[petsc-users] MatCreateSBAIJ

Sam Guo sam.guo at cd-adapco.com
Tue Mar 22 14:53:37 CDT 2022


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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