[petsc-users] PetscInt overflow

Jan Grießer griesser.jan at googlemail.com
Wed Oct 24 11:29:49 CDT 2018


I also run it with the -log_summary :
---------------------------------------------- PETSc Performance Summary:
----------------------------------------------



      ##########################################################
      #                                                        #
      #                          WARNING!!!                    #
      #                                                        #
      #   This code was compiled with a debugging option,      #
      #   To get timing results run ./configure                #
      #   using --with-debugging=no, the performance will      #
      #   be generally two or three times faster.              #
      #                                                        #
      ##########################################################


/work/ws/nemo/fr_jg1080-FreeSurface_Glass-0/GlassSystems/PeriodicSystems/N500000T0.001/SolveEigenvalueProblem_par/Test/Eigensolver_petsc_slepc_no_argparse.py
on a arch-linux2-c-debug named int02.nemo.privat with 20 processors, by
fr_jg1080 Wed Oct 24 18:26:30 2018
Using Petsc Release Version 3.9.4, Sep, 11, 2018

                         Max       Max/Min        Avg      Total
Time (sec):           7.474e+02      1.00000   7.474e+02
Objects:              3.600e+01      1.00000   3.600e+01
Flop:                 1.090e+11      1.00346   1.089e+11  2.177e+12
Flop/sec:            1.459e+08      1.00346   1.457e+08  2.913e+09
Memory:               3.950e+08      1.00296              7.891e+09
MPI Messages:         3.808e+04      1.00000   3.808e+04  7.615e+05
MPI Message Lengths:  2.211e+10      1.00217   5.802e+05  4.419e+11
MPI Reductions:       1.023e+05      1.00000

Flop counting convention: 1 flop = 1 real number operation of type
(multiply/divide/add/subtract)
                            e.g., VecAXPY() for real vectors of length N
--> 2N flop
                            and VecAXPY() for complex vectors of length N
--> 8N flop

Summary of Stages:   ----- Time ------  ----- Flop -----  --- Messages ---
-- Message Lengths --  -- Reductions --
                        Avg     %Total     Avg     %Total   counts
 %Total     Avg         %Total   counts   %Total
 0:      Main Stage: 7.4739e+02 100.0%  2.1773e+12 100.0%  7.615e+05
100.0%  5.802e+05      100.0%  1.022e+05 100.0%

------------------------------------------------------------------------------------------------------------------------
See the 'Profiling' chapter of the users' manual for details on
interpreting output.
Phase summary info:
   Count: number of times phase was executed
   Time and Flop: Max - maximum over all processors
                   Ratio - ratio of maximum to minimum over all processors
   Mess: number of messages sent
   Avg. len: average message length (bytes)
   Reduct: number of global reductions
   Global: entire computation
   Stage: stages of a computation. Set stages with PetscLogStagePush() and
PetscLogStagePop().
      %T - percent time in this phase         %F - percent flop in this
phase
      %M - percent messages in this phase     %L - percent message lengths
in this phase
      %R - percent reductions in this phase
   Total Mflop/s: 10e-6 * (sum of flop over all processors)/(max time over
all processors)
------------------------------------------------------------------------------------------------------------------------


      ##########################################################
      #                                                        #
      #                          WARNING!!!                    #
      #                                                        #
      #   This code was compiled with a debugging option,      #
      #   To get timing results run ./configure                #
      #   using --with-debugging=no, the performance will      #
      #   be generally two or three times faster.              #
      #                                                        #
      ##########################################################


Event                Count      Time (sec)     Flop
     --- Global ---  --- Stage ---   Total
                   Max Ratio  Max     Ratio   Max  Ratio  Mess   Avg len
Reduct  %T %F %M %L %R  %T %F %M %L %R Mflop/s
------------------------------------------------------------------------------------------------------------------------

--- Event Stage 0: Main Stage

BuildTwoSidedF         2 1.0 2.6670e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
0.0e+00  0  0  0  0  0   0  0  0  0  0     0
VecSet                 2 1.0 6.8650e-03 1.8 0.00e+00 0.0 0.0e+00 0.0e+00
0.0e+00  0  0  0  0  0   0  0  0  0  0     0
VecScatterBegin     2002 1.0 1.4380e+01 1.0 0.00e+00 0.0 7.6e+05 5.8e+05
0.0e+00  2  0100100  0   2  0100100  0     0
VecScatterEnd       2002 1.0 3.7604e+01 1.5 0.00e+00 0.0 0.0e+00 0.0e+00
0.0e+00  4  0  0  0  0   4  0  0  0  0     0
VecSetRandom           1 1.0 1.6440e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
0.0e+00  0  0  0  0  0   0  0  0  0  0     0
MatMult             2002 1.0 6.0846e+02 1.2 1.03e+11 1.0 7.6e+05 5.8e+05
0.0e+00 71 94100100  0  71 94100100  0  3376
MatAssemblyBegin       3 1.0 2.8129e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
6.0e+00  0  0  0  0  0   0  0  0  0  0     0
MatAssemblyEnd         3 1.0 8.5094e+00 1.0 0.00e+00 0.0 7.6e+02 1.5e+05
3.6e+01  1  0  0  0  0   1  0  0  0  0     0
EPSSetUp               1 1.0 1.7351e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
7.6e+01  0  0  0  0  0   0  0  0  0  0     0
EPSSolve               1 1.0 6.7891e+02 1.0 1.09e+11 1.0 7.6e+05 5.8e+05
1.0e+05 91100100100100  91100100100100  3207
STSetUp                1 1.0 2.2221e-04 1.3 0.00e+00 0.0 0.0e+00 0.0e+00
6.0e+00  0  0  0  0  0   0  0  0  0  0     0
STApply             2002 1.0 6.0879e+02 1.2 1.03e+11 1.0 7.6e+05 5.8e+05
0.0e+00 71 94100100  0  71 94100100  0  3374
BVCopy               999 1.0 2.7157e-01 1.2 0.00e+00 0.0 0.0e+00 0.0e+00
0.0e+00  0  0  0  0  0   0  0  0  0  0     0
BVMultVec           4004 1.0 2.2918e+00 1.0 2.10e+09 1.0 0.0e+00 0.0e+00
1.6e+04  0  2  0  0 16   0  2  0  0 16 18332
BVMultInPlace        999 1.0 4.8399e+01 1.0 1.20e+09 1.0 0.0e+00 0.0e+00
0.0e+00  6  1  0  0  0   6  1  0  0  0   495
BVDotVec            4004 1.0 1.0835e+01 1.0 2.70e+09 1.0 0.0e+00 0.0e+00
2.0e+04  1  2  0  0 20   1  2  0  0 20  4986
BVOrthogonalizeV    2003 1.0 1.3272e+01 1.0 4.80e+09 1.0 0.0e+00 0.0e+00
5.2e+04  2  4  0  0 51   2  4  0  0 51  7236
BVScale             2003 1.0 2.3521e-01 1.0 1.50e+08 1.0 0.0e+00 0.0e+00
0.0e+00  0  0  0  0  0   0  0  0  0  0 12773
BVSetRandom            1 1.0 1.6456e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
4.0e+00  0  0  0  0  0   0  0  0  0  0     0
DSSolve             1000 1.0 3.3338e+00 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
0.0e+00  0  0  0  0  0   0  0  0  0  0     0
DSVectors           1000 1.0 6.0029e-03 1.1 0.00e+00 0.0 0.0e+00 0.0e+00
0.0e+00  0  0  0  0  0   0  0  0  0  0     0
DSOther             2999 1.0 7.8770e-01 1.0 0.00e+00 0.0 0.0e+00 0.0e+00
0.0e+00  0  0  0  0  0   0  0  0  0  0     0
------------------------------------------------------------------------------------------------------------------------

Memory usage is given in bytes:

Object Type          Creations   Destructions     Memory  Descendants' Mem.
Reports information only for process 0.

--- Event Stage 0: Main Stage

              Viewer     2              1          840     0.
         PetscRandom     1              1          646     0.
           Index Set     4              4      5510472     0.
              Vector     9              9     11629608     0.
         Vec Scatter     2              2         1936     0.
              Matrix    10             10    331855732     0.
      Preconditioner     1              1         1000     0.
       Krylov Solver     1              1         1176     0.
          EPS Solver     1              1         1600     0.
  Spectral Transform     2              2         1624     0.
       Basis Vectors     1              1         2168     0.
       Direct Solver     1              1         2520     0.
              Region     1              1          672     0.
========================================================================================================================
Average time to get PetscTime(): 1.19209e-07
Average time for MPI_Barrier(): 2.67982e-05
Average time for zero size MPI_Send(): 1.08957e-05
#PETSc Option Table entries:
-bv_type mat
-eps_view_pre
-log_summary
#End of PETSc Option Table entries
Compiled without FORTRAN kernels
Compiled with full precision matrices (default)
sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8
sizeof(PetscScalar) 8 sizeof(PetscInt) 4
Configure options: --with-cc=mpicc --with-cxx=mpicxx --with-fc=mpif90
--download-mumps --with-shared-libraries=True --download-scalapack
-----------------------------------------
Libraries compiled on 2018-10-17 20:02:31 on login2.nemo.privat
Machine characteristics:
Linux-3.10.0-693.21.1.el7.x86_64-x86_64-with-centos-7.4.1708-Core
Using PETSc directory: /home/fr/fr_fr/fr_jg1080/Libaries/petsc-3.9.4
Using PETSc arch: arch-linux2-c-debug
-----------------------------------------

Using C compiler: mpicc  -fPIC  -wd1572 -g
Using Fortran compiler: mpif90  -fPIC -g
-----------------------------------------

Using include paths:
-I/home/fr/fr_fr/fr_jg1080/Libaries/petsc-3.9.4/include
-I/home/fr/fr_fr/fr_jg1080/Libaries/petsc-3.9.4/arch-linux2-c-debug/include
-----------------------------------------

Using C linker: mpicc
Using Fortran linker: mpif90
Using libraries:
-Wl,-rpath,/home/fr/fr_fr/fr_jg1080/Libaries/petsc-3.9.4/arch-linux2-c-debug/lib
-L/home/fr/fr_fr/fr_jg1080/Libaries/petsc-3.9.4/arch-linux2-c-debug/lib
-lpetsc
-Wl,-rpath,/home/fr/fr_fr/fr_jg1080/Libaries/petsc-3.9.4/arch-linux2-c-debug/lib
-L/home/fr/fr_fr/fr_jg1080/Libaries/petsc-3.9.4/arch-linux2-c-debug/lib
-Wl,-rpath,/opt/bwhpc/common/compiler/intel/2018.3.222/compilers_and_libraries/linux/mpi/intel64/lib/debug_mt
-L/opt/bwhpc/common/compiler/intel/2018.3.222/compilers_and_libraries/linux/mpi/intel64/lib/debug_mt
-Wl,-rpath,/opt/bwhpc/common/compiler/intel/2018.3.222/compilers_and_libraries/linux/mpi/intel64/lib
-L/opt/bwhpc/common/compiler/intel/2018.3.222/compilers_and_libraries/linux/mpi/intel64/lib
-Wl,-rpath,/opt/bwhpc/common/compiler/intel/2018.3.222/compilers_and_libraries/linux/lib/intel64
-L/opt/bwhpc/common/compiler/intel/2018.3.222/compilers_and_libraries/linux/lib/intel64
-Wl,-rpath,/opt/bwhpc/common/compiler/intel/2018.3.222/compilers_and_libraries_2018.3.222/linux/compiler/lib/intel64_lin
-L/opt/bwhpc/common/compiler/intel/2018.3.222/compilers_and_libraries_2018.3.222/linux/compiler/lib/intel64_lin
-Wl,-rpath,/usr/lib/gcc/x86_64-redhat-linux/4.8.5
-L/usr/lib/gcc/x86_64-redhat-linux/4.8.5
-Wl,-rpath,/opt/intel/mpi-rt/2017.0.0/intel64/lib/debug_mt
-Wl,-rpath,/opt/intel/mpi-rt/2017.0.0/intel64/lib -lcmumps -ldmumps
-lsmumps -lzmumps -lmumps_common -lpord -lscalapack -llapack -lblas -lX11
-lstdc++ -ldl -lmpifort -lmpi -lmpigi -lrt -lpthread -lifport
-lifcoremt_pic -limf -lsvml -lm -lipgo -lirc -lgcc_s -lirc_s -lstdc++ -ldl
-----------------------------------------



      ##########################################################
      #                                                        #
      #                          WARNING!!!                    #
      #                                                        #
      #   This code was compiled with a debugging option,      #
      #   To get timing results run ./configure                #
      #   using --with-debugging=no, the performance will      #
      #   be generally two or three times faster.              #
      #                                                        #
      ##########################################################


Am Mi., 24. Okt. 2018 um 18:07 Uhr schrieb Jan Grießer <
griesser.jan at googlemail.com>:

> For some reason i get only this error message, also when is use the
> -eps_view_pre. I started the program with nev=1, there the output is  (with
> -bv_type vecs -bv_type mat -eps_view_pre)
> EPS Object: 20 MPI processes
>   type: krylovschur
>     50% of basis vectors kept after restart
>     using the locking variant
>   problem type: symmetric eigenvalue problem
>   selected portion of the spectrum: smallest real parts
>   number of eigenvalues (nev): 1
>   number of column vectors (ncv): 3
>   maximum dimension of projected problem (mpd): 2
>   maximum number of iterations: 1000
>   tolerance: 1e-08
>   convergence test: relative to the eigenvalue
> BV Object: 20 MPI processes
>   type: mat
>   4 columns of global length 1500000
>   vector orthogonalization method: classical Gram-Schmidt
>   orthogonalization refinement: if needed (eta: 0.7071)
>   block orthogonalization method: GS
>   doing matmult as a single matrix-matrix product
> DS Object: 20 MPI processes
>   type: hep
>   parallel operation mode: REDUNDANT
>   solving the problem with: Implicit QR method (_steqr)
> ST Object: 20 MPI processes
>   type: shift
>   shift: 0.
>   number of matrices: 1
>
>
>
>
> Am Mi., 24. Okt. 2018 um 16:14 Uhr schrieb Matthew Knepley <
> knepley at gmail.com>:
>
>> On Wed, Oct 24, 2018 at 10:03 AM Jan Grießer <griesser.jan at googlemail.com>
>> wrote:
>>
>>> This is the error message i get from my program:
>>> Shape of the dynamical matrix:  (1500000, 1500000)
>>>
>>
>> Petsc installs a signal handler, so there should be a PETSc-specific
>> message before this one. Is something eating
>> your output?
>>
>>   Thanks,
>>
>>      Matt
>>
>>
>>>
>>> ===================================================================================
>>> =   BAD TERMINATION OF ONE OF YOUR APPLICATION PROCESSES
>>> =   PID 122676 RUNNING AT n3512.nemo.privat
>>> =   EXIT CODE: 9
>>> =   CLEANING UP REMAINING PROCESSES
>>> =   YOU CAN IGNORE THE BELOW CLEANUP MESSAGES
>>>
>>> ===================================================================================
>>>    Intel(R) MPI Library troubleshooting guide:
>>>       https://software.intel.com/node/561764
>>>
>>> ===================================================================================
>>>
>>>
>>> Am Mi., 24. Okt. 2018 um 16:01 Uhr schrieb Matthew Knepley <
>>> knepley at gmail.com>:
>>>
>>>> On Wed, Oct 24, 2018 at 9:38 AM Jan Grießer <
>>>> griesser.jan at googlemail.com> wrote:
>>>>
>>>>> Hey,
>>>>> i tried to run my program as you said with -bv_type vecs and/or
>>>>> -bv_type mat, but instead of the PETScInt overflow i now get an MPI Error 9
>>>>>
>>>>
>>>> Send the actual error.
>>>>
>>>>   Thanks,
>>>>
>>>>     Matt
>>>>
>>>>
>>>>> message, which i assume (after googling a little bit around) should be
>>>>> a memory problem. I tried to run it also on slightly bigger compute nodes
>>>>> on our cluster with 20 cores with each 12 GB and 24 GB but the problem
>>>>> still remains. The actual limit appears to be a 1.5 Million x 1.5 Million
>>>>> where i  searched for NEV = 1500 and MPD = 500/ 200 eigenvalues.
>>>>> Do you have maybe an idea what the error could be? I appended also the
>>>>> python method i used to solve the problem. I also tried to solve the
>>>>> problem with spectrum solving but the error message remains the same.
>>>>>
>>>>> def solve_eigensystem(DynMatrix_nn, NEV, MPD, Dimension):
>>>>> # Create the solver
>>>>> # E is used as an acronym for the EPS solver (EPS = Eigenvalue problem
>>>>> solver)
>>>>> E = SLEPc.EPS().create()
>>>>>
>>>>> # Set the preconditioner
>>>>> pc = PETSc.PC().create()
>>>>> pc.setType(pc.Type.BJACOBI)
>>>>>
>>>>> # Set the linear solver
>>>>> # Create the KSP object
>>>>> ksp = PETSc.KSP().create()
>>>>> # Create the solver, in this case GMRES
>>>>> ksp.setType(ksp.Type.GMRES)
>>>>> # Set the tolerances of the GMRES solver
>>>>>         # Link it to the PC
>>>>> ksp.setPC(pc)
>>>>>
>>>>> # Set up the spectral transformations
>>>>> st = SLEPc.ST().create()
>>>>> st.setType("shift")
>>>>> st.setKSP(ksp)
>>>>> # MPD stands for "maximum projected dimension". It has to due with
>>>>> computational cost, please read Chap. 2.6.5 of SLEPc docu for
>>>>> # an explanation. At the moment mpd is only a guess
>>>>> E.setDimensions(nev=NEV, mpd = MPD)
>>>>> # Eigenvalues should be real, therefore we start to order them from
>>>>> the smallest real value |l.real|
>>>>> E.setWhichEigenpairs(E.Which.SMALLEST_REAL)
>>>>> # Since the dynamical matrix is symmetric and real it is hermitian
>>>>> E.setProblemType(SLEPc.EPS.ProblemType.HEP)
>>>>> # Use the Krylov Schur method to solve the eigenvalue problem
>>>>> E.setType(E.Type.KRYLOVSCHUR)
>>>>> # Set the convergence criterion to relative to the eigenvalue and the
>>>>> maximal number of iterations
>>>>> E.setConvergenceTest(E.Conv.REL)
>>>>> E.setTolerances(tol = 1e-8, max_it = 5000)
>>>>> # Set the matrix in order to solve
>>>>> E.setOperators(DynMatrix_nn, None)
>>>>> # Sets EPS options from the options database. This routine must be
>>>>> called before `setUp()` if the user is to be allowed to set dthe solver
>>>>> type.
>>>>> E.setFromOptions()
>>>>> # Sets up all the internal data structures necessary for the execution
>>>>> of the eigensolver.
>>>>> E.setUp()
>>>>>
>>>>> # Solve eigenvalue problem
>>>>> E.solve()
>>>>>
>>>>> Print = PETSc.Sys.Print
>>>>>
>>>>> Print()
>>>>> Print("****************************")
>>>>> Print("***SLEPc Solution Results***")
>>>>> Print("****************************")
>>>>>
>>>>> its = E.getIterationNumber()
>>>>> Print("Number of iterations of the method: ", its)
>>>>> eps_type = E.getType()
>>>>> Print("Solution method: ", eps_type)
>>>>> nev, ncv, mpd = E.getDimensions()
>>>>> Print("Number of requested eigenvalues: ", nev)
>>>>> Print("Number of computeded eigenvectors: ", ncv)
>>>>> tol, maxit = E.getTolerances()
>>>>> Print("Stopping condition: (tol, maxit)", (tol, maxit))
>>>>> # Get the type of convergence
>>>>> conv_test = E.getConvergenceTest()
>>>>> Print("Selected convergence test: ", conv_test)
>>>>> # Get the used spectral transformation
>>>>> get_st = E.getST()
>>>>> Print("Selected spectral transformation: ", get_st)
>>>>> # Get the applied direct solver
>>>>> get_ksp = E.getDS()
>>>>> Print("Selected direct solver: ", get_ksp)
>>>>> nconv = E.getConverged()
>>>>> Print("Number of converged eigenpairs: ", nconv)
>>>>> .....
>>>>>
>>>>>
>>>>>
>>>>> Am Fr., 19. Okt. 2018 um 21:00 Uhr schrieb Smith, Barry F. <
>>>>> bsmith at mcs.anl.gov>:
>>>>>
>>>>>>
>>>>>>
>>>>>> > On Oct 19, 2018, at 7:56 AM, Zhang, Junchao <jczhang at mcs.anl.gov>
>>>>>> wrote:
>>>>>> >
>>>>>> >
>>>>>> > On Fri, Oct 19, 2018 at 4:02 AM Jan Grießer <
>>>>>> griesser.jan at googlemail.com> wrote:
>>>>>> > With more than 1 MPI process you mean i should use spectrum slicing
>>>>>> in divide the full problem in smaller subproblems?
>>>>>> > The --with-64-bit-indices is not a possibility for me since i
>>>>>> configured petsc with mumps, which does not allow to use the 64-bit version
>>>>>> (At least this was the error message when i tried to configure PETSc )
>>>>>> >
>>>>>> > MUMPS 5.1.2 manual chapter 2.4.2 says it supports "Selective 64-bit
>>>>>> integer feature" and "full 64-bit integer version" as well.
>>>>>>
>>>>>>     They use to achieve this by compiling with special Fortran flags
>>>>>> to promote integers to 64 bit; this is too fragile for our taste so we
>>>>>> never hooked PETSc up wit it. If they have a dependable way of using 64 bit
>>>>>> integers we should add that to our mumps.py and test it.
>>>>>>
>>>>>>    Barry
>>>>>>
>>>>>> >
>>>>>> > Am Mi., 17. Okt. 2018 um 18:24 Uhr schrieb Jose E. Roman <
>>>>>> jroman at dsic.upv.es>:
>>>>>> > To use BVVECS just add the command-line option -bv_type vecs
>>>>>> > This causes to use a separate Vec for each column, instead of a
>>>>>> single long Vec of size n*m. But it is considerably slower than the default.
>>>>>> >
>>>>>> > Anyway, for such large problems you should consider using more than
>>>>>> 1 MPI process. In that case the error may disappear because the local size
>>>>>> is smaller than 768000.
>>>>>> >
>>>>>> > Jose
>>>>>> >
>>>>>> >
>>>>>> > > El 17 oct 2018, a las 17:58, Matthew Knepley <knepley at gmail.com>
>>>>>> escribió:
>>>>>> > >
>>>>>> > > On Wed, Oct 17, 2018 at 11:54 AM Jan Grießer <
>>>>>> griesser.jan at googlemail.com> wrote:
>>>>>> > > Hi all,
>>>>>> > > i am using slepc4py and petsc4py to solve for the smallest real
>>>>>> eigenvalues and eigenvectors. For my test cases with a matrix A of the size
>>>>>> 30k x 30k solving for the smallest soutions works quite well, but when i
>>>>>> increase the dimension of my system to around A = 768000 x 768000 or 3
>>>>>> million x 3 million and ask for the smallest real 3000 (the number is
>>>>>> increasing with increasing system size) eigenvalues and eigenvectors i get
>>>>>> the output (for the 768000):
>>>>>> > >  The product 4001 times 768000 overflows the size of PetscInt;
>>>>>> consider reducing the number of columns, or use BVVECS instead
>>>>>> > > i understand that the requested number of eigenvectors and
>>>>>> eigenvalues is causing an overflow but i do not understand the solution of
>>>>>> the problem which is stated in the error message. Can someone tell me what
>>>>>> exactly BVVECS is and how i can use it? Or is there any other solution to
>>>>>> my problem ?
>>>>>> > >
>>>>>> > > You can also reconfigure with 64-bit integers:
>>>>>> --with-64-bit-indices
>>>>>> > >
>>>>>> > >   Thanks,
>>>>>> > >
>>>>>> > >     Matt
>>>>>> > >
>>>>>> > > Thank you very much in advance,
>>>>>> > > Jan
>>>>>> > >
>>>>>> > >
>>>>>> > >
>>>>>> > > --
>>>>>> > > 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/
>>>>>> >
>>>>>>
>>>>>>
>>>>
>>>> --
>>>> 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/>
>>>>
>>>
>>
>> --
>> 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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