PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat A,Mat P,PetscReal fill,Mat *C)
{
PetscErrorCode ierr;
PetscFreeSpaceList free_space=NULL,current_space=NULL;
Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
MatScalar *ca;
PetscBT lnkbt;
PetscReal afill;
PetscFunctionBegin;
/* Get ij structure of P^T */
ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
ptJ = ptj;
/* Allocate ci array, arrays for fill computation and */
/* free space for accumulating nonzero column info */
ierr = PetscMalloc1(pn+1,&ci);CHKERRQ(ierr);
ci[0] = 0;
ierr = PetscCalloc1(2*an+1,&ptadenserow);CHKERRQ(ierr);
ptasparserow = ptadenserow + an;
/* create and initialize a linked list */
nlnk = pn+1;
ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
/* Set initial free space to be fill*(nnz(A)+ nnz(P)) */
ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],pi[pm])),&free_space);CHKERRQ(ierr);
current_space = free_space;
/* Determine symbolic info for each row of C: */
for (i=0; i<pn; i++) {
ptnzi = pti[i+1] - pti[i];
ptanzi = 0;
/* Determine symbolic row of PtA: */
for (j=0; j<ptnzi; j++) {
arow = *ptJ++;
anzj = ai[arow+1] - ai[arow];
ajj = aj + ai[arow];
for (k=0; k<anzj; k++) {
if (!ptadenserow[ajj[k]]) {
ptadenserow[ajj[k]] = -1;
ptasparserow[ptanzi++] = ajj[k];
}
}
}
/* Using symbolic info for row of PtA, determine symbolic info for row of C: */
ptaj = ptasparserow;
cnzi = 0;
for (j=0; j<ptanzi; j++) {
prow = *ptaj++;
pnzj = pi[prow+1] - pi[prow];
pjj = pj + pi[prow];
/* add non-zero cols of P into the sorted linked list lnk */
ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
cnzi += nlnk;
}
/* If free space is not available, make more free space */
/* Double the amount of total space in the list */
if (current_space->local_remaining<cnzi) {
ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),¤t_space);CHKERRQ(ierr);
nspacedouble++;
}
/* Copy data into free space, and zero out denserows */
ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
current_space->array += cnzi;
current_space->local_used += cnzi;
current_space->local_remaining -= cnzi;
for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;
/* Aside: Perhaps we should save the pta info for the numerical factorization. */
/* For now, we will recompute what is needed. */
ci[i+1] = ci[i] + cnzi;
}
/* nnz is now stored in ci[ptm], column indices are in the list of free space */
/* Allocate space for cj, initialize cj, and */
/* destroy list of free space and other temporary array(s) */
ierr = PetscMalloc1(ci[pn]+1,&cj);CHKERRQ(ierr);
ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
ierr = PetscFree(ptadenserow);CHKERRQ(ierr);
ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
ierr = PetscCalloc1(ci[pn]+1,&ca);CHKERRQ(ierr);
/* put together the new matrix */
ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),pn,pn,ci,cj,ca,C);CHKERRQ(ierr);
ierr = MatSetBlockSizes(*C,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
/* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
/* Since these are PETSc arrays, change flags to free them as necessary. */
c = (Mat_SeqAIJ*)((*C)->data);
c->free_a = PETSC_TRUE;
c->free_ij = PETSC_TRUE;
c->nonew = 0;
(*C)->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy;
/* set MatInfo */
afill = (PetscReal)ci[pn]/(ai[am]+pi[pm] + 1.e-5);
if (afill < 1.0) afill = 1.0;
c->maxnz = ci[pn];
c->nz = ci[pn];
(*C)->info.mallocs = nspacedouble;
(*C)->info.fill_ratio_given = fill;
(*C)->info.fill_ratio_needed = afill;
/* Clean up. */
ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
#if defined(PETSC_USE_INFO)
if (ci[pn] != 0) {
ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
} else {
ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
}
#endif
PetscFunctionReturn(0);
}
PetscErrorCode MatLUFactorSymbolic_SeqBAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
{
Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b;
PetscInt n =a->mbs,bs = A->rmap->bs,bs2=a->bs2;
PetscBool row_identity,col_identity,both_identity;
IS isicol;
PetscErrorCode ierr;
const PetscInt *r,*ic;
PetscInt i,*ai=a->i,*aj=a->j;
PetscInt *bi,*bj,*ajtmp;
PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
PetscReal f;
PetscInt nlnk,*lnk,k,**bi_ptr;
PetscFreeSpaceList free_space=NULL,current_space=NULL;
PetscBT lnkbt;
PetscBool missing;
PetscFunctionBegin;
if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square");
ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
/* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
ierr = PetscMalloc1(n+1,&bi);CHKERRQ(ierr);
ierr = PetscMalloc1(n+1,&bdiag);CHKERRQ(ierr);
bi[0] = bdiag[0] = 0;
/* linked list for storing column indices of the active row */
nlnk = n + 1;
ierr = PetscLLCreate(n,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
ierr = PetscMalloc2(n+1,&bi_ptr,n+1,&im);CHKERRQ(ierr);
/* initial FreeSpace size is f*(ai[n]+1) */
f = info->fill;
ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);CHKERRQ(ierr);
current_space = free_space;
for (i=0; i<n; i++) {
/* copy previous fill into linked list */
nzi = 0;
nnz = ai[r[i]+1] - ai[r[i]];
ajtmp = aj + ai[r[i]];
ierr = PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);CHKERRQ(ierr);
nzi += nlnk;
/* add pivot rows into linked list */
row = lnk[n];
while (row < i) {
nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
ierr = PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);CHKERRQ(ierr);
nzi += nlnk;
row = lnk[row];
}
bi[i+1] = bi[i] + nzi;
im[i] = nzi;
/* mark bdiag */
nzbd = 0;
nnz = nzi;
k = lnk[n];
while (nnz-- && k < i) {
nzbd++;
k = lnk[k];
}
bdiag[i] = bi[i] + nzbd;
/* if free space is not available, make more free space */
if (current_space->local_remaining<nzi) {
nnz = PetscIntMultTruncate(n - i,nzi); /* estimated and max additional space needed */
ierr = PetscFreeSpaceGet(nnz,¤t_space);CHKERRQ(ierr);
reallocs++;
}
/* copy data into free space, then initialize lnk */
ierr = PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
bi_ptr[i] = current_space->array;
current_space->array += nzi;
current_space->local_used += nzi;
current_space->local_remaining -= nzi;
}
#if defined(PETSC_USE_INFO)
if (ai[n] != 0) {
PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);CHKERRQ(ierr);
ierr = PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);CHKERRQ(ierr);
ierr = PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);CHKERRQ(ierr);
ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
} else {
ierr = PetscInfo(A,"Empty matrix\n");CHKERRQ(ierr);
}
#endif
ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
/* destroy list of free space and other temporary array(s) */
ierr = PetscMalloc1(bi[n]+1,&bj);CHKERRQ(ierr);
ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
ierr = PetscFree2(bi_ptr,im);CHKERRQ(ierr);
/* put together the new matrix */
ierr = MatSeqBAIJSetPreallocation_SeqBAIJ(B,bs,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr);
ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);CHKERRQ(ierr);
b = (Mat_SeqBAIJ*)(B)->data;
b->free_a = PETSC_TRUE;
b->free_ij = PETSC_TRUE;
b->singlemalloc = PETSC_FALSE;
ierr = PetscMalloc1((bi[n]+1)*bs2,&b->a);CHKERRQ(ierr);
b->j = bj;
b->i = bi;
b->diag = bdiag;
b->free_diag = PETSC_TRUE;
b->ilen = 0;
b->imax = 0;
b->row = isrow;
b->col = iscol;
b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;
ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
b->icol = isicol;
ierr = PetscMalloc1(bs*n+bs,&b->solve_work);CHKERRQ(ierr);
ierr = PetscLogObjectMemory((PetscObject)B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)*bs2));CHKERRQ(ierr);
b->maxnz = b->nz = bi[n];
(B)->factortype = MAT_FACTOR_LU;
(B)->info.factor_mallocs = reallocs;
(B)->info.fill_ratio_given = f;
if (ai[n] != 0) {
(B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
} else {
(B)->info.fill_ratio_needed = 0.0;
}
ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
both_identity = (PetscBool) (row_identity && col_identity);
ierr = MatSeqBAIJSetNumericFactorization_inplace(B,both_identity);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy2(Mat A,Mat P,PetscReal fill,Mat *C)
{
PetscErrorCode ierr;
PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*p = (Mat_SeqAIJ*)P->data,*c;
PetscInt *pti,*ptj,*ptJ,*ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pjj;
PetscInt *ci,*cj,*ptadenserow,*ptasparserow,*ptaj,nspacedouble=0;
PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N;
PetscInt i,j,k,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,nlnk,*lnk;
MatScalar *ca;
PetscBT lnkbt;
PetscFunctionBegin;
/* Get ij structure of P^T */
ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
ptJ=ptj;
/* Allocate ci array, arrays for fill computation and */
/* free space for accumulating nonzero column info */
ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
ci[0] = 0;
ierr = PetscMalloc((2*an+1)*sizeof(PetscInt),&ptadenserow);CHKERRQ(ierr);
ierr = PetscMemzero(ptadenserow,(2*an+1)*sizeof(PetscInt));CHKERRQ(ierr);
ptasparserow = ptadenserow + an;
/* create and initialize a linked list */
nlnk = pn+1;
ierr = PetscLLCreate(pn,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
/* Set initial free space to be fill*nnz(A). */
/* This should be reasonable if sparsity of PtAP is similar to that of A. */
ierr = PetscFreeSpaceGet((PetscInt)(fill*ai[am]),&free_space);
current_space = free_space;
/* Determine symbolic info for each row of C: */
for (i=0;i<pn;i++) {
ptnzi = pti[i+1] - pti[i];
ptanzi = 0;
/* Determine symbolic row of PtA: */
for (j=0;j<ptnzi;j++) {
arow = *ptJ++;
anzj = ai[arow+1] - ai[arow];
ajj = aj + ai[arow];
for (k=0;k<anzj;k++) {
if (!ptadenserow[ajj[k]]) {
ptadenserow[ajj[k]] = -1;
ptasparserow[ptanzi++] = ajj[k];
}
}
}
/* Using symbolic info for row of PtA, determine symbolic info for row of C: */
ptaj = ptasparserow;
cnzi = 0;
for (j=0;j<ptanzi;j++) {
prow = *ptaj++;
pnzj = pi[prow+1] - pi[prow];
pjj = pj + pi[prow];
/* add non-zero cols of P into the sorted linked list lnk */
ierr = PetscLLAddSorted(pnzj,pjj,pn,nlnk,lnk,lnkbt);CHKERRQ(ierr);
cnzi += nlnk;
}
/* If free space is not available, make more free space */
/* Double the amount of total space in the list */
if (current_space->local_remaining<cnzi) {
ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,¤t_space);CHKERRQ(ierr);
nspacedouble++;
}
/* Copy data into free space, and zero out denserows */
ierr = PetscLLClean(pn,pn,cnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
current_space->array += cnzi;
current_space->local_used += cnzi;
current_space->local_remaining -= cnzi;
for (j=0;j<ptanzi;j++) {
ptadenserow[ptasparserow[j]] = 0;
}
/* Aside: Perhaps we should save the pta info for the numerical factorization. */
/* For now, we will recompute what is needed. */
ci[i+1] = ci[i] + cnzi;
}
/* nnz is now stored in ci[ptm], column indices are in the list of free space */
/* Allocate space for cj, initialize cj, and */
/* destroy list of free space and other temporary array(s) */
ierr = PetscMalloc((ci[pn]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
ierr = PetscFree(ptadenserow);CHKERRQ(ierr);
ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
/* Allocate space for ca */
ierr = PetscMalloc((ci[pn]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
ierr = PetscMemzero(ca,(ci[pn]+1)*sizeof(MatScalar));CHKERRQ(ierr);
/* put together the new matrix */
ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,pn,pn,ci,cj,ca,C);CHKERRQ(ierr);
(*C)->rmap->bs = P->cmap->bs;
(*C)->cmap->bs = P->cmap->bs;
PetscPrintf(PETSC_COMM_SELF,"************%s C.bs=%d,%d\n",__FUNCT__,(*C)->rmap->bs,(*C)->cmap->bs);
/* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
/* Since these are PETSc arrays, change flags to free them as necessary. */
c = (Mat_SeqAIJ *)((*C)->data);
c->free_a = PETSC_TRUE;
c->free_ij = PETSC_TRUE;
c->nonew = 0;
A->ops->ptapnumeric = MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy2; /* should use *C->ops until PtAP insterface is updated to double dispatch as MatMatMult() */
/* Clean up. */
ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
#if defined(PETSC_USE_INFO)
if (ci[pn] != 0) {
PetscReal afill = ((PetscReal)ci[pn])/ai[am];
if (afill < 1.0) afill = 1.0;
ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
ierr = PetscInfo1((*C),"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr);
} else {
ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
}
#endif
PetscFunctionReturn(0);
}
PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
{
PetscErrorCode ierr;
Mat Cmpi;
Mat_PtAPMPI *ptap;
PetscFreeSpaceList free_space=NULL,current_space=NULL;
Mat_MPIAIJ *a =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
Mat_SeqAIJ *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
Mat_SeqAIJ *p_loc,*p_oth;
PetscInt *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pdti,*pdtj,*poti,*potj,*ptJ;
PetscInt *adi=ad->i,*aj,*aoi=ao->i,nnz;
PetscInt *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
PetscInt am=A->rmap->n,pN=P->cmap->N,pm=P->rmap->n,pn=P->cmap->n;
PetscBT lnkbt;
MPI_Comm comm;
PetscMPIInt size,rank,tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0;
PetscInt **buf_rj,**buf_ri,**buf_ri_k;
PetscInt len,proc,*dnz,*onz,*owners;
PetscInt nzi,*pti,*ptj;
PetscInt nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
MPI_Request *swaits,*rwaits;
MPI_Status *sstatus,rstatus;
Mat_Merge_SeqsToMPI *merge;
PetscInt *api,*apj,*Jptr,apnz,*prmap=p->garray,pon,nspacedouble=0,j,ap_rmax=0;
PetscReal afill=1.0,afill_tmp;
PetscInt rmax;
#if defined(PTAP_PROFILE)
PetscLogDouble t0,t1,t2,t3,t4;
#endif
PetscFunctionBegin;
ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
#if defined(PTAP_PROFILE)
ierr = PetscTime(&t0);CHKERRQ(ierr);
#endif
/* check if matrix local sizes are compatible */
if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) {
SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%D, %D) != Prow (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
}
if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) {
SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%D, %D) != Prow (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
}
ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
/* create struct Mat_PtAPMPI and attached it to C later */
ierr = PetscNew(&ptap);CHKERRQ(ierr);
ierr = PetscNew(&merge);CHKERRQ(ierr);
ptap->merge = merge;
ptap->reuse = MAT_INITIAL_MATRIX;
/* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
/* get P_loc by taking all local rows of P */
ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
pi_loc = p_loc->i; pj_loc = p_loc->j;
pi_oth = p_oth->i; pj_oth = p_oth->j;
#if defined(PTAP_PROFILE)
ierr = PetscTime(&t1);CHKERRQ(ierr);
#endif
/* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
/*-------------------------------------------------------------------*/
ierr = PetscMalloc1((am+1),&api);CHKERRQ(ierr);
api[0] = 0;
/* create and initialize a linked list */
ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
/* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) -OOM for ex56, np=8k on Intrepid! */
ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);CHKERRQ(ierr);
current_space = free_space;
for (i=0; i<am; i++) {
/* diagonal portion of A */
nzi = adi[i+1] - adi[i];
aj = ad->j + adi[i];
for (j=0; j<nzi; j++) {
row = aj[j];
pnz = pi_loc[row+1] - pi_loc[row];
Jptr = pj_loc + pi_loc[row];
/* add non-zero cols of P into the sorted linked list lnk */
ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
}
/* off-diagonal portion of A */
nzi = aoi[i+1] - aoi[i];
aj = ao->j + aoi[i];
for (j=0; j<nzi; j++) {
row = aj[j];
pnz = pi_oth[row+1] - pi_oth[row];
Jptr = pj_oth + pi_oth[row];
ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
}
apnz = lnk[0];
api[i+1] = api[i] + apnz;
if (ap_rmax < apnz) ap_rmax = apnz;
/* if free space is not available, double the total space in the list */
if (current_space->local_remaining<apnz) {
ierr = PetscFreeSpaceGet(apnz+current_space->total_array_size,¤t_space);CHKERRQ(ierr);
nspacedouble++;
}
/* Copy data into free space, then initialize lnk */
ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
current_space->array += apnz;
current_space->local_used += apnz;
current_space->local_remaining -= apnz;
}
/* Allocate space for apj, initialize apj, and */
/* destroy list of free space and other temporary array(s) */
ierr = PetscMalloc1((api[am]+1),&apj);CHKERRQ(ierr);
ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
afill_tmp = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1);
if (afill_tmp > afill) afill = afill_tmp;
#if defined(PTAP_PROFILE)
ierr = PetscTime(&t2);CHKERRQ(ierr);
#endif
/* determine symbolic Co=(p->B)^T*AP - send to others */
/*----------------------------------------------------*/
ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
/* then, compute symbolic Co = (p->B)^T*AP */
pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
>= (num of nonzero rows of C_seq) - pn */
ierr = PetscMalloc1((pon+1),&coi);CHKERRQ(ierr);
coi[0] = 0;
/* set initial free space to be fill*(nnz(p->B) + nnz(AP)) */
nnz = fill*(poti[pon] + api[am]);
ierr = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
current_space = free_space;
for (i=0; i<pon; i++) {
pnz = poti[i+1] - poti[i];
ptJ = potj + poti[i];
for (j=0; j<pnz; j++) {
row = ptJ[j]; /* row of AP == col of Pot */
apnz = api[row+1] - api[row];
Jptr = apj + api[row];
/* add non-zero cols of AP into the sorted linked list lnk */
ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
}
nnz = lnk[0];
/* If free space is not available, double the total space in the list */
if (current_space->local_remaining<nnz) {
ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,¤t_space);CHKERRQ(ierr);
nspacedouble++;
}
/* Copy data into free space, and zero out denserows */
ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
current_space->array += nnz;
current_space->local_used += nnz;
current_space->local_remaining -= nnz;
coi[i+1] = coi[i] + nnz;
}
ierr = PetscMalloc1((coi[pon]+1),&coj);CHKERRQ(ierr);
ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
afill_tmp = (PetscReal)coi[pon]/(poti[pon] + api[am]+1);
if (afill_tmp > afill) afill = afill_tmp;
ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
/* send j-array (coj) of Co to other processors */
/*----------------------------------------------*/
/* determine row ownership */
ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
merge->rowmap->n = pn;
merge->rowmap->bs = 1;
ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
owners = merge->rowmap->range;
/* determine the number of messages to send, their lengths */
ierr = PetscMalloc2(size,&len_si,size,&sstatus);CHKERRQ(ierr);
ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
len_s = merge->len_s;
merge->nsend = 0;
ierr = PetscMalloc1((size+2),&owners_co);CHKERRQ(ierr);
proc = 0;
for (i=0; i<pon; i++) {
while (prmap[i] >= owners[proc+1]) proc++;
len_si[proc]++; /* num of rows in Co to be sent to [proc] */
len_s[proc] += coi[i+1] - coi[i];
}
len = 0; /* max length of buf_si[] */
owners_co[0] = 0;
for (proc=0; proc<size; proc++) {
owners_co[proc+1] = owners_co[proc] + len_si[proc];
if (len_si[proc]) {
merge->nsend++;
len_si[proc] = 2*(len_si[proc] + 1);
len += len_si[proc];
}
}
/* determine the number and length of messages to receive for coi and coj */
ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
/* post the Irecv and Isend of coj */
ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
ierr = PetscMalloc1((merge->nsend+1),&swaits);CHKERRQ(ierr);
for (proc=0, k=0; proc<size; proc++) {
if (!len_s[proc]) continue;
i = owners_co[proc];
ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
k++;
}
/* receives and sends of coj are complete */
for (i=0; i<merge->nrecv; i++) {
ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
}
ierr = PetscFree(rwaits);CHKERRQ(ierr);
if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
/* send and recv coi */
/*-------------------*/
ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
ierr = PetscMalloc1((len+1),&buf_s);CHKERRQ(ierr);
buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
for (proc=0,k=0; proc<size; proc++) {
if (!len_s[proc]) continue;
/* form outgoing message for i-structure:
buf_si[0]: nrows to be sent
[1:nrows]: row index (global)
[nrows+1:2*nrows+1]: i-structure index
*/
/*-------------------------------------------*/
nrows = len_si[proc]/2 - 1;
buf_si_i = buf_si + nrows+1;
buf_si[0] = nrows;
buf_si_i[0] = 0;
nrows = 0;
for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
nzi = coi[i+1] - coi[i];
buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
buf_si[nrows+1] = prmap[i] -owners[proc]; /* local row index */
nrows++;
}
ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
k++;
buf_si += len_si[proc];
}
i = merge->nrecv;
while (i--) {
ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
}
ierr = PetscFree(rwaits);CHKERRQ(ierr);
if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
ierr = PetscFree2(len_si,sstatus);CHKERRQ(ierr);
ierr = PetscFree(len_ri);CHKERRQ(ierr);
ierr = PetscFree(swaits);CHKERRQ(ierr);
ierr = PetscFree(buf_s);CHKERRQ(ierr);
#if defined(PTAP_PROFILE)
ierr = PetscTime(&t3);CHKERRQ(ierr);
#endif
/* compute the local portion of C (mpi mat) */
/*------------------------------------------*/
ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
/* allocate pti array and free space for accumulating nonzero column info */
ierr = PetscMalloc1((pn+1),&pti);CHKERRQ(ierr);
pti[0] = 0;
/* set initial free space to be fill*(nnz(P) + nnz(AP)) */
nnz = fill*(pi_loc[pm] + api[am]);
ierr = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
current_space = free_space;
ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
for (k=0; k<merge->nrecv; k++) {
buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
nrows = *buf_ri_k[k];
nextrow[k] = buf_ri_k[k] + 1; /* next row number of k-th recved i-structure */
nextci[k] = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure */
}
ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
rmax = 0;
for (i=0; i<pn; i++) {
/* add pdt[i,:]*AP into lnk */
pnz = pdti[i+1] - pdti[i];
ptJ = pdtj + pdti[i];
for (j=0; j<pnz; j++) {
row = ptJ[j]; /* row of AP == col of Pt */
apnz = api[row+1] - api[row];
Jptr = apj + api[row];
/* add non-zero cols of AP into the sorted linked list lnk */
ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
}
/* add received col data into lnk */
for (k=0; k<merge->nrecv; k++) { /* k-th received message */
if (i == *nextrow[k]) { /* i-th row */
nzi = *(nextci[k]+1) - *nextci[k];
Jptr = buf_rj[k] + *nextci[k];
ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
nextrow[k]++; nextci[k]++;
}
}
nnz = lnk[0];
/* if free space is not available, make more free space */
if (current_space->local_remaining<nnz) {
ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,¤t_space);CHKERRQ(ierr);
nspacedouble++;
}
/* copy data into free space, then initialize lnk */
ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
current_space->array += nnz;
current_space->local_used += nnz;
current_space->local_remaining -= nnz;
pti[i+1] = pti[i] + nnz;
if (nnz > rmax) rmax = nnz;
}
ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
ierr = PetscMalloc1((pti[pn]+1),&ptj);CHKERRQ(ierr);
ierr = PetscFreeSpaceContiguous(&free_space,ptj);CHKERRQ(ierr);
afill_tmp = (PetscReal)pti[pn]/(pi_loc[pm] + api[am]+1);
if (afill_tmp > afill) afill = afill_tmp;
ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
/* create symbolic parallel matrix Cmpi */
/*--------------------------------------*/
ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetBlockSizes(Cmpi,P->cmap->bs,P->cmap->bs);CHKERRQ(ierr);
ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
merge->bi = pti; /* Cseq->i */
merge->bj = ptj; /* Cseq->j */
merge->coi = coi; /* Co->i */
merge->coj = coj; /* Co->j */
merge->buf_ri = buf_ri;
merge->buf_rj = buf_rj;
merge->owners_co = owners_co;
merge->destroy = Cmpi->ops->destroy;
merge->duplicate = Cmpi->ops->duplicate;
/* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
Cmpi->assembled = PETSC_FALSE;
Cmpi->ops->destroy = MatDestroy_MPIAIJ_PtAP;
Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatPtAP;
/* attach the supporting struct to Cmpi for reuse */
c = (Mat_MPIAIJ*)Cmpi->data;
c->ptap = ptap;
ptap->api = api;
ptap->apj = apj;
ptap->rmax = ap_rmax;
*C = Cmpi;
/* flag 'scalable' determines which implementations to be used:
0: do dense axpy in MatPtAPNumeric() - fast, but requires storage of a nonscalable dense array apa;
1: do sparse axpy in MatPtAPNumeric() - might slow, uses a sparse array apa */
/* set default scalable */
ptap->scalable = PETSC_TRUE;
ierr = PetscOptionsGetBool(((PetscObject)Cmpi)->prefix,"-matptap_scalable",&ptap->scalable,NULL);CHKERRQ(ierr);
if (!ptap->scalable) { /* Do dense axpy */
ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
} else {
ierr = PetscCalloc1(ap_rmax+1,&ptap->apa);CHKERRQ(ierr);
}
#if defined(PTAP_PROFILE)
ierr = PetscTime(&t4);CHKERRQ(ierr);
if (rank==1) PetscPrintf(MPI_COMM_SELF," [%d] PtAPSymbolic %g/P + %g/AP + %g/comm + %g/PtAP = %g\n",rank,t1-t0,t2-t1,t3-t2,t4-t3,t4-t0);CHKERRQ(ierr);
#endif
#if defined(PETSC_USE_INFO)
if (pti[pn] != 0) {
ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
ierr = PetscInfo1(Cmpi,"Use MatPtAP(A,P,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr);
} else {
ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
}
#endif
PetscFunctionReturn(0);
}
PetscErrorCode MatApplyPAPt_Symbolic_SeqAIJ_SeqAIJ(Mat A,Mat P,Mat *C)
{
/* Note: This code is virtually identical to that of MatApplyPtAP_SeqAIJ_Symbolic */
/* and MatMatMult_SeqAIJ_SeqAIJ_Symbolic. Perhaps they could be merged nicely. */
PetscErrorCode ierr;
PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*p=(Mat_SeqAIJ*)P->data,*c;
PetscInt *ai=a->i,*aj=a->j,*ajj,*pi=p->i,*pj=p->j,*pti,*ptj,*ptjj;
PetscInt *ci,*cj,*paj,*padenserow,*pasparserow,*denserow,*sparserow;
PetscInt an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N;
PetscInt i,j,k,pnzi,arow,anzj,panzi,ptrow,ptnzj,cnzi;
MatScalar *ca;
PetscFunctionBegin;
/* some error checking which could be moved into interface layer */
if (pn!=am) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",pn,am);
if (am!=an) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %D != %D",am, an);
/* Set up timers */
ierr = PetscLogEventBegin(MAT_Applypapt_symbolic,A,P,0,0);CHKERRQ(ierr);
/* Create ij structure of P^T */
ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
/* Allocate ci array, arrays for fill computation and */
/* free space for accumulating nonzero column info */
ierr = PetscMalloc(((pm+1)*1)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
ci[0] = 0;
ierr = PetscMalloc4(an,PetscInt,&padenserow,an,PetscInt,&pasparserow,pm,PetscInt,&denserow,pm,PetscInt,&sparserow);CHKERRQ(ierr);
ierr = PetscMemzero(padenserow,an*sizeof(PetscInt));CHKERRQ(ierr);
ierr = PetscMemzero(pasparserow,an*sizeof(PetscInt));CHKERRQ(ierr);
ierr = PetscMemzero(denserow,pm*sizeof(PetscInt));CHKERRQ(ierr);
ierr = PetscMemzero(sparserow,pm*sizeof(PetscInt));CHKERRQ(ierr);
/* Set initial free space to be nnz(A) scaled by aspect ratio of Pt. */
/* This should be reasonable if sparsity of PAPt is similar to that of A. */
ierr = PetscFreeSpaceGet((ai[am]/pn)*pm,&free_space);CHKERRQ(ierr);
current_space = free_space;
/* Determine fill for each row of C: */
for (i=0;i<pm;i++) {
pnzi = pi[i+1] - pi[i];
panzi = 0;
/* Get symbolic sparse row of PA: */
for (j=0;j<pnzi;j++) {
arow = *pj++;
anzj = ai[arow+1] - ai[arow];
ajj = aj + ai[arow];
for (k=0;k<anzj;k++) {
if (!padenserow[ajj[k]]) {
padenserow[ajj[k]] = -1;
pasparserow[panzi++] = ajj[k];
}
}
}
/* Using symbolic row of PA, determine symbolic row of C: */
paj = pasparserow;
cnzi = 0;
for (j=0;j<panzi;j++) {
ptrow = *paj++;
ptnzj = pti[ptrow+1] - pti[ptrow];
ptjj = ptj + pti[ptrow];
for (k=0;k<ptnzj;k++) {
if (!denserow[ptjj[k]]) {
denserow[ptjj[k]] = -1;
sparserow[cnzi++] = ptjj[k];
}
}
}
/* sort sparse representation */
ierr = PetscSortInt(cnzi,sparserow);CHKERRQ(ierr);
/* If free space is not available, make more free space */
/* Double the amount of total space in the list */
if (current_space->local_remaining<cnzi) {
ierr = PetscFreeSpaceGet(cnzi+current_space->total_array_size,¤t_space);CHKERRQ(ierr);
}
/* Copy data into free space, and zero out dense row */
ierr = PetscMemcpy(current_space->array,sparserow,cnzi*sizeof(PetscInt));CHKERRQ(ierr);
current_space->array += cnzi;
current_space->local_used += cnzi;
current_space->local_remaining -= cnzi;
for (j=0;j<panzi;j++) {
padenserow[pasparserow[j]] = 0;
}
for (j=0;j<cnzi;j++) {
denserow[sparserow[j]] = 0;
}
ci[i+1] = ci[i] + cnzi;
}
/* column indices are in the list of free space */
/* Allocate space for cj, initialize cj, and */
/* destroy list of free space and other temporary array(s) */
ierr = PetscMalloc((ci[pm]+1)*sizeof(PetscInt),&cj);CHKERRQ(ierr);
ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
ierr = PetscFree4(padenserow,pasparserow,denserow,sparserow);CHKERRQ(ierr);
/* Allocate space for ca */
ierr = PetscMalloc((ci[pm]+1)*sizeof(MatScalar),&ca);CHKERRQ(ierr);
ierr = PetscMemzero(ca,(ci[pm]+1)*sizeof(MatScalar));CHKERRQ(ierr);
/* put together the new matrix */
ierr = MatCreateSeqAIJWithArrays(((PetscObject)A)->comm,pm,pm,ci,cj,ca,C);CHKERRQ(ierr);
(*C)->rmap->bs = P->cmap->bs;
(*C)->cmap->bs = P->cmap->bs;
/* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
/* Since these are PETSc arrays, change flags to free them as necessary. */
c = (Mat_SeqAIJ *)((*C)->data);
c->free_a = PETSC_TRUE;
c->free_ij = PETSC_TRUE;
c->nonew = 0;
/* Clean up. */
ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
ierr = PetscLogEventEnd(MAT_Applypapt_symbolic,A,P,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
