[petsc-users] DMPlexCreateExodusFromFile() does not work on macOS Sierra
Kong, Fande
fande.kong at inl.gov
Tue Jan 24 10:39:35 CST 2017
Thanks, Blaise and Matt,
I possibly mess up the brew installation somehow. I will clean up
everything and start over, and report back.
Fande,
On Tue, Jan 24, 2017 at 9:26 AM, Matthew Knepley <knepley at gmail.com> wrote:
> Thanks!
>
> Matt
>
> On Tue, Jan 24, 2017 at 8:57 AM, Blaise A Bourdin <bourdin at lsu.edu> wrote:
>
>> Hi,
>>
>> I was able to build petsc master with home-brew gcc 6.3 and intel 17.0
>> under macOS sierra. As Mark said, it is important to reinstall the entire
>> home-brew compiler + libs after upgrading macOS (and often Xcode).
>> I am able to read / write exodus files. I am attaching my configure
>> command lines:
>>
>> with intel 17.0:
>> ./configure ./configure \
>> --download-chaco=1 \
>> --download-exodusii=1 \
>> --download-hdf5=1 \
>> --download-hypre=1 \
>> --download-metis=1 \
>> --download-ml=1 \
>> --download-netcdf=1 \
>> --download-parmetis=1 \
>> --download-triangle=1 \
>> --with-blas-lapack-dir=$MKLROOT \
>> --with-debugging=1 \
>> --with-mpi-dir=$MPI_HOME \
>> --with-pic \
>> --with-shared-libraries=1 \
>> --with-vendor-compilers=intel \
>> --with-x11=1
>>
>> with gcc:
>> ./configure \
>> --download-exodusii=1 \
>> --download-chaco=1 \
>> --download-ctetgen=1 \
>> --download-hdf5=1 \
>> --download-hypre=1 \
>> --download-metis=1 \
>> --download-ml=1 \
>> --download-netcdf=1 \
>> --download-parmetis=1 \
>> --download-triangle=1 \
>> --download-yaml=1 \
>> --with-debugging=1 \
>> --with-shared-libraries=1 \
>> --with-x11=1
>>
>> Blaise
>>
>> On Jan 23, 2017, at 7:55 AM, Mark Adams <mfadams at lbl.gov> wrote:
>>
>> And I trust you updated all system software (like gcc, NetCDF and
>> ExodusII). OSX upgrades are hell.
>>
>> On Mon, Jan 23, 2017 at 12:36 AM, Matthew Knepley <knepley at gmail.com>
>> wrote:
>>
>>> On Sun, Jan 22, 2017 at 11:18 PM, Fande Kong <fdkong.jd at gmail.com>
>>> wrote:
>>>
>>>> Thanks, Matt,
>>>>
>>>> Clang does not have this issue. The code runs fine with clang.
>>>>
>>>
>>> Okay, it sounds like a gcc bug on Mac 10.6, or at least in the version
>>> you have.
>>>
>>> Matt
>>>
>>>
>>>> Fande,
>>>>
>>>> On Sun, Jan 22, 2017 at 8:03 PM, Matthew Knepley <knepley at gmail.com>
>>>> wrote:
>>>>
>>>>> On Sun, Jan 22, 2017 at 8:40 PM, Fande Kong <fdkong.jd at gmail.com>
>>>>> wrote:
>>>>>
>>>>>> Thanks, Matt.
>>>>>>
>>>>>> It is a weird bug.
>>>>>>
>>>>>> Do we have an alternative solution to this? I was wondering whether
>>>>>> it is possible to read the ".exo" files without using the ExodusII. For
>>>>>> example, can we read the ".exo" files using the netcdf only?
>>>>>>
>>>>>
>>>>> Well, ExodusII is only a think layer on NetCDF, just like other
>>>>> wrappers are thin layers on HDF5. It is
>>>>> really NetCDF that is failing. Can you switch compilers and see if
>>>>> that helps?
>>>>>
>>>>> Matt
>>>>>
>>>>>
>>>>>> Fande Kong,
>>>>>>
>>>>>>
>>>>>>
>>>>>> On Sun, Jan 22, 2017 at 6:50 PM, Matthew Knepley <knepley at gmail.com>
>>>>>> wrote:
>>>>>>
>>>>>>> On Sun, Jan 22, 2017 at 5:28 PM, Fande Kong <fdkong.jd at gmail.com>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> On Sun, Jan 22, 2017 at 12:35 PM, Matthew Knepley <
>>>>>>>> knepley at gmail.com> wrote:
>>>>>>>>
>>>>>>>>> On Sun, Jan 22, 2017 at 12:41 PM, Fande Kong <fdkong.jd at gmail.com>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>>> On Sat, Jan 21, 2017 at 10:47 PM, Matthew Knepley <
>>>>>>>>>> knepley at gmail.com> wrote:
>>>>>>>>>>
>>>>>>>>>>> On Sat, Jan 21, 2017 at 10:38 PM, Fande Kong <
>>>>>>>>>>> fdkong.jd at gmail.com> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> Hi All,
>>>>>>>>>>>>
>>>>>>>>>>>> I upgraded the OS system to macOS Sierra, and observed that
>>>>>>>>>>>> PETSc can not read the exodus file any more. The same code runs fine
>>>>>>>>>>>> on macOS Capitan. I also tested the function DMPlexCreateExodusFromFile()
>>>>>>>>>>>> against different versions of the GCC compiler such as GCC-5.4 and GCC-6,
>>>>>>>>>>>> and neither of them work. I guess this issue is related to the external
>>>>>>>>>>>> package *exodus*, and PETSc might not pick up the right
>>>>>>>>>>>> enveriment variables for the *exodus.*
>>>>>>>>>>>>
>>>>>>>>>>>> This issue can be reproduced using the following simple code:
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> 1) This is just a standard check. Have you reconfigured so that
>>>>>>>>>>> you know ExodusII was built with the same compilers and system libraries?
>>>>>>>>>>>
>>>>>>>>>>> 2) If so, can you get a stack trace with gdb or lldb?
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> 0 libsystem_kernel.dylib 0x00007fffad8b8dda
>>>>>>>>>> __pthread_kill + 10
>>>>>>>>>> 1 libsystem_pthread.dylib 0x00007fffad9a4787
>>>>>>>>>> pthread_kill + 90
>>>>>>>>>> 2 libsystem_c.dylib 0x00007fffad81e420 abort + 129
>>>>>>>>>> 3 libpetsc.3.7.dylib 0x00000001100eb9ee
>>>>>>>>>> PetscAbortErrorHandler + 506 (errstop.c:40)
>>>>>>>>>> 4 libpetsc.3.7.dylib 0x00000001100e631d PetscError
>>>>>>>>>> + 916 (err.c:379)
>>>>>>>>>> 5 libpetsc.3.7.dylib 0x00000001100ed830
>>>>>>>>>> PetscSignalHandlerDefault + 1927 (signal.c:160)
>>>>>>>>>> 6 libpetsc.3.7.dylib 0x00000001100ed088
>>>>>>>>>> PetscSignalHandler_Private(int) + 630 (signal.c:49)
>>>>>>>>>> 7 libsystem_platform.dylib 0x00007fffad997bba _sigtramp
>>>>>>>>>> + 26
>>>>>>>>>> 8 ??? 0x000000011ea09370
>>>>>>>>>> initialPoolContent + 19008
>>>>>>>>>> 9 libnetcdf.7.dylib 0x000000011228fc62
>>>>>>>>>> utf8proc_map + 210 (dutf8proc.c:543)
>>>>>>>>>> 10 libnetcdf.7.dylib 0x000000011228fd0f
>>>>>>>>>> utf8proc_NFC + 38 (dutf8proc.c:568)
>>>>>>>>>> 11 libnetcdf.7.dylib 0x00000001122a7928 NC_findattr
>>>>>>>>>> + 110 (attr.c:341)
>>>>>>>>>> 12 libnetcdf.7.dylib 0x00000001122a7a4e
>>>>>>>>>> NC_lookupattr + 119 (attr.c:384)
>>>>>>>>>> 13 libnetcdf.7.dylib 0x00000001122a93ef NC3_get_att
>>>>>>>>>> + 47 (attr.c:1138)
>>>>>>>>>> 14 libnetcdf.7.dylib 0x0000000112286126
>>>>>>>>>> nc_get_att_float + 90 (dattget.c:192)
>>>>>>>>>> 15 libpetsc.3.7.dylib 0x00000001117f3a5b
>>>>>>>>>> ex_open_int + 171 (ex_open.c:259)
>>>>>>>>>> 16 libpetsc.3.7.dylib 0x0000000110c36609
>>>>>>>>>> DMPlexCreateExodusFromFile + 781 (plexexodusii.c:43)
>>>>>>>>>> 17 DMPlexCreateExodusFromFile 0x000000010fed4cfc main + 397
>>>>>>>>>> (DMPlexCreateExodusFromFile.cpp:24)
>>>>>>>>>> 18 libdyld.dylib 0x00007fffad78a255 start + 1
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> This is a NetCDF error on ex_open_int(). My guess is that your
>>>>>>>>> NetCDF build is old and when it calls the system DLL
>>>>>>>>> you bomb. Can you do a completely new build, meaning either
>>>>>>>>> reclone PETSc somewhere else, or delete the whole
>>>>>>>>> $PETSC_DIR/$PETSC_ARCH/externalpackage directory and
>>>>>>>>> reconfigure/build?
>>>>>>>>>
>>>>>>>>> Thanks,
>>>>>>>>>
>>>>>>>>> Matt
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Hi Matt,
>>>>>>>>
>>>>>>>> Thanks for reply. I recloned PETSc (the old petsc folder is
>>>>>>>> deleted completely) and reconfigure. And still has the same issue. I also
>>>>>>>> checked if the binary is complied against any other netcdf. The binary is
>>>>>>>> actually complied against the right netcdf installed through PETSc.
>>>>>>>>
>>>>>>>
>>>>>>> You can see that this crash happens on the call to
>>>>>>>
>>>>>>> int CPU_word_size = 0, IO_word_size = 0, exoid = -1;
>>>>>>> float version;
>>>>>>>
>>>>>>> exoid = ex_open(filename, EX_READ, &CPU_word_size, &IO_word_size,
>>>>>>> &version);
>>>>>>>
>>>>>>> which means the fault is not in PETSc, but rather in ExodusII for
>>>>>>> your machine. We could definitely
>>>>>>> confirm this if you made a 5 line program that only called this, but
>>>>>>> I don't see why it should be different.
>>>>>>> I am not sure what to do, since I am not in control of anything
>>>>>>> about ExodusII. Can you report this to
>>>>>>> their dev team? It is strange since Blaise has not reported this,
>>>>>>> and I know he uses it all the time.
>>>>>>>
>>>>>>> Thanks,
>>>>>>>
>>>>>>> Matt
>>>>>>>
>>>>>>>
>>>>>>>> *LiviadeMacBook-Pro:partition livia$ otool -L
>>>>>>>> DMPlexCreateExodusFromFile*
>>>>>>>> *DMPlexCreateExodusFromFile:*
>>>>>>>> */Users/livia/math/petsc/arch-darwin-cxx-debug/lib/libpetsc.3.7.dylib
>>>>>>>> (compatibility version 3.7.0, current version 3.7.5)*
>>>>>>>> */Users/livia/math/petsc/arch-darwin-cxx-debug/lib/libsuperlu_dist.5.dylib
>>>>>>>> (compatibility version 5.0.0, current version 5.1.3)*
>>>>>>>> */Users/livia/math/petsc/arch-darwin-cxx-debug/lib/libparmetis.dylib
>>>>>>>> (compatibility version 0.0.0, current version 0.0.0)*
>>>>>>>> */Users/livia/math/petsc/arch-darwin-cxx-debug/lib/libmetis.dylib
>>>>>>>> (compatibility version 0.0.0, current version 0.0.0)*
>>>>>>>> */Users/livia/math/petsc/arch-darwin-cxx-debug/lib/libnetcdf.7.dylib
>>>>>>>> (compatibility version 10.0.0, current version 10.0.0)*
>>>>>>>> */Users/livia/math/petsc/arch-darwin-cxx-debug/lib/libhdf5_hl.8.dylib
>>>>>>>> (compatibility version 9.0.0, current version 9.1.0)*
>>>>>>>> */Users/livia/math/petsc/arch-darwin-cxx-debug/lib/libhdf5.8.dylib
>>>>>>>> (compatibility version 9.0.0, current version 9.1.0)*
>>>>>>>> */opt/X11/lib/libX11.6.dylib (compatibility version 10.0.0, current
>>>>>>>> version 10.0.0)*
>>>>>>>> */Users/livia/math/mpich-3.2_install/lib/libmpifort.12.dylib
>>>>>>>> (compatibility version 14.0.0, current version 14.0.0)*
>>>>>>>> */usr/local/opt/gcc at 5/lib/gcc/5/libgfortran.3.dylib (compatibility
>>>>>>>> version 4.0.0, current version 4.0.0)*
>>>>>>>> */usr/local/opt/gcc at 5/lib/gcc/5/libquadmath.0.dylib (compatibility
>>>>>>>> version 1.0.0, current version 1.0.0)*
>>>>>>>> */Users/livia/math/mpich-3.2_install/lib/libmpicxx.12.dylib
>>>>>>>> (compatibility version 14.0.0, current version 14.0.0)*
>>>>>>>> */usr/local/opt/gcc at 5/lib/gcc/5/libstdc++.6.dylib (compatibility
>>>>>>>> version 7.0.0, current version 7.21.0)*
>>>>>>>> */usr/local/opt/gcc at 5/lib/gcc/5/libgcc_s.1.dylib (compatibility
>>>>>>>> version 1.0.0, current version 1.0.0)*
>>>>>>>> */Users/livia/math/mpich-3.2_install/lib/libmpi.12.dylib
>>>>>>>> (compatibility version 14.0.0, current version 14.0.0)*
>>>>>>>> */Users/livia/math/mpich-3.2_install/lib/libpmpi.12.dylib
>>>>>>>> (compatibility version 14.0.0, current version 14.0.0)*
>>>>>>>> */usr/lib/libSystem.B.dylib (compatibility version 1.0.0, current
>>>>>>>> version 1238.0.0)*
>>>>>>>> */usr/local/lib/gcc/5/libgcc_s.1.dylib (compatibility version
>>>>>>>> 1.0.0, current version 1.0.0)*
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>> Matt
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>> *static char help[] = " create mesh from exodus.\n\n";*
>>>>>>>>>>>>
>>>>>>>>>>>> *#include <petscdm.h>*
>>>>>>>>>>>> *#include <petsc/private/dmpleximpl.h>*
>>>>>>>>>>>>
>>>>>>>>>>>> *#undef __FUNCT__*
>>>>>>>>>>>> *#define __FUNCT__ "main"*
>>>>>>>>>>>> *int main(int argc,char **argv)*
>>>>>>>>>>>> *{*
>>>>>>>>>>>> * char fineMeshFileName[2048];*
>>>>>>>>>>>> * DM dm;*
>>>>>>>>>>>> * MPI_Comm comm;*
>>>>>>>>>>>> * PetscBool flg;*
>>>>>>>>>>>>
>>>>>>>>>>>> * PetscErrorCode ierr;*
>>>>>>>>>>>>
>>>>>>>>>>>> * ierr = PetscInitialize(&argc,&argv,(char
>>>>>>>>>>>> *)0,help);CHKERRQ(ierr);*
>>>>>>>>>>>> * comm = PETSC_COMM_WORLD;*
>>>>>>>>>>>> * ierr =
>>>>>>>>>>>> PetscOptionsGetString(NULL,NULL,"-file",fineMeshFileName,sizeof(fineMeshFileName),&flg);CHKERRQ(ierr);*
>>>>>>>>>>>> * if(!flg){*
>>>>>>>>>>>> *SETERRQ(comm,PETSC_ERR_ARG_NULL,"please specify a fine mesh
>>>>>>>>>>>> file \n");*
>>>>>>>>>>>> * }*
>>>>>>>>>>>> * ierr = DMPlexCreateExodusFromFile( comm,fineMeshFileName,
>>>>>>>>>>>> PETSC_FALSE, &dm);CHKERRQ(ierr);*
>>>>>>>>>>>> * ierr = DMDestroy(&dm);CHKERRQ(ierr);*
>>>>>>>>>>>> * ierr = PetscFinalize();CHKERRQ(ierr);*
>>>>>>>>>>>> *}*
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> *LiviadeMacBook-Pro:partition livia$
>>>>>>>>>>>> ./DMPlexCreateExodusFromFile -file Tri3.exo *
>>>>>>>>>>>> *[0]PETSC ERROR:
>>>>>>>>>>>> ------------------------------------------------------------------------*
>>>>>>>>>>>> *[0]PETSC ERROR: Caught signal number 11 SEGV: Segmentation
>>>>>>>>>>>> Violation, probably memory access out of range*
>>>>>>>>>>>> *[0]PETSC ERROR: Try option -start_in_debugger or
>>>>>>>>>>>> -on_error_attach_debugger*
>>>>>>>>>>>> *[0]PETSC ERROR: or see
>>>>>>>>>>>> http://www.mcs.anl.gov/petsc/documentation/faq.html#valgrind
>>>>>>>>>>>> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mcs.anl.gov_petsc_documentation_faq.html-23valgrind&d=DQMFaQ&c=54IZrppPQZKX9mLzcGdPfFD1hxrcB__aEkJFOKJFd00&r=DUUt3SRGI0_JgtNaS3udV68GRkgV4ts7XKfj2opmiCY&m=nkRPgIUrB5lOg1etuJMY1nEqzxd7KeOXIvjnjV7-FqA&s=XmOq0yF0m99l0UmsNv88t0hiFq9Fkb3pO3cOOd0lwNs&e=>*
>>>>>>>>>>>> *[0]PETSC ERROR: or try http://valgrind.org
>>>>>>>>>>>> <https://urldefense.proofpoint.com/v2/url?u=http-3A__valgrind.org_&d=DQMFaQ&c=54IZrppPQZKX9mLzcGdPfFD1hxrcB__aEkJFOKJFd00&r=DUUt3SRGI0_JgtNaS3udV68GRkgV4ts7XKfj2opmiCY&m=nkRPgIUrB5lOg1etuJMY1nEqzxd7KeOXIvjnjV7-FqA&s=AV7Rf6LhmCS9mEf9kD8G2oX27ZLeXpFZ-j59UbuWffU&e=>
>>>>>>>>>>>> on GNU/linux and Apple Mac OS X to find memory corruption errors*
>>>>>>>>>>>> *[0]PETSC ERROR: likely location of problem given in stack
>>>>>>>>>>>> below*
>>>>>>>>>>>> *[0]PETSC ERROR: --------------------- Stack Frames
>>>>>>>>>>>> ------------------------------------*
>>>>>>>>>>>> *[0]PETSC ERROR: Note: The EXACT line numbers in the stack are
>>>>>>>>>>>> not available,*
>>>>>>>>>>>> *[0]PETSC ERROR: INSTEAD the line number of the start of
>>>>>>>>>>>> the function*
>>>>>>>>>>>> *[0]PETSC ERROR: is given.*
>>>>>>>>>>>> *[0]PETSC ERROR: [0] DMPlexCreateExodusFromFile line 38
>>>>>>>>>>>> /Users/livia/math/petsc/src/dm/impls/plex/plexexodusii.c*
>>>>>>>>>>>> *[0]PETSC ERROR: --------------------- Error Message
>>>>>>>>>>>> --------------------------------------------------------------*
>>>>>>>>>>>> *[0]PETSC ERROR: Signal received*
>>>>>>>>>>>> *[0]PETSC ERROR: See
>>>>>>>>>>>> http://www.mcs.anl.gov/petsc/documentation/faq.html
>>>>>>>>>>>> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mcs.anl.gov_petsc_documentation_faq.html&d=DQMFaQ&c=54IZrppPQZKX9mLzcGdPfFD1hxrcB__aEkJFOKJFd00&r=DUUt3SRGI0_JgtNaS3udV68GRkgV4ts7XKfj2opmiCY&m=nkRPgIUrB5lOg1etuJMY1nEqzxd7KeOXIvjnjV7-FqA&s=XjLUqdMLvzNjWQGVVaiJek1trAYMSDHAWY-ojgI9Tdo&e=>
>>>>>>>>>>>> for trouble shooting.*
>>>>>>>>>>>> *[0]PETSC ERROR: Petsc Release Version 3.7.5, unknown *
>>>>>>>>>>>> *[0]PETSC ERROR: ./DMPlexCreateExodusFromFile on a
>>>>>>>>>>>> arch-darwin-cxx-debug named LiviadeMacBook-Pro.local by livia Sat Jan 21
>>>>>>>>>>>> 21:04:22 2017*
>>>>>>>>>>>> *[0]PETSC ERROR: Configure options --with-clanguage=cxx
>>>>>>>>>>>> --with-shared-libraries=1 --download-fblaslapack=1 --with-mpi=1
>>>>>>>>>>>> --download-parmetis=1 --download-metis=1 --download-netcdf=1
>>>>>>>>>>>> --download-exodusii=1 --download-hdf5=1 --with-debugging=yes
>>>>>>>>>>>> --with-c2html=0 --download-hypre=1 --with-64-bit-indices=1
>>>>>>>>>>>> --download-superlu_dist=1 PETSC_ARCH=arch-darwin-cxx-debug*
>>>>>>>>>>>> *[0]PETSC ERROR: #1 User provided function() line 0 in unknown
>>>>>>>>>>>> file*
>>>>>>>>>>>> *application called MPI_Abort(MPI_COMM_WORLD, 59) - process 0*
>>>>>>>>>>>> *[unset]: write_line error; fd=-1 buf=:cmd=abort exitcode=59*
>>>>>>>>>>>> *:*
>>>>>>>>>>>> *system msg for write_line failure : Bad file descriptor*
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> The log files of make and configuration are also attached. If
>>>>>>>>>>>> you have any idea on this issue, please let me know!
>>>>>>>>>>>>
>>>>>>>>>>>> Fande Kong,
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> --
>>>>>>>>>>> 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
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> --
>>>>>>>>> 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
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> 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
>>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> 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
>>>>>
>>>>
>>>>
>>>
>>>
>>> --
>>> 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
>>>
>>
>>
>> --
>> Department of Mathematics and Center for Computation & Technology
>> Louisiana State University, Baton Rouge, LA 70803, USA
>> Tel. +1 (225) 578 1612 <(225)%20578-1612>, Fax +1 (225) 578 4276
>> <(225)%20578-4276> http://www.math.lsu.edu/~bourdin
>> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.math.lsu.edu_-7Ebourdin&d=DQMFaQ&c=54IZrppPQZKX9mLzcGdPfFD1hxrcB__aEkJFOKJFd00&r=DUUt3SRGI0_JgtNaS3udV68GRkgV4ts7XKfj2opmiCY&m=nkRPgIUrB5lOg1etuJMY1nEqzxd7KeOXIvjnjV7-FqA&s=39UrCY8TvVOvCDQnDT5DlOiClLfYKr-s73fY0TzCcSM&e=>
>>
>>
>>
>>
>>
>>
>>
>>
>
>
> --
> 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
>
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