[petsc-users] how is snes_test_jacobian_view computing the matrix difference?

[Barry Smith]

   Stefano hit the nail on the head!

   The matrices are of the same type it is just that MatView() for DMDA AIJ matrices MatView_MPI_DA()  causes them to printed out in “natural ordering” related to the grid instead of PETSc parallel ordering.  It is perhaps a case of Barry being too clever for his own good.

   SNESTestJacobian() has the code:

```
    PetscCall(MatGetType(A, &mattype));
    PetscCall(MatGetSize(A, &M, &N));
    PetscCall(MatGetLocalSize(A, &m, &n));
    PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    PetscCall(MatSetType(B, mattype));
    PetscCall(MatSetSizes(B, m, n, M, N));
    PetscCall(MatSetBlockSizesFromMats(B, A, A));
    PetscCall(MatSetUp(B));
    PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));

    PetscCall(SNESGetFunction(snes, NULL, NULL, &functx));
    PetscCall(SNESComputeJacobianDefault(snes, x, B, B, functx));
```

    It does not use MatDuplicate() hence the B (finite difference matrix) does not inherit the MatView_MPI_DA()  function.

    Could you please try the following. Edit src/snes/interface/snes.c and locate the routine SNESTestJacobian()  and replace the block of code  that creates the B matrix above with 

```
   PetscCall(MatDuplicate(B, MAT_DO_NOT_COPY_VALUES, &D));
```

   Then run make all in the PETSc home directory. Then rerun your program. The plan is now both matrices will be displayed in the same ordering (natural ordering on the multidimensional grid) and so the three matrices displayed should make sense.

   Barry




> On Mar 2, 2026, at 6:00 PM, Matteo Semplice via petsc-users <petsc-users at mcs.anl.gov> wrote:
> 
> It's indeed a DMDA (with 2 dofs per point), but the code is run with
> 
> -snes_test_jacobian -snes_test_jacobian_view
> 
> Would the hand-coded and the f.d. jacobian be different matrix type in this case?
> 
> Matteo
> 
> Il 02/03/26 21:32, Stefano Zampini ha scritto:
>> Maybe you are using a DMDA, with one matrix coming from it and the other not? DMDA changes the View to dump in natural ordering. 
>> 
>> Il giorno lun 2 mar 2026 alle ore 18:10 Matteo Semplice via petsc-users <petsc-users at mcs.anl.gov <mailto:petsc-users at mcs.anl.gov>> ha scritto:
>>> Dear all,
>>> 
>>>     the following output from -snes_test_jacobian_view lokks clear enough to pinpoint my mistake (I must be putting jacobian elements in the wrong place), but it nevertheless left me suprised.
>>> 
>>> 0 SNES Function norm 2.945516399303e-01
>>>   ---------- Testing Jacobian -------------
>>>   Testing hand-coded Jacobian, if (for double precision runs) ||J - Jfd||_F/||J||_F is
>>>     O(1.e-8), the hand-coded Jacobian is probably correct.
>>>   ||J - Jfd||_F/||J||_F = 0.000121529, ||J - Jfd||_F = 0.395752
>>>   Hand-coded Jacobian ----------
>>> Mat Object: 4 MPI processes
>>>   row 84:     (84, 60.)      (85, 0.)      (3446, -80.)      (3447, 0.)      (6808, 20.)      (6809, 0.)     
>>>   row 85:     (84, 0.00914434)      (85, 1.)      (3446, 0.)      (3447, 0.)      (6808, 0.)      (6809, 0.)    
>>>     
>>>    Finite difference Jacobian ----------
>>> Mat Object: 4 MPI processes
>>>   type: mpiaij
>>>   row 84:   (84, 60.)    (1806, -80.)    (3528, 20.)   
>>>   row 85:   (85, 0.999971)
>>> 
>>>   Hand-coded minus finite-difference Jacobian with tolerance 1e-05 ----------
>>> Mat Object: 4 MPI processes
>>>   type: mpiaij
>>>   row 84:  
>>>   row 85:   (84, 0.00914434)    (85, 2.9293e-05)
>>> The difference of the two matrices shoudl be nonzero in row 84 for all elements 1806, 3528, 3446, 6808. Is it intended that the difference is shown only for matrix elements that are present in both the hand-coded and the FD jacobian?
>>> 
>>> I would have expected an output like
>>> 
>>> row 84: (1806,80.)   (3446,-80.), etc
>>> 
>>> (This was on  PETSc Release Version 3.24.2)
>>> 
>>> Thanks
>>> 
>>>     Matteo
>>> 
>>> -- 
>>> Prof. Matteo Semplice
>>> Università degli Studi dell’Insubria
>>> Dipartimento di Scienza e Alta Tecnologia – DiSAT
>>> Professore Associato
>>> Via Valleggio, 11 – 22100 Como (CO) – Italia
>>> tel.: +39 031 2386316
>> 
>> 
>> 
>> --
>> Stefano
> -- 
> ---
> Professore Associato in Analisi Numerica
> Dipartimento di Scienza e Alta Tecnologia
> Università degli Studi dell'Insubria
> Via Valleggio, 11 - Como

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