/*
Implements the Cayley spectral transform.
*/
#include "src/st/stimpl.h" /*I "slepcst.h" I*/
typedef struct {
PetscScalar tau;
PetscTruth tau_set;
Vec w2;
} ST_CAYLEY;
#undef __FUNCT__
#define __FUNCT__ "STApply_Cayley"
PetscErrorCode STApply_Cayley(ST st,Vec x,Vec y)
{
PetscErrorCode ierr;
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
PetscScalar tau = ctx->tau;
PetscFunctionBegin;
if (st->shift_matrix == STMATMODE_INPLACE) { tau = tau + st->sigma; };
if (st->B) {
/* generalized eigenproblem: y = (A - sB)^-1 (A + tB)x */
ierr = MatMult(st->A,x,st->w);CHKERRQ(ierr);
ierr = MatMult(st->B,x,ctx->w2);CHKERRQ(ierr);
ierr = VecAXPY(st->w,tau,ctx->w2);CHKERRQ(ierr);
ierr = STAssociatedKSPSolve(st,st->w,y);CHKERRQ(ierr);
}
else {
/* standard eigenproblem: y = (A - sI)^-1 (A + tI)x */
ierr = MatMult(st->A,x,st->w);CHKERRQ(ierr);
ierr = VecAXPY(st->w,tau,x);CHKERRQ(ierr);
ierr = STAssociatedKSPSolve(st,st->w,y);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "STApplyTranspose_Cayley"
PetscErrorCode STApplyTranspose_Cayley(ST st,Vec x,Vec y)
{
PetscErrorCode ierr;
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
PetscScalar tau = ctx->tau;
PetscFunctionBegin;
if (st->shift_matrix == STMATMODE_INPLACE) { tau = tau + st->sigma; };
if (st->B) {
/* generalized eigenproblem: y = (A + tB)^T (A - sB)^-T x */
ierr = STAssociatedKSPSolve(st,x,st->w);CHKERRQ(ierr);
ierr = MatMult(st->A,st->w,y);CHKERRQ(ierr);
ierr = MatMult(st->B,st->w,ctx->w2);CHKERRQ(ierr);
ierr = VecAXPY(y,tau,ctx->w2);CHKERRQ(ierr);
}
else {
/* standard eigenproblem: y = (A + tI)^T (A - sI)^-T x */
ierr = STAssociatedKSPSolve(st,x,st->w);CHKERRQ(ierr);
ierr = MatMult(st->A,st->w,y);CHKERRQ(ierr);
ierr = VecAXPY(y,tau,st->w);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "STApplyB_Cayley"
PetscErrorCode STApplyB_Cayley(ST st,Vec x,Vec y)
{
PetscErrorCode ierr;
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
PetscScalar tau = ctx->tau;
PetscFunctionBegin;
if (st->shift_matrix == STMATMODE_INPLACE) { tau = tau + st->sigma; };
if (st->B) {
/* generalized eigenproblem: y = (A + tB)x */
ierr = MatMult(st->A,x,y);CHKERRQ(ierr);
ierr = MatMult(st->B,x,ctx->w2);CHKERRQ(ierr);
ierr = VecAXPY(y,tau,ctx->w2);CHKERRQ(ierr);
}
else {
/* standard eigenproblem: y = (A + tI)x */
ierr = MatMult(st->A,x,y);CHKERRQ(ierr);
ierr = VecAXPY(y,tau,x);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "STBackTransform_Cayley"
PetscErrorCode STBackTransform_Cayley(ST st,PetscScalar *eigr,PetscScalar *eigi)
{
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
#ifndef PETSC_USE_COMPLEX
PetscScalar t,i,r;
PetscFunctionBegin;
PetscValidPointer(eigr,2);
PetscValidPointer(eigi,3);
if (*eigi == 0.0) *eigr = (ctx->tau + *eigr * st->sigma) / (*eigr - 1.0);
else {
r = *eigr;
i = *eigi;
r = st->sigma * (r * r + i * i - r) + ctx->tau * (r - 1);
i = - st->sigma * i - ctx->tau * i;
t = i * i + r * (r - 2.0) + 1.0;
*eigr = r / t;
*eigi = i / t;
}
#else
PetscFunctionBegin;
PetscValidPointer(eigr,2);
*eigr = (ctx->tau + *eigr * st->sigma) / (*eigr - 1.0);
#endif
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "STPostSolve_Cayley"
PetscErrorCode STPostSolve_Cayley(ST st)
{
PetscErrorCode ierr;
PetscFunctionBegin;
if (st->shift_matrix == STMATMODE_INPLACE) {
if (st->B) {
ierr = MatAXPY(st->A,st->sigma,st->B,st->str);CHKERRQ(ierr);
} else {
ierr = MatShift(st->A,st->sigma); CHKERRQ(ierr);
}
st->setupcalled = 0;
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "STSetUp_Cayley"
PetscErrorCode STSetUp_Cayley(ST st)
{
PetscErrorCode ierr;
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
PetscFunctionBegin;
if (st->mat) { ierr = MatDestroy(st->mat);CHKERRQ(ierr); }
if (!ctx->tau_set) { ctx->tau = st->sigma; }
if (ctx->tau == 0.0 && st->sigma == 0.0) {
SETERRQ(1,"Values of shift and antishift cannot be zero simultaneously");
}
switch (st->shift_matrix) {
case STMATMODE_INPLACE:
st->mat = PETSC_NULL;
if (st->sigma != 0.0) {
if (st->B) {
ierr = MatAXPY(st->A,-st->sigma,st->B,st->str);CHKERRQ(ierr);
} else {
ierr = MatShift(st->A,-st->sigma);CHKERRQ(ierr);
}
}
/* In the following line, the SAME_NONZERO_PATTERN flag has been used to
* improve performance when solving a number of related eigenproblems */
ierr = KSPSetOperators(st->ksp,st->A,st->A,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
break;
case STMATMODE_SHELL:
ierr = STMatShellCreate(st,&st->mat);CHKERRQ(ierr);
ierr = KSPSetOperators(st->ksp,st->mat,st->mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
break;
default:
ierr = MatDuplicate(st->A,MAT_COPY_VALUES,&st->mat);CHKERRQ(ierr);
if (st->sigma != 0.0) {
if (st->B) {
ierr = MatAXPY(st->mat,-st->sigma,st->B,st->str);CHKERRQ(ierr);
} else {
ierr = MatShift(st->mat,-st->sigma);CHKERRQ(ierr);
}
}
/* In the following line, the SAME_NONZERO_PATTERN flag has been used to
* improve performance when solving a number of related eigenproblems */
ierr = KSPSetOperators(st->ksp,st->mat,st->mat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
}
if (st->B) {
if (ctx->w2) { ierr = VecDestroy(ctx->w2);CHKERRQ(ierr); }
ierr = MatGetVecs(st->B,&ctx->w2,PETSC_NULL);CHKERRQ(ierr);
}
ierr = KSPSetUp(st->ksp);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "STSetShift_Cayley"
PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)
{
PetscErrorCode ierr;
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
PetscFunctionBegin;
/* Nothing to be done if STSetUp has not been called yet */
if (!st->setupcalled) PetscFunctionReturn(0);
switch (st->shift_matrix) {
case STMATMODE_INPLACE:
/* Undo previous operations */
if (st->sigma != 0.0) {
if (st->B) {
ierr = MatAXPY(st->A,st->sigma,st->B,st->str);CHKERRQ(ierr);
} else {
ierr = MatShift(st->A,st->sigma);CHKERRQ(ierr);
}
}
/* Apply new shift */
if (newshift != 0.0) {
if (st->B) {
ierr = MatAXPY(st->A,-newshift,st->B,st->str);CHKERRQ(ierr);
} else {
ierr = MatShift(st->A,-newshift);CHKERRQ(ierr);
}
}
ierr = KSPSetOperators(st->ksp,st->A,st->A,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
break;
case STMATMODE_SHELL:
ierr = KSPSetOperators(st->ksp,st->mat,st->mat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
break;
default:
ierr = MatCopy(st->A, st->mat,SUBSET_NONZERO_PATTERN); CHKERRQ(ierr);
if (newshift != 0.0) {
if (st->B) { ierr = MatAXPY(st->mat,-newshift,st->B,st->str);CHKERRQ(ierr); }
else { ierr = MatShift(st->mat,-newshift);CHKERRQ(ierr); }
}
/* In the following line, the SAME_NONZERO_PATTERN flag has been used to
* improve performance when solving a number of related eigenproblems */
ierr = KSPSetOperators(st->ksp,st->mat,st->mat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
}
st->sigma = newshift;
if (!ctx->tau_set) { ctx->tau = newshift; }
ierr = KSPSetUp(st->ksp);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "STSetFromOptions_Cayley"
PetscErrorCode STSetFromOptions_Cayley(ST st)
{
PetscErrorCode ierr;
PetscScalar tau;
PetscTruth flg;
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
PetscFunctionBegin;
ierr = PetscOptionsHead("ST Cayley Options");CHKERRQ(ierr);
ierr = PetscOptionsScalar("-st_antishift","Value of the antishift","STSetAntishift",ctx->tau,&tau,&flg); CHKERRQ(ierr);
if (flg) {
ierr = STCayleySetAntishift(st,tau);CHKERRQ(ierr);
}
ierr = PetscOptionsTail();CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "STCayleySetAntishift_Cayley"
PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)
{
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
PetscFunctionBegin;
ctx->tau = newshift;
ctx->tau_set = PETSC_TRUE;
PetscFunctionReturn(0);
}
EXTERN_C_END
#undef __FUNCT__
#define __FUNCT__ "STCayleySetAntishift"
/*@
STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
spectral transformation.
Collective on ST
Input Parameters:
+ st - the spectral transformation context
- tau - the anti-shift
Options Database Key:
. -st_antishift - Sets the value of the anti-shift
Level: intermediate
Note:
In the generalized Cayley transform, the operator can be expressed as
OP = inv(A - sigma B)*(A + tau B). This function sets the value of tau.
Use STSetShift() for setting sigma.
.seealso: STSetShift()
@*/
PetscErrorCode STCayleySetAntishift(ST st,PetscScalar tau)
{
PetscErrorCode ierr, (*f)(ST,PetscScalar);
PetscFunctionBegin;
PetscValidHeaderSpecific(st,ST_COOKIE,1);
ierr = PetscObjectQueryFunction((PetscObject)st,"STCayleySetAntishift_C",(void (**)(void))&f);CHKERRQ(ierr);
if (f) {
ierr = (*f)(st,tau);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "STView_Cayley"
PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
{
PetscErrorCode ierr;
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
PetscFunctionBegin;
#if !defined(PETSC_USE_COMPLEX)
ierr = PetscViewerASCIIPrintf(viewer," antishift: %g\n",ctx->tau);CHKERRQ(ierr);
#else
ierr = PetscViewerASCIIPrintf(viewer," antishift: %g+%g i\n",PetscRealPart(ctx->tau),PetscImaginaryPart(ctx->tau));CHKERRQ(ierr);
#endif
ierr = STView_Default(st,viewer);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "STDestroy_Cayley"
PetscErrorCode STDestroy_Cayley(ST st)
{
PetscErrorCode ierr;
ST_CAYLEY *ctx = (ST_CAYLEY *) st->data;
PetscFunctionBegin;
if (ctx->w2) { ierr = VecDestroy(ctx->w2);CHKERRQ(ierr); }
ierr = PetscFree(ctx);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "STCreate_Cayley"
PetscErrorCode STCreate_Cayley(ST st)
{
PetscErrorCode ierr;
ST_CAYLEY *ctx;
PetscFunctionBegin;
ierr = PetscNew(ST_CAYLEY,&ctx); CHKERRQ(ierr);
PetscLogObjectMemory(st,sizeof(ST_CAYLEY));
st->data = (void *) ctx;
st->ops->apply = STApply_Cayley;
st->ops->applyB = STApplyB_Cayley;
st->ops->applytrans = STApplyTranspose_Cayley;
st->ops->postsolve = STPostSolve_Cayley;
st->ops->backtr = STBackTransform_Cayley;
st->ops->setfromoptions = STSetFromOptions_Cayley;
st->ops->setup = STSetUp_Cayley;
st->ops->setshift = STSetShift_Cayley;
st->ops->destroy = STDestroy_Cayley;
st->ops->view = STView_Cayley;
st->checknullspace = STCheckNullSpace_Default;
ctx->tau = 0.0;
ctx->tau_set = PETSC_FALSE;
ierr = PetscObjectComposeFunctionDynamic((PetscObject)st,"STCayleySetAntishift_C","STCayleySetAntishift_Cayley",
STCayleySetAntishift_Cayley);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_END