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_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 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);
}
