/*@
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 TSMonitorSPEig(TS ts,PetscInt step,PetscReal ptime,Vec v,void *monctx)
{
TSMonitorSPEigCtx ctx = (TSMonitorSPEigCtx) monctx;
PetscErrorCode ierr;
KSP ksp = ctx->ksp;
PetscInt n,N,nits,neig,i,its = 200;
PetscReal *r,*c,time_step_save;
PetscDrawSP drawsp = ctx->drawsp;
Mat A,B;
Vec xdot;
SNES snes;
PetscFunctionBegin;
if (!step) PetscFunctionReturn(0);
if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
ierr = VecDuplicate(v,&xdot);CHKERRQ(ierr);
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
ierr = SNESGetJacobian(snes,&A,&B,NULL,NULL);CHKERRQ(ierr);
ierr = MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&B);CHKERRQ(ierr);
/*
This doesn't work because methods keep and use internal information about the shift so it
seems we would need code for each method to trick the correct Jacobian in being computed.
*/
time_step_save = ts->time_step;
ts->time_step = PETSC_MAX_REAL;
ierr = SNESComputeJacobian(snes,v,A,B);CHKERRQ(ierr);
ts->time_step = time_step_save;
ierr = KSPSetOperators(ksp,B,B);CHKERRQ(ierr);
ierr = VecGetSize(v,&n);CHKERRQ(ierr);
if (n < 200) its = n;
ierr = KSPSetTolerances(ksp,1.e-10,PETSC_DEFAULT,PETSC_DEFAULT,its);CHKERRQ(ierr);
ierr = VecSetRandom(xdot,ctx->rand);CHKERRQ(ierr);
ierr = KSPSolve(ksp,xdot,xdot);CHKERRQ(ierr);
ierr = VecDestroy(&xdot);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&nits);CHKERRQ(ierr);
N = nits+2;
if (nits) {
PetscDraw draw;
PetscReal pause;
PetscDrawAxis axis;
PetscReal xmin,xmax,ymin,ymax;
ierr = PetscDrawSPReset(drawsp);CHKERRQ(ierr);
ierr = PetscDrawSPSetLimits(drawsp,ctx->xmin,ctx->xmax,ctx->ymin,ctx->ymax);CHKERRQ(ierr);
ierr = PetscMalloc2(PetscMax(n,N),&r,PetscMax(n,N),&c);CHKERRQ(ierr);
if (ctx->computeexplicitly) {
ierr = KSPComputeEigenvaluesExplicitly(ksp,n,r,c);CHKERRQ(ierr);
neig = n;
} else {
ierr = KSPComputeEigenvalues(ksp,N,r,c,&neig);CHKERRQ(ierr);
}
/* We used the positive operator to be able to reuse KSPs that require positive definiteness, now flip the spectrum as is conventional for ODEs */
for (i=0; i<neig; i++) r[i] = -r[i];
for (i=0; i<neig; i++) {
if (ts->ops->linearstability) {
PetscReal fr,fi;
ierr = TSComputeLinearStability(ts,r[i],c[i],&fr,&fi);CHKERRQ(ierr);
if ((fr*fr + fi*fi) > 1.0) {
ierr = PetscPrintf(ctx->comm,"Linearized Eigenvalue %g + %g i linear stability function %g norm indicates unstable scheme \n",(double)r[i],(double)c[i],(double)(fr*fr + fi*fi));CHKERRQ(ierr);
}
}
ierr = PetscDrawSPAddPoint(drawsp,r+i,c+i);CHKERRQ(ierr);
}
ierr = PetscFree2(r,c);CHKERRQ(ierr);
ierr = PetscDrawSPGetDraw(drawsp,&draw);CHKERRQ(ierr);
ierr = PetscDrawGetPause(draw,&pause);CHKERRQ(ierr);
ierr = PetscDrawSetPause(draw,0.0);CHKERRQ(ierr);
ierr = PetscDrawSPDraw(drawsp,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscDrawSetPause(draw,pause);CHKERRQ(ierr);
if (ts->ops->linearstability) {
ierr = PetscDrawSPGetAxis(drawsp,&axis);CHKERRQ(ierr);
ierr = PetscDrawAxisGetLimits(axis,&xmin,&xmax,&ymin,&ymax);CHKERRQ(ierr);
ierr = PetscDrawIndicatorFunction(draw,xmin,xmax,ymin,ymax,PETSC_DRAW_CYAN,(PetscErrorCode (*)(void*,PetscReal,PetscReal,PetscBool*))TSLinearStabilityIndicator,ts);CHKERRQ(ierr);
ierr = PetscDrawSPDraw(drawsp,PETSC_FALSE);CHKERRQ(ierr);
}
}
ierr = MatDestroy(&B);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*@
EPSSolve - Solves the eigensystem.
Collective on EPS
Input Parameter:
. eps - eigensolver context obtained from EPSCreate()
Options Database Keys:
+ -eps_view - print information about the solver used
. -eps_view_mat0 binary - save the first matrix (A) to the default binary viewer
. -eps_view_mat1 binary - save the second matrix (B) to the default binary viewer
- -eps_plot_eigs - plot computed eigenvalues
Level: beginner
.seealso: EPSCreate(), EPSSetUp(), EPSDestroy(), EPSSetTolerances()
@*/
PetscErrorCode EPSSolve(EPS eps)
{
PetscErrorCode ierr;
PetscInt i,nmat;
PetscReal re,im;
PetscScalar dot;
PetscBool flg,iscayley;
PetscViewer viewer;
PetscViewerFormat format;
PetscDraw draw;
PetscDrawSP drawsp;
STMatMode matmode;
Mat A,B;
Vec w,x;
PetscFunctionBegin;
PetscValidHeaderSpecific(eps,EPS_CLASSID,1);
ierr = PetscLogEventBegin(EPS_Solve,eps,0,0,0);CHKERRQ(ierr);
/* call setup */
ierr = EPSSetUp(eps);CHKERRQ(ierr);
eps->nconv = 0;
eps->its = 0;
for (i=0;i<eps->ncv;i++) {
eps->eigr[i] = 0.0;
eps->eigi[i] = 0.0;
eps->errest[i] = 0.0;
}
ierr = EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,eps->ncv);CHKERRQ(ierr);
/* call solver */
ierr = (*eps->ops->solve)(eps);CHKERRQ(ierr);
eps->state = EPS_STATE_SOLVED;
ierr = STGetMatMode(eps->st,&matmode);CHKERRQ(ierr);
if (matmode == ST_MATMODE_INPLACE && eps->ispositive) {
/* Purify eigenvectors before reverting operator */
ierr = EPSComputeVectors(eps);CHKERRQ(ierr);
}
ierr = STPostSolve(eps->st);CHKERRQ(ierr);
if (!eps->reason) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason");
/* Map eigenvalues back to the original problem, necessary in some
* spectral transformations */
if (eps->ops->backtransform) {
ierr = (*eps->ops->backtransform)(eps);CHKERRQ(ierr);
}
#if !defined(PETSC_USE_COMPLEX)
/* reorder conjugate eigenvalues (positive imaginary first) */
for (i=0; i<eps->nconv-1; i++) {
if (eps->eigi[i] != 0) {
if (eps->eigi[i] < 0) {
eps->eigi[i] = -eps->eigi[i];
eps->eigi[i+1] = -eps->eigi[i+1];
/* the next correction only works with eigenvectors */
ierr = EPSComputeVectors(eps);CHKERRQ(ierr);
ierr = BVScaleColumn(eps->V,i+1,-1.0);CHKERRQ(ierr);
}
i++;
}
}
#endif
ierr = STGetNumMatrices(eps->st,&nmat);CHKERRQ(ierr);
ierr = STGetOperators(eps->st,0,&A);CHKERRQ(ierr);
if (nmat>1) { ierr = STGetOperators(eps->st,1,&B);CHKERRQ(ierr); }
/* In the case of Cayley transform, eigenvectors need to be B-normalized */
ierr = PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);CHKERRQ(ierr);
if (iscayley && eps->isgeneralized && eps->ishermitian) {
ierr = MatGetVecs(B,NULL,&w);CHKERRQ(ierr);
ierr = EPSComputeVectors(eps);CHKERRQ(ierr);
for (i=0;i<eps->nconv;i++) {
ierr = BVGetColumn(eps->V,i,&x);CHKERRQ(ierr);
ierr = MatMult(B,x,w);CHKERRQ(ierr);
ierr = VecDot(w,x,&dot);CHKERRQ(ierr);
ierr = VecScale(x,1.0/PetscSqrtScalar(dot));CHKERRQ(ierr);
ierr = BVRestoreColumn(eps->V,i,&x);CHKERRQ(ierr);
}
ierr = VecDestroy(&w);CHKERRQ(ierr);
}
/* sort eigenvalues according to eps->which parameter */
ierr = SlepcSortEigenvalues(eps->sc,eps->nconv,eps->eigr,eps->eigi,eps->perm);CHKERRQ(ierr);
ierr = PetscLogEventEnd(EPS_Solve,eps,0,0,0);CHKERRQ(ierr);
/* various viewers */
ierr = MatViewFromOptions(A,((PetscObject)eps)->prefix,"-eps_view_mat0");CHKERRQ(ierr);
if (nmat>1) { ierr = MatViewFromOptions(B,((PetscObject)eps)->prefix,"-eps_view_mat1");CHKERRQ(ierr); }
ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)eps),((PetscObject)eps)->prefix,"-eps_view",&viewer,&format,&flg);CHKERRQ(ierr);
if (flg && !PetscPreLoadingOn) {
ierr = PetscViewerPushFormat(viewer,format);CHKERRQ(ierr);
ierr = EPSView(eps,viewer);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(((PetscObject)eps)->prefix,"-eps_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<eps->nconv;i++) {
#if defined(PETSC_USE_COMPLEX)
re = PetscRealPart(eps->eigr[i]);
im = PetscImaginaryPart(eps->eigi[i]);
#else
re = eps->eigr[i];
im = eps->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 deflation and initial subspaces */
eps->nds = 0;
eps->nini = 0;
PetscFunctionReturn(0);
}
void PETSC_STDCALL petscdrawspaddpoint_(PetscDrawSP sp,PetscReal *x,PetscReal *y, int *__ierr ){
*__ierr = PetscDrawSPAddPoint(
(PetscDrawSP)PetscToPointer((sp) ),x,y);
}
