The phrase Hermitian symmetric was originally an attempt to make the text
clearer, but in fact it is confusing and wrong. The phrase Hermitian
symmetric should be removed and just Hermitian used.
Real matrices are either either both symmetric and Hermitian or not
symmetric and not Hermitian
Complex matrices can be set to symmetric or Hermitian. For SBAIJ this
changes the meaning of the values in the matrix; for matrices with full storage
this means the user is stating that the matrix values are actually symmetric or
Hermitian in the storage.
Currently for complex matrices one can state the matrix is both symmetric
and Hermitian which would mean one is stating the imaginary parts are all zero;
if this is the case then it doesn't matter if the
MatMult_SeqSBAIJ_1_Hermitian() or the MatMult_SeqSBAIJ_1() is used for SeqBAIJ.
Note that calling both of these doesn't mean the imaginary parts will be zeroed
out, it is statement by the user that the imaginary parts are zero.
For parallel matrices, even in debug node, checking the user is telling
the truth when they set symmetric or Hermitian is considered too expensive so
we just trust the user.
With the replacement of Hermitian symmetric by Hermitian will the text now
be clear or should more clarification be given in the manual pages (as above)?
Barry
case MAT_HERMITIAN:
#if defined(PETSC_USE_COMPLEX) /* MAT_HERMITIAN is a synonym for MAT_SYMMETRIC
with reals */
if (!A->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must
call MatAssemblyEnd() first");
if (A->cmap->n < 65536 && A->cmap->bs == 1) {
A->ops->mult = MatMult_SeqSBAIJ_1_Hermitian_ushort;
} else if (A->cmap->bs == 1) {
A->ops->mult = MatMult_SeqSBAIJ_1_Hermitian;
} else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for Hermitian with
block size greater than 1");
#endif
case MAT_SYMMETRIC:
mat->symmetric = flg;
if (flg) mat->structurally_symmetric = PETSC_TRUE;
mat->symmetric_set = PETSC_TRUE;
mat->structurally_symmetric_set = flg;
#if !defined(PETSC_USE_COMPLEX)
mat->hermitian = flg;
mat->hermitian_set = PETSC_TRUE;
#endif
break;
case MAT_HERMITIAN:
mat->hermitian = flg;
if (flg) mat->structurally_symmetric = PETSC_TRUE;
mat->hermitian_set = PETSC_TRUE;
mat->structurally_symmetric_set = flg;
#if !defined(PETSC_USE_COMPLEX)
mat->symmetric = flg;
mat->symmetric_set = PETSC_TRUE;
#endif
> On Sep 11, 2019, at 5:55 AM, Pierre Jolivet via petsc-dev
> <petsc-dev@mcs.anl.gov> wrote:
>
> (Putting back petsc-dev on c/c)
> I don’t think you are the one that needs to do the changes.
> There should be clarifications from the PETSc side of things, first.
> From the man page your are quoting
> (https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MATSEQSBAIJ.html):
> 1) how to make a SBAIJ Mat Hermitian but not symmetric? Is this handled by
> PETSc? Is this legal to do MatSetOption(A, MAT_SYMMETRIC, PETSC_FALSE)
> followed by MatSetOption(A, MAT_HERMITIAN, PETSC_TRUE)? I think this is the
> case where bs>1 is not handled internally by PETSc, so for this case it
> should be OK to error out.
> 2) “Hermitian symmetric” is a fancy way of saying that the matrix has no
> imaginary part. Or is just “Hermitian" what is supposed to be written on the
> page? In which case, how do you tell to PETSc that you are indeed dealing
> with a matrix with no imaginary part.
>
> Thanks,
> Pierre
>
>> On 11 Sep 2019, at 11:51 AM, Jose E. Roman <jro...@dsic.upv.es> wrote:
>>
>> Now I understand better. You are right. Maybe I should do some changes in
>> SLEPc. I will think about this next week.
>>
>>
>>> El 11 sept 2019, a las 11:38, Pierre Jolivet <pierre.joli...@enseeiht.fr>
>>> escribió:
>>>
>>>
>>>
>>>> On 11 Sep 2019, at 11:21 AM, Jose E. Roman <jro...@dsic.upv.es> wrote:
>>>>
>>>> In
>>>> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MATSEQSBAIJ.html
>>>> it says "To make it Hermitian symmetric you can call MatSetOption(Mat,
>>>> MAT_HERMITIAN);" So my understanding is that in SBAIJ assumes
>>>> MAT_SYMMETRIC and the user must set MAT_HERMITIAN if desired.
>>>
>>> Right, that is exactly what you do in STMatSetHermitian. You get from the
>>> user a SBAIJ matrix (so SYMMETRIC = true), and you set yourself HERMITIAN =
>>> true.
>>>
>>>> I don't think it makes sense to set both MAT_HERMITIAN and MAT_SYMMETRIC.
>>>
>>> Why? A symmetric (or Hermitian) matrix with no imaginary part is both
>>> Hermitian and symmetric, so at least this set of options defines correctly
>>> the structure of the matrix (which is not the case if you only assume it is
>>> _either_ symmetric or Hermitian).
>>>
>>>> But I may be wrong because I find this part of PETSc very confusing.
>>>>
>>>>
>>>>> El 11 sept 2019, a las 11:08, Jose E. Roman <jro...@dsic.upv.es> escribió:
>>>>>
>>>>> Do you mean setting both flags MAT_HERMITIAN and MAT_SYMMETRIC? Is this
>>>>> possible?
>>>
>>> It was possible before my commit for bs == 1, but not for bs > 1.
>>>
>>> At least now my tests are not failing.
>>>
>>>>>> El 11 sept 2019, a las 11:04, Pierre Jolivet
>>>>>> <pierre.joli...@enseeiht.fr> escribió:
>>>>>>
>>>>>> Symmetric <=> a_ij = a_ji
>>>>>> Hermitian <=> a_ij = conj(a_ji)
>>>>>>
>>>>>> Symmetric + Hermitian <=> a_ij = conj(a_ji) = a_ji <=> imag(a_ji) = 0
>>>>>> \forall ij
>>>>>>
>>>>>> Or am I stupid?
>>>>>>
>>>>>>> On 11 Sep 2019, at 10:59 AM, Jose E. Roman <jro...@dsic.upv.es> wrote:
>>>>>>>
>>>>>>> Not sure if I understand you. Do you mean that a complex SBAIJ Mat with
>>>>>>> MAT_HERMITIAN flag can be assumed to have zero imaginary part? I don't
>>>>>>> think so. This matrix should have real diagonal entries, but
>>>>>>> off-diagonal entries should be allowed to have nonzero imaginary part.
>>>>>>> This is what is done in MatMult_SeqSBAIJ_1_Hermitian(), where
>>>>>>> off-diagonal entries are conjugated when used for the strict lower
>>>>>>> triangular part. So I guess the right fix is to implement
>>>>>>> MatMult_SeqSBAIJ_2_Hermitian(), MatMult_SeqSBAIJ_3_Hermitian() and so
>>>>>>> on with appropriate use of PetscConj().
>>>>>>>
>>>>>>> Jose
>>>>>>>
>>>>>>>> El 11 sept 2019, a las 10:36, Pierre Jolivet
>>>>>>>> <pierre.joli...@enseeiht.fr> escribió:
>>>>>>>>
>>>>>>>> Nevermind, this is the wrong fix.
>>>>>>>> The proper fix is in PETSc. It should not error out if the matrix is
>>>>>>>> also symmetric.
>>>>>>>> Indeed, complex symmetric Hermitian => complex with no imaginary part.
>>>>>>>> Thus all operations like MatMult, MatMultHermitianTranspose, Cholesky…
>>>>>>>> will work for bs > 1, since all is filled with zeroes.
>>>>>>>> I will take care of this, I’m c/c’ing petsc-dev so that they don’t
>>>>>>>> have to “reverse engineer” the trivial change to MatSetOption_SeqSBAIJ.
>>>>>>>>
>>>>>>>> Sorry about the noise.
>>>>>>>>
>>>>>>>> Thank you,
>>>>>>>> Pierre
>>>>>>>>
>>>>>>>>> On 10 Sep 2019, at 8:37 AM, Pierre Jolivet
>>>>>>>>> <pierre.joli...@enseeiht.fr> wrote:
>>>>>>>>>
>>>>>>>>> Hello,
>>>>>>>>> Could you consider not setting MAT_HERMITIAN here
>>>>>>>>> http://slepc.upv.es/documentation/current/src/sys/classes/st/interface/stsles.c.html#line276
>>>>>>>>> when using SBAIJ matrices with bs > 1?
>>>>>>>>> This makes PETSc error out with
>>>>>>>>> # [1]PETSC ERROR: No support for this operation for this object
>>>>>>>>> type
>>>>>>>>> # [1]PETSC ERROR: No support for Hermitian with block size
>>>>>>>>> greater than 1
>>>>>>>>>
>>>>>>>>> The change does not bring any regression, since PETSc is always
>>>>>>>>> giving an error without it, but on the contrary, it improves the
>>>>>>>>> range of applicability of SLEPc, e.g., for complex Hermitian problems
>>>>>>>>> with SBAIJ matrices and bs > 1 that _don’t_ require the flag
>>>>>>>>> MAT_HERMITIAN set to true.
>>>>>>>>>
>>>>>>>>> Thanks,
>>>>>>>>> Pierre
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>
>>>>
>>>
>>
>
