PetscErrorCode MatGetOrdering_myordering(Mat mat,MatOrderingType type,IS *irow,IS *icol)
{
PetscErrorCode ierr;
PetscInt n,i,*ii;
PetscBool done;
MPI_Comm comm;
PetscFunctionBegin;
ierr = PetscObjectGetComm((PetscObject)mat,&comm);
CHKERRQ(ierr);
ierr = MatGetRowIJ(mat,0,PETSC_FALSE,PETSC_TRUE,&n,NULL,NULL,&done);
CHKERRQ(ierr);
ierr = MatRestoreRowIJ(mat,0,PETSC_FALSE,PETSC_TRUE,NULL,NULL,NULL,&done);
CHKERRQ(ierr);
if (done) { /* matrix may be "compressed" in symbolic factorization, due to i-nodes or block storage */
ierr = PetscMalloc(n*sizeof(PetscInt),&ii);
CHKERRQ(ierr);
for (i=0; i<n; i++) ii[i] = n-i-1; /* replace your index here */
ierr = ISCreateGeneral(PETSC_COMM_SELF,n,ii,PETSC_COPY_VALUES,irow);
CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,n,ii,PETSC_OWN_POINTER,icol);
CHKERRQ(ierr);
} else SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"MatRestoreRowIJ fails!");
ierr = ISSetIdentity(*irow);
CHKERRQ(ierr);
ierr = ISSetIdentity(*icol);
CHKERRQ(ierr);
ierr = ISSetPermutation(*irow);
CHKERRQ(ierr);
ierr = ISSetPermutation(*icol);
CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode ISInvertPermutation_Block(IS is,PetscInt nlocal,IS *isout)
{
IS_Block *sub = (IS_Block*)is->data;
PetscInt i,*ii,bs,n,*idx = sub->idx;
PetscMPIInt size;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = MPI_Comm_size(PetscObjectComm((PetscObject)is),&size);
CHKERRQ(ierr);
ierr = PetscLayoutGetBlockSize(is->map, &bs);
CHKERRQ(ierr);
ierr = PetscLayoutGetLocalSize(is->map, &n);
CHKERRQ(ierr);
n /= bs;
if (size == 1) {
ierr = PetscMalloc1(n,&ii);
CHKERRQ(ierr);
for (i=0; i<n; i++) ii[idx[i]] = i;
ierr = ISCreateBlock(PETSC_COMM_SELF,bs,n,ii,PETSC_OWN_POINTER,isout);
CHKERRQ(ierr);
ierr = ISSetPermutation(*isout);
CHKERRQ(ierr);
} else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No inversion written yet for block IS");
PetscFunctionReturn(0);
}
PetscErrorCode ISInvertPermutation_General(IS is,PetscInt nlocal,IS *isout)
{
IS_General *sub = (IS_General*)is->data;
PetscInt i,*ii,n,nstart;
const PetscInt *idx = sub->idx;
PetscMPIInt size;
IS istmp,nistmp;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscLayoutGetLocalSize(is->map, &n);CHKERRQ(ierr);
ierr = MPI_Comm_size(PetscObjectComm((PetscObject)is),&size);CHKERRQ(ierr);
if (size == 1) {
ierr = PetscMalloc1(n,&ii);CHKERRQ(ierr);
for (i=0; i<n; i++) ii[idx[i]] = i;
ierr = ISCreateGeneral(PETSC_COMM_SELF,n,ii,PETSC_OWN_POINTER,isout);CHKERRQ(ierr);
ierr = ISSetPermutation(*isout);CHKERRQ(ierr);
} else {
/* crude, nonscalable get entire IS on each processor */
if (nlocal == PETSC_DECIDE) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Do not yet support nlocal of PETSC_DECIDE");
ierr = ISAllGather(is,&istmp);CHKERRQ(ierr);
ierr = ISSetPermutation(istmp);CHKERRQ(ierr);
ierr = ISInvertPermutation(istmp,PETSC_DECIDE,&nistmp);CHKERRQ(ierr);
ierr = ISDestroy(&istmp);CHKERRQ(ierr);
/* get the part we need */
ierr = MPI_Scan(&nlocal,&nstart,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)is));CHKERRQ(ierr);
#if defined(PETSC_USE_DEBUG)
{
PetscInt N;
PetscMPIInt rank;
ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)is),&rank);CHKERRQ(ierr);
ierr = PetscLayoutGetSize(is->map, &N);CHKERRQ(ierr);
if (rank == size-1) {
if (nstart != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of nlocal lengths %d != total IS length %d",nstart,N);
}
}
#endif
nstart -= nlocal;
ierr = ISGetIndices(nistmp,&idx);CHKERRQ(ierr);
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is),nlocal,idx+nstart,PETSC_COPY_VALUES,isout);CHKERRQ(ierr);
ierr = ISRestoreIndices(nistmp,&idx);CHKERRQ(ierr);
ierr = ISDestroy(&nistmp);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*@
ISSetIdentity - Informs the index set that it is an identity.
Logically Collective on IS
Input Parmeters:
. is - the index set
Level: intermediate
Concepts: identity mapping
Concepts: index sets^is identity
.seealso: ISIdentity()
@*/
PetscErrorCode ISSetIdentity(IS is)
{
PetscErrorCode ierr;
PetscFunctionBegin;
PetscValidHeaderSpecific(is,IS_CLASSID,1);
is->isidentity = PETSC_TRUE;
ierr = ISSetPermutation(is);
CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@
ISInvertPermutation - Creates a new permutation that is the inverse of
a given permutation.
Collective on IS
Input Parameter:
+ is - the index set
- nlocal - number of indices on this processor in result (ignored for 1 proccessor) or
use PETSC_DECIDE
Output Parameter:
. isout - the inverse permutation
Level: intermediate
Notes: For parallel index sets this does the complete parallel permutation, but the
code is not efficient for huge index sets (10,000,000 indices).
Concepts: inverse permutation
Concepts: permutation^inverse
Concepts: index sets^inverting
@*/
PetscErrorCode ISInvertPermutation(IS is,PetscInt nlocal,IS *isout)
{
PetscErrorCode ierr;
PetscFunctionBegin;
PetscValidHeaderSpecific(is,IS_CLASSID,1);
PetscValidPointer(isout,3);
if (!is->isperm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Not a permutation, must call ISSetPermutation() on the IS first");
ierr = (*is->ops->invertpermutation)(is,nlocal,isout);CHKERRQ(ierr);
ierr = ISSetPermutation(*isout);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@
ISPartitioningToNumbering - Takes an ISPartitioning and on each processor
generates an IS that contains a new global node number for each index based
on the partitioing.
Collective on IS
Input Parameters
. partitioning - a partitioning as generated by MatPartitioningApply()
Output Parameter:
. is - on each processor the index set that defines the global numbers
(in the new numbering) for all the nodes currently (before the partitioning)
on that processor
Level: advanced
.seealso: MatPartitioningCreate(), AOCreateBasic(), ISPartitioningCount()
@*/
PetscErrorCode ISPartitioningToNumbering(IS part,IS *is)
{
MPI_Comm comm;
PetscInt i,np,npt,n,*starts = NULL,*sums = NULL,*lsizes = NULL,*newi = NULL;
const PetscInt *indices = NULL;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscObjectGetComm((PetscObject)part,&comm);CHKERRQ(ierr);
/* count the number of partitions, i.e., virtual processors */
ierr = ISGetLocalSize(part,&n);CHKERRQ(ierr);
ierr = ISGetIndices(part,&indices);CHKERRQ(ierr);
np = 0;
for (i=0; i<n; i++) np = PetscMax(np,indices[i]);
ierr = MPI_Allreduce(&np,&npt,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
np = npt+1; /* so that it looks like a MPI_Comm_size output */
/*
lsizes - number of elements of each partition on this particular processor
sums - total number of "previous" nodes for any particular partition
starts - global number of first element in each partition on this processor
*/
ierr = PetscMalloc3(np,&lsizes,np,&starts,np,&sums);CHKERRQ(ierr);
ierr = PetscMemzero(lsizes,np*sizeof(PetscInt));CHKERRQ(ierr);
for (i=0; i<n; i++) lsizes[indices[i]]++;
ierr = MPI_Allreduce(lsizes,sums,np,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
ierr = MPI_Scan(lsizes,starts,np,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
for (i=0; i<np; i++) starts[i] -= lsizes[i];
for (i=1; i<np; i++) {
sums[i] += sums[i-1];
starts[i] += sums[i-1];
}
/*
For each local index give it the new global number
*/
ierr = PetscMalloc1(n,&newi);CHKERRQ(ierr);
for (i=0; i<n; i++) newi[i] = starts[indices[i]]++;
ierr = PetscFree3(lsizes,starts,sums);CHKERRQ(ierr);
ierr = ISRestoreIndices(part,&indices);CHKERRQ(ierr);
ierr = ISCreateGeneral(comm,n,newi,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
ierr = ISSetPermutation(*is);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ISInvertPermutation_Stride(IS is,PetscInt nlocal,IS *perm)
{
IS_Stride *isstride = (IS_Stride*)is->data;
PetscErrorCode ierr;
PetscFunctionBegin;
if (is->isidentity) {
ierr = ISCreateStride(PETSC_COMM_SELF,isstride->n,0,1,perm);CHKERRQ(ierr);
} else {
IS tmp;
const PetscInt *indices,n = isstride->n;
ierr = ISGetIndices(is,&indices);CHKERRQ(ierr);
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is),n,indices,PETSC_COPY_VALUES,&tmp);CHKERRQ(ierr);
ierr = ISSetPermutation(tmp);CHKERRQ(ierr);
ierr = ISRestoreIndices(is,&indices);CHKERRQ(ierr);
ierr = ISInvertPermutation(tmp,nlocal,perm);CHKERRQ(ierr);
ierr = ISDestroy(&tmp);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscMPIInt rank,size;
PetscInt i,n,*indices;
const PetscInt *ii;
IS is,newis;
PetscBool flg;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
/*
Test IS of size 0
*/
ierr = ISCreateGeneral(PETSC_COMM_SELF,0,&n,PETSC_COPY_VALUES,&is);CHKERRQ(ierr);
ierr = ISGetSize(is,&n);CHKERRQ(ierr);
if (n != 0) SETERRQ(PETSC_COMM_SELF,1,"ISGetSize");
ierr = ISDestroy(&is);CHKERRQ(ierr);
/*
Create large IS and test ISGetIndices()
*/
n = 10000 + rank;
ierr = PetscMalloc1(n,&indices);CHKERRQ(ierr);
for (i=0; i<n; i++) indices[i] = rank + i;
ierr = ISCreateGeneral(PETSC_COMM_SELF,n,indices,PETSC_COPY_VALUES,&is);CHKERRQ(ierr);
ierr = ISGetIndices(is,&ii);CHKERRQ(ierr);
for (i=0; i<n; i++) {
if (ii[i] != indices[i]) SETERRQ(PETSC_COMM_SELF,1,"ISGetIndices");
}
ierr = ISRestoreIndices(is,&ii);CHKERRQ(ierr);
/*
Check identity and permutation
*/
ierr = ISPermutation(is,&flg);CHKERRQ(ierr);
if (flg) SETERRQ(PETSC_COMM_SELF,1,"ISPermutation");
ierr = ISIdentity(is,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,1,"ISIdentity");
ierr = ISSetPermutation(is);CHKERRQ(ierr);
ierr = ISSetIdentity(is);CHKERRQ(ierr);
ierr = ISPermutation(is,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,1,"ISPermutation");
ierr = ISIdentity(is,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,1,"ISIdentity");
/*
Check equality of index sets
*/
ierr = ISEqual(is,is,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,1,"ISEqual");
/*
Sorting
*/
ierr = ISSort(is);CHKERRQ(ierr);
ierr = ISSorted(is,&flg);CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,1,"ISSort");
/*
Thinks it is a different type?
*/
ierr = PetscObjectTypeCompare((PetscObject)is,ISSTRIDE,&flg);CHKERRQ(ierr);
if (flg) SETERRQ(PETSC_COMM_SELF,1,"ISStride");
ierr = PetscObjectTypeCompare((PetscObject)is,ISBLOCK,&flg);CHKERRQ(ierr);
if (flg) SETERRQ(PETSC_COMM_SELF,1,"ISBlock");
ierr = ISDestroy(&is);CHKERRQ(ierr);
/*
Inverting permutation
*/
for (i=0; i<n; i++) indices[i] = n - i - 1;
ierr = ISCreateGeneral(PETSC_COMM_SELF,n,indices,PETSC_COPY_VALUES,&is);CHKERRQ(ierr);
ierr = PetscFree(indices);CHKERRQ(ierr);
ierr = ISSetPermutation(is);CHKERRQ(ierr);
ierr = ISInvertPermutation(is,PETSC_DECIDE,&newis);CHKERRQ(ierr);
ierr = ISGetIndices(newis,&ii);CHKERRQ(ierr);
for (i=0; i<n; i++) {
if (ii[i] != n - i - 1) SETERRQ(PETSC_COMM_SELF,1,"ISInvertPermutation");
}
ierr = ISRestoreIndices(newis,&ii);CHKERRQ(ierr);
ierr = ISDestroy(&newis);CHKERRQ(ierr);
ierr = ISDestroy(&is);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
static PetscErrorCode MatPartitioningApply_PTScotch_Private(MatPartitioning part, PetscBool useND, IS *partitioning)
{
MPI_Comm pcomm,comm;
MatPartitioning_PTScotch *scotch = (MatPartitioning_PTScotch*)part->data;
PetscErrorCode ierr;
PetscMPIInt rank;
Mat mat = part->adj;
Mat_MPIAdj *adj = (Mat_MPIAdj*)mat->data;
PetscBool flg,distributed;
PetscBool proc_weight_flg;
PetscInt i,j,p,bs=1,nold;
PetscInt *NDorder = NULL;
PetscReal *vwgttab,deltval;
SCOTCH_Num *locals,*velotab,*veloloctab,*edloloctab,vertlocnbr,edgelocnbr,nparts=part->n;
PetscFunctionBegin;
ierr = PetscObjectGetComm((PetscObject)part,&pcomm);CHKERRQ(ierr);
/* Duplicate the communicator to be sure that PTSCOTCH attribute caching does not interfere with PETSc. */
ierr = MPI_Comm_dup(pcomm,&comm);CHKERRQ(ierr);
ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIADJ,&flg);CHKERRQ(ierr);
if (!flg) {
/* bs indicates if the converted matrix is "reduced" from the original and hence the
resulting partition results need to be stretched to match the original matrix */
nold = mat->rmap->n;
ierr = MatConvert(mat,MATMPIADJ,MAT_INITIAL_MATRIX,&mat);CHKERRQ(ierr);
if (mat->rmap->n > 0) bs = nold/mat->rmap->n;
adj = (Mat_MPIAdj*)mat->data;
}
proc_weight_flg = PETSC_TRUE;
ierr = PetscOptionsGetBool(NULL, NULL, "-mat_partitioning_ptscotch_proc_weight", &proc_weight_flg, NULL);CHKERRQ(ierr);
ierr = PetscMalloc1(mat->rmap->n+1,&locals);CHKERRQ(ierr);
if (useND) {
#if defined(PETSC_HAVE_SCOTCH_PARMETIS_V3_NODEND)
PetscInt *sizes, *seps, log2size, subd, *level, base = 0;
PetscMPIInt size;
ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
log2size = PetscLog2Real(size);
subd = PetscPowInt(2,log2size);
if (subd != size) SETERRQ(comm,PETSC_ERR_SUP,"Only power of 2 communicator sizes");
ierr = PetscMalloc1(mat->rmap->n,&NDorder);CHKERRQ(ierr);
ierr = PetscMalloc3(2*size,&sizes,4*size,&seps,size,&level);CHKERRQ(ierr);
SCOTCH_ParMETIS_V3_NodeND(mat->rmap->range,adj->i,adj->j,&base,NULL,NDorder,sizes,&comm);
ierr = MatPartitioningSizesToSep_Private(subd,sizes,seps,level);CHKERRQ(ierr);
for (i=0;i<mat->rmap->n;i++) {
PetscInt loc;
ierr = PetscFindInt(NDorder[i],2*subd,seps,&loc);CHKERRQ(ierr);
if (loc < 0) {
loc = -(loc+1);
if (loc%2) { /* part of subdomain */
locals[i] = loc/2;
} else {
ierr = PetscFindInt(NDorder[i],2*(subd-1),seps+2*subd,&loc);CHKERRQ(ierr);
loc = loc < 0 ? -(loc+1)/2 : loc/2;
locals[i] = level[loc];
}
} else locals[i] = loc/2;
}
ierr = PetscFree3(sizes,seps,level);CHKERRQ(ierr);
#else
SETERRQ(pcomm,PETSC_ERR_SUP,"Need libptscotchparmetis.a compiled with -DSCOTCH_METIS_PREFIX");
#endif
} else {
velotab = NULL;
if (proc_weight_flg) {
ierr = PetscMalloc1(nparts,&vwgttab);CHKERRQ(ierr);
ierr = PetscMalloc1(nparts,&velotab);CHKERRQ(ierr);
for (j=0; j<nparts; j++) {
if (part->part_weights) vwgttab[j] = part->part_weights[j]*nparts;
else vwgttab[j] = 1.0;
}
for (i=0; i<nparts; i++) {
deltval = PetscAbsReal(vwgttab[i]-PetscFloorReal(vwgttab[i]+0.5));
if (deltval>0.01) {
for (j=0; j<nparts; j++) vwgttab[j] /= deltval;
}
}
for (i=0; i<nparts; i++) velotab[i] = (SCOTCH_Num)(vwgttab[i] + 0.5);
ierr = PetscFree(vwgttab);CHKERRQ(ierr);
}
vertlocnbr = mat->rmap->range[rank+1] - mat->rmap->range[rank];
edgelocnbr = adj->i[vertlocnbr];
veloloctab = part->vertex_weights;
edloloctab = adj->values;
/* detect whether all vertices are located at the same process in original graph */
for (p = 0; !mat->rmap->range[p+1] && p < nparts; ++p);
distributed = (mat->rmap->range[p+1] == mat->rmap->N) ? PETSC_FALSE : PETSC_TRUE;
if (distributed) {
SCOTCH_Arch archdat;
SCOTCH_Dgraph grafdat;
SCOTCH_Dmapping mappdat;
SCOTCH_Strat stradat;
ierr = SCOTCH_dgraphInit(&grafdat,comm);CHKERRQ(ierr);
ierr = SCOTCH_dgraphBuild(&grafdat,0,vertlocnbr,vertlocnbr,adj->i,adj->i+1,veloloctab,
NULL,edgelocnbr,edgelocnbr,adj->j,NULL,edloloctab);CHKERRQ(ierr);
#if defined(PETSC_USE_DEBUG)
ierr = SCOTCH_dgraphCheck(&grafdat);CHKERRQ(ierr);
#endif
ierr = SCOTCH_archInit(&archdat);CHKERRQ(ierr);
ierr = SCOTCH_stratInit(&stradat);CHKERRQ(ierr);
ierr = SCOTCH_stratDgraphMapBuild(&stradat,scotch->strategy,nparts,nparts,scotch->imbalance);CHKERRQ(ierr);
if (velotab) {
ierr = SCOTCH_archCmpltw(&archdat,nparts,velotab);CHKERRQ(ierr);
} else {
ierr = SCOTCH_archCmplt( &archdat,nparts);CHKERRQ(ierr);
}
ierr = SCOTCH_dgraphMapInit(&grafdat,&mappdat,&archdat,locals);CHKERRQ(ierr);
ierr = SCOTCH_dgraphMapCompute(&grafdat,&mappdat,&stradat);CHKERRQ(ierr);
SCOTCH_dgraphMapExit(&grafdat,&mappdat);
SCOTCH_archExit(&archdat);
SCOTCH_stratExit(&stradat);
SCOTCH_dgraphExit(&grafdat);
} else if (rank == p) {
SCOTCH_Graph grafdat;
SCOTCH_Strat stradat;
ierr = SCOTCH_graphInit(&grafdat);CHKERRQ(ierr);
ierr = SCOTCH_graphBuild(&grafdat,0,vertlocnbr,adj->i,adj->i+1,veloloctab,NULL,edgelocnbr,adj->j,edloloctab);CHKERRQ(ierr);
#if defined(PETSC_USE_DEBUG)
ierr = SCOTCH_graphCheck(&grafdat);CHKERRQ(ierr);
#endif
ierr = SCOTCH_stratInit(&stradat);CHKERRQ(ierr);
ierr = SCOTCH_stratGraphMapBuild(&stradat,scotch->strategy,nparts,scotch->imbalance);CHKERRQ(ierr);
ierr = SCOTCH_graphPart(&grafdat,nparts,&stradat,locals);CHKERRQ(ierr);
SCOTCH_stratExit(&stradat);
SCOTCH_graphExit(&grafdat);
}
ierr = PetscFree(velotab);CHKERRQ(ierr);
}
ierr = MPI_Comm_free(&comm);CHKERRQ(ierr);
if (bs > 1) {
PetscInt *newlocals;
ierr = PetscMalloc1(bs*mat->rmap->n,&newlocals);CHKERRQ(ierr);
for (i=0;i<mat->rmap->n;i++) {
for (j=0;j<bs;j++) {
newlocals[bs*i+j] = locals[i];
}
}
ierr = PetscFree(locals);CHKERRQ(ierr);
ierr = ISCreateGeneral(pcomm,bs*mat->rmap->n,newlocals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
} else {
ierr = ISCreateGeneral(pcomm,mat->rmap->n,locals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
}
if (useND) {
IS ndis;
if (bs > 1) {
ierr = ISCreateBlock(pcomm,bs,mat->rmap->n,NDorder,PETSC_OWN_POINTER,&ndis);CHKERRQ(ierr);
} else {
ierr = ISCreateGeneral(pcomm,mat->rmap->n,NDorder,PETSC_OWN_POINTER,&ndis);CHKERRQ(ierr);
}
ierr = ISSetPermutation(ndis);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject)(*partitioning),"_petsc_matpartitioning_ndorder",(PetscObject)ndis);CHKERRQ(ierr);
ierr = ISDestroy(&ndis);CHKERRQ(ierr);
}
if (!flg) {
ierr = MatDestroy(&mat);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
Mat A,B;
Vec xx,s1,s2,yy;
PetscErrorCode ierr;
PetscInt m=45,rows[2],cols[2],bs=1,i,row,col,*idx,M;
PetscScalar rval,vals1[4],vals2[4];
PetscRandom rdm;
IS is1,is2;
PetscReal s1norm,s2norm,rnorm,tol = 1.e-4;
PetscTruth flg;
MatFactorInfo info;
PetscInitialize(&argc,&args,(char *)0,help);
/* Test MatSetValues() and MatGetValues() */
ierr = PetscOptionsGetInt(PETSC_NULL,"-mat_block_size",&bs,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-mat_size",&m,PETSC_NULL);CHKERRQ(ierr);
M = m*bs;
ierr = MatCreateSeqBAIJ(PETSC_COMM_SELF,bs,M,M,1,PETSC_NULL,&A);CHKERRQ(ierr);
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,M,M,15,PETSC_NULL,&B);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,M,&xx);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(xx,&yy);CHKERRQ(ierr);
/* For each row add atleast 15 elements */
for (row=0; row<M; row++) {
for (i=0; i<25*bs; i++) {
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
col = (PetscInt)(PetscRealPart(rval)*M);
ierr = MatSetValues(A,1,&row,1,&col,&rval,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(B,1,&row,1,&col,&rval,INSERT_VALUES);CHKERRQ(ierr);
}
}
/* Now set blocks of values */
for (i=0; i<20*bs; i++) {
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[0] = (PetscInt)(PetscRealPart(rval)*M);
vals1[0] = rval;
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[1] = (PetscInt)(PetscRealPart(rval)*M);
vals1[1] = rval;
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[0] = (PetscInt)(PetscRealPart(rval)*M);
vals1[2] = rval;
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[1] = (PetscInt)(PetscRealPart(rval)*M);
vals1[3] = rval;
ierr = MatSetValues(A,2,rows,2,cols,vals1,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(B,2,rows,2,cols,vals1,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&s1norm);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_FROBENIUS,&s2norm);CHKERRQ(ierr);
rnorm = PetscAbsScalar(s2norm-s1norm)/s2norm;
if ( rnorm>tol ) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&s1norm);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_INFINITY,&s2norm);CHKERRQ(ierr);
rnorm = PetscAbsScalar(s2norm-s1norm)/s2norm;
if ( rnorm>tol ) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&s1norm);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_1,&s2norm);CHKERRQ(ierr);
rnorm = PetscAbsScalar(s2norm-s1norm)/s2norm;
if ( rnorm>tol ) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_NORM_1()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
/* MatShift() */
rval = 10*s1norm;
ierr = MatShift(A,rval);CHKERRQ(ierr);
ierr = MatShift(B,rval);CHKERRQ(ierr);
/* Test MatTranspose() */
ierr = MatTranspose(A,MAT_REUSE_MATRIX,&A);CHKERRQ(ierr);
ierr = MatTranspose(B,MAT_REUSE_MATRIX,&B);CHKERRQ(ierr);
/* Now do MatGetValues() */
for (i=0; i<30; i++) {
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[0] = (PetscInt)(PetscRealPart(rval)*M);
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
cols[1] = (PetscInt)(PetscRealPart(rval)*M);
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[0] = (PetscInt)(PetscRealPart(rval)*M);
ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
rows[1] = (PetscInt)(PetscRealPart(rval)*M);
ierr = MatGetValues(A,2,rows,2,cols,vals1);CHKERRQ(ierr);
ierr = MatGetValues(B,2,rows,2,cols,vals2);CHKERRQ(ierr);
ierr = PetscMemcmp(vals1,vals2,4*sizeof(PetscScalar),&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetValues bs = %D\n",bs);CHKERRQ(ierr);
}
}
/* Test MatMult(), MatMultAdd() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = VecSet(s2,0.0);CHKERRQ(ierr);
ierr = MatMult(A,xx,s1);CHKERRQ(ierr);
ierr = MatMultAdd(A,xx,s2,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatMult not equal to MatMultAdd Norm1=%e Norm2=%e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatMult() */
ierr = MatMultEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult()\n");CHKERRQ(ierr);
}
/* Test MatMultAdd() */
ierr = MatMultAddEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultAdd()\n");CHKERRQ(ierr);
}
/* Test MatMultTranspose() */
ierr = MatMultTransposeEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultTranspose()\n");CHKERRQ(ierr);
}
/* Test MatMultTransposeAdd() */
ierr = MatMultTransposeAddEqual(A,B,10,&flg);CHKERRQ(ierr);
if (!flg){
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultTransposeAdd()\n");CHKERRQ(ierr);
}
/* Do LUFactor() on both the matrices */
ierr = PetscMalloc(M*sizeof(PetscInt),&idx);CHKERRQ(ierr);
for (i=0; i<M; i++) idx[i] = i;
ierr = ISCreateGeneral(PETSC_COMM_SELF,M,idx,&is1);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,M,idx,&is2);CHKERRQ(ierr);
ierr = PetscFree(idx);CHKERRQ(ierr);
ierr = ISSetPermutation(is1);CHKERRQ(ierr);
ierr = ISSetPermutation(is2);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
info.fill = 2.0;
info.dtcol = 0.0;
info.zeropivot = 1.e-14;
info.pivotinblocks = 1.0;
ierr = MatLUFactor(B,is1,is2,&info);CHKERRQ(ierr);
ierr = MatLUFactor(A,is1,is2,&info);CHKERRQ(ierr);
/* Test MatSolveAdd() */
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(yy,rdm);CHKERRQ(ierr);
ierr = MatSolveAdd(B,xx,yy,s2);CHKERRQ(ierr);
ierr = MatSolveAdd(A,xx,yy,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveAdd - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatSolveAdd() when x = A'b +x */
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(s1,rdm);CHKERRQ(ierr);
ierr = VecCopy(s2,s1);CHKERRQ(ierr);
ierr = MatSolveAdd(B,xx,s2,s2);CHKERRQ(ierr);
ierr = MatSolveAdd(A,xx,s1,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveAdd(same) - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatSolve() */
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = MatSolve(B,xx,s2);CHKERRQ(ierr);
ierr = MatSolve(A,xx,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolve - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
/* Test MatSolveTranspose() */
if (bs < 8) {
for (i=0; i<10; i++) {
ierr = VecSetRandom(xx,rdm);CHKERRQ(ierr);
ierr = MatSolveTranspose(B,xx,s2);CHKERRQ(ierr);
ierr = MatSolveTranspose(A,xx,s1);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
rnorm = s2norm-s1norm;
if (rnorm<-tol || rnorm>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveTranspose - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
}
}
}
ierr = MatDestroy(A);CHKERRQ(ierr);
ierr = MatDestroy(B);CHKERRQ(ierr);
ierr = VecDestroy(xx);CHKERRQ(ierr);
ierr = VecDestroy(s1);CHKERRQ(ierr);
ierr = VecDestroy(s2);CHKERRQ(ierr);
ierr = VecDestroy(yy);CHKERRQ(ierr);
ierr = ISDestroy(is1);CHKERRQ(ierr);
ierr = ISDestroy(is2);CHKERRQ(ierr);
ierr = PetscRandomDestroy(rdm);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
static PetscErrorCode MatPartitioningApply_Parmetis_Private(MatPartitioning part, PetscBool useND, IS *partitioning)
{
MatPartitioning_Parmetis *pmetis = (MatPartitioning_Parmetis*)part->data;
PetscErrorCode ierr;
PetscInt *locals = NULL;
Mat mat = part->adj,amat,pmat;
PetscBool flg;
PetscInt bs = 1;
PetscFunctionBegin;
ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIADJ,&flg);CHKERRQ(ierr);
if (flg) {
amat = mat;
ierr = PetscObjectReference((PetscObject)amat);CHKERRQ(ierr);
} else {
/* bs indicates if the converted matrix is "reduced" from the original and hence the
resulting partition results need to be stretched to match the original matrix */
ierr = MatConvert(mat,MATMPIADJ,MAT_INITIAL_MATRIX,&amat);CHKERRQ(ierr);
if (amat->rmap->n > 0) bs = mat->rmap->n/amat->rmap->n;
}
ierr = MatMPIAdjCreateNonemptySubcommMat(amat,&pmat);CHKERRQ(ierr);
ierr = MPI_Barrier(PetscObjectComm((PetscObject)part));CHKERRQ(ierr);
if (pmat) {
MPI_Comm pcomm,comm;
Mat_MPIAdj *adj = (Mat_MPIAdj*)pmat->data;
PetscInt *vtxdist = pmat->rmap->range;
PetscInt *xadj = adj->i;
PetscInt *adjncy = adj->j;
PetscInt *NDorder = NULL;
PetscInt itmp = 0,wgtflag=0, numflag=0, ncon=1, nparts=part->n, options[24], i, j;
real_t *tpwgts,*ubvec,itr=0.1;
int status;
ierr = PetscObjectGetComm((PetscObject)pmat,&pcomm);CHKERRQ(ierr);
#if defined(PETSC_USE_DEBUG)
/* check that matrix has no diagonal entries */
{
PetscInt rstart;
ierr = MatGetOwnershipRange(pmat,&rstart,NULL);CHKERRQ(ierr);
for (i=0; i<pmat->rmap->n; i++) {
for (j=xadj[i]; j<xadj[i+1]; j++) {
if (adjncy[j] == i+rstart) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Row %d has diagonal entry; Parmetis forbids diagonal entry",i+rstart);
}
}
}
#endif
ierr = PetscMalloc1(pmat->rmap->n,&locals);CHKERRQ(ierr);
if (adj->values && !part->vertex_weights)
wgtflag = 1;
if (part->vertex_weights && !adj->values)
wgtflag = 2;
if (part->vertex_weights && adj->values)
wgtflag = 3;
if (PetscLogPrintInfo) {itmp = pmetis->printout; pmetis->printout = 127;}
ierr = PetscMalloc1(ncon*nparts,&tpwgts);CHKERRQ(ierr);
for (i=0; i<ncon; i++) {
for (j=0; j<nparts; j++) {
if (part->part_weights) {
tpwgts[i*nparts+j] = part->part_weights[i*nparts+j];
} else {
tpwgts[i*nparts+j] = 1./nparts;
}
}
}
ierr = PetscMalloc1(ncon,&ubvec);CHKERRQ(ierr);
for (i=0; i<ncon; i++) {
ubvec[i] = 1.05;
}
/* This sets the defaults */
options[0] = 0;
for (i=1; i<24; i++) {
options[i] = -1;
}
/* Duplicate the communicator to be sure that ParMETIS attribute caching does not interfere with PETSc. */
ierr = MPI_Comm_dup(pcomm,&comm);CHKERRQ(ierr);
if (useND) {
PetscInt *sizes, *seps, log2size, subd, *level;
PetscMPIInt size;
idx_t mtype = PARMETIS_MTYPE_GLOBAL, rtype = PARMETIS_SRTYPE_2PHASE, p_nseps = 1, s_nseps = 1;
real_t ubfrac = 1.05;
ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
ierr = PetscMalloc1(pmat->rmap->n,&NDorder);CHKERRQ(ierr);
ierr = PetscMalloc3(2*size,&sizes,4*size,&seps,size,&level);CHKERRQ(ierr);
PetscStackCallParmetis(ParMETIS_V32_NodeND,((idx_t*)vtxdist,(idx_t*)xadj,(idx_t*)adjncy,(idx_t*)part->vertex_weights,(idx_t*)&numflag,&mtype,&rtype,&p_nseps,&s_nseps,&ubfrac,NULL/* seed */,NULL/* dbglvl */,(idx_t*)NDorder,(idx_t*)(sizes),&comm));
log2size = PetscLog2Real(size);
subd = PetscPowInt(2,log2size);
ierr = MatPartitioningSizesToSep_Private(subd,sizes,seps,level);CHKERRQ(ierr);
for (i=0;i<pmat->rmap->n;i++) {
PetscInt loc;
ierr = PetscFindInt(NDorder[i],2*subd,seps,&loc);CHKERRQ(ierr);
if (loc < 0) {
loc = -(loc+1);
if (loc%2) { /* part of subdomain */
locals[i] = loc/2;
} else {
ierr = PetscFindInt(NDorder[i],2*(subd-1),seps+2*subd,&loc);CHKERRQ(ierr);
loc = loc < 0 ? -(loc+1)/2 : loc/2;
locals[i] = level[loc];
}
} else locals[i] = loc/2;
}
ierr = PetscFree3(sizes,seps,level);CHKERRQ(ierr);
} else {
if (pmetis->repartition) {
PetscStackCallParmetis(ParMETIS_V3_AdaptiveRepart,((idx_t*)vtxdist,(idx_t*)xadj,(idx_t*)adjncy,(idx_t*)part->vertex_weights,(idx_t*)part->vertex_weights,(idx_t*)adj->values,(idx_t*)&wgtflag,(idx_t*)&numflag,(idx_t*)&ncon,(idx_t*)&nparts,tpwgts,ubvec,&itr,(idx_t*)options,(idx_t*)&pmetis->cuts,(idx_t*)locals,&comm));
} else {
PetscStackCallParmetis(ParMETIS_V3_PartKway,((idx_t*)vtxdist,(idx_t*)xadj,(idx_t*)adjncy,(idx_t*)part->vertex_weights,(idx_t*)adj->values,(idx_t*)&wgtflag,(idx_t*)&numflag,(idx_t*)&ncon,(idx_t*)&nparts,tpwgts,ubvec,(idx_t*)options,(idx_t*)&pmetis->cuts,(idx_t*)locals,&comm));
}
}
ierr = MPI_Comm_free(&comm);CHKERRQ(ierr);
ierr = PetscFree(tpwgts);CHKERRQ(ierr);
ierr = PetscFree(ubvec);CHKERRQ(ierr);
if (PetscLogPrintInfo) pmetis->printout = itmp;
if (bs > 1) {
PetscInt i,j,*newlocals;
ierr = PetscMalloc1(bs*pmat->rmap->n,&newlocals);CHKERRQ(ierr);
for (i=0; i<pmat->rmap->n; i++) {
for (j=0; j<bs; j++) {
newlocals[bs*i + j] = locals[i];
}
}
ierr = PetscFree(locals);CHKERRQ(ierr);
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),bs*pmat->rmap->n,newlocals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
} else {
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),pmat->rmap->n,locals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
}
if (useND) {
IS ndis;
if (bs > 1) {
ierr = ISCreateBlock(PetscObjectComm((PetscObject)part),bs,pmat->rmap->n,NDorder,PETSC_OWN_POINTER,&ndis);CHKERRQ(ierr);
} else {
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),pmat->rmap->n,NDorder,PETSC_OWN_POINTER,&ndis);CHKERRQ(ierr);
}
ierr = ISSetPermutation(ndis);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject)(*partitioning),"_petsc_matpartitioning_ndorder",(PetscObject)ndis);CHKERRQ(ierr);
ierr = ISDestroy(&ndis);CHKERRQ(ierr);
}
} else {
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),0,NULL,PETSC_COPY_VALUES,partitioning);CHKERRQ(ierr);
if (useND) {
IS ndis;
if (bs > 1) {
ierr = ISCreateBlock(PetscObjectComm((PetscObject)part),bs,0,NULL,PETSC_COPY_VALUES,&ndis);CHKERRQ(ierr);
} else {
ierr = ISCreateGeneral(PetscObjectComm((PetscObject)part),0,NULL,PETSC_COPY_VALUES,&ndis);CHKERRQ(ierr);
}
ierr = ISSetPermutation(ndis);CHKERRQ(ierr);
ierr = PetscObjectCompose((PetscObject)(*partitioning),"_petsc_matpartitioning_ndorder",(PetscObject)ndis);CHKERRQ(ierr);
ierr = ISDestroy(&ndis);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&pmat);CHKERRQ(ierr);
ierr = MatDestroy(&amat);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
const struct {PetscInt i,j; PetscScalar v;} entries[] = {{0,3,1.},{1,2,2.},{2,1,3.},{2,4,4.},{3,0,5.},{3,3,6.},{4,1,7.},{4,4,8.}};
const PetscInt ixrow[5] = {4,2,1,3,0},ixcol[5] = {3,2,1,4,0};
Mat A,B;
PetscErrorCode ierr;
PetscInt i,rstart,rend,cstart,cend;
IS isrow,iscol;
PetscViewer viewer,sviewer;
PetscBool view_sparse;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
/* ------- Assemble matrix, --------- */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,5,5);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
ierr = MatGetOwnershipRangeColumn(A,&cstart,&cend);CHKERRQ(ierr);
for (i=0; i<(PetscInt)(sizeof(entries)/sizeof(entries[0])); i++) {
ierr = MatSetValue(A,entries[i].i,entries[i].j,entries[i].v,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* ------ Prepare index sets ------ */
ierr = ISCreateGeneral(PETSC_COMM_WORLD,rend-rstart,ixrow+rstart,PETSC_USE_POINTER,&isrow);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,5,ixcol,PETSC_USE_POINTER,&iscol);CHKERRQ(ierr);
ierr = ISSetPermutation(isrow);CHKERRQ(ierr);
ierr = ISSetPermutation(iscol);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr);
view_sparse = PETSC_FALSE;
ierr = PetscOptionsGetBool(PETSC_NULL, "-view_sparse", &view_sparse, PETSC_NULL);CHKERRQ(ierr);
if (!view_sparse) {
ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_DENSE);CHKERRQ(ierr);
}
ierr = PetscViewerASCIIPrintf(viewer,"Original matrix\n");CHKERRQ(ierr);
ierr = MatView(A,viewer);CHKERRQ(ierr);
ierr = MatPermute(A,isrow,iscol,&B);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Permuted matrix\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Row permutation\n");CHKERRQ(ierr);
ierr = ISView(isrow,viewer);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Column permutation\n");CHKERRQ(ierr);
ierr = PetscViewerGetSingleton(viewer,&sviewer);CHKERRQ(ierr);
ierr = ISView(iscol,sviewer);CHKERRQ(ierr);
ierr = PetscViewerRestoreSingleton(viewer,&sviewer);CHKERRQ(ierr);
/* Free data structures */
ierr = ISDestroy(&isrow);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
void PETSC_STDCALL issetpermutation_(IS is, int *__ierr ){
*__ierr = ISSetPermutation(
(IS)PetscToPointer((is) ));
}
PETSC_EXTERN PetscErrorCode MatGetOrdering_AWBM(Mat A, MatOrderingType type, IS *permR, IS *permC)
{
Vec *scalR, *scalC, scalRVec, scalCVec;
scalR = &scalRVec; scalC = &scalCVec;
/* EVERYTHING IS WRITTEN AS IF THE MATRIX WERE COLUMN-MAJOR */
Mat_SeqAIJ *aij = (Mat_SeqAIJ *) A->data;
PetscInt n = A->rmap->n; /* Number of local columns */
PetscInt m = A->cmap->n; /* Number of local rows */
PetscInt *match; /* The row matched to each column, and inverse column permutation */
PetscInt *matchR; /* The column matched to each row */
PetscInt *p; /* The column permutation */
const PetscInt *ia = aij->i;
const PetscInt *ja = aij->j;
const MatScalar *a = aij->a;
Vec colMax;
PetscScalar *a_j, *sr, *sc;
PetscReal *weights /* c_ij */, *u /* u_i */, *v /* v_j */, eps = PETSC_SQRT_MACHINE_EPSILON;
PetscInt debug = 0, r, c, r1, c1;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscOptionsGetInt(NULL, "-debug", &debug, NULL);CHKERRQ(ierr);
ierr = MatGetVecs(A, NULL, &colMax);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(A, colMax, NULL);CHKERRQ(ierr);
ierr = PetscMalloc2(n, &match, m, &matchR);CHKERRQ(ierr);
ierr = PetscMalloc1(n, &p);CHKERRQ(ierr);
ierr = PetscCalloc3(m, &u, n, &v, ia[n], &weights);CHKERRQ(ierr);
for (c = 0; c < n; ++c) match[c] = -1;
/* Compute weights */
ierr = VecGetArray(colMax, &a_j);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
for (r = ia[c]; r < ia[c+1]; ++r) {
PetscReal ar = PetscAbsScalar(a[r]);
if (ar == 0.0) weights[r] = PETSC_MAX_REAL;
else weights[r] = log(a_j[c]/ar);
}
}
/* Compute local row weights */
for (r = 0; r < m; ++r) u[r] = PETSC_MAX_REAL;
for (c = 0; c < n; ++c) {
for (r = ia[c]; r < ia[c+1]; ++r) {
u[ja[r]] = PetscMin(u[ja[r]], weights[r]);
}
}
/* Compute local column weights */
for (c = 0; c < n; ++c) {
v[c] = PETSC_MAX_REAL;
for (r = ia[c]; r < ia[c+1]; ++r) {
v[c] = PetscMin(v[c], weights[r] - u[ja[r]]);
}
}
for (r = 0; r < m; ++r) matchR[r] = -1;
/* Match columns */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
/* if (match[c] >= 0) continue; */
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "Row %d\n Weights:", c);CHKERRQ(ierr);}
for (r = ia[c]; r < ia[c+1]; ++r) {
PetscReal weight = weights[r] - u[ja[r]] - v[c];
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, " %g", weight);CHKERRQ(ierr);}
if ((weight <= eps) && (matchR[ja[r]] < 0)) {
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "Matched %d -- %d\n", c, ja[r]);CHKERRQ(ierr);}
match[c] = ja[r];
matchR[ja[r]] = c;
break;
}
}
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "\n");CHKERRQ(ierr);}
}
/* Deal with unmatched columns */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
if (match[c] >= 0) continue;
for (r = ia[c]; r < ia[c+1]; ++r) {
PetscReal weight = weights[r] - u[ja[r]] - v[c];
if (weight > eps) continue;
/* \bar c_ij = 0 and (r, j1) \in M */
c1 = matchR[ja[r]];
for (r1 = ia[c1]; r1 < ia[c1+1]; ++r1) {
PetscReal weight1 = weights[r1] - u[ja[r1]] - v[c1];
if ((matchR[ja[r1]] < 0) && (weight1 <= eps)) {
/* (r, c1) in M is replaced by (r, c) and (r1, c1) */
if (debug) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Replaced match %d -- %d\n", c1, ja[r]);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, " Added match %d -- %d\n", c, ja[r]);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, " Added match %d -- %d\n", c1, ja[r1]);CHKERRQ(ierr);
}
match[c] = ja[r];
matchR[ja[r]] = c;
match[c1] = ja[r1];
matchR[ja[r1]] = c1;
break;
}
}
if (match[c] >= 0) break;
}
}
/* Allow matching with non-optimal rows */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
if (match[c] >= 0) continue;
for (r = ia[c]; r < ia[c+1]; ++r) {
if (matchR[ja[r]] < 0) {
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "Matched non-opt %d -- %d\n", c, ja[r]);CHKERRQ(ierr);}
match[c] = ja[r];
matchR[ja[r]] = c;
break;
}
}
}
/* Deal with non-optimal unmatched columns */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
if (match[c] >= 0) continue;
for (r = ia[c]; r < ia[c+1]; ++r) {
/* \bar c_ij = 0 and (r, j1) \in M */
c1 = matchR[ja[r]];
for (r1 = ia[c1]; r1 < ia[c1+1]; ++r1) {
if (matchR[ja[r1]] < 0) {
/* (r, c1) in M is replaced by (r, c) and (r1, c1) */
if (debug) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Replaced match %d -- %d\n", c1, ja[r]);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, " Added match %d -- %d\n", c, ja[r]);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, " Added match %d -- %d\n", c1, ja[r1]);CHKERRQ(ierr);
}
match[c] = ja[r];
matchR[ja[r]] = c;
match[c1] = ja[r1];
matchR[ja[r1]] = c1;
break;
}
}
if (match[c] >= 0) break;
}
}
/* Complete matching */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0, r = 0; c < n; ++c) {
if (match[c] >= n) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Column %d matched to invalid row %d", c, match[c]);
if (match[c] < 0) {
for (; r < n; ++r) {
if (matchR[r] < 0) {
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "Matched default %d -- %d\n", c, r);CHKERRQ(ierr);}
match[c] = r;
matchR[r] = c;
break;
}
}
}
}
/* Check matching */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
if (match[c] < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Column %d unmatched", c);
if (match[c] >= n) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Column %d matched to invalid row %d", c, match[c]);
}
/* Make permutation */
for (c = 0; c < n; ++c) {p[match[c]] = c;}
ierr = ISCreateGeneral(PETSC_COMM_SELF, n, p, PETSC_OWN_POINTER, permR);CHKERRQ(ierr);
ierr = ISSetPermutation(*permR);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF, n, 0, 1, permC);CHKERRQ(ierr);
ierr = ISSetPermutation(*permC);CHKERRQ(ierr);
ierr = PetscFree2(match, matchR);CHKERRQ(ierr);
/* Make scaling */
ierr = VecCreateSeq(PETSC_COMM_SELF, n, scalR);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF, n, scalC);CHKERRQ(ierr);
ierr = VecGetArray(*scalR, &sr);CHKERRQ(ierr);
ierr = VecGetArray(*scalC, &sc);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
sr[c] = PetscExpReal(v[c])/a_j[c];
sc[c] = PetscExpReal(u[c]);
}
ierr = VecRestoreArray(*scalR, &sr);CHKERRQ(ierr);
ierr = VecRestoreArray(*scalC, &sc);CHKERRQ(ierr);
ierr = VecRestoreArray(colMax, &a_j);CHKERRQ(ierr);
ierr = VecDestroy(&colMax);CHKERRQ(ierr);
ierr = PetscFree3(u,v,weights);CHKERRQ(ierr);
ierr = VecDestroy(scalR);CHKERRQ(ierr);
ierr = VecDestroy(scalC);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc, char **args)
{
Mat A, L;
AppCtx ctx;
PetscViewer viewer;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc, &args, (char *) 0, help);CHKERRQ(ierr);
ierr = ProcessOptions(&ctx);CHKERRQ(ierr);
/* Load matrix */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD, ctx.matFilename, FILE_MODE_READ, &viewer);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD, &A);CHKERRQ(ierr);
ierr = MatLoad(A, viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
/* Make graph Laplacian from matrix */
ierr = MatLaplacian(A, 1.0e-12, &L);CHKERRQ(ierr);
/* Check Laplacian */
PetscReal norm;
Vec x, y;
ierr = MatGetVecs(L, &x, NULL);CHKERRQ(ierr);
ierr = VecDuplicate(x, &y);CHKERRQ(ierr);
ierr = VecSet(x, 1.0);CHKERRQ(ierr);
ierr = MatMult(L, x, y);CHKERRQ(ierr);
ierr = VecNorm(y, NORM_INFINITY, &norm);CHKERRQ(ierr);
if (norm > 1.0e-10) SETERRQ(PetscObjectComm((PetscObject) y), PETSC_ERR_PLIB, "Invalid graph Laplacian");
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
/* Compute Fiedler vector, and perhaps more vectors */
Mat LD;
PetscScalar *a, *realpart, *imagpart, *eigvec, *work, sdummy;
PetscBLASInt bn, bN, lwork, lierr, idummy;
PetscInt n, i;
ierr = MatConvert(L, MATDENSE, MAT_INITIAL_MATRIX, &LD);CHKERRQ(ierr);
ierr = MatGetLocalSize(LD, &n, NULL);CHKERRQ(ierr);
ierr = MatDenseGetArray(LD, &a);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n, &bn);CHKERRQ(ierr);
ierr = PetscBLASIntCast(n, &bN);CHKERRQ(ierr);
ierr = PetscBLASIntCast(5*n,&lwork);CHKERRQ(ierr);
ierr = PetscBLASIntCast(1,&idummy);CHKERRQ(ierr);
ierr = PetscMalloc4(n,PetscScalar,&realpart,n,PetscScalar,&imagpart,n*n,PetscScalar,&eigvec,lwork,PetscScalar,&work);CHKERRQ(ierr);
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
PetscStackCall("LAPACKgeev", LAPACKgeev_("N","V",&bn,a,&bN,realpart,imagpart,&sdummy,&idummy,eigvec,&bN,work,&lwork,&lierr));
if (lierr) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in LAPACK routine %d", (int) lierr);
ierr = PetscFPTrapPop();CHKERRQ(ierr);
PetscReal *r, *c;
PetscInt *perm;
ierr = PetscMalloc3(n,PetscInt,&perm,n,PetscReal,&r,n,PetscReal,&c);CHKERRQ(ierr);
for (i = 0; i < n; ++i) perm[i] = i;
ierr = PetscSortRealWithPermutation(n,realpart,perm);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {
r[i] = realpart[perm[i]];
c[i] = imagpart[perm[i]];
}
for (i = 0; i < n; ++i) {
realpart[i] = r[i];
imagpart[i] = c[i];
}
/* Output spectrum */
if (ctx.showSpectrum) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Spectrum\n");CHKERRQ(ierr);
for (i = 0; i < n; ++i) {ierr = PetscPrintf(PETSC_COMM_SELF, "%d: Real %g Imag %g\n", i, realpart[i], imagpart[i]);CHKERRQ(ierr);}
}
/* Check lowest eigenvalue and eigenvector */
PetscInt evInd = perm[0];
if ((realpart[0] > 1.0e-12) || (imagpart[0] > 1.0e-12)) SETERRQ(PetscObjectComm((PetscObject) L), PETSC_ERR_PLIB, "Graph Laplacian must have lowest eigenvalue 0");
for (i = 0; i < n; ++i) {
if (fabs(eigvec[evInd*n+i] - eigvec[evInd*n+0]) > 1.0e-10) SETERRQ3(PetscObjectComm((PetscObject) L), PETSC_ERR_PLIB, "Graph Laplacian must have constant lowest eigenvector ev_%d %g != ev_0 %g", i, eigvec[evInd*n+i], eigvec[evInd*n+0]);
}
/* Output Fiedler vector */
evInd = perm[1];
if (ctx.showFiedler) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Fiedler vector, Re{ev} %g\n", realpart[1]);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {ierr = PetscPrintf(PETSC_COMM_SELF, "%d: %g\n", i, eigvec[evInd*n+i]);CHKERRQ(ierr);}
}
/* Construct Fiedler partition */
IS fIS, fIS2;
PetscInt *fperm, *fperm2, pos, neg, posSize = 0;
ierr = PetscMalloc(n * sizeof(PetscInt), &fperm);CHKERRQ(ierr);
for (i = 0; i < n; ++i) {
if (eigvec[evInd*n+i] > 0.0) ++posSize;
}
ierr = PetscMalloc(n * sizeof(PetscInt), &fperm2);CHKERRQ(ierr);
for (i = 0; i < n; ++i) fperm[i] = i;
ierr = PetscSortRealWithPermutation(n, &eigvec[evInd*n], fperm);CHKERRQ(ierr);
for (i = 0; i < n; ++i) fperm2[n-1-i] = fperm[i];
for (i = 0, pos = 0, neg = posSize; i < n; ++i) {
if (eigvec[evInd*n+i] > 0.0) fperm[pos++] = i;
else fperm[neg++] = i;
}
ierr = ISCreateGeneral(PetscObjectComm((PetscObject) L), n, fperm, PETSC_OWN_POINTER, &fIS);CHKERRQ(ierr);
ierr = ISSetPermutation(fIS);CHKERRQ(ierr);
ierr = ISCreateGeneral(PetscObjectComm((PetscObject) L), n, fperm2, PETSC_OWN_POINTER, &fIS2);CHKERRQ(ierr);
ierr = ISSetPermutation(fIS2);CHKERRQ(ierr);
ierr = PetscFree3(perm,r,c);CHKERRQ(ierr);
ierr = PetscFree4(realpart,imagpart,eigvec,work);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(LD, &a);CHKERRQ(ierr);
ierr = MatDestroy(&LD);CHKERRQ(ierr);
ierr = MatDestroy(&L);CHKERRQ(ierr);
/* Permute matrix */
Mat AR, AR2;
ierr = MatPermute(A, fIS, fIS, &AR);CHKERRQ(ierr);
ierr = MatView(A, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(AR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&fIS);CHKERRQ(ierr);
ierr = MatPermute(A, fIS2, fIS2, &AR2);CHKERRQ(ierr);
ierr = MatView(AR2, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&fIS2);CHKERRQ(ierr);
ierr = MatDestroy(&AR);CHKERRQ(ierr);
AR = AR2;
/* Extract blocks and reorder */
Mat AP, AN, APR, ANR;
IS ispos, isneg, rpermpos, cpermpos, rpermneg, cpermneg;
PetscInt bw, bwr;
ierr = ISCreateStride(PETSC_COMM_SELF, posSize, 0, 1, &ispos);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF, n - posSize, posSize, 1, &isneg);CHKERRQ(ierr);
ierr = MatGetSubMatrix(AR, ispos, ispos, MAT_INITIAL_MATRIX, &AP);CHKERRQ(ierr);
ierr = MatGetSubMatrix(AR, isneg, isneg, MAT_INITIAL_MATRIX, &AN);CHKERRQ(ierr);
ierr = ISDestroy(&ispos);CHKERRQ(ierr);
ierr = ISDestroy(&isneg);CHKERRQ(ierr);
ierr = MatGetOrdering(AP, ctx.matOrdtype, &rpermpos, &cpermpos);CHKERRQ(ierr);
ierr = MatGetOrdering(AN, ctx.matOrdtype, &rpermneg, &cpermneg);CHKERRQ(ierr);
ierr = MatPermute(AP, rpermpos, cpermpos, &APR);CHKERRQ(ierr);
ierr = MatComputeBandwidth(AP, 0.0, &bw);CHKERRQ(ierr);
ierr = MatComputeBandwidth(APR, 0.0, &bwr);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Reduced positive bandwidth from %d to %d\n", bw, bwr);CHKERRQ(ierr);
ierr = MatPermute(AN, rpermneg, cpermneg, &ANR);CHKERRQ(ierr);
ierr = MatComputeBandwidth(AN, 0.0, &bw);CHKERRQ(ierr);
ierr = MatComputeBandwidth(ANR, 0.0, &bwr);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD, "Reduced negative bandwidth from %d to %d\n", bw, bwr);CHKERRQ(ierr);
ierr = MatView(AP, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(APR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(AN, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(ANR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
/* Reorder original matrix */
Mat ARR;
IS rperm, cperm;
PetscInt *idx;
const PetscInt *cidx;
ierr = PetscMalloc(n * sizeof(PetscInt), &idx);CHKERRQ(ierr);
ierr = ISGetIndices(rpermpos, &cidx);CHKERRQ(ierr);
for (i = 0; i < posSize; ++i) idx[i] = cidx[i];
ierr = ISRestoreIndices(rpermpos, &cidx);CHKERRQ(ierr);
ierr = ISGetIndices(rpermneg, &cidx);CHKERRQ(ierr);
for (i = posSize; i < n; ++i) idx[i] = cidx[i-posSize] + posSize;
ierr = ISRestoreIndices(rpermneg, &cidx);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF, n, idx, PETSC_OWN_POINTER, &rperm);CHKERRQ(ierr);
ierr = ISSetPermutation(rperm);CHKERRQ(ierr);
ierr = PetscMalloc(n * sizeof(PetscInt), &idx);CHKERRQ(ierr);
ierr = ISGetIndices(cpermpos, &cidx);CHKERRQ(ierr);
for (i = 0; i < posSize; ++i) idx[i] = cidx[i];
ierr = ISRestoreIndices(cpermpos, &cidx);CHKERRQ(ierr);
ierr = ISGetIndices(cpermneg, &cidx);CHKERRQ(ierr);
for (i = posSize; i < n; ++i) idx[i] = cidx[i-posSize] + posSize;
ierr = ISRestoreIndices(cpermneg, &cidx);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF, n, idx, PETSC_OWN_POINTER, &cperm);CHKERRQ(ierr);
ierr = ISSetPermutation(cperm);CHKERRQ(ierr);
ierr = MatPermute(AR, rperm, cperm, &ARR);CHKERRQ(ierr);
ierr = MatView(ARR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&rperm);CHKERRQ(ierr);
ierr = ISDestroy(&cperm);CHKERRQ(ierr);
ierr = ISDestroy(&rpermpos);CHKERRQ(ierr);
ierr = ISDestroy(&cpermpos);CHKERRQ(ierr);
ierr = ISDestroy(&rpermneg);CHKERRQ(ierr);
ierr = ISDestroy(&cpermneg);CHKERRQ(ierr);
ierr = MatDestroy(&AP);CHKERRQ(ierr);
ierr = MatDestroy(&AN);CHKERRQ(ierr);
ierr = MatDestroy(&APR);CHKERRQ(ierr);
ierr = MatDestroy(&ANR);CHKERRQ(ierr);
/* Compare bands */
Mat B, BR;
ierr = MatCreateSubMatrixBanded(A, 50, 0.95, &B);CHKERRQ(ierr);
ierr = MatCreateSubMatrixBanded(ARR, 50, 0.95, &BR);CHKERRQ(ierr);
ierr = MatView(B, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatView(BR, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
ierr = MatDestroy(&B);CHKERRQ(ierr);
ierr = MatDestroy(&BR);CHKERRQ(ierr);
/* Cleanup */
ierr = MatDestroy(&ARR);CHKERRQ(ierr);
ierr = MatDestroy(&AR);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}