PetscErrorCode EPSSetUp_Lanczos(EPS eps)
{
EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
BVOrthogRefineType refine;
PetscReal eta;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);CHKERRQ(ierr);
if (eps->ncv>eps->nev+eps->mpd) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must not be larger than nev+mpd");
if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
if (!eps->which) { ierr = EPSSetWhichEigenpairs_Default(eps);CHKERRQ(ierr); }
switch (eps->which) {
case EPS_LARGEST_IMAGINARY:
case EPS_SMALLEST_IMAGINARY:
case EPS_TARGET_IMAGINARY:
SETERRQ(PetscObjectComm((PetscObject)eps),1,"Wrong value of eps->which");
default: ; /* default case to remove warning */
}
if (!eps->extraction) {
ierr = EPSSetExtraction(eps,EPS_RITZ);CHKERRQ(ierr);
} else if (eps->extraction!=EPS_RITZ) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not supported in this solver");
ierr = EPSAllocateSolution(eps,1);CHKERRQ(ierr);
ierr = EPS_SetInnerProduct(eps);CHKERRQ(ierr);
if (lanczos->reorthog != EPS_LANCZOS_REORTHOG_FULL) {
ierr = BVGetOrthogonalization(eps->V,NULL,&refine,&eta);CHKERRQ(ierr);
ierr = BVSetOrthogonalization(eps->V,BV_ORTHOG_MGS,refine,eta);CHKERRQ(ierr);
ierr = PetscInfo(eps,"Switching to MGS orthogonalization\n");CHKERRQ(ierr);
}
if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_SELECTIVE) {
ierr = BVDuplicate(eps->V,&lanczos->AV);CHKERRQ(ierr);
}
ierr = DSSetType(eps->ds,DSHEP);CHKERRQ(ierr);
ierr = DSSetCompact(eps->ds,PETSC_TRUE);CHKERRQ(ierr);
ierr = DSAllocate(eps->ds,eps->ncv+1);CHKERRQ(ierr);
if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_LOCAL) {
ierr = EPSSetWorkVecs(eps,1);CHKERRQ(ierr);
}
/* dispatch solve method */
if (!eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Requested method is only available for Hermitian problems");
if (eps->isgeneralized && eps->ishermitian && !eps->ispositive) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Requested method does not work for indefinite problems");
eps->ops->solve = EPSSolve_Lanczos;
PetscFunctionReturn(0);
}
PetscErrorCode SVDSetUp_TRLanczos(SVD svd)
{
PetscErrorCode ierr;
PetscInt N;
PetscFunctionBegin;
ierr = SVDMatGetSize(svd,NULL,&N);CHKERRQ(ierr);
ierr = SVDSetDimensions_Default(svd);CHKERRQ(ierr);
if (svd->ncv>svd->nsv+svd->mpd) SETERRQ(PetscObjectComm((PetscObject)svd),1,"The value of ncv must not be larger than nev+mpd");
if (!svd->max_it) svd->max_it = PetscMax(N/svd->ncv,100);
svd->leftbasis = PETSC_TRUE;
ierr = SVDAllocateSolution(svd,1);CHKERRQ(ierr);
ierr = DSSetType(svd->ds,DSSVD);CHKERRQ(ierr);
ierr = DSSetCompact(svd->ds,PETSC_TRUE);CHKERRQ(ierr);
ierr = DSAllocate(svd->ds,svd->ncv);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
DS ds;
SlepcSC sc;
PetscReal *T,*s,re,im;
PetscScalar *eigr,*eigi;
PetscInt i,n=10,l=2,k=5,ld;
PetscViewer viewer;
PetscBool verbose;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type GHIEP with compact storage - dimension %D.\n",n);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-l",&l,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-k",&k,NULL);CHKERRQ(ierr);
if (l>n || k>n || l>k) SETERRQ(PETSC_COMM_WORLD,1,"Wrong value of dimensions");
ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr);
/* Create DS object */
ierr = DSCreate(PETSC_COMM_WORLD,&ds);CHKERRQ(ierr);
ierr = DSSetType(ds,DSGHIEP);CHKERRQ(ierr);
ierr = DSSetFromOptions(ds);CHKERRQ(ierr);
ld = n+2; /* test leading dimension larger than n */
ierr = DSAllocate(ds,ld);CHKERRQ(ierr);
ierr = DSSetDimensions(ds,n,0,l,k);CHKERRQ(ierr);
ierr = DSSetCompact(ds,PETSC_TRUE);CHKERRQ(ierr);
/* Set up viewer */
ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr);
ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr);
ierr = DSView(ds,viewer);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
if (verbose) {
ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
}
/* Fill arrow-tridiagonal matrix */
ierr = DSGetArrayReal(ds,DS_MAT_T,&T);CHKERRQ(ierr);
ierr = DSGetArrayReal(ds,DS_MAT_D,&s);CHKERRQ(ierr);
for (i=0;i<n;i++) T[i] = (PetscReal)(i+1);
for (i=k;i<n-1;i++) T[i+ld] = 1.0;
for (i=l;i<k;i++) T[i+2*ld] = 1.0;
T[2*ld+l+1] = -7; T[ld+k+1] = -7;
/* Signature matrix */
for (i=0;i<n;i++) s[i] = 1.0;
s[l+1] = -1.0;
s[k+1] = -1.0;
ierr = DSRestoreArrayReal(ds,DS_MAT_T,&T);CHKERRQ(ierr);
ierr = DSRestoreArrayReal(ds,DS_MAT_D,&s);CHKERRQ(ierr);
if (l==0 && k==0) {
ierr = DSSetState(ds,DS_STATE_INTERMEDIATE);CHKERRQ(ierr);
} else {
ierr = DSSetState(ds,DS_STATE_RAW);CHKERRQ(ierr);
}
if (verbose) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");CHKERRQ(ierr);
ierr = DSView(ds,viewer);CHKERRQ(ierr);
}
/* Solve */
ierr = PetscCalloc2(n,&eigr,n,&eigi);CHKERRQ(ierr);
ierr = DSGetSlepcSC(ds,&sc);CHKERRQ(ierr);
sc->comparison = SlepcCompareLargestMagnitude;
sc->comparisonctx = NULL;
sc->map = NULL;
sc->mapobj = NULL;
ierr = DSSolve(ds,eigr,eigi);CHKERRQ(ierr);
ierr = DSSort(ds,eigr,eigi,NULL,NULL,NULL);CHKERRQ(ierr);
if (verbose) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");CHKERRQ(ierr);
ierr = DSView(ds,viewer);CHKERRQ(ierr);
}
/* Print eigenvalues */
ierr = PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalues =\n",n);CHKERRQ(ierr);
for (i=0;i<n;i++) {
#if defined(PETSC_USE_COMPLEX)
re = PetscRealPart(eigr[i]);
im = PetscImaginaryPart(eigr[i]);
#else
re = eigr[i];
im = eigi[i];
#endif
if (PetscAbs(im)<1e-10) {
ierr = PetscViewerASCIIPrintf(viewer," %.5f\n",(double)re);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(viewer," %.5f%+.5fi\n",(double)re,(double)im);CHKERRQ(ierr);
}
}
ierr = PetscFree2(eigr,eigi);CHKERRQ(ierr);
ierr = DSDestroy(&ds);CHKERRQ(ierr);
ierr = SlepcFinalize();
return 0;
}
PetscErrorCode EPSSetUp_KrylovSchur(EPS eps)
{
PetscErrorCode ierr;
EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
enum { EPS_KS_DEFAULT,EPS_KS_SYMM,EPS_KS_SLICE,EPS_KS_INDEF } variant;
PetscFunctionBegin;
/* spectrum slicing requires special treatment of default values */
if (eps->which==EPS_ALL) {
ierr = EPSSetUp_KrylovSchur_Slice(eps);CHKERRQ(ierr);
} else {
ierr = EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);CHKERRQ(ierr);
if (eps->ncv>eps->nev+eps->mpd) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must not be larger than nev+mpd");
if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
if (!eps->which) { ierr = EPSSetWhichEigenpairs_Default(eps);CHKERRQ(ierr); }
}
if (eps->isgeneralized && eps->ishermitian && !eps->ispositive && eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not implemented for indefinite problems");
if (eps->ishermitian && eps->ispositive && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY)) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Wrong value of eps->which");
if (!eps->extraction) {
ierr = EPSSetExtraction(eps,EPS_RITZ);CHKERRQ(ierr);
} else if (eps->extraction!=EPS_RITZ && eps->extraction!=EPS_HARMONIC)
SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
if (!ctx->keep) ctx->keep = 0.5;
ierr = EPSAllocateSolution(eps,1);CHKERRQ(ierr);
ierr = EPS_SetInnerProduct(eps);CHKERRQ(ierr);
if (eps->arbitrary) {
ierr = EPSSetWorkVecs(eps,2);CHKERRQ(ierr);
} else if (eps->ishermitian && !eps->ispositive){
ierr = EPSSetWorkVecs(eps,1);CHKERRQ(ierr);
}
/* dispatch solve method */
if (eps->ishermitian) {
if (eps->which==EPS_ALL) {
if (eps->isgeneralized && !eps->ispositive) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing not implemented for indefinite problems");
else variant = EPS_KS_SLICE;
} else if (eps->isgeneralized && !eps->ispositive) {
variant = EPS_KS_INDEF;
} else {
switch (eps->extraction) {
case EPS_RITZ: variant = EPS_KS_SYMM; break;
case EPS_HARMONIC: variant = EPS_KS_DEFAULT; break;
default: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
}
}
} else {
switch (eps->extraction) {
case EPS_RITZ: variant = EPS_KS_DEFAULT; break;
case EPS_HARMONIC: variant = EPS_KS_DEFAULT; break;
default: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
}
}
switch (variant) {
case EPS_KS_DEFAULT:
eps->ops->solve = EPSSolve_KrylovSchur_Default;
eps->ops->computevectors = EPSComputeVectors_Schur;
ierr = DSSetType(eps->ds,DSNHEP);CHKERRQ(ierr);
ierr = DSAllocate(eps->ds,eps->ncv+1);CHKERRQ(ierr);
break;
case EPS_KS_SYMM:
eps->ops->solve = EPSSolve_KrylovSchur_Symm;
eps->ops->computevectors = EPSComputeVectors_Hermitian;
ierr = DSSetType(eps->ds,DSHEP);CHKERRQ(ierr);
ierr = DSSetCompact(eps->ds,PETSC_TRUE);CHKERRQ(ierr);
ierr = DSSetExtraRow(eps->ds,PETSC_TRUE);CHKERRQ(ierr);
ierr = DSAllocate(eps->ds,eps->ncv+1);CHKERRQ(ierr);
break;
case EPS_KS_SLICE:
eps->ops->solve = EPSSolve_KrylovSchur_Slice;
eps->ops->computevectors = NULL;
ierr = DSSetType(eps->ds,DSHEP);CHKERRQ(ierr);
ierr = DSSetCompact(eps->ds,PETSC_TRUE);CHKERRQ(ierr);
ierr = DSAllocate(eps->ds,ctx->ncv+1);CHKERRQ(ierr);
break;
case EPS_KS_INDEF:
eps->ops->solve = EPSSolve_KrylovSchur_Indefinite;
eps->ops->computevectors = EPSComputeVectors_Indefinite;
ierr = DSSetType(eps->ds,DSGHIEP);CHKERRQ(ierr);
ierr = DSSetCompact(eps->ds,PETSC_TRUE);CHKERRQ(ierr);
ierr = DSAllocate(eps->ds,eps->ncv+1);CHKERRQ(ierr);
break;
default: SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error");
}
PetscFunctionReturn(0);
}
