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);
}
int main(int argc,char **argv)
{
Mat A,R,C,C_dense,C_sparse,Rt_dense,P,PtAP;
PetscInt row,col,m,n;
PetscErrorCode ierr;
MatScalar one =1.0,val;
MatColoring mc;
MatTransposeColoring matcoloring = 0;
ISColoring iscoloring;
PetscBool equal;
PetscMPIInt size;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
/* Create seqaij A */
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,4,4,4,4);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
row = 0; col=0; val=1.0; ierr = MatSetValues(A,1,&row,1,&col,&val,ADD_VALUES);CHKERRQ(ierr);
row = 1; col=3; val=2.0; ierr = MatSetValues(A,1,&row,1,&col,&val,ADD_VALUES);CHKERRQ(ierr);
row = 2; col=2; val=3.0; ierr = MatSetValues(A,1,&row,1,&col,&val,ADD_VALUES);CHKERRQ(ierr);
row = 3; col=0; val=4.0; ierr = MatSetValues(A,1,&row,1,&col,&val,ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(A,"A_");CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr);
/* Create seqaij R */
ierr = MatCreate(PETSC_COMM_SELF,&R);CHKERRQ(ierr);
ierr = MatSetSizes(R,2,4,2,4);CHKERRQ(ierr);
ierr = MatSetType(R,MATSEQAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(R);CHKERRQ(ierr);
ierr = MatSetUp(R);CHKERRQ(ierr);
row = 0; col=0; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
row = 0; col=1; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
row = 1; col=1; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
row = 1; col=2; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
row = 1; col=3; ierr = MatSetValues(R,1,&row,1,&col,&one,ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(R,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(R,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(R,"R_");CHKERRQ(ierr);
ierr = MatView(R,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr);
/* C = A*R^T */
ierr = MatMatTransposeMult(A,R,MAT_INITIAL_MATRIX,2.0,&C);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(C,"ARt_");CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr);
/* Create MatTransposeColoring from symbolic C=A*R^T */
ierr = MatColoringCreate(C,&mc);CHKERRQ(ierr);
ierr = MatColoringSetDistance(mc,2);CHKERRQ(ierr);
/* ierr = MatColoringSetType(mc,MATCOLORINGSL);CHKERRQ(ierr); */
ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
ierr = MatColoringApply(mc,&iscoloring);CHKERRQ(ierr);
ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
ierr = MatTransposeColoringCreate(C,iscoloring,&matcoloring);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
/* Create Rt_dense */
ierr = MatCreate(PETSC_COMM_WORLD,&Rt_dense);CHKERRQ(ierr);
ierr = MatSetSizes(Rt_dense,4,matcoloring->ncolors,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
ierr = MatSetType(Rt_dense,MATDENSE);CHKERRQ(ierr);
ierr = MatSeqDenseSetPreallocation(Rt_dense,NULL);CHKERRQ(ierr);
ierr = MatAssemblyBegin(Rt_dense,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Rt_dense,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatGetLocalSize(Rt_dense,&m,&n);CHKERRQ(ierr);
printf("Rt_dense: %d,%d\n",(int)m,(int)n);
/* Get Rt_dense by Apply MatTransposeColoring to R */
ierr = MatTransColoringApplySpToDen(matcoloring,R,Rt_dense);CHKERRQ(ierr);
/* C_dense = A*Rt_dense */
ierr = MatMatMult(A,Rt_dense,MAT_INITIAL_MATRIX,2.0,&C_dense);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(C_dense,"ARt_dense_");CHKERRQ(ierr);
/*ierr = MatView(C_dense,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
/*ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr); */
/* Recover C from C_dense */
ierr = MatDuplicate(C,MAT_DO_NOT_COPY_VALUES,&C_sparse);CHKERRQ(ierr);
ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C_sparse);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(C_sparse,"ARt_color_");CHKERRQ(ierr);
ierr = MatView(C_sparse,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"\n");CHKERRQ(ierr);
ierr = MatDestroy(&C_dense);CHKERRQ(ierr);
ierr = MatDestroy(&C_sparse);CHKERRQ(ierr);
ierr = MatDestroy(&Rt_dense);CHKERRQ(ierr);
ierr = MatTransposeColoringDestroy(&matcoloring);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
/* Test PtAP = P^T*A*P, P = R^T */
ierr = MatTranspose(R,MAT_INITIAL_MATRIX,&P);CHKERRQ(ierr);
ierr = MatPtAP(A,P,MAT_INITIAL_MATRIX,2.0,&PtAP);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(PtAP,"PtAP_");CHKERRQ(ierr);
ierr = MatView(PtAP,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = MatDestroy(&P);CHKERRQ(ierr);
/* Test C = RARt */
ierr = MatRARt(A,R,MAT_INITIAL_MATRIX,2.0,&C);CHKERRQ(ierr);
ierr = MatRARt(A,R,MAT_REUSE_MATRIX,2.0,&C);CHKERRQ(ierr);
ierr = MatEqual(C,PtAP,&equal);CHKERRQ(ierr);
if (!equal) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: PtAP != RARt");CHKERRQ(ierr);
}
/* Free spaces */
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&R);CHKERRQ(ierr);
ierr = MatDestroy(&PtAP);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat R,PetscReal fill,Mat *C)
{
PetscErrorCode ierr;
Mat P;
PetscInt *rti,*rtj;
Mat_RARt *rart;
PetscContainer container;
MatTransposeColoring matcoloring;
ISColoring iscoloring;
Mat Rt_dense,RARt_dense;
PetscLogDouble GColor=0.0,MCCreate=0.0,MDenCreate=0.0,t0,tf,etime=0.0;
Mat_SeqAIJ *c;
PetscFunctionBegin;
ierr = PetscGetTime(&t0);CHKERRQ(ierr);
/* 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,PETSC_NULL,&P);CHKERRQ(ierr);
/* get symbolic C=Pt*A*P */
ierr = MatPtAPSymbolic_SeqAIJ_SeqAIJ(A,P,fill,C);CHKERRQ(ierr);
(*C)->rmap->bs = R->rmap->bs;
(*C)->cmap->bs = R->rmap->bs;
/* create a supporting struct */
ierr = PetscNew(Mat_RARt,&rart);CHKERRQ(ierr);
/* attach the supporting struct to C */
ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
ierr = PetscContainerSetPointer(container,rart);CHKERRQ(ierr);
ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_RARt);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject)(*C),"Mat_RARt",(PetscObject)container);CHKERRQ(ierr);
ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
ierr = PetscGetTime(&tf);CHKERRQ(ierr);
etime += tf - t0;
/* Create MatTransposeColoring from symbolic C=R*A*R^T */
c=(Mat_SeqAIJ*)(*C)->data;
ierr = PetscGetTime(&t0);CHKERRQ(ierr);
ierr = MatGetColoring(*C,MATCOLORINGLF,&iscoloring);CHKERRQ(ierr);
ierr = PetscGetTime(&tf);CHKERRQ(ierr);
GColor += tf - t0;
ierr = PetscGetTime(&t0);CHKERRQ(ierr);
ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
rart->matcoloring = matcoloring;
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
ierr = PetscGetTime(&tf);CHKERRQ(ierr);
MCCreate += tf - t0;
ierr = PetscGetTime(&t0);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,PETSC_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,PETSC_NULL);CHKERRQ(ierr);
rart->RARt = RARt_dense;
/* Allocate work array to store columns of A*R^T used in MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense() */
ierr = PetscMalloc(A->rmap->n*4*sizeof(PetscScalar),&rart->work);CHKERRQ(ierr);
ierr = PetscGetTime(&tf);CHKERRQ(ierr);
MDenCreate += tf - t0;
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 = PetscInfo6(*C,"RARt_den %D %D; Rt_den %D %D, (RARt->nz %D)/(m*ncolors)=%g\n",RARt_dense->rmap->n,RARt_dense->cmap->n,Rt_dense->rmap->n,Rt_dense->cmap->n,c->nz,density);CHKERRQ(ierr);
ierr = PetscInfo5(*C,"Sym = GetColor %g + MColorCreate %g + MDenCreate %g + other %g = %g\n",GColor,MCCreate,MDenCreate,etime,GColor+MCCreate+MDenCreate+etime);CHKERRQ(ierr);
}
#endif
PetscFunctionReturn(0);
}
