void QuasiNewton<dcomplex>::symmHerDiag(int NTrial, ostream &output){
/*
* Solve S(R)| X(R) > = E(R)| X(R) > (1/ω)
*
* | X(R) > = | X(R)_g >
* | X(R)_u >
*
* The opposite (1/ω vs ω) is solved because the metric is not positive definite
* and can therefore not be solved using DSYGV because of the involved Cholesky
* decomposition.
*
*/
char JOBV = 'V';
char UPLO = 'L';
int iType = 1;
int TwoNTrial = 2*NTrial;
int INFO;
ComplexCMMap SSuper(this->SSuperMem, 2*NTrial,2*NTrial);
ComplexCMMap SCPY(this->SCPYMem, TwoNTrial,TwoNTrial);
SCPY = SSuper; // Copy of original matrix to use for re-orthogonalization
// Perform diagonalization of reduced subspace using DSYGV
zhegv_(&iType,&JOBV,&UPLO,&TwoNTrial,this->SSuperMem,&TwoNTrial,
this->ASuperMem,&TwoNTrial,this->RealEMem,this->WORK,&this->LWORK,
this->RWORK,&INFO);
if(INFO!=0) CErr("ZHEGV failed to converge in Davison Iterations",output);
// Grab the "positive paired" roots (throw away other element of the pair)
this->RealEMem += NTrial;
RealVecMap ER (this->RealEMem,NTrial);
new (&SSuper) ComplexCMMap(this->SSuperMem+2*NTrial*NTrial,2*NTrial,NTrial);
// Swap the ordering because we solve for (1/ω)
for(auto i = 0 ; i < NTrial; i++) ER(i) = 1.0/ER(i);
for(auto i = 0 ; i < NTrial/2; i++){
SSuper.col(i).swap(SSuper.col(NTrial - i - 1));
double tmp = ER(i);
ER(i) = ER(NTrial - i - 1);
ER(NTrial - i - 1) = tmp;
}
/*
* Re-orthogonalize the eigenvectors with respect to the metric S(R)
* because DSYGV orthogonalzies the vectors with respect to E(R)
* because we solve the opposite problem.
*
* Gramm-Schmidt
*/
this->metBiOrth(SSuper,SCPY);
// Separate the eigenvectors into gerade and ungerade parts
ComplexCMMap XTSigmaR(this->XTSigmaRMem,NTrial,NTrial);
ComplexCMMap XTSigmaL(this->XTSigmaLMem,NTrial,NTrial);
XTSigmaR = SSuper.block(0, 0,NTrial,NTrial);
XTSigmaL = SSuper.block(NTrial,0,NTrial,NTrial);
} // symmHerDiag
int LapackGHEPEPairs(int hn, complex<double>* A, complex<double>* B, double* lami)
{
integer n = hn;
char jobzm = 'V' , uplo = 'U';
integer lwork=8*n;
std::complex<double>* work = new std::complex<double>[lwork];
double* rwork = new double[lwork];
integer info;
integer itype =1;
integer lda = n;
integer ldb = n;
cout << " zhegv " << endl;
cout << " A s " << endl;
for(int j=0;j<n;j++)
{
for(int k=0;k<n;k++)
cout << A[j*n+k] << " \t " ;
cout << endl;
}
cout << " M " << endl;
for(int j=0;j<n;j++)
{
for(int k=0;k<n;k++)
cout << B[j*n+k] << " \t " ;
cout << endl;
}
zhegv_(&itype,&jobzm,&uplo , &n , A , &lda, B, &ldb, lami, work, &lwork, rwork, &info);
cout << " ... is back " << endl;
if(info != 0)
{
cout << "LapackGHEPEPairs Info " << info << endl;
cout << "n = " << n << endl;
}
delete [] work;
delete [] rwork;
return(info);
}