[petsc-users] Update DMDA attached to DMSWARM

Matthew Knepley knepley at gmail.com
Tue Jan 28 10:24:24 CST 2025 

No problem. Sorry I did not think of it sooner.

   Matt

On Tue, Jan 28, 2025 at 10:45 AM MIGUEL MOLINOS PEREZ <mmolinos at us.es>
wrote:

> It works! Thank you again Matt.
>
> Miguel
>
>
> On 24 Jan 2025, at 17:07, MIGUEL MOLINOS PEREZ <mmolinos at us.es> wrote:
>
> Ohh, I wasn't aware of this function. Thank you Matt, I’ll see if that
> solves the problem.
>
> Miguel
>
> On 24 Jan 2025, at 17:00, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Fri, Jan 24, 2025 at 10:56 AM MIGUEL MOLINOS PEREZ <mmolinos at us.es>
> wrote:
>
>> Sorry I wasn’t clear enough. By “the box is updated” I mean: I run
>> DMGetBoundingBox and the resulting coordinates are updated according to the
>> deformation gradient “F".
>>
>
> Oh, if you change the periodic extent, which you are, you have to recall
> DMSetPeriodicity(), which is what DMGetBoundaingBox() consults for the
> periodic extent (because the coordinates cannot be trusted).
>
>   Thanks,
>
>      Matt
>
>
>> Thanks,
>> Miguel
>>
>> On 24 Jan 2025, at 16:50, Matthew Knepley <knepley at gmail.com> wrote:
>>
>> On Fri, Jan 24, 2025 at 10:36 AM MIGUEL MOLINOS PEREZ <mmolinos at us.es>
>> wrote:
>>
>>> Thanks Matt, I tried that too, and the problem remains. The box is
>>> updated only if I set no periodic bcc.
>>>
>>
>> What do you mean by "The box is updated"? I am trying to understand how
>> you test things. Clearly the coordinates are updated,
>> even in the periodic case. Thus, I need to understand the test. Once we
>> do that, we can work backwards to the first broken thing.
>>
>>   Thanks,
>>
>>       Matt
>>
>>
>>> Miguel
>>>
>>> On 24 Jan 2025, at 14:20, Matthew Knepley <knepley at gmail.com> wrote:
>>>
>>> On Fri, Jan 24, 2025 at 4:41 AM MIGUEL MOLINOS PEREZ <mmolinos at us.es>
>>> wrote:
>>>
>>>> Dear Matt, the error was in the implementation of the volume expansion
>>>> function. I updated it, and it works finte under finite domains. However,
>>>> if I include periodic boundary conditions the volume of the cell does not
>>>> accommodate the volume expansion of the particles. The deformation gradient
>>>> is not the identity… I guess I am missing the fine detail on how periodic
>>>> bcc are implemented in DMDA mesh, I’m right?
>>>>
>>>
>>> DMDA identifies vertices using a VecScatter to implement periodic BC.
>>> This should be insensitive to coordinates. However, I don't think the
>>> algorithm below is correct for local coordinates. You use GlobalToLocal(),
>>> which means that some global coordinate "wins" for each local cell, so
>>> cells on the periodic boundary can be wrong. I would set the local
>>> coordinates by hand as well.
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> Thanks,
>>>> Miguel
>>>>
>>>> static PetscErrorCode Volumetric_Expansion_DMDA(DM * da,
>>>> const Eigen::Matrix3d& F) {
>>>>
>>>> PetscInt i, j, mstart, m, nstart, n, pstart, p, k;
>>>> Vec local, global;
>>>> DMDACoor3d ***coors, ***coorslocal;
>>>> DM cda;
>>>>
>>>> PetscFunctionBeginUser;
>>>> PetscCall(DMGetCoordinateDM(*da, &cda));
>>>> PetscCall(DMGetCoordinates(*da, &global));
>>>> PetscCall(DMGetCoordinatesLocal(*da, &local));
>>>> PetscCall(DMDAVecGetArray(cda, global, &coors));
>>>> PetscCall(DMDAVecGetArrayRead(cda, local, &coorslocal));
>>>> PetscCall(DMDAGetCorners(cda, &mstart, &nstart, &pstart, &m, &n, &p));
>>>> for (i = mstart; i < mstart + m; i++) {
>>>> for (j = nstart; j < nstart + n; j++) {
>>>> for (k = pstart; k < pstart + p; k++) {
>>>> coors[k][j][i].x = coorslocal[k][j][i].x * F(0, 0);
>>>> coors[k][j][i].y = coorslocal[k][j][i].y * F(1, 1);
>>>> coors[k][j][i].z = coorslocal[k][j][i].z * F(2, 2);
>>>> }
>>>> }
>>>> }
>>>> PetscCall(DMDAVecRestoreArray(cda, global, &coors));
>>>> PetscCall(DMDAVecRestoreArrayRead(cda, local, &coorslocal));
>>>>
>>>> PetscCall(DMGlobalToLocalBegin(cda, global, INSERT_VALUES, local));
>>>> PetscCall(DMGlobalToLocalEnd(cda, global, INSERT_VALUES, local));
>>>>
>>>> PetscFunctionReturn(PETSC_SUCCESS);
>>>> }
>>>>
>>>> On 17 Jan 2025, at 18:01, MIGUEL MOLINOS PEREZ <mmolinos at us.es> wrote:
>>>>
>>>> You are right!! Thank you again!
>>>>
>>>> Miguel
>>>>
>>>> On Jan 17, 2025, at 5:18 PM, Matthew Knepley <knepley at gmail.com> wrote:
>>>>
>>>> On Fri, Jan 17, 2025 at 10:49 AM MIGUEL MOLINOS PEREZ <mmolinos at us.es>
>>>> wrote:
>>>>
>>>>> Now the error is in the call to DMSwarmMigrate
>>>>>
>>>>
>>>> You have almost certainly overwritten memory somewhere. Can you use
>>>> vlagrind or Address Sanitizer?
>>>>
>>>>    Thanks,
>>>>
>>>>       Matt
>>>>
>>>>
>>>>> Miguel
>>>>>
>>>>> [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 https://urldefense.us/v3/__https://petsc.org/release/faq/*valgrind__;Iw!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUxxZ4fooO$  and
>>>>> https://urldefense.us/v3/__https://petsc.org/release/faq/__;!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx15Kn1xQ$ 
>>>>> [0]PETSC ERROR: ---------------------  Stack Frames
>>>>> ------------------------------------
>>>>> [0]PETSC ERROR: The line numbers in the error traceback are not always
>>>>> exact.
>>>>> [0]PETSC ERROR: #1 DMSwarmDataBucketGetSizes() at
>>>>> /Users/migmolper/petsc/src/dm/impls/swarm/data_bucket.c:297
>>>>> [0]PETSC ERROR: #2 DMSwarmMigrate_CellDMScatter() at
>>>>> /Users/migmolper/petsc/src/dm/impls/swarm/swarm_migrate.c:201
>>>>> [0]PETSC ERROR: #3 DMSwarmMigrate() at
>>>>> /Users/migmolper/petsc/src/dm/impls/swarm/swarm.c:1349
>>>>> [0]PETSC ERROR: #4 main() at
>>>>> /Users/migmolper/DMD/driver-tasting-SOLERA.cpp:41
>>>>> application called MPI_Abort(MPI_COMM_WORLD, 59) - process 0
>>>>>
>>>>> On Jan 17, 2025, at 4:22 PM, Matthew Knepley <knepley at gmail.com>
>>>>> wrote:
>>>>>
>>>>> On Fri, Jan 17, 2025 at 10:08 AM MIGUEL MOLINOS PEREZ <mmolinos at us.es>
>>>>> wrote:
>>>>>
>>>>>> Thank you Matt, this the piece of code I use to change the
>>>>>> coordinates of the DM obtained using:
>>>>>>
>>>>>
>>>>> You do not need the call to DMSetCoordinates(). What happens when you
>>>>> remove it?
>>>>>
>>>>>   Thanks,
>>>>>
>>>>>     Matt
>>>>>
>>>>>
>>>>>>
>>>>>> DMSwarmGetCellDM(Simulation.atomistic_data, &bounding_cell);
>>>>>> DMGetApplicationContext(bounding_cell, &background_mesh);
>>>>>>
>>>>>> Thanks,
>>>>>> Miguel
>>>>>>
>>>>>>
>>>>>> /************************************************************************/
>>>>>>
>>>>>> PetscErrorCode Volumetric_Expansion(DM dm, const Eigen::Matrix3d& F)
>>>>>> {
>>>>>> PetscErrorCode ierr;
>>>>>> Vec coordinates;
>>>>>> PetscScalar* coordArray;
>>>>>> PetscInt xs, ys, zs, xm, ym, zm, i, j, k;
>>>>>> PetscInt dim, M, N, P;
>>>>>>
>>>>>> PetscFunctionBegin;
>>>>>> // Get DMDA information
>>>>>> ierr = DMDAGetInfo(dm, &dim, &M, &N, &P, NULL, NULL, NULL, NULL, NULL,
>>>>>> NULL,
>>>>>> NULL, NULL, NULL);
>>>>>> CHKERRQ(ierr);
>>>>>> ierr = DMDAGetCorners(dm, &xs, &ys, &zs, &xm, &ym, &zm);
>>>>>> CHKERRQ(ierr);
>>>>>>
>>>>>> // Get the coordinates vector
>>>>>> ierr = DMGetCoordinates(dm, &coordinates);
>>>>>> CHKERRQ(ierr);
>>>>>> ierr = VecGetArray(coordinates, &coordArray);
>>>>>> CHKERRQ(ierr);
>>>>>>
>>>>>> // Update the coordinates based on the desired transformation
>>>>>> for (k = zs; k < zs + zm; k++) {
>>>>>> for (j = ys; j < ys + ym; j++) {
>>>>>> for (i = xs; i < xs + xm; i++) {
>>>>>> PetscInt idx =
>>>>>> ((k * N + j) * M + i) * dim; // Index for the i, j, k point
>>>>>> coordArray[idx] = coordArray[idx] * F(0,0); // Update x-coordinate
>>>>>> coordArray[idx + 1] = coordArray[idx + 1] * F(1,1); // Update
>>>>>> y-coordinate
>>>>>> coordArray[idx + 2] = coordArray[idx + 2] * F(2,2); // Update
>>>>>> z-coordinate
>>>>>> }
>>>>>> }
>>>>>> }
>>>>>>
>>>>>> // Restore the coordinates vector
>>>>>> ierr = VecRestoreArray(coordinates, &coordArray);
>>>>>> CHKERRQ(ierr);
>>>>>>
>>>>>> // Set the updated coordinates back to the DMDA
>>>>>> ierr = DMSetCoordinates(dm, coordinates);
>>>>>> CHKERRQ(ierr);
>>>>>>
>>>>>> PetscFunctionReturn(0);
>>>>>> }
>>>>>>
>>>>>>
>>>>>> /************************************************************************/
>>>>>>
>>>>>> On 17 Jan 2025, at 16:00, Matthew Knepley <knepley at gmail.com> wrote:
>>>>>>
>>>>>> On Fri, Jan 17, 2025 at 9:45 AM MIGUEL MOLINOS PEREZ <mmolinos at us.es>
>>>>>> wrote:
>>>>>>
>>>>>>> I tried what you suggested, but still I got this error message.
>>>>>>> Maybe I should use main release?
>>>>>>>
>>>>>>
>>>>>> No. I suspect something is wrong with the way you are setting
>>>>>> coordinates. Can you share the code?
>>>>>>
>>>>>>   Thanks,
>>>>>>
>>>>>>      Matt
>>>>>>
>>>>>>
>>>>>>> Miguel
>>>>>>>
>>>>>>> [4]PETSC ERROR:
>>>>>>> ------------------------------------------------------------------------
>>>>>>> [4]PETSC ERROR: Caught signal number 11 SEGV: Segmentation
>>>>>>> Violation, probably memory access out of range
>>>>>>> [4]PETSC ERROR: Try option -start_in_debugger or
>>>>>>> -on_error_attach_debugger
>>>>>>> [4]PETSC ERROR: or see https://urldefense.us/v3/__https://petsc.org/release/faq/*valgrind__;Iw!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUxxZ4fooO$  and
>>>>>>> https://urldefense.us/v3/__https://petsc.org/release/faq/__;!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx15Kn1xQ$ 
>>>>>>> [4]PETSC ERROR: ---------------------  Stack Frames
>>>>>>> ------------------------------------
>>>>>>> [4]PETSC ERROR: The line numbers in the error traceback are not
>>>>>>> always exact.
>>>>>>> [4]PETSC ERROR: #1 Pack_PetscReal_1_0() at
>>>>>>> /Users/migmolper/petsc/src/vec/is/sf/impls/basic/sfpack.c:373
>>>>>>> [4]PETSC ERROR: #2 PetscSFLinkPackRootData_Private() at
>>>>>>> /Users/migmolper/petsc/src/vec/is/sf/impls/basic/sfpack.c:932
>>>>>>> [4]PETSC ERROR: #3 PetscSFLinkPackRootData() at
>>>>>>> /Users/migmolper/petsc/src/vec/is/sf/impls/basic/sfpack.c:966
>>>>>>> [4]PETSC ERROR: #4 PetscSFBcastBegin_Basic() at
>>>>>>> /Users/migmolper/petsc/src/vec/is/sf/impls/basic/sfbasic.c:357
>>>>>>> [4]PETSC ERROR: #5 PetscSFBcastWithMemTypeBegin() at
>>>>>>> /Users/migmolper/petsc/src/vec/is/sf/interface/sf.c:1513
>>>>>>> [4]PETSC ERROR: #6 VecScatterBegin_Internal() at
>>>>>>> /Users/migmolper/petsc/src/vec/is/sf/interface/vscat.c:70
>>>>>>> [4]PETSC ERROR: #7 VecScatterBegin() at
>>>>>>> /Users/migmolper/petsc/src/vec/is/sf/interface/vscat.c:1316
>>>>>>> [4]PETSC ERROR: #8 DMGlobalToLocalBegin_DA() at
>>>>>>> /Users/migmolper/petsc/src/dm/impls/da/dagtol.c:15
>>>>>>> [4]PETSC ERROR: #9 DMGlobalToLocalBegin() at
>>>>>>> /Users/migmolper/petsc/src/dm/interface/dm.c:2844
>>>>>>> [4]PETSC ERROR: #10 DMGetCoordinatesLocalSetUp() at
>>>>>>> /Users/migmolper/petsc/src/dm/interface/dmcoordinates.c:565
>>>>>>> [4]PETSC ERROR: #11 DMGetCoordinatesLocal() at
>>>>>>> /Users/migmolper/petsc/src/dm/interface/dmcoordinates.c:599
>>>>>>> [4]PETSC ERROR: #12 _DMLocatePoints_DMDARegular_IS() at
>>>>>>> /Users/migmolper/DMD/SOLERA/Atoms/Atom.cpp:531
>>>>>>> [4]PETSC ERROR: #13 DMLocatePoints_DMDARegular() at
>>>>>>> /Users/migmolper/DMD/SOLERA/Atoms/Atom.cpp:586
>>>>>>> [4]PETSC ERROR: #14 DMLocatePoints() at
>>>>>>> /Users/migmolper/petsc/src/dm/interface/dmcoordinates.c:1194
>>>>>>> [4]PETSC ERROR: #15 DMSwarmMigrate_CellDMScatter() at
>>>>>>> /Users/migmolper/petsc/src/dm/impls/swarm/swarm_migrate.c:219
>>>>>>> [4]PETSC ERROR: #16 DMSwarmMigrate() at
>>>>>>> /Users/migmolper/petsc/src/dm/impls/swarm/swarm.c:1349
>>>>>>> [4]PETSC ERROR: #17 main() at
>>>>>>> /Users/migmolper/DMD/driver-tasting-SOLERA.cpp:41
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> On Jan 15, 2025, at 4:56 PM, MIGUEL MOLINOS PEREZ <mmolinos at us.es>
>>>>>>> wrote:
>>>>>>>
>>>>>>> Thank you Matt for the useful info. I’ll try your idea.
>>>>>>>
>>>>>>> Miguel
>>>>>>>
>>>>>>> On 15 Jan 2025, at 16:48, Matthew Knepley <knepley at gmail.com> wrote:
>>>>>>>
>>>>>>> On Wed, Jan 15, 2025 at 10:41 AM MIGUEL MOLINOS PEREZ <
>>>>>>> mmolinos at us.es> wrote:
>>>>>>>
>>>>>>>> Thank you Matt.
>>>>>>>>
>>>>>>>> Yes, I am getting the "CellDM" from the DMSwarm.
>>>>>>>>
>>>>>>>> 1. I have recently overhauled this functionality because it was not
>>>>>>>> flexible enough for the plasma simulation we do. Thus main and release work
>>>>>>>> differently.
>>>>>>>>
>>>>>>>>
>>>>>>>> Nice to hear that. Should I move to main?
>>>>>>>>
>>>>>>>
>>>>>>> The changes allow you to have several cell DMs. I want to bin
>>>>>>> particles in space, but also in velocity, and then in the tensor product of
>>>>>>> space and velocity. Moreover, sometimes I want to use different Swarm
>>>>>>> fields as the DM field for the solver. You can do all that with main now.
>>>>>>> If you just need a single DM with the same DM fields, release is fine.
>>>>>>>
>>>>>>>
>>>>>>>> 2. I assume you are using release
>>>>>>>>
>>>>>>>>
>>>>>>>> You are correct.
>>>>>>>>
>>>>>>>> 3. In both main and release, if you change the coordinates of your
>>>>>>>> CellDM mesh, you need to rebin the particles. The easiest way to do this is
>>>>>>>> to call DMSwarmMigrate(sw, PETSC_FALSE).
>>>>>>>>
>>>>>>>>
>>>>>>>> What do you mean by rebin?
>>>>>>>>
>>>>>>>
>>>>>>> When you provide the cell DM, Swrm makes a "sort context" that bins
>>>>>>> the particles into DM cells. If you change the coordinates, this binning
>>>>>>> will change, so you need it to "rebin" or recreate the sort context.
>>>>>>>
>>>>>>>   Thanks,
>>>>>>>
>>>>>>>     Matt
>>>>>>>
>>>>>>>
>>>>>>>> Miguel
>>>>>>>>
>>>>>>>>
>>>>>>>>   Thanks,
>>>>>>>>
>>>>>>>>      Matt
>>>>>>>>
>>>>>>>>
>>>>>>>>> Best,
>>>>>>>>> Miguel
>>>>>>>>>
>>>>>>>> --
>>>>>>>> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx5LqFJcU$ 
>>>>>>>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx06JLsWL$ >
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx5LqFJcU$ 
>>>>>>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx06JLsWL$ >
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> --
>>>>>> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx5LqFJcU$ 
>>>>>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx06JLsWL$ >
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>> --
>>>>> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx5LqFJcU$ 
>>>>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx06JLsWL$ >
>>>>>
>>>>>
>>>>>
>>>>
>>>> --
>>>> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx5LqFJcU$ 
>>>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx06JLsWL$ >
>>>>
>>>>
>>>>
>>>>
>>>
>>> --
>>> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx5LqFJcU$ 
>>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx06JLsWL$ >
>>>
>>>
>>>
>>
>> --
>> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx5LqFJcU$ 
>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx06JLsWL$ >
>>
>>
>>
>
> --
> 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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx5LqFJcU$ 
> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx06JLsWL$ >
>
>
>
>

-- 
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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx5LqFJcU$  <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!ee2AOndSc3M8PXEGVjufaWIa3rs_TPHCCbPc7Y2s8ri6DAQ5tamfRac_Wqy3I_kP85xjohwRbXcUx06JLsWL$ >
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