthew,
>
> we do not know if DMPlexNaturalToGlobalBegin/End is buggy or if it is our
> comprehension of what it should do that is wrong...
>
> Would you just check if what we try to do from line 313 to 356 is good or
> wrong?
>
> The expected result is that the global vector "lGlobalVec" contains the
> element numbers from the initial partition that have been put into
> "lNatVec".
>
> Thanks a lot for any insights!!
>
> Okay, I have found the problem.I confess to not actually looking very
closely at the implementation before. GlobalToNatural was assuming that
the "natural" was also sequential, and looking at it all the tests are
eq-to-parallel distribution. I need to fix it for a parallel natural state.
Hopefully
it will not take me long.
Thanks,
Matt
> Eric
>
>
> On 2021-10-27 2:32 p.m., Eric Chamberland wrote:
>
> Hi Matthew,
>
> we continued the example. Now it must be our misuse of PETSc that
> produced the wrong result.
>
> As stated into the code:
>
> // The call to DMPlexNaturalToGlobalBegin/End does not produce our
> expected result...
> // In lGlobalVec, we expect to have:
> /*
> * Process [0]
> * 2.
> * 4.
> * 8.
> * 3.
> * 9.
> * Process [1]
> * 1.
> * 5.
> * 7.
> * 0.
> * 6.
> *
> * but we obtained:
> *
> * Process [0]
> * 2.
> * 4.
> * 8.
> * 0.
> * 0.
> * Process [1]
> * 0.
> * 0.
> * 0.
> * 0.
> * 0.
> */
>
> (see attached ex44.c)
>
> Thanks,
>
> Eric
> On 2021-10-27 1:25 p.m., Eric Chamberland wrote:
>
> Great!
>
> Thanks Matthew, it is working for me up to that point!
>
> We are continuing the ex44.c and forward it to you at the next blocking
> point...
>
> Eric
> On 2021-10-27 11:14 a.m., Matthew Knepley wrote:
>
> On Wed, Oct 27, 2021 at 8:29 AM Eric Chamberland <
> Eric.Chamberland at giref.ulaval.ca> wrote:
>
>> Hi Matthew,
>>
>> the smallest mesh which crashes the code is a 2x5 mesh:
>>
>> See the modified ex44.c
>>
>> With smaller meshes(2x2, 2x4, etc), it passes... But it bugs latter when
>> I try to use DMPlexNaturalToGlobalBegin but let's keep that other problem
>> for later...
>>
>> Thanks a lot for helping digging into this! :)
>>
> I have made a small fix in this branch
>
> https://gitlab.com/petsc/petsc/-/commits/knepley/fix-plex-g2n
>
> It seems to run for me. Can you check it?
>
> Thanks,
>
> Matt
>
>
>> Eric
>>
>> (sorry if you received this for a 2nd times, I have trouble with my mail)
>> On 2021-10-26 4:35 p.m., Matthew Knepley wrote:
>>
>> On Tue, Oct 26, 2021 at 1:35 PM Eric Chamberland <
>> Eric.Chamberland at giref.ulaval.ca> wrote:
>>
>>> Here is a screenshot of the partition I hard coded (top) and
>>> vertices/element numbers (down):
>>>
>>> I have not yet modified the ex44.c example to properly assign the
>>> coordinates...
>>>
>>> (but I would not have done it like it is in the last version because the
>>> sCoords array is the global array with global vertices number)
>>>
>>> I will have time to do this tomorrow...
>>>
>>> Maybe I can first try to reproduce all this with a smaller mesh?
>>>
>>
>> That might make it easier to find a problem.
>>
>> Thanks!
>>
>> Matt
>>
>>
>>> Eric
>>> On 2021-10-26 9:46 a.m., Matthew Knepley wrote:
>>>
>>> Okay, I ran it. Something seems off with the mesh. First, I cannot
>>> simply explain the partition. The number of shared vertices and edges
>>> does not seem to come from a straight cut. Second, the mesh look
>>> scrambled on output.
>>>
>>> Thanks,
>>>
>>> Matt
>>>
>>> On Sun, Oct 24, 2021 at 11:49 PM Eric Chamberland <
>>> Eric.Chamberland at giref.ulaval.ca> wrote:
>>>
>>>> Hi Matthew,
>>>>
>>>> ok, I started back from your ex44.c example and added the global array
>>>> of coordinates. I just have to code the creation of the local coordinates
>>>> now.
>>>>
>>>> Eric
>>>> On 2021-10-20 6:55 p.m., Matthew Knepley wrote:
>>>>
>>>> On Wed, Oct 20, 2021 at 3:06 PM Eric Chamberland <
>>>> Eric.Chamberland at giref.ulaval.ca> wrote:
>>>>
>>>>> Hi Matthew,
>>>>>
>>>>> we tried to reproduce the error in a simple example.
>>>>>
>>>>> The context is the following: We hard coded the mesh and initial
>>>>> partition into the code (see sConnectivity and sInitialPartition) for 2
>>>>> ranks and try to create a section in order to use the
>>>>> DMPlexNaturalToGlobalBegin function to retreive our initial element numbers.
>>>>>
>>>>> Now the call to DMPlexDistribute give different errors depending on
>>>>> what type of component we ask the field to be created. For our objective,
>>>>> we would like a global field to be created on elements only (like a P0
>>>>> interpolation).
>>>>>
>>>>> We now have the following error generated:
>>>>>
>>>>> [0]PETSC ERROR: --------------------- Error Message
>>>>> --------------------------------------------------------------
>>>>> [0]PETSC ERROR: Petsc has generated inconsistent data
>>>>> [0]PETSC ERROR: Inconsistency in indices, 18 should be 17
>>>>> [0]PETSC ERROR: See
>>>>> https://www.mcs.anl.gov/petsc/documentation/faq.html for trouble
>>>>> shooting.
>>>>> [0]PETSC ERROR: Petsc Release Version 3.15.0, Mar 30, 2021
>>>>> [0]PETSC ERROR: ./bug on a named rohan by ericc Wed Oct 20 14:52:36
>>>>> 2021
>>>>> [0]PETSC ERROR: Configure options
>>>>> --prefix=/opt/petsc-3.15.0_debug_openmpi-4.1.0_gcc7 --with-mpi-compilers=1
>>>>> --with-mpi-dir=/opt/openmpi-4.1.0_gcc7 --with-cxx-dialect=C++14
>>>>> --with-make-np=12 --with-shared-libraries=1 --with-debugging=yes
>>>>> --with-memalign=64 --with-visibility=0 --with-64-bit-indices=0
>>>>> --download-ml=yes --download-mumps=yes --download-superlu=yes
>>>>> --download-hpddm=yes --download-slepc=yes --download-superlu_dist=yes
>>>>> --download-parmetis=yes --download-ptscotch=yes --download-metis=yes
>>>>> --download-strumpack=yes --download-suitesparse=yes --download-hypre=yes
>>>>> --with-blaslapack-dir=/opt/intel/oneapi/mkl/2021.1.1/env/../lib/intel64
>>>>> --with-mkl_pardiso-dir=/opt/intel/oneapi/mkl/2021.1.1/env/..
>>>>> --with-mkl_cpardiso-dir=/opt/intel/oneapi/mkl/2021.1.1/env/..
>>>>> --with-scalapack=1
>>>>> --with-scalapack-include=/opt/intel/oneapi/mkl/2021.1.1/env/../include
>>>>> --with-scalapack-lib="-L/opt/intel/oneapi/mkl/2021.1.1/env/../lib/intel64
>>>>> -lmkl_scalapack_lp64 -lmkl_blacs_openmpi_lp64"
>>>>> [0]PETSC ERROR: #1 PetscSFCreateSectionSF() at
>>>>> /tmp/ompi-opt/petsc-3.15.0-debug/src/vec/is/sf/utils/sfutils.c:409
>>>>> [0]PETSC ERROR: #2 DMPlexCreateGlobalToNaturalSF() at
>>>>> /tmp/ompi-opt/petsc-3.15.0-debug/src/dm/impls/plex/plexnatural.c:184
>>>>> [0]PETSC ERROR: #3 DMPlexDistribute() at
>>>>> /tmp/ompi-opt/petsc-3.15.0-debug/src/dm/impls/plex/plexdistribute.c:1733
>>>>> [0]PETSC ERROR: #4 main() at bug_section.cc:159
>>>>> [0]PETSC ERROR: No PETSc Option Table entries
>>>>> [0]PETSC ERROR: ----------------End of Error Message -------send
>>>>> entire error message to petsc-maint at mcs.anl.gov----------
>>>>>
>>>>> Hope the attached code is self-explaining, note that to make it short,
>>>>> we have not included the final part of it, just the buggy part we are
>>>>> encountering right now...
>>>>>
>>>>> Thanks for your insights,
>>>>>
>>>> Thanks for making the example. I tweaked it slightly. I put in a test
>>>> case that just makes a parallel 7 x 10 quad mesh. This works
>>>> fine. Thus I think it must be something connected with the original
>>>> mesh. It is hard to get a handle on it without the coordinates.
>>>> Do you think you could put the coordinate array in? I have added the
>>>> code to load them (see attached file).
>>>>
>>>> Thanks,
>>>>
>>>> Matt
>>>>
>>>>> Eric
>>>>> On 2021-10-06 9:23 p.m., Matthew Knepley wrote:
>>>>>
>>>>> On Wed, Oct 6, 2021 at 5:43 PM Eric Chamberland <
>>>>> Eric.Chamberland at giref.ulaval.ca> wrote:
>>>>>
>>>>>> Hi Matthew,
>>>>>>
>>>>>> we tried to use that. Now, we discovered that:
>>>>>>
>>>>>> 1- even if we "ask" for sfNatural creation with DMSetUseNatural, it
>>>>>> is not created because DMPlexCreateGlobalToNaturalSF looks for a "section":
>>>>>> this is not documented in DMSetUseNaturalso we are asking ourselfs: "is
>>>>>> this a permanent feature or a temporary situation?"
>>>>>>
>>>>> I think explaining this will help clear up a lot.
>>>>>
>>>>> What the Natural2Global map does is permute a solution vector into the
>>>>> ordering that it would have had prior to mesh distribution.
>>>>> Now, in order to do this permutation, I need to know the original
>>>>> (global) data layout. If it is not specified _before_ distribution, we
>>>>> cannot build the permutation. The section describes the data layout,
>>>>> so I need it before distribution.
>>>>>
>>>>> I cannot think of another way that you would implement this, but if
>>>>> you want something else, let me know.
>>>>>
>>>>>> 2- We then tried to create a "section" in different manners: we took
>>>>>> the code into the example petsc/src/dm/impls/plex/tests/ex15.c. However,
>>>>>> we ended up with a segfault:
>>>>>>
>>>>>> corrupted size vs. prev_size
>>>>>> [rohan:07297] *** Process received signal ***
>>>>>> [rohan:07297] Signal: Aborted (6)
>>>>>> [rohan:07297] Signal code: (-6)
>>>>>> [rohan:07297] [ 0] /lib64/libpthread.so.0(+0x13f80)[0x7f6f13be3f80]
>>>>>> [rohan:07297] [ 1] /lib64/libc.so.6(gsignal+0x10b)[0x7f6f109b718b]
>>>>>> [rohan:07297] [ 2] /lib64/libc.so.6(abort+0x175)[0x7f6f109b8585]
>>>>>> [rohan:07297] [ 3] /lib64/libc.so.6(+0x7e2f7)[0x7f6f109fb2f7]
>>>>>> [rohan:07297] [ 4] /lib64/libc.so.6(+0x857ea)[0x7f6f10a027ea]
>>>>>> [rohan:07297] [ 5] /lib64/libc.so.6(+0x86036)[0x7f6f10a03036]
>>>>>> [rohan:07297] [ 6] /lib64/libc.so.6(+0x861a3)[0x7f6f10a031a3]
>>>>>> [rohan:07297] [ 7] /lib64/libc.so.6(+0x88740)[0x7f6f10a05740]
>>>>>> [rohan:07297] [ 8]
>>>>>> /lib64/libc.so.6(__libc_malloc+0x1b8)[0x7f6f10a070c8]
>>>>>> [rohan:07297] [ 9]
>>>>>> /lib64/libc.so.6(__backtrace_symbols+0x134)[0x7f6f10a8b064]
>>>>>> [rohan:07297] [10]
>>>>>> /home/mefpp_ericc/GIREF/bin/MEF++.dev(_Z12reqBacktraceRNSt7__cxx1112basic_stringIcSt11char_traitsIcESaIcEEE+0x4e)[0x4538ce]
>>>>>> [rohan:07297] [11]
>>>>>> /home/mefpp_ericc/GIREF/bin/MEF++.dev(_Z15attacheDebuggerv+0x120)[0x4523c0]
>>>>>> [rohan:07297] [12]
>>>>>> /home/mefpp_ericc/GIREF/lib/libgiref_dev_Util.so(traitementSignal+0x612)[0x7f6f28f503a2]
>>>>>> [rohan:07297] [13] /lib64/libc.so.6(+0x3a210)[0x7f6f109b7210]
>>>>>>
>>>>>> [rohan:07297] [14]
>>>>>> /opt/petsc-3.15.0_debug_openmpi-4.1.0_gcc7/lib/libpetsc.so.3.15(PetscTrMallocDefault+0x6fd)[0x7f6f22f1b8ed]
>>>>>> [rohan:07297] [15]
>>>>>> /opt/petsc-3.15.0_debug_openmpi-4.1.0_gcc7/lib/libpetsc.so.3.15(PetscMallocA+0x5cd)[0x7f6f22f19c2d]
>>>>>> [rohan:07297] [16]
>>>>>> /opt/petsc-3.15.0_debug_openmpi-4.1.0_gcc7/lib/libpetsc.so.3.15(PetscSFCreateSectionSF+0xb48)[0x7f6f23268e18]
>>>>>> [rohan:07297] [17]
>>>>>> /opt/petsc-3.15.0_debug_openmpi-4.1.0_gcc7/lib/libpetsc.so.3.15(DMPlexCreateGlobalToNaturalSF+0x13b2)[0x7f6f241a5602]
>>>>>> [rohan:07297] [18]
>>>>>> /opt/petsc-3.15.0_debug_openmpi-4.1.0_gcc7/lib/libpetsc.so.3.15(DMPlexDistribute+0x39b1)[0x7f6f23fdca21]
>>>>>>
>>>>> I am not sure what happened here, but if you could send a sample code,
>>>>> I will figure it out.
>>>>>
>>>>>> If we do not create a section, the call to DMPlexDistribute is
>>>>>> successful, but DMPlexGetGlobalToNaturalSF return a null SF pointer...
>>>>>>
>>>>> Yes, it just ignores it in this case because it does not have a global
>>>>> layout.
>>>>>
>>>>>> Here are the operations we are calling ( this is almost the code we
>>>>>> are using, I just removed verifications and creation of the connectivity
>>>>>> which use our parallel structure and code):
>>>>>>
>>>>>> ===========
>>>>>>
>>>>>> PetscInt* lCells = 0;
>>>>>> PetscInt lNumCorners = 0;
>>>>>> PetscInt lDimMail = 0;
>>>>>> PetscInt lnumCells = 0;
>>>>>>
>>>>>> //At this point we create the cells for PETSc expected input for
>>>>>> DMPlexBuildFromCellListParallel and set lNumCorners, lDimMail and lnumCells
>>>>>> to correct values.
>>>>>> ...
>>>>>>
>>>>>> DM lDMBete = 0
>>>>>> DMPlexCreate(lMPIComm,&lDMBete);
>>>>>>
>>>>>> DMSetDimension(lDMBete, lDimMail);
>>>>>>
>>>>>> DMPlexBuildFromCellListParallel(lDMBete,
>>>>>> lnumCells,
>>>>>> PETSC_DECIDE,
>>>>>>
>>>>>> pLectureElementsLocaux.reqNbTotalSommets(),
>>>>>> lNumCorners,
>>>>>> lCells,
>>>>>> PETSC_NULL);
>>>>>>
>>>>>> DM lDMBeteInterp = 0;
>>>>>> DMPlexInterpolate(lDMBete, &lDMBeteInterp);
>>>>>> DMDestroy(&lDMBete);
>>>>>> lDMBete = lDMBeteInterp;
>>>>>>
>>>>>> DMSetUseNatural(lDMBete,PETSC_TRUE);
>>>>>>
>>>>>> PetscSF lSFMigrationSansOvl = 0;
>>>>>> PetscSF lSFMigrationOvl = 0;
>>>>>> DM lDMDistribueSansOvl = 0;
>>>>>> DM lDMAvecOverlap = 0;
>>>>>>
>>>>>> PetscPartitioner lPart;
>>>>>> DMPlexGetPartitioner(lDMBete, &lPart);
>>>>>> PetscPartitionerSetFromOptions(lPart);
>>>>>>
>>>>>> PetscSection section;
>>>>>> PetscInt numFields = 1;
>>>>>> PetscInt numBC = 0;
>>>>>> PetscInt numComp[1] = {1};
>>>>>> PetscInt numDof[4] = {1, 0, 0, 0};
>>>>>> PetscInt bcFields[1] = {0};
>>>>>> IS bcPoints[1] = {NULL};
>>>>>>
>>>>>> DMSetNumFields(lDMBete, numFields);
>>>>>>
>>>>>> DMPlexCreateSection(lDMBete, NULL, numComp, numDof, numBC,
>>>>>> bcFields, bcPoints, NULL, NULL, §ion);
>>>>>> DMSetLocalSection(lDMBete, section);
>>>>>>
>>>>>> DMPlexDistribute(lDMBete, 0, &lSFMigrationSansOvl,
>>>>>> &lDMDistribueSansOvl); // segfault!
>>>>>>
>>>>>> ===========
>>>>>>
>>>>>> So we have other question/remarks:
>>>>>>
>>>>>> 3- Maybe PETSc expect something specific that is missing/not
>>>>>> verified: for example, we didn't gave any coordinates since we just want to
>>>>>> partition and compute overlap for the mesh... and then recover our element
>>>>>> numbers in a "simple way"
>>>>>>
>>>>>> 4- We are telling ourselves it is somewhat a "big price to pay" to
>>>>>> have to build an unused section to have the global to natural ordering set
>>>>>> ? Could this requirement be avoided?
>>>>>>
>>>>> I don't think so. There would have to be _some_ way of describing your
>>>>> data layout in terms of mesh points, and I do not see how you could use
>>>>> less memory doing that.
>>>>>
>>>>>> 5- Are there any improvement towards our usages in 3.16 release?
>>>>>>
>>>>> Let me try and run the code above.
>>>>>
>>>>> Thanks,
>>>>>
>>>>> Matt
>>>>>
>>>>>> Thanks,
>>>>>>
>>>>>> Eric
>>>>>>
>>>>>>
>>>>>> On 2021-09-29 7:39 p.m., Matthew Knepley wrote:
>>>>>>
>>>>>> On Wed, Sep 29, 2021 at 5:18 PM Eric Chamberland <
>>>>>> Eric.Chamberland at giref.ulaval.ca> wrote:
>>>>>>
>>>>>>> Hi,
>>>>>>>
>>>>>>> I come back with _almost_ the original question:
>>>>>>>
>>>>>>> I would like to add an integer information (*our* original element
>>>>>>> number, not petsc one) on each element of the DMPlex I create with
>>>>>>> DMPlexBuildFromCellListParallel.
>>>>>>>
>>>>>>> I would like this interger to be distribruted by or the same way
>>>>>>> DMPlexDistribute distribute the mesh.
>>>>>>>
>>>>>>> Is it possible to do this?
>>>>>>>
>>>>>>
>>>>>> I think we already have support for what you want. If you call
>>>>>>
>>>>>> https://petsc.org/main/docs/manualpages/DM/DMSetUseNatural.html
>>>>>>
>>>>>> before DMPlexDistribute(), it will compute a PetscSF encoding the
>>>>>> global to natural map. You
>>>>>> can get it with
>>>>>>
>>>>>>
>>>>>> https://petsc.org/main/docs/manualpages/DMPLEX/DMPlexGetGlobalToNaturalSF.html
>>>>>>
>>>>>> and use it with
>>>>>>
>>>>>>
>>>>>> https://petsc.org/main/docs/manualpages/DMPLEX/DMPlexGlobalToNaturalBegin.html
>>>>>>
>>>>>> Is this sufficient?
>>>>>>
>>>>>> Thanks,
>>>>>>
>>>>>> Matt
>>>>>>
>>>>>>
>>>>>>> Thanks,
>>>>>>>
>>>>>>> Eric
>>>>>>>
>>>>>>> On 2021-07-14 1:18 p.m., Eric Chamberland wrote:
>>>>>>> > Hi,
>>>>>>> >
>>>>>>> > I want to use DMPlexDistribute from PETSc for computing
>>>>>>> overlapping
>>>>>>> > and play with the different partitioners supported.
>>>>>>> >
>>>>>>> > However, after calling DMPlexDistribute, I noticed the elements
>>>>>>> are
>>>>>>> > renumbered and then the original number is lost.
>>>>>>> >
>>>>>>> > What would be the best way to keep track of the element
>>>>>>> renumbering?
>>>>>>> >
>>>>>>> > a) Adding an optional parameter to let the user retrieve a vector
>>>>>>> or
>>>>>>> > "IS" giving the old number?
>>>>>>> >
>>>>>>> > b) Adding a DMLabel (seems a wrong good solution)
>>>>>>> >
>>>>>>> > c) Other idea?
>>>>>>> >
>>>>>>> > Of course, I don't want to loose performances with the need of
>>>>>>> this
>>>>>>> > "mapping"...
>>>>>>> >
>>>>>>> > Thanks,
>>>>>>> >
>>>>>>> > Eric
>>>>>>> >
>>>>>>> --
>>>>>>> Eric Chamberland, ing., M. Ing
>>>>>>> Professionnel de recherche
>>>>>>> GIREF/Université Laval
>>>>>>> (418) 656-2131 poste 41 22 42
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> --
>>>>>> What most experimenters take for granted before they begin their
>>>>>> experiments is infinitely more interesting than any results to which their
>>>>>> experiments lead.
>>>>>> -- Norbert Wiener
>>>>>>
>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>>
>>>>>> --
>>>>>> Eric Chamberland, ing., M. Ing
>>>>>> Professionnel de recherche
>>>>>> GIREF/Université Laval
>>>>>> (418) 656-2131 poste 41 22 42
>>>>>>
>>>>>>
>>>>>
>>>>> --
>>>>> What most experimenters take for granted before they begin their
>>>>> experiments is infinitely more interesting than any results to which their
>>>>> experiments lead.
>>>>> -- Norbert Wiener
>>>>>
>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>
>>>>> --
>>>>> Eric Chamberland, ing., M. Ing
>>>>> Professionnel de recherche
>>>>> GIREF/Université Laval
>>>>> (418) 656-2131 poste 41 22 42
>>>>>
>>>>>
>>>>
>>>> --
>>>> What most experimenters take for granted before they begin their
>>>> experiments is infinitely more interesting than any results to which their
>>>> experiments lead.
>>>> -- Norbert Wiener
>>>>
>>>> https://www.cse.buffalo.edu/~knepley/
>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>
>>>> --
>>>> Eric Chamberland, ing., M. Ing
>>>> Professionnel de recherche
>>>> GIREF/Université Laval
>>>> (418) 656-2131 poste 41 22 42
>>>>
>>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>> https://www.cse.buffalo.edu/~knepley/
>>> <http://www.cse.buffalo.edu/~knepley/>
>>>
>>> --
>>> Eric Chamberland, ing., M. Ing
>>> Professionnel de recherche
>>> GIREF/Université Laval
>>> (418) 656-2131 poste 41 22 42
>>>
>>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>> https://www.cse.buffalo.edu/~knepley/
>> <http://www.cse.buffalo.edu/~knepley/>
>>
>> --
>> Eric Chamberland, ing., M. Ing
>> Professionnel de recherche
>> GIREF/Université Laval
>> (418) 656-2131 poste 41 22 42
>>
>>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
> --
> Eric Chamberland, ing., M. Ing
> Professionnel de recherche
> GIREF/Université Laval
> (418) 656-2131 poste 41 22 42
>
> --
> Eric Chamberland, ing., M. Ing
> Professionnel de recherche
> GIREF/Université Laval
> (418) 656-2131 poste 41 22 42
>
> --
> Eric Chamberland, ing., M. Ing
> Professionnel de recherche
> GIREF/Université Laval
> (418) 656-2131 poste 41 22 42
>
>
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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