/*
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
SLEPc - Scalable Library for Eigenvalue Problem Computations
Copyright (c) 2002-2011, Universitat 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 <slepc-private/psimpl.h> /*I "slepcps.h" I*/
#include <slepcblaslapack.h>
/*
compute X = X - Y*s^{-1}*Y^T*B*X where s=Y^T*B*Y
B diagonal (signature matrix)
*/
#undef __FUNCT__
#define __FUNCT__ "PSOrthog_private"
static PetscErrorCode PSOrthog_private(PetscScalar *B, PetscScalar *Y, PetscReal ss, PetscScalar *X, PetscScalar *h,PetscInt n)
{
PetscInt i;
PetscScalar h_,r;
PetscFunctionBegin;
if(Y){
h_ = 0.0; /* h_=(Y^Tdiag(B)*Y)^{-1}*Y^T*diag(B)*X*/
for(i=0;i<n;i++){ h_+=Y[i]*B[i]*X[i];}
h_ /= ss;
for(i=0;i<n;i++){X[i] -= h_*Y[i];} /* X = X-h_*Y */
/* repeat */
r = 0.0;
for(i=0;i<n;i++){ r+=Y[i]*B[i]*X[i];}
r /= ss;
for(i=0;i<n;i++){X[i] -= r*Y[i];}
h_ += r;
}else h_ = 0.0;
if(h) *h = h_;
PetscFunctionReturn(0);
}
/* normalization with a indefinite norm */
#undef __FUNCT__
#define __FUNCT__ "PSNormIndef_private"
static PetscErrorCode PSNormIndef_private(PetscScalar *B,PetscScalar *X, PetscScalar *norm,PetscInt n)
{
PetscInt i;
PetscReal norm_;
/* s-normalization */
norm_ = 0.0;
for(i=0;i<n;i++){norm_ += X[i]*B[i]*X[i];}
if(norm_<0){norm_ = -PetscSqrtReal(-norm_);}
else {norm_ = PetscSqrtReal(norm_);}
for(i=0;i<n;i++)X[i] /= norm_;
if(norm) *norm = norm_;
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "PSAllocate_GHIEP"
PetscErrorCode PSAllocate_GHIEP(PS ps,PetscInt ld)
{
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PSAllocateMat_Private(ps,PS_MAT_A);CHKERRQ(ierr);
ierr = PSAllocateMat_Private(ps,PS_MAT_B);CHKERRQ(ierr);
ierr = PSAllocateMat_Private(ps,PS_MAT_Q);CHKERRQ(ierr);
ierr = PSAllocateMatReal_Private(ps,PS_MAT_T);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "PSSwitchFormat_GHIEP"
PetscErrorCode PSSwitchFormat_GHIEP(PS ps,PetscBool tocompact)
{
PetscReal *T;
PetscScalar *A,*B;
PetscInt i,k,ld;
PetscFunctionBegin;
A = ps->mat[PS_MAT_A];
B = ps->mat[PS_MAT_B];
T = ps->rmat[PS_MAT_T];
k = ps->k;
ld = ps->ld;
if(tocompact){ /* switch from dense (arrow) to compact */
for(i=0; i < k; i++){
T[i] = PetscRealPart(A[i*(1+ld)]);
T[ld +i] = PetscRealPart(A[k+i*ld]);
T[2*ld +i] = PetscRealPart(B[i*(1+ld)]);
}
for(i=k; i < ps->n; i++){
T[i] = PetscRealPart(A[i*(1+ld)]);
T[ld +i] = PetscRealPart(A[i*(ld+1)+1]);
T[2*ld +i] = PetscRealPart(B[i*(1+ld)]);
}
}else{ /* switch from compact (arrow) to dense */
for(i=0; i < k; i++){
A[i*(1+ld)] = T[i];
A[k+i*ld] = T[ld+i];
A[i+k*ld] = T[ld+i];
B[i*(1+ld)] = T[2*ld+i];
}
A[k*(ld+1)] = T[k];
B[k*(ld+1)] = T[2*ld+k];
for(i=k+1; i < ps->n; i++){
A[i*(1+ld)] = T[i];
A[i*ld + i-1] = T[i-1+ld];
A[(i-1)*ld + i] = T[i-1+ld];
B[i*(1+ld)] = T[2*ld+i];
}
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "PSView_GHIEP"
PetscErrorCode PSView_GHIEP(PS ps,PetscViewer viewer)
{
PetscErrorCode ierr;
PetscViewerFormat format;
PetscInt i,j,r,c;
PetscReal value;
const char *methodname[] = {
"QR method",
"QR + Inverse Iteration"
};
PetscFunctionBegin;
ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
ierr = PetscViewerASCIIPrintf(viewer,"solving the problem with: %s\n",methodname[ps->method]);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (ps->compact) {
ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
if (format == PETSC_VIEWER_ASCII_MATLAB) {
ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ps->n,ps->n);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"zzz = zeros(%D,3);\n",3*ps->n);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"zzz = [\n");CHKERRQ(ierr);
for (i=0;i<ps->n;i++) {
ierr = PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",i+1,i+1,*(ps->rmat[PS_MAT_T]+i));CHKERRQ(ierr);
}
for (i=0;i<ps->n-1;i++) {
r = PetscMax(i+2,ps->k+1);
c = i+1;
ierr = PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",r,c,*(ps->rmat[PS_MAT_T]+ps->ld+i));CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",c,r,*(ps->rmat[PS_MAT_T]+ps->ld+i));CHKERRQ(ierr);
}
ierr = PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(zzz);\n",PSMatName[PS_MAT_T]);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"%% Size = %D %D\n",ps->n,ps->n);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"omega = zeros(%D,3);\n",3*ps->n);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"omega = [\n");CHKERRQ(ierr);
for (i=0;i<ps->n;i++) {
ierr = PetscViewerASCIIPrintf(viewer,"%D %D %18.16e\n",i+1,i+1,*(ps->rmat[PS_MAT_T]+2*(ps->ld)+i));CHKERRQ(ierr);
}
ierr = PetscViewerASCIIPrintf(viewer,"];\n%s = spconvert(omega);\n",PSMatName[PS_MAT_B]);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(viewer,"T\n");CHKERRQ(ierr);
for (i=0;i<ps->n;i++) {
for (j=0;j<ps->n;j++) {
if (i==j) value = *(ps->rmat[PS_MAT_T]+i);
else if ((i<ps->k && j==ps->k) || (i==ps->k && j<ps->k)) value = *(ps->rmat[PS_MAT_T]+ps->ld+PetscMin(i,j));
else if (i==j+1 && i>ps->k) value = *(ps->rmat[PS_MAT_T]+ps->ld+i-1);
else if (i+1==j && j>ps->k) value = *(ps->rmat[PS_MAT_T]+ps->ld+j-1);
else value = 0.0;
ierr = PetscViewerASCIIPrintf(viewer," %18.16e ",value);CHKERRQ(ierr);
}
ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
}
ierr = PetscViewerASCIIPrintf(viewer,"omega\n");CHKERRQ(ierr);
for (i=0;i<ps->n;i++) {
for (j=0;j<ps->n;j++) {
if (i==j) value = *(ps->rmat[PS_MAT_T]+2*(ps->ld)+i);
else value = 0.0;
ierr = PetscViewerASCIIPrintf(viewer," %18.16e ",value);CHKERRQ(ierr);
}
ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
}
}
ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
} else {
ierr = PSViewMat_Private(ps,viewer,PS_MAT_A);CHKERRQ(ierr);
ierr = PSViewMat_Private(ps,viewer,PS_MAT_B);CHKERRQ(ierr);
}
if (ps->state>PS_STATE_INTERMEDIATE) {
ierr = PSViewMat_Private(ps,viewer,PS_MAT_Q);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "PSVectors_GHIEP_Eigen_Some"
PetscErrorCode PSVectors_GHIEP_Eigen_Some(PS ps,PetscInt *k,PetscReal *rnorm,PetscBool left)
{
/// to complete /////
PetscScalar *Q = ps->mat[PS_MAT_Q];
PetscReal s1,s2,d1,d2,b;
PetscInt ld = ps->ld,k_;
PetscErrorCode ierr;
PSMatType mat;
PetscFunctionBegin;
if (left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for left eigenvectors");
else mat = PS_MAT_Q;
k_ = *k;
if(k_ < ps->n-1){
b = (ps->compact)?*(ps->rmat[PS_MAT_T]+ld+k_):*(ps->mat[PS_MAT_A]+(k_+1)+ld*k_);
}else b = 0;
if(b==0){/* real */
ierr = PetscMemcpy(ps->mat[mat]+(k_)*ld,Q+(k_)*ld,ld*sizeof(PetscScalar));CHKERRQ(ierr);
}else{ /* complex block */
if(ps->compact){
s1 = *(ps->rmat[PS_MAT_T]+2*ld+k_);
d1 = *(ps->rmat[PS_MAT_T]+k_);
s2 = *(ps->rmat[PS_MAT_T]+2*ld+k_+1);
d2 = *(ps->rmat[PS_MAT_T]+k_+1);
}else{
s1 = PetscRealPart(*(ps->mat[PS_MAT_B]+2*ld+k_));
d1 = PetscRealPart(*(ps->mat[PS_MAT_A]+k_));
s2 = PetscRealPart(*(ps->mat[PS_MAT_B]+2*ld+k_+1));
d2 = PetscRealPart(*(ps->mat[PS_MAT_A]+k_+1));
}
}
if (rnorm) *rnorm = PetscAbsScalar(Q[ps->n-1+(k_)*ld]);
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "PSVectors_GHIEP"
PetscErrorCode PSVectors_GHIEP(PS ps,PSMatType mat,PetscInt *k,PetscReal *rnorm)
{
PetscInt i;
PetscBool left;
PetscErrorCode ierr;
PetscFunctionBegin;
if (ps->state<PS_STATE_CONDENSED) SETERRQ(((PetscObject)ps)->comm,PETSC_ERR_ORDER,"Must call PSSolve() first");
switch (mat) {
case PS_MAT_Y:
left = PETSC_TRUE;
case PS_MAT_X:
if (k){
ierr = PSVectors_GHIEP_Eigen_Some(ps,k,rnorm,left);CHKERRQ(ierr);
}else{
for(i=0; i<ps->n; i++){
ierr = PSVectors_GHIEP_Eigen_Some(ps,&i,rnorm,left);CHKERRQ(ierr);
}
}
break;
case PS_MAT_U:
case PS_MAT_VT:
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented yet");
break;
default:
SETERRQ(((PetscObject)ps)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "PSComplexEigs_private"
static PetscErrorCode PSComplexEigs_private(PS ps, PetscInt n0, PetscInt n1, PetscScalar *wr, PetscScalar *wi){
PetscInt j,ld;
PetscScalar *A,*B;
PetscReal *d,*e,*s,d1,d2,e1,e2,disc;
PetscFunctionBegin;
ld = ps->ld;
if (ps->compact){
d = ps->rmat[PS_MAT_T];
e = d + ld;
s = e + ld;
for (j=n0;j<n1;j++) {
if (j==n1-1 || e[j] == 0.0) {
/* real eigenvalue */
wr[j] = d[j]/s[j];
wi[j] = 0.0 ;
} else {
/* diagonal block */
d1 = d[j]/s[j]; d2 = d[j+1]/s[j+1]; e1 = e[j]/s[j+1]; e2 = e[j]/s[j];
wr[j] = (d1+d2)/2; wr[j+1] = wr[j];
disc = (d1-d2)*(d1-d2) - (e1-e2)*(e1-e2);
if (disc<0){ /* complex eigenvalues */
wi[j] = PetscSqrtReal(-disc)/2; wi[j+1] = -wi[j];
}else{ /* real eigenvalues */
disc = PetscSqrtReal(disc)/2;
wr[j] = wr[j]+disc; wr[j+1]=wr[j+1]-disc; wi[j] = 0.0; wi[j+1] = 0.0;
}
j++;
}
}
}else{
A = ps->mat[PS_MAT_A];
B = ps->mat[PS_MAT_B];
for (j=n0;j<n1;j++) {
if (j==n1-1 || A[(j+1)+j*ld] == 0.0) {
/* real eigenvalue */
wr[j] = A[j+j*ld]/B[j+j*ld];
wi[j] = 0.0 ;
} else {
/* diagonal block */
d1 = A[j+j*ld]/B[j+j*ld]; d2 = A[(j+1)+(j+1)*ld]/B[(j+1)+(j+1)*ld];
e1 = A[j+(j+1)*ld]/B[j+j*ld]; e2 = A[(j+1)+j*ld]/B[(j+1)+(j+1)*ld];
wr[j] = (d1+d2)/2; wr[j+1] = wr[j];
disc = (d1-d2)*(d1-d2) - (e1-e2)*(e1-e2);
if (disc<0){ /* complex eigenvalues */
wi[j] = PetscSqrtReal(-disc)/2; wi[j+1] = -wi[j];
}else{ /* real eigenvalues */
disc = PetscSqrtReal(disc)/2;
wr[j] = wr[j]+disc; wr[j+1]=wr[j+1]-disc; wi[j] = 0.0; wi[j+1] = 0.0;
}
j++;
}
}
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "PSSolve_GHIEP_QR_II"
PetscErrorCode PSSolve_GHIEP_QR_II(PS ps,PetscScalar *wr,PetscScalar *wi)
{
#if defined(SLEPC_MISSING_LAPACK_GEHRD) || defined(SLEPC_MISSING_LAPACK_ORGHR) || defined(PETSC_MISSING_LAPACK_HSEQR) || defined(PETSC_MISSING_LAPACK_HSEIN)
PetscFunctionBegin;
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEHRD/ORGHR/HSEQR/HSEIN - Lapack routines are unavailable.");
#else
PetscErrorCode ierr;
PetscInt i,j,off;
PetscBLASInt lwork,info,n1,one,ld,*select,*infoC,mout;
PetscScalar *A,*B,*W,*Q,*work,*tau,zero,oneS;
PetscScalar h;
PetscReal *d,*e,*s,*ss,toldeg=1e-5,d1,d2;
PetscFunctionBegin;
n1 = PetscBLASIntCast(ps->n - ps->l);
one = PetscBLASIntCast(1);
oneS = 1.0;
zero = 0.0;
ld = PetscBLASIntCast(ps->ld);
off = ps->l + ps->l*ld;
A = ps->mat[PS_MAT_A];
B = ps->mat[PS_MAT_B];
Q = ps->mat[PS_MAT_Q];
d = ps->rmat[PS_MAT_T];
e = ps->rmat[PS_MAT_T] + ld;
s = ps->rmat[PS_MAT_T] + 2*ld;
ierr = PSAllocateWork_Private(ps,ld+ld*ld,ld,ld*2);CHKERRQ(ierr);
tau = ps->work;
work = ps->work+ld;
lwork = ld*ld;
select = ps->iwork;
infoC = ps->iwork + ld;
/* initialize orthogonal matrix */
ierr = PetscMemzero(Q,ld*ld*sizeof(PetscScalar));CHKERRQ(ierr);
for (i=0;i< ps->n;i++)
Q[i+i*ld] = 1.0;
if (n1 == 1) {
if(ps->compact){
wr[ps->l] = d[ps->l]/s[ps->l]; wi[ps->l] = 0.0;
}else{
d[ps->l] = PetscRealPart(A[off]); s[ps->l] = PetscRealPart(B[off]);
wr[ps->l] = d[ps->l]/s[ps->l]; wi[ps->l] = 0.0;
}
PetscFunctionReturn(0);
}
/* form standard problem in A */
if (ps->compact) {
ierr = PetscMemzero(A,ld*ld*sizeof(PetscScalar));CHKERRQ(ierr);
for(i=ps->l; i < ps->k; i++){
A[i+i*ld] = d[i]/s[i];
A[ps->k+i*ld] = e[i]/s[ps->k];
A[i + ps->k*ld] = e[i]/s[i];
}
A[ps->k + ps->k*ld] = d[ps->k]/s[ps->k];
for(i=ps->k+1; i < ps->n; i++){
A[i+i*ld] = d[i]/s[i];
A[(i-1)+i*ld] = e[i-1]/s[i-1];
A[i+(i-1)*ld] = e[i-1]/s[i];
}
}else{
for(j=ps->l; j<ps->n; j++){
for(i=ps->l; i<ps->n; i++){
A[i+j*ld] /= B[i+i*ld];
}
}
}
/* reduce to upper Hessemberg form */
if (ps->state<PS_STATE_INTERMEDIATE) {
LAPACKgehrd_(&n1,&one,&n1,A+off,&ld,tau,work,&lwork,&info);
if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEHRD %d",&info);
for (j=ps->l;j<ps->n-1;j++) {
for (i=j+2;i<ps->n;i++) {
Q[i+j*ld] = A[i+j*ld];
A[i+j*ld] = 0.0;
}
}
LAPACKorghr_(&n1,&one,&n1,Q+off,&ld,tau,work,&lwork,&info);
if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGHR %d",&info);
}
/* Compute Eigenvalues (QR)*/
ierr = PSAllocateMat_Private(ps,PS_MAT_W);CHKERRQ(ierr);
W = ps->mat[PS_MAT_W];
ierr = PetscMemcpy(W,A,ld*ld*sizeof(PetscScalar));CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
LAPACKhseqr_("E","N",&n1,&one,&n1,W+off,&ld,wr+ps->l,wi+ps->l,PETSC_NULL,&ld,work,&lwork,&info);
#else
LAPACKhseqr_("E","N",&n1,&one,&n1,W+off,&ld,wr+ps->l,PETSC_NULL,&ld,work,&lwork,&info);
#endif
if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",&info);
/* Compute Eigenvectors with Inverse Iteration */
#if !defined(PETSC_USE_COMPLEX)
for(i=0;i<n1;i++)select[i]=1;
LAPACKhsein_("R","N","N",select,&n1,A+off,&ld,wr+ps->l,wi+ps->l,PETSC_NULL,&ld,W+off,&ld,&n1,&mout,work,PETSC_NULL,infoC,&info);
#else
SETERRQ1(((PetscObject)ps)->comm,PETSC_ERR_SUP," In PSSolve, QR + II method not implemented for complex indefinite problems",info);
#endif
/* accumulate previous Q */
if (ps->state<PS_STATE_INTERMEDIATE) {
BLASgemm_("N","N",&n1,&n1,&n1,&oneS,Q+off,&ld,W+off,&ld,&zero,A+off,&ld);
ierr = PSCopyMatrix_Private(ps,PS_MAT_Q,PS_MAT_A);CHKERRQ(ierr);
}else {ierr = PSCopyMatrix_Private(ps,PS_MAT_Q,PS_MAT_W);CHKERRQ(ierr);}
/* compute real s-orthonormal base */
ss = ps->rwork;
for(i=ps->l;i<ps->n;i++){
if(wi[i]==0.0){/* real */
for(j=i-1;j>=ps->l;j--){
/* s-orthogonalization with close eigenvalues */
if(wi[j]==0 && PetscAbsReal(wr[j]-wr[i])<toldeg){
ierr = PSOrthog_private(s+ps->l, Q+j*ld+ps->l, ss[j],Q+i*ld+ps->l, PETSC_NULL,n1);CHKERRQ(ierr);
}
}
ierr = PSNormIndef_private(s+ps->l,Q+i*ld+ps->l,&h,n1);CHKERRQ(ierr);
ss[i] = (h<0)?-1:1;
d[i] = wr[i]*ss[i]; e[i] = 0.0;
}else{
for(j=i-1;j>=ps->l;j--){
/* s-orthogonalization of Qi and Qi+1*/
if(PetscAbsReal(wr[j]-wr[i])<toldeg && PetscAbsReal(PetscAbsReal(wi[j])-PetscAbsReal(wi[i]))<toldeg){
ierr = PSOrthog_private(s+ps->l, Q+j*ld+ps->l, ss[j],Q+i*ld+ps->l, PETSC_NULL,n1);CHKERRQ(ierr);
ierr = PSOrthog_private(s+ps->l, Q+j*ld+ps->l, ss[j],Q+(i+1)*ld+ps->l, PETSC_NULL,n1);CHKERRQ(ierr);
}
}
ierr = PSNormIndef_private(s+ps->l,Q+i*ld+ps->l,&d1,n1);CHKERRQ(ierr);
ss[i] = (d1<0)?-1:1;
ierr = PSOrthog_private(s+ps->l, Q+i*ld+ps->l, ss[i],Q+(i+1)*ld+ps->l, &h,n1);CHKERRQ(ierr);
ierr = PSNormIndef_private(s+ps->l,Q+(i+1)*ld+ps->l,&d2,n1);CHKERRQ(ierr);
ss[i+1] = (d2<0)?-1:1;
d[i] = (wr[i]-wi[i]*h/d1)*ss[i]; d[i+1] = (wr[i]+wi[i]*h/d1)*ss[i+1];
e[i] = wi[i]*d2/d1*ss[i]; e[i+1] = 0.0;
i++;
}
}
for(i=ps->l;i<ps->n;i++) s[i] = ss[i];
ps->k = ps->l;
/* The result is stored in both places (compact and regular) */
if (!ps->compact) {
ierr = PetscMemzero(A+ps->l*ld,n1*ld*sizeof(PetscScalar));CHKERRQ(ierr);
ierr = PSSwitchFormat_GHIEP(ps,PETSC_FALSE);CHKERRQ(ierr);
}
/* Recover eigenvalues from diagonal */
//ierr = PSComplexEigs_private(ps, 0, ps->n, wr, wi);CHKERRQ(ierr);
#endif
PetscFunctionReturn(0);
}
/*
Parameters:
ps (In/Out): On input the ps object contains (T,S) symmetric pencil with S indefinite diagonal (signature matrix)
On output ps contains Q and (D,SS), equivalent symmetric pencil whit D block diagonal and SS diagonal,
verifying: Q^T*T*Q = D and Q^T*S*Q = SS
wr,wi (Out): eigenvalues of equivalent pencils
(Modified only rows and columns ps->l to ps->n in T and S)
*/
#undef __FUNCT__
#define __FUNCT__ "PSSolve_GHIEP_QR"
PetscErrorCode PSSolve_GHIEP_QR(PS ps,PetscScalar *wr,PetscScalar *wi)
{
#if defined(SLEPC_MISSING_LAPACK_GEHRD) || defined(SLEPC_MISSING_LAPACK_ORGHR) || defined(PETSC_MISSING_LAPACK_HSEQR)
PetscFunctionBegin;
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GEHRD/ORGHR/HSEQR - Lapack routines are unavailable.");
#else
PetscErrorCode ierr;
PetscInt i,j,off;
PetscBLASInt lwork,info,n1,one,mout,ld;
PetscScalar *A,*B,*Q,*work,*tau;
PetscScalar h;
PetscReal *d,*e,*s,*ss,toldeg=1e-5,d1,d2;
PetscFunctionBegin;
n1 = PetscBLASIntCast(ps->n - ps->l);
one = PetscBLASIntCast(1);
ld = PetscBLASIntCast(ps->ld);
off = ps->l + ps->l*ld;
A = ps->mat[PS_MAT_A];
B = ps->mat[PS_MAT_B];
Q = ps->mat[PS_MAT_Q];
d = ps->rmat[PS_MAT_T];
e = ps->rmat[PS_MAT_T] + ld;
s = ps->rmat[PS_MAT_T] + 2*ld;
ierr = PSAllocateWork_Private(ps,ld+ld*ld,ld,0);CHKERRQ(ierr);
tau = ps->work;
work = ps->work+ld;
lwork = ld*ld;
/* initialize orthogonal matrix */
ierr = PetscMemzero(Q,ld*ld*sizeof(PetscScalar));CHKERRQ(ierr);
for (i=0;i< ps->n;i++)
Q[i+i*ld] = 1.0;
if (n1 == 1) {
if(ps->compact){
wr[ps->l] = d[ps->l]/s[ps->l]; wi[ps->l] = 0.0;
}else{
d[ps->l] = PetscRealPart(A[off]); s[ps->l] = PetscRealPart(B[off]);
wr[ps->l] = d[ps->l]/s[ps->l]; wi[ps->l] = 0.0;
}
PetscFunctionReturn(0);
}
/* form standard problem in A */
if (ps->compact) {
ierr = PetscMemzero(A,ld*ld*sizeof(PetscScalar));CHKERRQ(ierr);
for(i=ps->l; i < ps->k; i++){
A[i+i*ld] = d[i]/s[i];
A[ps->k+i*ld] = e[i]/s[ps->k];
A[i + ps->k*ld] = e[i]/s[i];
}
A[ps->k + ps->k*ld] = d[ps->k]/s[ps->k];
for(i=ps->k+1; i < ps->n; i++){
A[i+i*ld] = d[i]/s[i];
A[(i-1)+i*ld] = e[i-1]/s[i-1];
A[i+(i-1)*ld] = e[i-1]/s[i];
}
}else{
for(j=ps->l; j<ps->n; j++){
for(i=ps->l; i<ps->n; i++){
A[i+j*ld] /= B[i+i*ld];
}
}
}
/* reduce to upper Hessemberg form */
if (ps->state<PS_STATE_INTERMEDIATE) {
LAPACKgehrd_(&n1,&one,&n1,A+off,&ld,tau,work,&lwork,&info);
if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGEHRD %d",&info);
for (j=ps->l;j<ps->n-1;j++) {
for (i=j+2;i<ps->n;i++) {
Q[i+j*ld] = A[i+j*ld];
A[i+j*ld] = 0.0;
}
}
LAPACKorghr_(&n1,&one,&n1,Q+off,&ld,tau,work,&lwork,&info);
if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xORGHR %d",&info);
}
/* compute the real Schur form */
#if !defined(PETSC_USE_COMPLEX)
LAPACKhseqr_("S","V",&n1,&one,&n1,A+off,&ld,wr+ps->l,wi+ps->l,Q+off,&ld,work,&lwork,&info);
#else
LAPACKhseqr_("S","V",&n1,&one,&n1,A+off,&ld,wr,Q+off,&ld,work,&lwork,&info);
#endif
if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xHSEQR %d",&info);
/* compute eigenvectors */
#if !defined(PETSC_USE_COMPLEX)
LAPACKtrevc_("R","B",PETSC_NULL,&n1,A+off,&ld,PETSC_NULL,&ld,Q+off,&ld,&n1,&mout,ps->work,&info);
#else
LAPACKtrevc_("R","B",PETSC_NULL,&n1,A+off,&ld,PETSC_NULL,&ld,Q+off,&ld,&n1,&mout,work,ps->rwork,&info);
#endif
if (info) SETERRQ1(((PetscObject)ps)->comm,PETSC_ERR_LIB,"Error in Lapack xTREVC %i",&info);
/* compute real s-orthonormal base */
#if !defined(PETSC_USE_COMPLEX)
ss = ps->rwork;
for(i=ps->l;i<ps->n;i++){
if(wi[i]==0.0){/* real */
for(j=i-1;j>=ps->l;j--){
/* s-orthogonalization with close eigenvalues */
if(wi[j]==0 && PetscAbsReal(wr[j]-wr[i])<toldeg){
ierr = PSOrthog_private(s+ps->l, Q+j*ld+ps->l, ss[j],Q+i*ld+ps->l, PETSC_NULL,n1);CHKERRQ(ierr);
}
}
ierr = PSNormIndef_private(s+ps->l,Q+i*ld+ps->l,&h,n1);CHKERRQ(ierr);
ss[i] = (h<0)?-1:1;
d[i] = wr[i]*ss[i]; e[i] = 0.0;
}else{
for(j=i-1;j>=ps->l;j--){
/* s-orthogonalization of Qi and Qi+1*/
if(PetscAbsReal(wr[j]-wr[i])<toldeg && PetscAbsReal(PetscAbsReal(wi[j])-PetscAbsReal(wi[i]))<toldeg){
ierr = PSOrthog_private(s+ps->l, Q+j*ld+ps->l, ss[j],Q+i*ld+ps->l, PETSC_NULL,n1);CHKERRQ(ierr);
ierr = PSOrthog_private(s+ps->l, Q+j*ld+ps->l, ss[j],Q+(i+1)*ld+ps->l, PETSC_NULL,n1);CHKERRQ(ierr);
}
}
ierr = PSNormIndef_private(s+ps->l,Q+i*ld+ps->l,&d1,n1);CHKERRQ(ierr);
ss[i] = (d1<0)?-1:1;
ierr = PSOrthog_private(s+ps->l, Q+i*ld+ps->l, ss[i],Q+(i+1)*ld+ps->l, &h,n1);CHKERRQ(ierr);
ierr = PSNormIndef_private(s+ps->l,Q+(i+1)*ld+ps->l,&d2,n1);CHKERRQ(ierr);
ss[i+1] = (d2<0)?-1:1;
d[i] = (wr[i]-wi[i]*h/d1)*ss[i]; d[i+1] = (wr[i]+wi[i]*h/d1)*ss[i+1];
e[i] = wi[i]*d2/d1*ss[i]; e[i+1] = 0.0;
i++;
}
}
for(i=ps->l;i<ps->n;i++) s[i] = ss[i];
ps->k = ps->l;
/* The result is stored in both places (compact and regular) */
if (!ps->compact) {
ierr = PetscMemzero(A+ps->l*ld,n1*ld*sizeof(PetscScalar));CHKERRQ(ierr);
ierr = PSSwitchFormat_GHIEP(ps,PETSC_FALSE);CHKERRQ(ierr);
}
/* Recover eigenvalues from diagonal */
//ierr = PSComplexEigs_private(ps, 0, ps->n, wr, wi);CHKERRQ(ierr);
#else
SETERRQ1(((PetscObject)ps)->comm,PETSC_ERR_SUP," In PSSolve, QR method not implemented for complex indefinite problems",info);
#endif
PetscFunctionReturn(0);
#endif
}
#undef __FUNCT__
#define __FUNCT__ "PSSortEigenvalues_Private"
static PetscErrorCode PSSortEigenvalues_Private(PS ps,PetscScalar *wr,PetscScalar *wi,PetscInt *perm,PetscErrorCode (*comp_func)(PetscScalar,PetscScalar,PetscScalar,PetscScalar,PetscInt*,void*),void *comp_ctx)
{
PetscErrorCode ierr;
PetscScalar re,im;
PetscInt i,j,result,tmp1,tmp2,d=1;
PetscFunctionBegin;
PetscValidScalarPointer(wi,3);
for (i=0;i<ps->n;i++) perm[i] = i;
/* insertion sort */
i=ps->l+1;
#if !defined(PETSC_USE_COMPLEX)
if(wi[perm[i-1]]!=0.0) i++; /* initial value is complex */
#else
if(PetscImaginaryPart(wr[perm[i-1]])!=0.0) i++;
#endif
for (;i<ps->n;i+=d) {
re = wr[perm[i]];
im = wi[perm[i]];
tmp1 = perm[i];
#if !defined(PETSC_USE_COMPLEX)
if(im!=0.0) {d = 2; tmp2 = perm[i+1];}else d = 1;
#else
if(PetscImaginaryPart(re)!=0.0) {d = 2; tmp2 = perm[i+1];}else d = 1;
#endif
j = i-1;
ierr = (*comp_func)(re,im,wr[perm[j]],wi[perm[j]],&result,comp_ctx);CHKERRQ(ierr);
while (result<0 && j>=ps->l) {
perm[j+d]=perm[j]; j--;
#if !defined(PETSC_USE_COMPLEX)
if(wi[perm[j+1]]!=0)
#else
if(PetscImaginaryPart(wr[perm[j+1]])!=0)
#endif
{perm[j+d]=perm[j]; j--;}
if (j>=ps->l) {
ierr = (*comp_func)(re,im,wr[perm[j]],wi[perm[j]],&result,comp_ctx);CHKERRQ(ierr);
}
}
perm[j+1] = tmp1;
if(d==2) perm[j+2] = tmp2;
}
PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "PSSort_GHIEP"
PetscErrorCode PSSort_GHIEP(PS ps,PetscScalar *wr,PetscScalar *wi,PetscErrorCode (*comp_func)(PetscScalar,PetscScalar,PetscScalar,PetscScalar,PetscInt*,void*),void *comp_ctx)
{
PetscErrorCode ierr;
PetscInt n,i,*perm;
PetscReal *d,*e,*s,*w;
PetscFunctionBegin;
n = ps->n;
d = ps->rmat[PS_MAT_T];
e = d + ps->ld;
s = d + 2*ps->ld;
w = ps->work;
ierr = PSAllocateWork_Private(ps,ps->ld,0,ps->ld);CHKERRQ(ierr);
perm = ps->iwork;
ierr = PSSortEigenvalues_Private(ps,wr,wi,perm,comp_func,comp_ctx);CHKERRQ(ierr);
ierr = PetscMemcpy(ps->work,wr,n*sizeof(PetscScalar));CHKERRQ(ierr);
for (i=ps->l;i<n;i++) {
wr[i] = w[perm[i]];
}
ierr = PetscMemcpy(ps->work,wi,n*sizeof(PetscScalar));CHKERRQ(ierr);
for (i=ps->l;i<n;i++) {
wi[i] = w[perm[i]];
}
ierr = PetscMemcpy(ps->work,s,n*sizeof(PetscScalar));CHKERRQ(ierr);
for (i=ps->l;i<n;i++) {
s[i] = w[perm[i]];
}
ierr = PetscMemcpy(w,d,n*sizeof(PetscScalar));CHKERRQ(ierr);
for (i=ps->l;i<n;i++) {
d[i] = w[perm[i]];
}
ierr = PetscMemcpy(w,e,n*sizeof(PetscScalar));CHKERRQ(ierr);
for (i=ps->l;i<n-1;i++) {
e[i] = w[perm[i]];
}
if(!ps->compact){ ierr = PSSwitchFormat_GHIEP(ps,PETSC_FALSE);CHKERRQ(ierr);}
ierr = PSPermuteColumns_Private(ps,ps->l,n,PS_MAT_Q,perm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "PSCreate_GHIEP"
PetscErrorCode PSCreate_GHIEP(PS ps)
{
PetscFunctionBegin;
ps->ops->allocate = PSAllocate_GHIEP;
ps->ops->view = PSView_GHIEP;
ps->ops->vectors = PSVectors_GHIEP;
ps->ops->solve[0] = PSSolve_GHIEP_QR;
ps->ops->solve[1] = PSSolve_GHIEP_QR_II;
ps->ops->sort = PSSort_GHIEP;
PetscFunctionReturn(0);
}
EXTERN_C_END