/*@
KSPComputeEigenvaluesExplicitly - Computes all of the eigenvalues of the
preconditioned operator using LAPACK.
Collective on KSP
Input Parameter:
+ ksp - iterative context obtained from KSPCreate()
- n - size of arrays r and c
Output Parameters:
+ r - real part of computed eigenvalues
- c - complex part of computed eigenvalues
Notes:
This approach is very slow but will generally provide accurate eigenvalue
estimates. This routine explicitly forms a dense matrix representing
the preconditioned operator, and thus will run only for relatively small
problems, say n < 500.
Many users may just want to use the monitoring routine
KSPMonitorSingularValue() (which can be set with option -ksp_monitor_singular_value)
to print the singular values at each iteration of the linear solve.
The preconditoner operator, rhs vector, solution vectors should be
set before this routine is called. i.e use KSPSetOperators(),KSPSolve() or
KSPSetOperators()
Level: advanced
.keywords: KSP, compute, eigenvalues, explicitly
.seealso: KSPComputeEigenvalues(), KSPMonitorSingularValue(), KSPComputeExtremeSingularValues(), KSPSetOperators(), KSPSolve()
@*/
PetscErrorCode KSPComputeEigenvaluesExplicitly(KSP ksp,PetscInt nmax,PetscReal *r,PetscReal *c)
{
Mat BA;
PetscErrorCode ierr;
PetscMPIInt size,rank;
MPI_Comm comm = ((PetscObject)ksp)->comm;
PetscScalar *array;
Mat A;
PetscInt m,row,nz,i,n,dummy;
const PetscInt *cols;
const PetscScalar *vals;
PetscFunctionBegin;
ierr = KSPComputeExplicitOperator(ksp,&BA);CHKERRQ(ierr);
ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
ierr = MatGetSize(BA,&n,&n);CHKERRQ(ierr);
if (size > 1) { /* assemble matrix on first processor */
ierr = MatCreate(((PetscObject)ksp)->comm,&A);CHKERRQ(ierr);
if (!rank) {
ierr = MatSetSizes(A,n,n,n,n);CHKERRQ(ierr);
} else {
ierr = MatSetSizes(A,0,0,n,n);CHKERRQ(ierr);
}
ierr = MatSetType(A,MATMPIDENSE);CHKERRQ(ierr);
ierr = MatMPIDenseSetPreallocation(A,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscLogObjectParent(BA,A);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(BA,&row,&dummy);CHKERRQ(ierr);
ierr = MatGetLocalSize(BA,&m,&dummy);CHKERRQ(ierr);
for (i=0; i<m; i++) {
ierr = MatGetRow(BA,row,&nz,&cols,&vals);CHKERRQ(ierr);
ierr = MatSetValues(A,1,&row,nz,cols,vals,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatRestoreRow(BA,row,&nz,&cols,&vals);CHKERRQ(ierr);
row++;
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatDenseGetArray(A,&array);CHKERRQ(ierr);
} else {
ierr = MatDenseGetArray(BA,&array);CHKERRQ(ierr);
}
#if defined(PETSC_HAVE_ESSL)
/* ESSL has a different calling sequence for dgeev() and zgeev() than standard LAPACK */
if (!rank) {
PetscScalar sdummy,*cwork;
PetscReal *work,*realpart;
PetscBLASInt clen,idummy,lwork,bn,zero = 0;
PetscInt *perm;
#if !defined(PETSC_USE_COMPLEX)
clen = n;
#else
clen = 2*n;
#endif
ierr = PetscMalloc(clen*sizeof(PetscScalar),&cwork);CHKERRQ(ierr);
idummy = -1; /* unused */
bn = PetscBLASIntCast(n);
lwork = 5*n;
ierr = PetscMalloc(lwork*sizeof(PetscReal),&work);CHKERRQ(ierr);
ierr = PetscMalloc(n*sizeof(PetscReal),&realpart);CHKERRQ(ierr);
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
LAPACKgeev_(&zero,array,&bn,cwork,&sdummy,&idummy,&idummy,&bn,work,&lwork);
ierr = PetscFPTrapPop();CHKERRQ(ierr);
ierr = PetscFree(work);CHKERRQ(ierr);
/* For now we stick with the convention of storing the real and imaginary
components of evalues separately. But is this what we really want? */
ierr = PetscMalloc(n*sizeof(PetscInt),&perm);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
for (i=0; i<n; i++) {
realpart[i] = cwork[2*i];
perm[i] = i;
}
ierr = PetscSortRealWithPermutation(n,realpart,perm);CHKERRQ(ierr);
for (i=0; i<n; i++) {
r[i] = cwork[2*perm[i]];
c[i] = cwork[2*perm[i]+1];
}
#else
for (i=0; i<n; i++) {
realpart[i] = PetscRealPart(cwork[i]);
perm[i] = i;
}
ierr = PetscSortRealWithPermutation(n,realpart,perm);CHKERRQ(ierr);
for (i=0; i<n; i++) {
r[i] = PetscRealPart(cwork[perm[i]]);
c[i] = PetscImaginaryPart(cwork[perm[i]]);
}
#endif
ierr = PetscFree(perm);CHKERRQ(ierr);
ierr = PetscFree(realpart);CHKERRQ(ierr);
ierr = PetscFree(cwork);CHKERRQ(ierr);
}
#elif !defined(PETSC_USE_COMPLEX)
if (!rank) {
PetscScalar *work;
PetscReal *realpart,*imagpart;
PetscBLASInt idummy,lwork;
PetscInt *perm;
idummy = n;
lwork = 5*n;
ierr = PetscMalloc(2*n*sizeof(PetscReal),&realpart);CHKERRQ(ierr);
imagpart = realpart + n;
ierr = PetscMalloc(5*n*sizeof(PetscReal),&work);CHKERRQ(ierr);
#if defined(PETSC_MISSING_LAPACK_GEEV)
SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_SUP,"GEEV - Lapack routine is unavailable\nNot able to provide eigen values.");
#else
{
PetscBLASInt lierr;
PetscScalar sdummy;
PetscBLASInt bn = PetscBLASIntCast(n);
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
LAPACKgeev_("N","N",&bn,array,&bn,realpart,imagpart,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,&lierr);
if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in LAPACK routine %d",(int)lierr);
ierr = PetscFPTrapPop();CHKERRQ(ierr);
}
#endif
ierr = PetscFree(work);CHKERRQ(ierr);
ierr = PetscMalloc(n*sizeof(PetscInt),&perm);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]];
}
ierr = PetscFree(perm);CHKERRQ(ierr);
ierr = PetscFree(realpart);CHKERRQ(ierr);
}
#else
if (!rank) {
PetscScalar *work,*eigs;
PetscReal *rwork;
PetscBLASInt idummy,lwork;
PetscInt *perm;
idummy = n;
lwork = 5*n;
ierr = PetscMalloc(5*n*sizeof(PetscScalar),&work);CHKERRQ(ierr);
ierr = PetscMalloc(2*n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
ierr = PetscMalloc(n*sizeof(PetscScalar),&eigs);CHKERRQ(ierr);
#if defined(PETSC_MISSING_LAPACK_GEEV)
SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_SUP,"GEEV - Lapack routine is unavailable\nNot able to provide eigen values.");
#else
{
PetscBLASInt lierr;
PetscScalar sdummy;
PetscBLASInt nb = PetscBLASIntCast(n);
ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
LAPACKgeev_("N","N",&nb,array,&nb,eigs,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,rwork,&lierr);
if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in LAPACK routine %d",(int)lierr);
ierr = PetscFPTrapPop();CHKERRQ(ierr);
}
#endif
ierr = PetscFree(work);CHKERRQ(ierr);
ierr = PetscFree(rwork);CHKERRQ(ierr);
ierr = PetscMalloc(n*sizeof(PetscInt),&perm);CHKERRQ(ierr);
for (i=0; i<n; i++) { perm[i] = i;}
for (i=0; i<n; i++) { r[i] = PetscRealPart(eigs[i]);}
ierr = PetscSortRealWithPermutation(n,r,perm);CHKERRQ(ierr);
for (i=0; i<n; i++) {
r[i] = PetscRealPart(eigs[perm[i]]);
c[i] = PetscImaginaryPart(eigs[perm[i]]);
}
ierr = PetscFree(perm);CHKERRQ(ierr);
ierr = PetscFree(eigs);CHKERRQ(ierr);
}
#endif
if (size > 1) {
ierr = MatDenseRestoreArray(A,&array);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
} else {
ierr = MatDenseRestoreArray(BA,&array);CHKERRQ(ierr);
}
ierr = MatDestroy(&BA);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PETSC_EXTERN void PETSC_STDCALL kspcomputeexplicitoperator_(KSP ksp,Mat *mat, int *__ierr ){
*__ierr = KSPComputeExplicitOperator(
(KSP)PetscToPointer((ksp) ),mat);
}
