[petsc-users] MatCreateSBAIJ
Sam Guo
sam.guo at cd-adapco.com
Tue Mar 22 15:20:41 CDT 2022
I am using SLEPc to solve a generalized eigenvalue problem.
On Tue, Mar 22, 2022 at 1:16 PM Sam Guo <sam.guo at cd-adapco.com> wrote:
> Here is one memory comparison (memory in MB)
> np=1np=2np=4np=8np=16
> shell 1614 1720 1874 1673 1248
> PETSc(using full matrix) 2108 2260 2364 2215 1734
> PETSc(using symmetric matrix) 1750 2100 2189 2094 1727Those are the total
> water mark memory added.
>
> On Tue, Mar 22, 2022 at 1:10 PM Barry Smith <bsmith at petsc.dev> wrote:
>
>>
>> Sam,
>>
>> MUMPS is a direct solver, as such, it requires much more memory than
>> the original matrix (stored as a PETSc matrix) to store the factored
>> matrix. The savings you will get by not having a PETSc copy of the matrix
>> and a MUMPS copy of the matrix at the same time is unlikely to be
>> significant. Do you have memory footprint measurements indicating that not
>> having the PETSc copy of the matrix in memory will allow you to run
>> measurably larger simulations?
>>
>> Barry
>>
>>
>>
>>
>> On Mar 22, 2022, at 3:58 PM, Sam Guo <sam.guo at cd-adapco.com> wrote:
>>
>> 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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