PetscErrorCode MatPtAP_SeqAIJ_SeqAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
{
PetscErrorCode ierr;
const char *algTypes[2] = {"scalable","nonscalable"};
PetscInt alg=0; /* set default algorithm */
PetscFunctionBegin;
if (scall == MAT_INITIAL_MATRIX) {
/*
Alg 'scalable' determines which implementations to be used:
"nonscalable": do dense axpy in MatPtAPNumeric() - fastest, but requires storage of struct A*P;
"scalable": do two sparse axpy in MatPtAPNumeric() - might slow, does not store structure of A*P.
*/
ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,2,algTypes[0],&alg,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
switch (alg) {
case 1:
ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_DenseAxpy(A,P,fill,C);CHKERRQ(ierr);
break;
default:
ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr);
break;
}
ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
}
ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr);
ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
{
PetscErrorCode ierr;
Mat_SeqAIJ *ap,*c;
PetscInt *api,*apj,*ci,pn=P->cmap->N;
MatScalar *ca;
Mat_PtAP *ptap;
Mat Pt,AP;
PetscBool sparse_axpy=PETSC_TRUE;
PetscFunctionBegin;
ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
/* flag 'sparse_axpy' determines which implementations to be used:
0: do dense axpy in MatPtAPNumeric() - fastest, but requires storage of struct A*P;
1: do two sparse axpy in MatPtAPNumeric() - slowest, does not store structure of A*P. */
ierr = PetscOptionsBool("-matptap_scalable","Use sparse axpy but slower MatPtAPNumeric()","",sparse_axpy,&sparse_axpy,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
if (sparse_axpy) {
ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* Get symbolic Pt = P^T */
ierr = MatTransposeSymbolic_SeqAIJ(P,&Pt);CHKERRQ(ierr);
/* Get symbolic AP = A*P */
ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,P,fill,&AP);CHKERRQ(ierr);
ap = (Mat_SeqAIJ*)AP->data;
api = ap->i;
apj = ap->j;
ap->free_ij = PETSC_FALSE; /* api and apj are kept in struct ptap, cannot be destroyed with AP */
/* Get C = Pt*AP */
ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(Pt,AP,fill,C);CHKERRQ(ierr);
c = (Mat_SeqAIJ*)(*C)->data;
ci = c->i;
ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr);
c->a = ca;
c->free_a = PETSC_TRUE;
/* Create a supporting struct for reuse by MatPtAPNumeric() */
ierr = PetscNew(Mat_PtAP,&ptap);CHKERRQ(ierr);
c->ptap = ptap;
ptap->destroy = (*C)->ops->destroy;
(*C)->ops->destroy = MatDestroy_SeqAIJ_PtAP;
/* Allocate temporary array for storage of one row of A*P */
ierr = PetscMalloc((pn+1)*sizeof(PetscScalar),&ptap->apa);CHKERRQ(ierr);
ierr = PetscMemzero(ptap->apa,(pn+1)*sizeof(PetscScalar));CHKERRQ(ierr);
(*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ;
ptap->api = api;
ptap->apj = apj;
/* Clean up. */
ierr = MatDestroy(&Pt);CHKERRQ(ierr);
ierr = MatDestroy(&AP);CHKERRQ(ierr);
#if defined(PETSC_USE_INFO)
ierr = PetscInfo2((*C),"given fill %G, use scalable %d\n",fill,sparse_axpy);CHKERRQ(ierr);
#endif
PetscFunctionReturn(0);
}
PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(Mat A,Mat R,PetscReal fill,Mat *C)
{
PetscErrorCode ierr;
Mat P;
PetscInt *rti,*rtj;
Mat_RARt *rart;
MatColoring coloring;
MatTransposeColoring matcoloring;
ISColoring iscoloring;
Mat Rt_dense,RARt_dense;
Mat_SeqAIJ *c;
PetscFunctionBegin;
/* create symbolic P=Rt */
ierr = MatGetSymbolicTranspose_SeqAIJ(R,&rti,&rtj);CHKERRQ(ierr);
ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,R->cmap->n,R->rmap->n,rti,rtj,NULL,&P);CHKERRQ(ierr);
/* get symbolic C=Pt*A*P */
ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(A,P,fill,C);CHKERRQ(ierr);
ierr = MatSetBlockSizes(*C,PetscAbs(R->rmap->bs),PetscAbs(R->rmap->bs));CHKERRQ(ierr);
(*C)->ops->rartnumeric = MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart;
/* create a supporting struct */
ierr = PetscNew(&rart);CHKERRQ(ierr);
c = (Mat_SeqAIJ*)(*C)->data;
c->rart = rart;
/* ------ Use coloring ---------- */
/* inode causes memory problem, don't know why */
if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
/* Create MatTransposeColoring from symbolic C=R*A*R^T */
ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr);
ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
rart->matcoloring = matcoloring;
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
/* Create Rt_dense */
ierr = MatCreate(PETSC_COMM_SELF,&Rt_dense);CHKERRQ(ierr);
ierr = MatSetSizes(Rt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
ierr = MatSetType(Rt_dense,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(Rt_dense,NULL);CHKERRQ(ierr);
Rt_dense->assembled = PETSC_TRUE;
rart->Rt = Rt_dense;
/* Create RARt_dense = R*A*Rt_dense */
ierr = MatCreate(PETSC_COMM_SELF,&RARt_dense);CHKERRQ(ierr);
ierr = MatSetSizes(RARt_dense,(*C)->rmap->n,matcoloring->ncolors,(*C)->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
ierr = MatSetType(RARt_dense,MATSEQDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(RARt_dense,NULL);CHKERRQ(ierr);
rart->RARt = RARt_dense;
/* Allocate work array to store columns of A*R^T used in MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense() */
ierr = PetscMalloc1(A->rmap->n*4,&rart->work);CHKERRQ(ierr);
rart->destroy = (*C)->ops->destroy;
(*C)->ops->destroy = MatDestroy_SeqAIJ_RARt;
/* clean up */
ierr = MatRestoreSymbolicTranspose_SeqAIJ(R,&rti,&rtj);CHKERRQ(ierr);
ierr = MatDestroy(&P);CHKERRQ(ierr);
#if defined(PETSC_USE_INFO)
{
PetscReal density= (PetscReal)(c->nz)/(RARt_dense->rmap->n*RARt_dense->cmap->n);
ierr = PetscInfo(*C,"C=R*(A*Rt) via coloring C - use sparse-dense inner products\n");CHKERRQ(ierr);
ierr = PetscInfo6(*C,"RARt_den %D %D; Rt %D %D (RARt->nz %D)/(m*ncolors)=%g\n",RARt_dense->rmap->n,RARt_dense->cmap->n,R->cmap->n,R->rmap->n,c->nz,density);CHKERRQ(ierr);
}
#endif
PetscFunctionReturn(0);
}
