[petsc-users] MatCreateSBAIJ
Sam Guo
sam.guo at cd-adapco.com
Tue Mar 22 14:58:43 CDT 2022
The reason I want to use shell matrix is to reduce memory footprint. If I
create a PETSc matrix and use MUMPS, I understand PETSc will create another
copy of the matrix for MUMPS. Is there any way to avoid the extra copy of
MUMPS?
On Tue, Mar 22, 2022 at 12:53 PM Sam Guo <sam.guo at cd-adapco.com> wrote:
> Barry,
> Thanks for the illustration. Is there an easy way to mimic the
> implementation using shell matrix? I have been studying how the sMvctx is
> created and it seems pretty involved.
>
> Thanks,
> Sam
>
> On Mon, Mar 21, 2022 at 2:48 PM Barry Smith <bsmith at petsc.dev> wrote:
>
>>
>>
>> On Mar 21, 2022, at 4:36 PM, Sam Guo <sam.guo at cd-adapco.com> wrote:
>>
>> Barry,
>> Thanks. Could you elaborate? I try to implement the matrix-vector
>> multiplication for a symmetric matrix using shell matrix.
>>
>>
>> Consider with three ranks
>>
>> (a) = ( A B D) (x)
>> (b) ( B' C E) (y)
>> (c) ( D' E' F) (w)
>>
>> Only the ones without the ' are stored on the rank. So for example
>> B is stored on rank 0.
>>
>> Rank 0 computes A x and keeps it in a. Rank 1 computes Cy and
>> keeps it in b Rank 2 computes Fw and keeps it in c
>>
>> Rank 0 computes B'x and D'x. It puts the nonzero entries of these
>> values as well as the values of x into slvec0
>>
>> Rank 1 computes E'y and puts the nonzero entries as well as the
>> values into slvec0
>>
>> Rank 2 puts the values of we needed by the other ranks into slvec0
>>
>> Rank 0 does B y_h + D z_h where it gets the y_h and z_h values
>> from slvec1 and adds it to a
>>
>> Rank 1 takes the B'x from slvec1 and adds it to b it then takes
>> the E y_h values where the y_h are pulled from slvec1 and adds them b
>>
>> Rank 2 takes the B'x and E'y from slvec0 and adds them to c.
>>
>>
>>
>> Thanks,
>> Sam
>>
>> On Mon, Mar 21, 2022 at 12:56 PM Barry Smith <bsmith at petsc.dev> wrote:
>>
>>>
>>> The "trick" is that though "more" communication is needed to complete
>>> the product the communication can still be done in a single VecScatter
>>> instead of two separate calls to VecScatter. We simply pack both pieces of
>>> information that needs to be sent into a single vector.
>>>
>>> /* copy x into the vec slvec0 */1111: VecGetArray <https://petsc.org/main/docs/manualpages/Vec/VecGetArray.html#VecGetArray>(a->slvec0,&from);1112: VecGetArrayRead <https://petsc.org/main/docs/manualpages/Vec/VecGetArrayRead.html#VecGetArrayRead>(xx,&x);
>>> 1114: PetscArraycpy <https://petsc.org/main/docs/manualpages/Sys/PetscArraycpy.html#PetscArraycpy>(from,x,bs*mbs);1115: VecRestoreArray <https://petsc.org/main/docs/manualpages/Vec/VecRestoreArray.html#VecRestoreArray>(a->slvec0,&from);1116: VecRestoreArrayRead <https://petsc.org/main/docs/manualpages/Vec/VecRestoreArrayRead.html#VecRestoreArrayRead>(xx,&x);
>>> 1118: VecScatterBegin <https://petsc.org/main/docs/manualpages/PetscSF/VecScatterBegin.html#VecScatterBegin>(a->sMvctx,a->slvec0,a->slvec1,ADD_VALUES <https://petsc.org/main/docs/manualpages/Sys/ADD_VALUES.html#ADD_VALUES>,SCATTER_FORWARD <https://petsc.org/main/docs/manualpages/Vec/SCATTER_FORWARD.html#SCATTER_FORWARD>);1119: VecScatterEnd <https://petsc.org/main/docs/manualpages/PetscSF/VecScatterEnd.html#VecScatterEnd>(a->sMvctx,a->slvec0,a->slvec1,ADD_VALUES <https://petsc.org/main/docs/manualpages/Sys/ADD_VALUES.html#ADD_VALUES>,SCATTER_FORWARD <https://petsc.org/main/docs/manualpages/Vec/SCATTER_FORWARD.html#SCATTER_FORWARD>);
>>>
>>> If you create two symmetric matrices, one with SBAIJ and one with BAIJ
>>> and compare the time to do the product you will find that the SBAIJ is not
>>> significantly slower but does save memory.
>>>
>>>
>>> On Mar 21, 2022, at 3:26 PM, Sam Guo <sam.guo at cd-adapco.com> wrote:
>>>
>>> Using following example from the MatCreateSBAIJ documentation
>>>
>>> 0 1 2 3 4 5 6 7 8 9 10 11
>>> --------------------------
>>> row 3 |. . . d d d o o o o o o
>>> row 4 |. . . d d d o o o o o o
>>> row 5 |. . . d d d o o o o o o
>>> --------------------------
>>>
>>>
>>> On a processor that owns rows 3, 4 and 5, rows 0-2 info are still needed. Is is that the processor that owns rows 0-2 will apply B symmetrical and then send the result
>>>
>>> to the processor that owns 3-5?
>>>
>>>
>>> On Mon, Mar 21, 2022 at 12:14 PM Mark Adams <mfadams at lbl.gov> wrote:
>>>
>>>> PETSc stores parallel matrices as two serial matrices. One for the
>>>> diagonal (d or A) block and one for the rest (o or B).
>>>> I would guess that for symmetric matrices it has a symmetric matrix for
>>>> the diagonal and a full AIJ matrix for the (upper) off-diagonal.
>>>> So the multtranspose is applying B symmetrically. This lower
>>>> off-diagonal and the diagonal block can be done without communication.
>>>> Then the off processor values are collected, and the upper off-diagonal
>>>> is applied.
>>>>
>>>> On Mon, Mar 21, 2022 at 2:35 PM Sam Guo <sam.guo at cd-adapco.com> wrote:
>>>>
>>>>> I am most interested in how the lower triangular part is
>>>>> redistributed. It seems that SBAJI saves memory but requires more
>>>>> communication than BAIJ.
>>>>>
>>>>> On Mon, Mar 21, 2022 at 11:27 AM Sam Guo <sam.guo at cd-adapco.com>
>>>>> wrote:
>>>>>
>>>>>> Mark, thanks for the quick response. I am more interested in parallel
>>>>>> implementation of MatMult for SBAIJ. I found following
>>>>>>
>>>>>> 1094: *PetscErrorCode <https://petsc.org/main/docs/manualpages/Sys/PetscErrorCode.html#PetscErrorCode> MatMult_MPISBAIJ(Mat <https://petsc.org/main/docs/manualpages/Mat/Mat.html#Mat> A,Vec <https://petsc.org/main/docs/manualpages/Vec/Vec.html#Vec> xx,Vec <https://petsc.org/main/docs/manualpages/Vec/Vec.html#Vec> yy)*1095: {1096: Mat_MPISBAIJ *a = (Mat_MPISBAIJ*)A->data;1097: PetscErrorCode <https://petsc.org/main/docs/manualpages/Sys/PetscErrorCode.html#PetscErrorCode> ierr;1098: PetscInt <https://petsc.org/main/docs/manualpages/Sys/PetscInt.html#PetscInt> mbs=a->mbs,bs=A->rmap->bs;1099: PetscScalar <https://petsc.org/main/docs/manualpages/Sys/PetscScalar.html#PetscScalar> *from;1100: const PetscScalar <https://petsc.org/main/docs/manualpages/Sys/PetscScalar.html#PetscScalar> *x;
>>>>>> 1103: /* diagonal part */1104: (*a->A->ops->mult)(a->A,xx,a->slvec1a);1105: VecSet <https://petsc.org/main/docs/manualpages/Vec/VecSet.html#VecSet>(a->slvec1b,0.0);
>>>>>> 1107: /* subdiagonal part */1108: (*a->B->ops->multtranspose)(a->B,xx,a->slvec0b);
>>>>>> 1110: /* copy x into the vec slvec0 */1111: VecGetArray <https://petsc.org/main/docs/manualpages/Vec/VecGetArray.html#VecGetArray>(a->slvec0,&from);1112: VecGetArrayRead <https://petsc.org/main/docs/manualpages/Vec/VecGetArrayRead.html#VecGetArrayRead>(xx,&x);
>>>>>> 1114: PetscArraycpy <https://petsc.org/main/docs/manualpages/Sys/PetscArraycpy.html#PetscArraycpy>(from,x,bs*mbs);1115: VecRestoreArray <https://petsc.org/main/docs/manualpages/Vec/VecRestoreArray.html#VecRestoreArray>(a->slvec0,&from);1116: VecRestoreArrayRead <https://petsc.org/main/docs/manualpages/Vec/VecRestoreArrayRead.html#VecRestoreArrayRead>(xx,&x);
>>>>>> 1118: VecScatterBegin <https://petsc.org/main/docs/manualpages/PetscSF/VecScatterBegin.html#VecScatterBegin>(a->sMvctx,a->slvec0,a->slvec1,ADD_VALUES <https://petsc.org/main/docs/manualpages/Sys/ADD_VALUES.html#ADD_VALUES>,SCATTER_FORWARD <https://petsc.org/main/docs/manualpages/Vec/SCATTER_FORWARD.html#SCATTER_FORWARD>);1119: VecScatterEnd <https://petsc.org/main/docs/manualpages/PetscSF/VecScatterEnd.html#VecScatterEnd>(a->sMvctx,a->slvec0,a->slvec1,ADD_VALUES <https://petsc.org/main/docs/manualpages/Sys/ADD_VALUES.html#ADD_VALUES>,SCATTER_FORWARD <https://petsc.org/main/docs/manualpages/Vec/SCATTER_FORWARD.html#SCATTER_FORWARD>);1120: /* supperdiagonal part */1121: (*a->B->ops->multadd)(a->B,a->slvec1b,a->slvec1a,yy);1122: return(0);1123: }
>>>>>>
>>>>>> I try to understand the algorithm.
>>>>>>
>>>>>>
>>>>>> Thanks,
>>>>>>
>>>>>> Sam
>>>>>>
>>>>>>
>>>>>> On Mon, Mar 21, 2022 at 11:14 AM Mark Adams <mfadams at lbl.gov> wrote:
>>>>>>
>>>>>>> This code looks fine to me and the code is
>>>>>>> in src/mat/impls/sbaij/seq/sbaij2.c
>>>>>>>
>>>>>>> On Mon, Mar 21, 2022 at 2:02 PM Sam Guo <sam.guo at cd-adapco.com>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> Dear PETSc dev team,
>>>>>>>> The documentation about MatCreateSBAIJ has following
>>>>>>>> "It is recommended that one use the MatCreate
>>>>>>>> <https://petsc.org/main/docs/manualpages/Mat/MatCreate.html#MatCreate>
>>>>>>>> (), MatSetType
>>>>>>>> <https://petsc.org/main/docs/manualpages/Mat/MatSetType.html#MatSetType>()
>>>>>>>> and/or MatSetFromOptions
>>>>>>>> <https://petsc.org/main/docs/manualpages/Mat/MatSetFromOptions.html#MatSetFromOptions>(),
>>>>>>>> MatXXXXSetPreallocation() paradigm instead of this routine directly.
>>>>>>>> [MatXXXXSetPreallocation() is, for example,
>>>>>>>> MatSeqAIJSetPreallocation
>>>>>>>> <https://petsc.org/main/docs/manualpages/Mat/MatSeqAIJSetPreallocation.html#MatSeqAIJSetPreallocation>
>>>>>>>> ]"
>>>>>>>> I currently call MatCreateSBAIJ directly as follows:
>>>>>>>> MatCreateSBAIJ (with d_nnz and o_nnz)
>>>>>>>> MatSetValues (to add row by row)
>>>>>>>> MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
>>>>>>>> MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
>>>>>>>> MatSetOption(A, MAT_SYMMETRIC, PETSC_TRUE);
>>>>>>>>
>>>>>>>> Two questions:
>>>>>>>> (1) I am wondering whether what I am doing is the
>>>>>>>> most efficient.
>>>>>>>>
>>>>>>>> (2) I try to find out how the matrix vector multiplication is
>>>>>>>> implemented in PETSc for SBAIJ storage.
>>>>>>>>
>>>>>>>> Thanks,
>>>>>>>> Sam
>>>>>>>>
>>>>>>>
>>>
>>
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