/*
SLEPc eigensolver: "davidson"
Step: improve the eigenvectors X
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SLEPc - Scalable Library for Eigenvalue Problem Computations
Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain
This file is part of SLEPc.
SLEPc is free software: you can redistribute it and/or modify it under the
terms of version 3 of the GNU Lesser General Public License as published by
the Free Software Foundation.
SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
more details.
You should have received a copy of the GNU Lesser General Public License
along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/
#include "davidson.h"
#include <slepcvec.h>
PetscErrorCode dvd_improvex_PfuncV(dvdDashboard *d, void *funcV, Vec *D,
PetscInt max_size_D, PetscInt r_s, PetscInt r_e, Vec *auxV,
PetscScalar *auxS);
PetscErrorCode dvd_matmult_jd(Mat A, Vec in, Vec out);
PetscErrorCode dvd_matgetvecs_jd(Mat A, Vec *right, Vec *left);
PetscErrorCode dvd_improvex_jd_d(dvdDashboard *d);
PetscErrorCode dvd_improvex_jd_start(dvdDashboard *d);
PetscErrorCode dvd_improvex_jd_end(dvdDashboard *d);
PetscErrorCode dvd_improvex_jd_gen(dvdDashboard *d, Vec *D,
PetscInt max_size_D, PetscInt r_s,
PetscInt r_e, PetscInt *size_D);
PetscErrorCode dvd_improvex_jd_proj_uv_KBXX(dvdDashboard *d, PetscInt i_s,
PetscInt i_e, Vec **u, Vec **v, Vec **kr, Vec **auxV_, PetscScalar *theta,
PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld);
PetscErrorCode dvd_improvex_jd_proj_uv_KBXY(dvdDashboard *d, PetscInt i_s,
PetscInt i_e, Vec **u, Vec **v, Vec **kr, Vec **auxV_, PetscScalar *theta,
PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld);
PetscErrorCode dvd_improvex_jd_proj_uv_KBXZ(dvdDashboard *d, PetscInt i_s,
PetscInt i_e, Vec **u, Vec **v, Vec **kr, Vec **auxV_, PetscScalar *theta,
PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld);
PetscErrorCode dvd_improvex_jd_proj_uv_KBXZY(dvdDashboard *d, PetscInt i_s,
PetscInt i_e, Vec **u, Vec **v, Vec **kr, Vec **auxV_, PetscScalar *theta,
PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld);
PetscErrorCode dvd_improvex_jd_lit_const_0(dvdDashboard *d, PetscInt i,
PetscScalar* theta, PetscScalar* thetai,
PetscInt *maxits, PetscReal *tol);
PetscErrorCode dvd_improvex_get_eigenvectors(dvdDashboard *d, PetscScalar *pX,
PetscScalar *pY, PetscInt ld_,
PetscScalar *auxS, PetscInt size_auxS);
#define size_Z (64*4)
/**** JD update step (I - Kfg'/(g'Kf)) K(A - sB) (I - Kfg'/(g'Kf)) t = (I - Kfg'/(g'Kf))r ****/
typedef struct {
PetscInt size_X;
void
*old_improveX_data; /* old improveX_data */
improveX_type
old_improveX; /* old improveX */
KSP ksp; /* correction equation solver */
Vec *u,*v, /* the projector is (I-v*u') */
friends, /* reference vector for composite vectors */
*auxV; /* auxiliar vectors */
PetscScalar *theta,
*thetai; /* the shifts used in the correction eq. */
PetscInt maxits, /* maximum number of iterations */
r_s, r_e, /* the selected eigenpairs to improve */
n_uv, /* number of vectors u, v and kr */
ksp_max_size; /* the ksp maximum subvectors size */
PetscReal tol, /* the maximum solution tolerance */
fix; /* tolerance for using the approx. eigenvalue */
dvdDashboard
*d; /* the currect dvdDashboard reference */
PC old_pc; /* old pc in ksp */
} dvdImprovex_jd;
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd"
PetscErrorCode dvd_improvex_jd(dvdDashboard *d, dvdBlackboard *b, KSP ksp,
PetscInt max_bs)
{
PetscErrorCode ierr;
dvdImprovex_jd *data;
PetscBool t;
PC pc;
PetscFunctionBegin;
/* Setting configuration constrains */
/* If the arithmetic is real and the problem is not Hermitian, then
the block size is incremented in one */
#if !defined(PETSC_USE_COMPLEX)
if (DVD_ISNOT(d->sEP, DVD_EP_HERMITIAN)) {
max_bs++;
b->max_size_X = PetscMax(b->max_size_X, max_bs);
}
#endif
b->max_size_auxV = PetscMax(b->max_size_auxV, b->max_size_X*4); /* u,v,kr,
auxV */
b->max_size_auxS = PetscMax(b->max_size_auxS,
b->max_size_X*3 + /* theta, thetai */
2*b->max_size_V*b->max_size_V + /* pX, pY */
11*b->max_size_V+4*b->max_size_V*b->max_size_V
/* dvd_improvex_get_eigenvectors */
);
/* Setup the preconditioner */
if (ksp) {
ierr = KSPGetPC(ksp, &pc); CHKERRQ(ierr);
ierr = dvd_static_precond_PC(d, b, pc); CHKERRQ(ierr);
} else {
ierr = dvd_static_precond_PC(d, b, 0); CHKERRQ(ierr);
}
/* Setup the step */
if (b->state >= DVD_STATE_CONF) {
ierr = PetscMalloc(sizeof(dvdImprovex_jd), &data); CHKERRQ(ierr);
data->size_X = b->max_size_X;
data->old_improveX_data = d->improveX_data;
d->improveX_data = data;
data->old_improveX = d->improveX;
ierr = PetscTypeCompare((PetscObject)ksp, KSPPREONLY, &t); CHKERRQ(ierr);
data->ksp = t?0:ksp;
data->d = d;
d->improveX = dvd_improvex_jd_gen;
data->ksp_max_size = max_bs;
/* Create the reference vector */
ierr = VecCreateCompWithVecs(d->V, max_bs, PETSC_NULL, &data->friends);
CHKERRQ(ierr);
DVD_FL_ADD(d->startList, dvd_improvex_jd_start);
DVD_FL_ADD(d->endList, dvd_improvex_jd_end);
DVD_FL_ADD(d->destroyList, dvd_improvex_jd_d);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_start"
PetscErrorCode dvd_improvex_jd_start(dvdDashboard *d)
{
PetscErrorCode ierr;
dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
PetscInt rA, cA, rlA, clA;
Mat A;
PetscBool t;
PC pc;
PetscFunctionBegin;
/* Setup the ksp */
if(data->ksp) {
/* Save the current pc and set a PCNONE */
ierr = KSPGetPC(data->ksp, &data->old_pc); CHKERRQ(ierr);
ierr = PetscTypeCompare((PetscObject)data->old_pc, PCNONE, &t);
CHKERRQ(ierr);
if (t) {
data->old_pc = 0;
} else {
ierr = PetscObjectReference((PetscObject)data->old_pc); CHKERRQ(ierr);
ierr = PCCreate(((PetscObject)d->eps)->comm, &pc); CHKERRQ(ierr);
ierr = PCSetType(pc, PCNONE); CHKERRQ(ierr);
ierr = PCSetOperators(pc, d->A, d->A, SAME_PRECONDITIONER); CHKERRQ(ierr);
ierr = KSPSetPC(data->ksp, pc); CHKERRQ(ierr);
ierr = PCDestroy(&pc); CHKERRQ(ierr);
}
/* Create the (I-v*u')*K*(A-s*B) matrix */
ierr = MatGetSize(d->A, &rA, &cA); CHKERRQ(ierr);
ierr = MatGetLocalSize(d->A, &rlA, &clA); CHKERRQ(ierr);
ierr = MatCreateShell(((PetscObject)d->A)->comm, rlA*data->ksp_max_size,
clA*data->ksp_max_size, rA*data->ksp_max_size,
cA*data->ksp_max_size, data, &A); CHKERRQ(ierr);
ierr = MatShellSetOperation(A, MATOP_MULT,
(void(*)(void))dvd_matmult_jd); CHKERRQ(ierr);
ierr = MatShellSetOperation(A, MATOP_GET_VECS,
(void(*)(void))dvd_matgetvecs_jd);
CHKERRQ(ierr);
ierr = KSPSetOperators(data->ksp, A, A, SAME_PRECONDITIONER);
CHKERRQ(ierr);
ierr = KSPSetUp(data->ksp); CHKERRQ(ierr);
ierr = MatDestroy(&A); CHKERRQ(ierr);
} else
data->old_pc = 0;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_end"
PetscErrorCode dvd_improvex_jd_end(dvdDashboard *d)
{
PetscErrorCode ierr;
dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
PetscFunctionBegin;
/* Restore the pc of ksp */
if (data->old_pc) {
ierr = KSPSetPC(data->ksp, data->old_pc); CHKERRQ(ierr);
ierr = PCDestroy(&data->old_pc); CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_d"
PetscErrorCode dvd_improvex_jd_d(dvdDashboard *d)
{
PetscErrorCode ierr;
dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
PetscFunctionBegin;
/* Restore changes in dvdDashboard */
d->improveX_data = data->old_improveX_data;
/* Free local data and objects */
ierr = VecDestroy(&data->friends); CHKERRQ(ierr);
ierr = PetscFree(data); CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_gen"
PetscErrorCode dvd_improvex_jd_gen(dvdDashboard *d, Vec *D,
PetscInt max_size_D, PetscInt r_s,
PetscInt r_e, PetscInt *size_D)
{
dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
PetscErrorCode ierr;
PetscInt i, j, n, maxits, maxits0, lits, s;
PetscScalar a, *pX, *pY, *auxS = d->auxS;
PetscReal tol, tol0;
Vec *u, *v, *kr, kr_comp, D_comp;
PetscFunctionBegin;
/* Quick exit */
if ((max_size_D == 0) || r_e-r_s <= 0) {
/* Callback old improveX */
if (data->old_improveX) {
d->improveX_data = data->old_improveX_data;
data->old_improveX(d, PETSC_NULL, 0, 0, 0, PETSC_NULL);
d->improveX_data = data;
}
PetscFunctionReturn(0);
}
n = PetscMin(PetscMin(data->size_X, max_size_D), r_e-r_s);
if (n == 0) SETERRQ(PETSC_COMM_SELF,1, "n == 0!\n");
if (data->size_X < r_e-r_s) SETERRQ(PETSC_COMM_SELF,1, "size_X < r_e-r_s!\n");
/* Compute the eigenvectors of the selected pairs */
pX = auxS; auxS+= d->size_H*d->size_H;
pY = auxS; auxS+= d->size_H*d->size_H;
ierr = dvd_improvex_get_eigenvectors(d, pX, pY, d->size_H, auxS,
d->size_auxS-(auxS-d->auxS));
CHKERRQ(ierr);
for(i=0, s=0; i<n; i+=s) {
/* If the selected eigenvalue is complex, but the arithmetic is real... */
#if !defined(PETSC_USE_COMPLEX)
if (PetscAbsScalar(d->eigi[i] != 0.0)) {
if (i+2 <= max_size_D) s=2; else break;
} else
#endif
s=1;
data->auxV = d->auxV;
data->r_s = r_s+i; data->r_e = r_s+i+s;
data->n_uv = s;
data->theta = auxS; data->thetai = auxS+2*s;
/* Compute theta, maximum iterations and tolerance */
maxits = 0; tol = 1;
for(j=0; j<s; j++) {
ierr = d->improvex_jd_lit(d, r_s+i+j, &data->theta[2*j],
&data->thetai[j], &maxits0, &tol0);
CHKERRQ(ierr);
maxits+= maxits0; tol*= tol0;
}
maxits/= s; tol = exp(log(tol)/s);
/* Compute u, v and kr */
ierr = d->improvex_jd_proj_uv(d, r_s+i, r_s+i+s, &u, &v, &kr,
&data->auxV, data->theta, data->thetai,
&pX[d->size_H*(r_s+i)],
&pY[d->size_H*(r_s+i)], d->size_H);
CHKERRQ(ierr);
data->u = u; data->v = v;
/* Check if the first eigenpairs are converged */
if (i == 0) {
ierr = d->preTestConv(d, 0, s, s, PETSC_NULL, PETSC_NULL, &d->npreconv);
CHKERRQ(ierr);
if (d->npreconv > 0) break;
}
/* Compute kr <- kr - u*(v'*kr) */
for(j=0; j<s; j++) {
ierr = VecDot(kr[j], v[j], &a); CHKERRQ(ierr);
ierr = VecAXPY(kr[j], -a, u[j]); CHKERRQ(ierr);
ierr = VecScale(kr[j], -1.0); CHKERRQ(ierr);
}
/* If KSP==0, D <- kr */
if (!data->ksp) {
for(j=0; j<s; j++) {
ierr = VecCopy(kr[j], D[j+i]); CHKERRQ(ierr);
}
} else {
/* Compouse kr and D */
ierr = VecCreateCompWithVecs(kr, data->ksp_max_size, data->friends,
&kr_comp); CHKERRQ(ierr);
ierr = VecCreateCompWithVecs(&D[i], data->ksp_max_size, data->friends,
&D_comp); CHKERRQ(ierr);
ierr = VecCompSetVecs(data->friends, PETSC_NULL, s); CHKERRQ(ierr);
/* Solve the correction equation */
ierr = KSPSetTolerances(data->ksp, tol, PETSC_DEFAULT, PETSC_DEFAULT,
maxits); CHKERRQ(ierr);
ierr = KSPSolve(data->ksp, kr_comp, D_comp); CHKERRQ(ierr);
ierr = KSPGetIterationNumber(data->ksp, &lits); CHKERRQ(ierr);
d->eps->OP->lineariterations+= lits;
/* Destroy the composed ks and D */
ierr = VecDestroy(&kr_comp); CHKERRQ(ierr);
ierr = VecDestroy(&D_comp); CHKERRQ(ierr);
}
}
*size_D = i;
/* Callback old improveX */
if (data->old_improveX) {
d->improveX_data = data->old_improveX_data;
data->old_improveX(d, PETSC_NULL, 0, 0, 0, PETSC_NULL);
d->improveX_data = data;
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_matmult_jd"
PetscErrorCode dvd_matmult_jd(Mat A, Vec in, Vec out)
{
PetscErrorCode ierr;
dvdImprovex_jd *data;
PetscScalar a;
PetscInt n, i;
const Vec *inx, *outx, *Bx;
PetscFunctionBegin;
ierr = MatShellGetContext(A, (void**)&data); CHKERRQ(ierr);
ierr = VecCompGetVecs(in, &inx, PETSC_NULL); CHKERRQ(ierr);
ierr = VecCompGetVecs(out, &outx, PETSC_NULL); CHKERRQ(ierr);
n = data->r_e - data->r_s;
/* aux <- theta[1]A*in - theta[0]*B*in */
for(i=0; i<n; i++) {
ierr = MatMult(data->d->A, inx[i], data->auxV[i]); CHKERRQ(ierr);
}
if (data->d->B) {
for(i=0; i<n; i++) {
ierr = MatMult(data->d->B, inx[i], outx[i]); CHKERRQ(ierr);
}
Bx = outx;
} else
Bx = inx;
for(i=0; i<n; i++) {
#if !defined(PETSC_USE_COMPLEX)
if(data->d->eigi[data->r_s+i] != 0.0) {
/* aux_i <- [ t_2i+1*A*inx_i - t_2i*Bx_i + ti_i*Bx_i+1;
aux_i+1 t_2i+1*A*inx_i+1 - ti_i*Bx_i - t_2i*Bx_i+1 ] */
ierr = VecAXPBYPCZ(data->auxV[i], -data->theta[2*i], data->thetai[i],
data->theta[2*i+1], Bx[i], Bx[i+1]);
CHKERRQ(ierr);
ierr = VecAXPBYPCZ(data->auxV[i+1], -data->thetai[i],
-data->theta[2*i], data->theta[2*i+1], Bx[i],
Bx[i+1]); CHKERRQ(ierr);
i++;
} else
#endif
{
ierr = VecAXPBY(data->auxV[i], -data->theta[i*2], data->theta[i*2+1],
Bx[i]); CHKERRQ(ierr);
}
}
/* out <- K * aux */
for(i=0; i<n; i++) {
ierr = data->d->improvex_precond(data->d, data->r_s+i, data->auxV[i],
outx[i]); CHKERRQ(ierr);
}
/* out <- out - u*(v'*out) */
for(i=0; i<n; i++) {
ierr = VecDot(outx[i], data->v[i], &a); CHKERRQ(ierr);
ierr = VecAXPY(outx[i], -a, data->u[i]); CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_matgetvecs_jd"
PetscErrorCode dvd_matgetvecs_jd(Mat A, Vec *right, Vec *left)
{
PetscErrorCode ierr;
Vec *r, *l;
dvdImprovex_jd *data;
PetscInt n, i;
PetscFunctionBegin;
ierr = MatShellGetContext(A, (void**)&data); CHKERRQ(ierr);
n = data->ksp_max_size;
if (right) {
ierr = PetscMalloc(sizeof(Vec)*n, &r); CHKERRQ(ierr);
}
if (left) {
ierr = PetscMalloc(sizeof(Vec)*n, &l); CHKERRQ(ierr);
}
for (i=0; i<n; i++) {
ierr = MatGetVecs(data->d->A, right?&r[i]:PETSC_NULL,
left?&l[i]:PETSC_NULL); CHKERRQ(ierr);
}
if(right) {
ierr = VecCreateCompWithVecs(r, n, data->friends, right); CHKERRQ(ierr);
for (i=0; i<n; i++) {
ierr = VecDestroy(&r[i]); CHKERRQ(ierr);
}
}
if(left) {
ierr = VecCreateCompWithVecs(l, n, data->friends, left); CHKERRQ(ierr);
for (i=0; i<n; i++) {
ierr = VecDestroy(&l[i]); CHKERRQ(ierr);
}
}
if (right) {
ierr = PetscFree(r); CHKERRQ(ierr);
}
if (left) {
ierr = PetscFree(l); CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_proj_uv"
PetscErrorCode dvd_improvex_jd_proj_uv(dvdDashboard *d, dvdBlackboard *b,
ProjType_t p)
{
PetscFunctionBegin;
/* Setup the step */
if (b->state >= DVD_STATE_CONF) {
switch(p) {
case DVD_PROJ_KBXX:
d->improvex_jd_proj_uv = dvd_improvex_jd_proj_uv_KBXX; break;
case DVD_PROJ_KBXY:
d->improvex_jd_proj_uv = dvd_improvex_jd_proj_uv_KBXY; break;
case DVD_PROJ_KBXZ:
d->improvex_jd_proj_uv = dvd_improvex_jd_proj_uv_KBXZ; break;
case DVD_PROJ_KBXZY:
d->improvex_jd_proj_uv = dvd_improvex_jd_proj_uv_KBXZY; break;
}
}
PetscFunctionReturn(0);
}
#define DVD_COMPLEX_RAYLEIGH_QUOTIENT(ur,ui,Axr,Axi,Bxr,Bxi,eigr,eigi,b,ierr)\
{ \
ierr = VecDot((Axr), (ur), &(b)[0]); CHKERRQ(ierr); /* r*A*r */ \
ierr = VecDot((Axr), (ui), &(b)[1]); CHKERRQ(ierr); /* i*A*r */ \
ierr = VecDot((Axi), (ur), &(b)[2]); CHKERRQ(ierr); /* r*A*i */ \
ierr = VecDot((Axi), (ui), &(b)[3]); CHKERRQ(ierr); /* i*A*i */ \
ierr = VecDot((Bxr), (ur), &(b)[4]); CHKERRQ(ierr); /* r*B*r */ \
ierr = VecDot((Bxr), (ui), &(b)[5]); CHKERRQ(ierr); /* i*B*r */ \
ierr = VecDot((Bxi), (ur), &(b)[6]); CHKERRQ(ierr); /* r*B*i */ \
ierr = VecDot((Bxi), (ui), &(b)[7]); CHKERRQ(ierr); /* i*B*i */ \
(b)[0] = (b)[0]+(b)[3]; /* rAr+iAi */ \
(b)[2] = (b)[2]-(b)[1]; /* rAi-iAr */ \
(b)[4] = (b)[4]+(b)[7]; /* rBr+iBi */ \
(b)[6] = (b)[6]-(b)[5]; /* rBi-iBr */ \
(b)[7] = (b)[4]*(b)[4] + (b)[6]*(b)[6]; /* k */ \
*(eigr) = ((b)[0]*(b)[4] + (b)[2]*(b)[6]) / (b)[7]; /* eig_r */ \
*(eigi) = ((b)[2]*(b)[4] - (b)[0]*(b)[6]) / (b)[7]; /* eig_i */ \
}
#if !defined(PETSC_USE_COMPLEX)
#define DVD_COMPUTE_N_RR(eps,i,i_s,n,eigr,eigi,u,Ax,Bx,b,ierr) \
for((i)=0; (i)<(n); (i)++) { \
if ((eigi)[(i_s)+(i)] != 0.0) { \
/* eig_r = [(rAr+iAi)*(rBr+iBi) + (rAi-iAr)*(rBi-iBr)]/k \
eig_i = [(rAi-iAr)*(rBr+iBi) - (rAr+iAi)*(rBi-iBr)]/k \
k = (rBr+iBi)*(rBr+iBi) + (rBi-iBr)*(rBi-iBr) */ \
DVD_COMPLEX_RAYLEIGH_QUOTIENT((u)[(i)], (u)[(i)+1], (Ax)[(i)], \
(Ax)[(i)+1], (Bx)[(i)], (Bx)[(i)+1], &(b)[8], &(b)[9], (b), (ierr)); \
if (PetscAbsScalar((eigr)[(i_s)+(i)] - (b)[8])/ \
PetscAbsScalar((eigr)[(i_s)+(i)]) > 1e-10 || \
PetscAbsScalar((eigi)[(i_s)+(i)] - (b)[9])/ \
PetscAbsScalar((eigi)[(i_s)+(i)]) > 1e-10 ) { \
(ierr) = PetscInfo4((eps), "The eigenvalue %g+%g is far from its "\
"Rayleigh quotient value %g+%g\n", \
(eigr)[(i_s)+(i)], \
(eigi)[(i_s)+1], (b)[8], (b)[9]); \
} \
(i)++; \
} \
}
#else
#define DVD_COMPUTE_N_RR(eps,i,i_s,n,eigr,eigi,u,Ax,Bx,b,ierr) \
for((i)=0; (i)<(n); (i)++) { \
(ierr) = VecDot((Ax)[(i)], (u)[(i)], &(b)[0]); CHKERRQ(ierr); \
(ierr) = VecDot((Bx)[(i)], (u)[(i)], &(b)[1]); CHKERRQ(ierr); \
(b)[0] = (b)[0]/(b)[1]; \
if (PetscAbsScalar((eigr)[(i_s)+(i)] - (b)[0])/ \
PetscAbsScalar((eigr)[(i_s)+(i)]) > 1e-10 ) { \
(ierr) = PetscInfo4((eps), "The eigenvalue %g+%g is far from its " \
"Rayleigh quotient value %g+%g\n", \
PetscRealPart((eigr)[(i_s)+(i)]), \
PetscImaginaryPart((eigr)[(i_s)+(i)]), PetscRealPart((b)[0]), \
PetscImaginaryPart((b)[0])); \
} \
}
#endif
#if !defined(PETSC_USE_COMPLEX)
#define DVD_NORM_FOR_UV(x) PetscAbsScalar(x)
#else
#define DVD_NORM_FOR_UV(x) (x)
#endif
#define DVD_NORMALIZE_UV(u,v,ierr,a) { \
(ierr) = VecDot((u), (v), &(a)); CHKERRQ(ierr); \
if ((a) == 0.0) { \
SETERRQ(((PetscObject)u)->comm,1, "Inappropriate approximate eigenvector norm"); \
} \
if ((u) == (v)) { \
ierr = VecScale((u), 1.0/PetscSqrtScalar(DVD_NORM_FOR_UV(a))); \
CHKERRQ(ierr); \
} else { \
ierr = VecScale((u), 1.0/(a)); CHKERRQ(ierr); \
} \
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_proj_uv_KBXZ"
/*
Compute: u <- K^{-1}*B*X, v <- (theta[0]*A+theta[1]*B)*X,
kr <- K^{-1}*(A-eig*B)*X, being X <- V*pX[i_s..i_e-1],
where
auxV, 4*(i_e-i_s) auxiliar global vectors
pX,pY, the right and left eigenvectors of the projected system
ld, the leading dimension of pX and pY
*/
PetscErrorCode dvd_improvex_jd_proj_uv_KBXZ(dvdDashboard *d, PetscInt i_s,
PetscInt i_e, Vec **u, Vec **v, Vec **kr, Vec **auxV_, PetscScalar *theta,
PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld)
{
PetscErrorCode ierr;
PetscInt n = i_e - i_s, i;
PetscScalar a, b[16];
Vec *Ax, *Bx, *r, *auxV = *auxV_, X[4];
/* The memory manager doen't allow to call a subroutines */
PetscScalar Z[size_Z];
PetscFunctionBegin;
/* Book space for u, v and kr */
*u = auxV; auxV+= n;
*kr = auxV; auxV+= n;
*v = auxV; auxV+= n;
/* Ax = v, Bx = r = auxV */
Ax = *v;
r = Bx = auxV; auxV+= n;
/* Ax <- A*X(i) */
ierr = SlepcUpdateVectorsZ(Ax, 0.0, 1.0, d->AV, d->size_AV, pX, ld,
d->size_H, n); CHKERRQ(ierr);
/* Bx <- B*X(i) */
for(i=i_s; i<i_e; i++) d->nX[i] = 1.0;
if (d->BV) {
ierr = SlepcUpdateVectorsZ(Bx, 0.0, 1.0, d->BV, d->size_BV, pX, ld,
d->size_H, n); CHKERRQ(ierr);
} else {
ierr = SlepcUpdateVectorsZ(d->B?*u:Bx, 0.0, 1.0, d->V, d->size_V, pX, ld,
d->size_H, n); CHKERRQ(ierr);
if (d->B) {
for(i=0; i<n; i++) {
ierr = MatMult(d->B, (*u)[i], Bx[i]); CHKERRQ(ierr);
}
}
}
/* Recompute the eigenvalue */
ierr = SlepcUpdateVectorsZ(*u, 0.0, 1.0, d->W?d->W:d->V, d->size_V, pY, ld,
d->size_H, n); CHKERRQ(ierr);
DVD_COMPUTE_N_RR(d->eps, i, i_s, n, d->eigr, d->eigi, *u, Ax, Bx, b, ierr);
/* u <- K^{-1} Bx */
for(i=0; i<n; i++) {
ierr = d->improvex_precond(d, i_s+i, Bx[i], (*u)[i]); CHKERRQ(ierr);
}
for(i=0; i<n; i++) {
if (d->eigi[i_s+i] == 0.0) {
/* [v r] <- [Ax Bx][theta_2i' 1 ]
[theta_2i+1 -eig] */
b[0] = PetscConj(theta[i*2]); b[1] = theta[2*i+1];
b[2] = 1.0; b[3] = -d->eigr[i_s+i];
ierr = SlepcUpdateVectorsS(&(*v)[i], n, 0.0, 1.0, &(*v)[i], 2*n, n,
b, 2, 2, 2); CHKERRQ(ierr);
} else {
/* [v_i v_i+1 r_i r_i+1]*= [tau_0' 0 1 0
0 tau_0' 0 1
tau_1 0 -eigr_i -eigi_i
0 tau_1 eigi_i -eigr_i ] */
b[0] = b[5] = PetscConj(theta[2*i]);
b[2] = b[7] = theta[2*i+1];
b[8] = b[13] = 1.0;
b[10] = b[15] = -d->eigr[i_s+i];
b[14] = -(b[11] = d->eigi[i_s+i]);
b[1] = b[3] = b[4] = b[6] = b[9] = b[12] = 0.0;
X[0] = (*v)[i]; X[1] = (*v)[i+1]; X[2] = r[i]; X[3] = r[i+1];
ierr = SlepcUpdateVectorsD(X, 4, 1.0, b, 4, 4, 4, Z, size_Z);
CHKERRQ(ierr);
i++;
}
}
/* kr <- K^{-1}*r */
d->calcpairs_proj_res(d, i_s, i_e, r);
for(i=0; i<n; i++) {
ierr = d->improvex_precond(d, i_s+i, r[i], (*kr)[i]); CHKERRQ(ierr);
}
/* Free r */
auxV-= n;
/* Normalize the projector */
for(i=0; i<n; i++) DVD_NORMALIZE_UV((*u)[i],(*v)[i],ierr,a);
/* Return the next free vector */
*auxV_ = auxV;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_proj_uv_KBXZY"
/*
Compute: u <- K^{-1}*B*X, v <- (theta[0]*A+theta[1]*B)*Y,
kr <- K^{-1}*(A-eig*B)*X, being X <- V*pX[i_s..i_e-1], Y <- W*pY[i_s..i_e-1]
where
auxV, 4*(i_e-i_s) auxiliar global vectors
pX,pY, the right and left eigenvectors of the projected system
ld, the leading dimension of pX and pY
*/
PetscErrorCode dvd_improvex_jd_proj_uv_KBXZY(dvdDashboard *d, PetscInt i_s,
PetscInt i_e, Vec **u, Vec **v, Vec **kr, Vec **auxV_, PetscScalar *theta,
PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld)
{
PetscErrorCode ierr;
PetscInt n = i_e - i_s, i;
PetscScalar a, b[16];
Vec *Ax, *Bx, *r, *auxV = *auxV_, X[4];
/* The memory manager doen't allow to call a subroutines */
PetscScalar Z[size_Z];
PetscFunctionBegin;
/* Book space for u, v and kr */
*u = auxV; auxV+= n;
*kr = auxV; auxV+= n;
*v = auxV; auxV+= n;
r = auxV; auxV+= n;
/* u <- Y(i) */
ierr = SlepcUpdateVectorsZ(*u, 0.0, 1.0, d->W?d->W:d->V, d->size_V, pY, ld,
d->size_H, n); CHKERRQ(ierr);
/* v <- theta[0]A*u + theta[1]*B*u */
for(i=0; i<n; i++) {
ierr = MatMult(d->A, (*u)[i], (*v)[i]); CHKERRQ(ierr);
}
if (d->B) {
for(i=0; i<n; i++) {
ierr = MatMult(d->B, (*u)[i], (*kr)[i]); CHKERRQ(ierr);
}
Bx = *kr;
} else
Bx = *u;
for(i=0; i<n; i++) {
#if !defined(PETSC_USE_COMPLEX)
if(d->eigi[i_s+i] != 0.0) {
/* [v_i v_i+1 Bx_i Bx_i+1]*= [ theta_2i' 0
0 theta_2i'
theta_2i+1 -thetai_i
thetai_i theta_2i+1 ] */
b[0] = b[5] = PetscConj(theta[2*i]);
b[2] = b[7] = -theta[2*i+1];
b[6] = -(b[3] = thetai[i]);
b[1] = b[4] = 0.0;
X[0] = (*v)[i]; X[1] = (*v)[i+1]; X[2] = Bx[i]; X[3] = Bx[i+1];
ierr = SlepcUpdateVectorsD(X, 4, 1.0, b, 4, 4, 2, Z, size_Z);
CHKERRQ(ierr);
i++;
} else
#endif
{
/* v_i <- v_i*theta_2i' + Bx_i*theta_2i+1 */
ierr = VecAXPBY((*v)[i], theta[i*2+1], PetscConj(theta[i*2]), Bx[i]);
CHKERRQ(ierr);
}
}
/* Bx <- B*X(i) */
Bx = *kr;
for(i=i_s; i<i_e; i++) d->nX[i] = 1.0;
if (d->BV) {
ierr = SlepcUpdateVectorsZ(Bx, 0.0, 1.0, d->BV, d->size_BV, pX, ld,
d->size_H, n); CHKERRQ(ierr);
} else {
ierr = SlepcUpdateVectorsZ(d->B?r:Bx, 0.0, 1.0, d->V, d->size_V, pX, ld,
d->size_H, n); CHKERRQ(ierr);
if (d->B) {
for(i=0; i<n; i++) {
ierr = MatMult(d->B, r[i], Bx[i]); CHKERRQ(ierr);
}
}
}
/* Ax <- A*X(i) */
Ax = r;
ierr = SlepcUpdateVectorsZ(Ax, 0.0, 1.0, d->AV, d->size_AV, pX, ld,
d->size_H, n); CHKERRQ(ierr);
/* Recompute the eigenvalue */
DVD_COMPUTE_N_RR(d->eps, i, i_s, n, d->eigr, d->eigi, *u, Ax, Bx, b, ierr);
/* u <- K^{-1} Bx */
for(i=0; i<n; i++) {
ierr = d->improvex_precond(d, i_s+i, Bx[i], (*u)[i]); CHKERRQ(ierr);
}
for(i=0; i<n; i++) {
if (d->eigi[i_s+i] == 0.0) {
/* r <- Ax -eig*Bx */
ierr = VecAXPBY(r[i], -d->eigr[i_s+i], 1.0, Bx[i]); CHKERRQ(ierr);
} else {
/* [r_i r_i+1 kr_i kr_i+1]*= [ 1 0
0 1
-eigr_i -eigi_i
eigi_i -eigr_i] */
b[0] = b[5] = 1.0;
b[2] = b[7] = -d->eigr[i_s+i];
b[6] = -(b[3] = d->eigi[i_s+i]);
b[1] = b[4] = 0.0;
X[0] = r[i]; X[1] = r[i+1]; X[2] = (*kr)[i]; X[3] = (*kr)[i+1];
ierr = SlepcUpdateVectorsD(X, 4, 1.0, b, 4, 4, 2, Z, size_Z);
CHKERRQ(ierr);
i++;
}
}
/* kr <- K^{-1}*r */
d->calcpairs_proj_res(d, i_s, i_e, r);
for(i=0; i<n; i++) {
ierr = d->improvex_precond(d, i_s+i, r[i], (*kr)[i]); CHKERRQ(ierr);
}
/* Free r */
auxV-= n;
/* Normalize the projector */
for(i=0; i<n; i++) DVD_NORMALIZE_UV((*u)[i],(*v)[i],ierr,a);
/* Return the next free vector */
*auxV_ = auxV;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_proj_uv_KBXX"
/*
Compute: u <- K^{-1}*B*X, v <- X,
kr <- K^{-1}*(A-eig*B)*X, being X <- V*pX[i_s..i_e-1]
where
auxV, 4*(i_e-i_s) auxiliar global vectors
pX,pY, the right and left eigenvectors of the projected system
ld, the leading dimension of pX and pY
*/
PetscErrorCode dvd_improvex_jd_proj_uv_KBXX(dvdDashboard *d, PetscInt i_s,
PetscInt i_e, Vec **u, Vec **v, Vec **kr, Vec **auxV_, PetscScalar *theta,
PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld)
{
PetscErrorCode ierr;
PetscInt n = i_e - i_s, i;
PetscScalar a, b[16];
Vec *Ax, *Bx, *r, *auxV = *auxV_, X[4];
/* The memory manager doen't allow to call a subroutines */
PetscScalar Z[size_Z];
PetscFunctionBegin;
/* Book space for u, v and kr */
*u = auxV; auxV+= n;
*kr = auxV; auxV+= n;
*v = auxV; auxV+= n;
r = auxV; auxV+= n;
/* [v u] <- X(i) Y(i) */
ierr = SlepcUpdateVectorsZ(*v, 0.0, 1.0, d->V, d->size_V, pX, ld,
d->size_H, n); CHKERRQ(ierr);
ierr = SlepcUpdateVectorsZ(*u, 0.0, 1.0, d->W?d->W:d->V, d->size_V, pY, ld,
d->size_H, n); CHKERRQ(ierr);
/* Bx <- B*X(i) */
Bx = *kr;
for(i=i_s; i<i_e; i++) d->nX[i] = 1.0;
if (d->BV) {
ierr = SlepcUpdateVectorsZ(Bx, 0.0, 1.0, d->BV, d->size_BV, pX, ld,
d->size_H, n); CHKERRQ(ierr);
} else {
if (d->B) {
for(i=0; i<n; i++) {
ierr = MatMult(d->B, (*v)[i], Bx[i]); CHKERRQ(ierr);
}
} else
Bx = *v;
}
/* Ax <- A*X(i) */
Ax = r;
ierr = SlepcUpdateVectorsZ(Ax, 0.0, 1.0, d->AV, d->size_AV, pX, ld,
d->size_H, n); CHKERRQ(ierr);
/* Recompute the eigenvalue */
DVD_COMPUTE_N_RR(d->eps, i, i_s, n, d->eigr, d->eigi, *u, Ax, Bx, b, ierr);
/* u <- K^{-1} Bx */
for(i=0; i<n; i++) {
ierr = d->improvex_precond(d, i_s+i, Bx[i], (*u)[i]); CHKERRQ(ierr);
}
for(i=0; i<n; i++) {
if (d->eigi[i_s+i] == 0.0) {
/* r <- Ax -eig*Bx */
ierr = VecAXPBY(r[i], -d->eigr[i_s+i], 1.0, Bx[i]); CHKERRQ(ierr);
} else {
/* [r_i r_i+1 kr_i kr_i+1]*= [ 1 0
0 1
-eigr_i -eigi_i
eigi_i -eigr_i] */
b[0] = b[5] = 1.0;
b[2] = b[7] = -d->eigr[i_s+i];
b[6] = -(b[3] = d->eigi[i_s+i]);
b[1] = b[4] = 0.0;
X[0] = r[i]; X[1] = r[i+1]; X[2] = (*kr)[i]; X[3] = (*kr)[i+1];
ierr = SlepcUpdateVectorsD(X, 4, 1.0, b, 4, 4, 2, Z, size_Z);
CHKERRQ(ierr);
i++;
}
}
/* kr <- K^{-1}*r */
d->calcpairs_proj_res(d, i_s, i_e, r);
for(i=0; i<n; i++) {
ierr = d->improvex_precond(d, i_s+i, r[i], (*kr)[i]); CHKERRQ(ierr);
}
/* Free r */
auxV-= n;
/* Normalize the projector */
for(i=0; i<n; i++) DVD_NORMALIZE_UV((*u)[i],(*v)[i],ierr,a);
/* Return the next free vector */
*auxV_ = auxV;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_proj_uv_KBXY"
/*
Compute: u <- K^{-1}*B*X, v <- Y,
kr <- K^{-1}*(A-eig*B)*X, being X <- V*pX[i_s..i_e-1], Y <- V*pY[i_s..i_e-1]
where
auxV, 4*(i_e-i_s) auxiliar global vectors
pX,pY, the right and left eigenvectors of the projected system
ld, the leading dimension of pX and pY
*/
PetscErrorCode dvd_improvex_jd_proj_uv_KBXY(dvdDashboard *d, PetscInt i_s,
PetscInt i_e, Vec **u, Vec **v, Vec **kr, Vec **auxV_, PetscScalar *theta,
PetscScalar *thetai, PetscScalar *pX, PetscScalar *pY, PetscInt ld)
{
PetscErrorCode ierr;
PetscInt n = i_e - i_s, i;
PetscScalar a, b[16];
Vec *Ax, *Bx, *r, *auxV = *auxV_, X[4];
/* The memory manager doen't allow to call a subroutines */
PetscScalar Z[size_Z];
PetscFunctionBegin;
/* Book space for u, v and kr */
*u = auxV; auxV+= n;
*kr = auxV; auxV+= n;
*v = auxV; auxV+= n;
r = auxV; auxV+= n;
/* v <- Y(i) */
ierr = SlepcUpdateVectorsZ(*v, 0.0, 1.0, d->W?d->W:d->V, d->size_V, pY, ld,
d->size_H, n); CHKERRQ(ierr);
/* Bx <- B*X(i) */
Bx = *kr;
for(i=i_s; i<i_e; i++) d->nX[i] = 1.0;
if (d->BV) {
ierr = SlepcUpdateVectorsZ(Bx, 0.0, 1.0, d->BV, d->size_BV, pX, ld,
d->size_H, n); CHKERRQ(ierr);
} else {
ierr = SlepcUpdateVectorsZ(d->B?*u:Bx, 0.0, 1.0, d->V, d->size_V, pX, ld,
d->size_H, n); CHKERRQ(ierr);
if (d->B) {
for(i=0; i<n; i++) {
ierr = MatMult(d->B, (*u)[i], Bx[i]); CHKERRQ(ierr);
}
}
}
/* Ax <- A*X(i) */
Ax = r;
ierr = SlepcUpdateVectorsZ(Ax, 0.0, 1.0, d->AV, d->size_AV, pX, ld,
d->size_H, n); CHKERRQ(ierr);
/* Recompute the eigenvalue */
DVD_COMPUTE_N_RR(d->eps, i, i_s, n, d->eigr, d->eigi, *v, Ax, Bx, b, ierr);
/* u <- K^{-1} Bx */
for(i=0; i<n; i++) {
ierr = d->improvex_precond(d, i_s+i, Bx[i], (*u)[i]); CHKERRQ(ierr);
}
for(i=0; i<n; i++) {
if (d->eigi[i_s+i] == 0.0) {
/* r <- Ax -eig*Bx */
ierr = VecAXPBY(r[i], -d->eigr[i_s+i], 1.0, Bx[i]); CHKERRQ(ierr);
} else {
/* [r_i r_i+1 kr_i kr_i+1]*= [ 1 0
0 1
-eigr_i -eigi_i
eigi_i -eigr_i] */
b[0] = b[5] = 1.0;
b[2] = b[7] = -d->eigr[i_s+i];
b[6] = -(b[3] = d->eigi[i_s+i]);
b[1] = b[4] = 0.0;
X[0] = r[i]; X[1] = r[i+1]; X[2] = (*kr)[i]; X[3] = (*kr)[i+1];
ierr = SlepcUpdateVectorsD(X, 4, 1.0, b, 4, 4, 2, Z, size_Z);
CHKERRQ(ierr);
i++;
}
}
/* kr <- K^{-1}*r */
d->calcpairs_proj_res(d, i_s, i_e, r);
for(i=0; i<n; i++) {
ierr = d->improvex_precond(d, i_s+i, r[i], (*kr)[i]); CHKERRQ(ierr);
}
/* Free r */
auxV-= n;
/* Normalize the projector */
for(i=0; i<n; i++) DVD_NORMALIZE_UV((*u)[i],(*v)[i],ierr,a);
/* Return the next free vector */
*auxV_ = auxV;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_lit_const"
PetscErrorCode dvd_improvex_jd_lit_const(dvdDashboard *d, dvdBlackboard *b,
PetscInt maxits, PetscReal tol,
PetscReal fix)
{
dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
PetscFunctionBegin;
/* Setup the step */
if (b->state >= DVD_STATE_CONF) {
data->maxits = maxits;
data->tol = tol;
data->fix = fix;
d->improvex_jd_lit = dvd_improvex_jd_lit_const_0;
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_jd_lit_const_0"
PetscErrorCode dvd_improvex_jd_lit_const_0(dvdDashboard *d, PetscInt i,
PetscScalar* theta, PetscScalar* thetai, PetscInt *maxits, PetscReal *tol)
{
dvdImprovex_jd *data = (dvdImprovex_jd*)d->improveX_data;
PetscReal a;
PetscFunctionBegin;
#if !defined(PETSC_USE_COMPLEX)
a = sqrt(d->eigr[i]*d->eigr[i]+d->eigi[i]*d->eigi[i]);
#else
a = PetscAbsScalar(d->eigr[i]);
#endif
if (d->nR[i]/a < data->fix) {
theta[0] = d->eigr[i];
theta[1] = 1.0;
#if !defined(PETSC_USE_COMPLEX)
*thetai = d->eigi[i];
#endif
} else {
theta[0] = d->target[0];
theta[1] = d->target[1];
#if !defined(PETSC_USE_COMPLEX)
*thetai = 0.0;
#endif
}
#if defined(PETSC_USE_COMPLEX)
if(thetai) *thetai = 0.0;
#endif
*maxits = data->maxits;
*tol = data->tol;
PetscFunctionReturn(0);
}
/**** Patterns implementation *************************************************/
typedef PetscInt (*funcV0_t)(dvdDashboard*, PetscInt, PetscInt, Vec*);
typedef PetscInt (*funcV1_t)(dvdDashboard*, PetscInt, PetscInt, Vec*,
PetscScalar*, Vec);
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_PfuncV"
/* Compute D <- K^{-1} * funcV[r_s..r_e] */
PetscErrorCode dvd_improvex_PfuncV(dvdDashboard *d, void *funcV, Vec *D,
PetscInt max_size_D, PetscInt r_s, PetscInt r_e, Vec *auxV,
PetscScalar *auxS)
{
PetscErrorCode ierr;
PetscInt i;
PetscFunctionBegin;
if (max_size_D >= r_e-r_s+1) {
/* The optimized version needs one vector extra of D */
/* D(1:r.size) = R(r_s:r_e-1) */
if (auxS) ((funcV1_t)funcV)(d, r_s, r_e, D+1, auxS, auxV[0]);
else ((funcV0_t)funcV)(d, r_s, r_e, D+1);
/* D = K^{-1} * R */
for (i=0; i<r_e-r_s; i++) {
ierr = d->improvex_precond(d, i+r_s, D[i+1], D[i]); CHKERRQ(ierr);
}
} else if (max_size_D == r_e-r_s) {
/* Non-optimized version */
/* auxV <- R[r_e-1] */
if (auxS) ((funcV1_t)funcV)(d, r_e-1, r_e, auxV, auxS, auxV[1]);
else ((funcV0_t)funcV)(d, r_e-1, r_e, auxV);
/* D(1:r.size-1) = R(r_s:r_e-2) */
if (auxS) ((funcV1_t)funcV)(d, r_s, r_e-1, D+1, auxS, auxV[1]);
else ((funcV0_t)funcV)(d, r_s, r_e-1, D+1);
/* D = K^{-1} * R */
for (i=0; i<r_e-r_s-1; i++) {
ierr = d->improvex_precond(d, i+r_s, D[i+1], D[i]); CHKERRQ(ierr);
}
ierr = d->improvex_precond(d, r_e-1, auxV[0], D[r_e-r_s-1]); CHKERRQ(ierr);
} else {
SETERRQ(PETSC_COMM_SELF,1, "Problem: r_e-r_s > max_size_D!");
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "dvd_improvex_get_eigenvectors"
/* Compute the left and right projected eigenvectors where,
pX, the returned right eigenvectors
pY, the returned left eigenvectors,
ld_, the leading dimension of pX and pY,
auxS, auxiliar vector of size length 6*d->size_H
*/
PetscErrorCode dvd_improvex_get_eigenvectors(dvdDashboard *d, PetscScalar *pX,
PetscScalar *pY, PetscInt ld, PetscScalar *auxS, PetscInt size_auxS)
{
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = SlepcDenseCopy(pY, ld, d->T?d->pY:d->pX, d->ldpX, d->size_H,
d->size_H); CHKERRQ(ierr);
ierr = SlepcDenseCopy(pX, ld, d->pX, d->ldpX, d->size_H, d->size_H);
CHKERRQ(ierr);
/* [qX, qY] <- eig(S, T); pX <- d->pX * qX; pY <- d->pY * qY */
ierr = dvd_compute_eigenvectors(d->size_H, d->S, d->ldS, d->T, d->ldT, pX,
ld, pY, ld, auxS, size_auxS, PETSC_TRUE);
CHKERRQ(ierr);
/* 2-Normalize the columns of pX an pY */
ierr = SlepcDenseNorm(pX, ld, d->size_H, d->size_H, d->eigi); CHKERRQ(ierr);
ierr = SlepcDenseNorm(pY, ld, d->size_H, d->size_H, d->eigi); CHKERRQ(ierr);
PetscFunctionReturn(0);
}