/*
PEPComputeScaleFactor - compute sfactor as described in [Betcke 2008].
*/
PetscErrorCode PEPComputeScaleFactor(PEP pep)
{
PetscErrorCode ierr;
PetscBool has0,has1,flg;
PetscReal norm0,norm1;
Mat T[2];
PEPBasis basis;
PetscFunctionBegin;
if (pep->scale==PEP_SCALE_NONE || pep->scale==PEP_SCALE_DIAGONAL) { /* no scalar scaling */
pep->sfactor = 1.0;
PetscFunctionReturn(0);
}
if (pep->sfactor_set) PetscFunctionReturn(0); /* user provided value */
ierr = PEPGetBasis(pep,&basis);CHKERRQ(ierr);
if (basis==PEP_BASIS_MONOMIAL) {
ierr = STGetTransform(pep->st,&flg);CHKERRQ(ierr);
if (flg) {
ierr = STGetTOperators(pep->st,0,&T[0]);CHKERRQ(ierr);
ierr = STGetTOperators(pep->st,pep->nmat-1,&T[1]);CHKERRQ(ierr);
} else {
T[0] = pep->A[0];
T[1] = pep->A[pep->nmat-1];
}
if (pep->nmat>2) {
ierr = MatHasOperation(T[0],MATOP_NORM,&has0);CHKERRQ(ierr);
ierr = MatHasOperation(T[1],MATOP_NORM,&has1);CHKERRQ(ierr);
if (has0 && has1) {
ierr = MatNorm(T[0],NORM_INFINITY,&norm0);CHKERRQ(ierr);
ierr = MatNorm(T[1],NORM_INFINITY,&norm1);CHKERRQ(ierr);
pep->sfactor = PetscPowReal(norm0/norm1,1.0/(pep->nmat-1));
} else {
pep->sfactor = 1.0;
}
}
} else pep->sfactor = 1.0;
PetscFunctionReturn(0);
}
/*@
PEPSolve - Solves the polynomial eigensystem.
Collective on PEP
Input Parameter:
. pep - eigensolver context obtained from PEPCreate()
Options Database Keys:
+ -pep_view - print information about the solver used
- -pep_plot_eigs - plot computed eigenvalues
Level: beginner
.seealso: PEPCreate(), PEPSetUp(), PEPDestroy(), PEPSetTolerances()
@*/
PetscErrorCode PEPSolve(PEP pep)
{
PetscErrorCode ierr;
PetscInt i;
PetscReal re,im;
PetscBool flg,islinear;
PetscViewer viewer;
PetscViewerFormat format;
PetscDraw draw;
PetscDrawSP drawsp;
PetscFunctionBegin;
PetscValidHeaderSpecific(pep,PEP_CLASSID,1);
ierr = PetscLogEventBegin(PEP_Solve,pep,0,0,0);CHKERRQ(ierr);
/* call setup */
ierr = PEPSetUp(pep);CHKERRQ(ierr);
pep->nconv = 0;
pep->its = 0;
for (i=0;i<pep->ncv;i++) {
pep->eigr[i] = 0.0;
pep->eigi[i] = 0.0;
pep->errest[i] = 0.0;
}
ierr = PEPMonitor(pep,pep->its,pep->nconv,pep->eigr,pep->eigi,pep->errest,pep->ncv);CHKERRQ(ierr);
ierr = (*pep->ops->solve)(pep);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)pep,PEPLINEAR,&islinear);CHKERRQ(ierr);
if (!islinear) {
ierr = STPostSolve(pep->st);CHKERRQ(ierr);
}
if (!pep->reason) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason");
if (!islinear) {
/* Map eigenvalues back to the original problem */
ierr = STGetTransform(pep->st,&flg);CHKERRQ(ierr);
if (flg) {
ierr = STBackTransform(pep->st,pep->nconv,pep->eigr,pep->eigi);CHKERRQ(ierr);
}
}
pep->state = PEP_STATE_SOLVED;
if (pep->refine==PEP_REFINE_SIMPLE && pep->rits>0) {
ierr = PEPComputeVectors(pep);CHKERRQ(ierr);
ierr = PEPNewtonRefinementSimple(pep,&pep->rits,&pep->rtol,pep->nconv);CHKERRQ(ierr);
pep->state = PEP_STATE_EIGENVECTORS;
}
#if !defined(PETSC_USE_COMPLEX)
/* reorder conjugate eigenvalues (positive imaginary first) */
for (i=0;i<pep->nconv-1;i++) {
if (pep->eigi[i] != 0) {
if (pep->eigi[i] < 0) {
pep->eigi[i] = -pep->eigi[i];
pep->eigi[i+1] = -pep->eigi[i+1];
/* the next correction only works with eigenvectors */
ierr = PEPComputeVectors(pep);CHKERRQ(ierr);
ierr = BVScaleColumn(pep->V,i+1,-1.0);CHKERRQ(ierr);
}
i++;
}
}
#endif
/* sort eigenvalues according to pep->which parameter */
ierr = SlepcSortEigenvalues(pep->sc,pep->nconv,pep->eigr,pep->eigi,pep->perm);CHKERRQ(ierr);
ierr = PetscLogEventEnd(PEP_Solve,pep,0,0,0);CHKERRQ(ierr);
/* various viewers */
ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)pep),((PetscObject)pep)->prefix,"-pep_view",&viewer,&format,&flg);CHKERRQ(ierr);
if (flg && !PetscPreLoadingOn) {
ierr = PetscViewerPushFormat(viewer,format);CHKERRQ(ierr);
ierr = PEPView(pep,viewer);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)pep)->prefix,"-pep_plot_eigs",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = PetscViewerDrawOpen(PETSC_COMM_SELF,0,"Computed Eigenvalues",PETSC_DECIDE,PETSC_DECIDE,300,300,&viewer);CHKERRQ(ierr);
ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
ierr = PetscDrawSPCreate(draw,1,&drawsp);CHKERRQ(ierr);
for (i=0;i<pep->nconv;i++) {
#if defined(PETSC_USE_COMPLEX)
re = PetscRealPart(pep->eigr[i]);
im = PetscImaginaryPart(pep->eigi[i]);
#else
re = pep->eigr[i];
im = pep->eigi[i];
#endif
ierr = PetscDrawSPAddPoint(drawsp,&re,&im);CHKERRQ(ierr);
}
ierr = PetscDrawSPDraw(drawsp,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscDrawSPDestroy(&drawsp);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
/* Remove the initial subspace */
pep->nini = 0;
PetscFunctionReturn(0);
}
PetscErrorCode PEPSetUp_Linear(PEP pep)
{
PetscErrorCode ierr;
PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
PetscInt i=0;
EPSWhich which;
PetscBool trackall,istrivial,flg;
PetscScalar sigma;
/* function tables */
PetscErrorCode (*fcreate[][2])(MPI_Comm,PEP_LINEAR*,Mat*) = {
{ MatCreateExplicit_Linear_N1A, MatCreateExplicit_Linear_N1B }, /* N1 */
{ MatCreateExplicit_Linear_N2A, MatCreateExplicit_Linear_N2B }, /* N2 */
{ MatCreateExplicit_Linear_S1A, MatCreateExplicit_Linear_S1B }, /* S1 */
{ MatCreateExplicit_Linear_S2A, MatCreateExplicit_Linear_S2B }, /* S2 */
{ MatCreateExplicit_Linear_H1A, MatCreateExplicit_Linear_H1B }, /* H1 */
{ MatCreateExplicit_Linear_H2A, MatCreateExplicit_Linear_H2B } /* H2 */
};
PetscErrorCode (*fmult[][2])(Mat,Vec,Vec) = {
{ MatMult_Linear_N1A, MatMult_Linear_N1B },
{ MatMult_Linear_N2A, MatMult_Linear_N2B },
{ MatMult_Linear_S1A, MatMult_Linear_S1B },
{ MatMult_Linear_S2A, MatMult_Linear_S2B },
{ MatMult_Linear_H1A, MatMult_Linear_H1B },
{ MatMult_Linear_H2A, MatMult_Linear_H2B }
};
PetscErrorCode (*fgetdiagonal[][2])(Mat,Vec) = {
{ MatGetDiagonal_Linear_N1A, MatGetDiagonal_Linear_N1B },
{ MatGetDiagonal_Linear_N2A, MatGetDiagonal_Linear_N2B },
{ MatGetDiagonal_Linear_S1A, MatGetDiagonal_Linear_S1B },
{ MatGetDiagonal_Linear_S2A, MatGetDiagonal_Linear_S2B },
{ MatGetDiagonal_Linear_H1A, MatGetDiagonal_Linear_H1B },
{ MatGetDiagonal_Linear_H2A, MatGetDiagonal_Linear_H2B }
};
PetscFunctionBegin;
if (!ctx->cform) ctx->cform = 1;
if (!pep->which) pep->which = PEP_LARGEST_MAGNITUDE;
if (pep->basis!=PEP_BASIS_MONOMIAL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver not implemented for non-monomial bases");
if (pep->nmat!=3) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver only available for quadratic problems");
if (pep->scale==PEP_SCALE_DIAGONAL || pep->scale==PEP_SCALE_BOTH) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Diagonal scaling not allowed in PEP linear solver");
ierr = STGetTransform(pep->st,&flg);CHKERRQ(ierr);
if (flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"ST transformation flag not allowed for PEP linear solver");
/* compute scale factor if no set by user */
ierr = PEPComputeScaleFactor(pep);CHKERRQ(ierr);
ierr = STGetOperators(pep->st,0,&ctx->K);CHKERRQ(ierr);
ierr = STGetOperators(pep->st,1,&ctx->C);CHKERRQ(ierr);
ierr = STGetOperators(pep->st,2,&ctx->M);CHKERRQ(ierr);
ctx->sfactor = pep->sfactor;
ierr = MatDestroy(&ctx->A);CHKERRQ(ierr);
ierr = MatDestroy(&ctx->B);CHKERRQ(ierr);
ierr = VecDestroy(&ctx->x1);CHKERRQ(ierr);
ierr = VecDestroy(&ctx->x2);CHKERRQ(ierr);
ierr = VecDestroy(&ctx->y1);CHKERRQ(ierr);
ierr = VecDestroy(&ctx->y2);CHKERRQ(ierr);
switch (pep->problem_type) {
case PEP_GENERAL: i = 0; break;
case PEP_HERMITIAN: i = 2; break;
case PEP_GYROSCOPIC: i = 4; break;
default: SETERRQ(PetscObjectComm((PetscObject)pep),1,"Wrong value of pep->problem_type");
}
i += ctx->cform-1;
if (ctx->explicitmatrix) {
ctx->x1 = ctx->x2 = ctx->y1 = ctx->y2 = NULL;
ierr = (*fcreate[i][0])(PetscObjectComm((PetscObject)pep),ctx,&ctx->A);CHKERRQ(ierr);
ierr = (*fcreate[i][1])(PetscObjectComm((PetscObject)pep),ctx,&ctx->B);CHKERRQ(ierr);
} else {
ierr = VecCreateMPIWithArray(PetscObjectComm((PetscObject)pep),1,pep->nloc,pep->n,NULL,&ctx->x1);CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PetscObjectComm((PetscObject)pep),1,pep->nloc,pep->n,NULL,&ctx->x2);CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PetscObjectComm((PetscObject)pep),1,pep->nloc,pep->n,NULL,&ctx->y1);CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PetscObjectComm((PetscObject)pep),1,pep->nloc,pep->n,NULL,&ctx->y2);CHKERRQ(ierr);
ierr = PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->x1);CHKERRQ(ierr);
ierr = PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->x2);CHKERRQ(ierr);
ierr = PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->y1);CHKERRQ(ierr);
ierr = PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->y2);CHKERRQ(ierr);
ierr = MatCreateShell(PetscObjectComm((PetscObject)pep),2*pep->nloc,2*pep->nloc,2*pep->n,2*pep->n,ctx,&ctx->A);CHKERRQ(ierr);
ierr = MatShellSetOperation(ctx->A,MATOP_MULT,(void(*)(void))fmult[i][0]);CHKERRQ(ierr);
ierr = MatShellSetOperation(ctx->A,MATOP_GET_DIAGONAL,(void(*)(void))fgetdiagonal[i][0]);CHKERRQ(ierr);
ierr = MatCreateShell(PetscObjectComm((PetscObject)pep),2*pep->nloc,2*pep->nloc,2*pep->n,2*pep->n,ctx,&ctx->B);CHKERRQ(ierr);
ierr = MatShellSetOperation(ctx->B,MATOP_MULT,(void(*)(void))fmult[i][1]);CHKERRQ(ierr);
ierr = MatShellSetOperation(ctx->B,MATOP_GET_DIAGONAL,(void(*)(void))fgetdiagonal[i][1]);CHKERRQ(ierr);
}
ierr = PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->A);CHKERRQ(ierr);
ierr = PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->B);CHKERRQ(ierr);
if (!ctx->eps) { ierr = PEPLinearGetEPS(pep,&ctx->eps);CHKERRQ(ierr); }
ierr = EPSSetOperators(ctx->eps,ctx->A,ctx->B);CHKERRQ(ierr);
if (pep->problem_type==PEP_HERMITIAN) {
ierr = EPSSetProblemType(ctx->eps,EPS_GHIEP);CHKERRQ(ierr);
} else {
ierr = EPSSetProblemType(ctx->eps,EPS_GNHEP);CHKERRQ(ierr);
}
switch (pep->which) {
case PEP_LARGEST_MAGNITUDE: which = EPS_LARGEST_MAGNITUDE; break;
case PEP_SMALLEST_MAGNITUDE: which = EPS_SMALLEST_MAGNITUDE; break;
case PEP_LARGEST_REAL: which = EPS_LARGEST_REAL; break;
case PEP_SMALLEST_REAL: which = EPS_SMALLEST_REAL; break;
case PEP_LARGEST_IMAGINARY: which = EPS_LARGEST_IMAGINARY; break;
case PEP_SMALLEST_IMAGINARY: which = EPS_SMALLEST_IMAGINARY; break;
case PEP_TARGET_MAGNITUDE: which = EPS_TARGET_MAGNITUDE; break;
case PEP_TARGET_REAL: which = EPS_TARGET_REAL; break;
case PEP_TARGET_IMAGINARY: which = EPS_TARGET_IMAGINARY; break;
default: SETERRQ(PetscObjectComm((PetscObject)pep),1,"Wrong value of which");
}
ierr = EPSSetWhichEigenpairs(ctx->eps,which);CHKERRQ(ierr);
ierr = EPSSetDimensions(ctx->eps,pep->nev,pep->ncv?pep->ncv:PETSC_DEFAULT,pep->mpd?pep->mpd:PETSC_DEFAULT);CHKERRQ(ierr);
ierr = EPSSetTolerances(ctx->eps,pep->tol==PETSC_DEFAULT?SLEPC_DEFAULT_TOL/10.0:pep->tol/10.0,pep->max_it?pep->max_it:PETSC_DEFAULT);CHKERRQ(ierr);
ierr = RGIsTrivial(pep->rg,&istrivial);CHKERRQ(ierr);
if (!istrivial) { ierr = EPSSetRG(ctx->eps,pep->rg);CHKERRQ(ierr); }
/* Transfer the trackall option from pep to eps */
ierr = PEPGetTrackAll(pep,&trackall);CHKERRQ(ierr);
ierr = EPSSetTrackAll(ctx->eps,trackall);CHKERRQ(ierr);
/* temporary change of target */
if (pep->sfactor!=1.0) {
ierr = EPSGetTarget(ctx->eps,&sigma);CHKERRQ(ierr);
ierr = EPSSetTarget(ctx->eps,sigma/pep->sfactor);CHKERRQ(ierr);
}
ierr = EPSSetUp(ctx->eps);CHKERRQ(ierr);
ierr = EPSGetDimensions(ctx->eps,NULL,&pep->ncv,&pep->mpd);CHKERRQ(ierr);
ierr = EPSGetTolerances(ctx->eps,NULL,&pep->max_it);CHKERRQ(ierr);
if (pep->nini>0) { ierr = PetscInfo(pep,"Ignoring initial vectors\n");CHKERRQ(ierr); }
ierr = PEPAllocateSolution(pep,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
