void GeneralizedEigenSystemSolverRealSymmetricMatrices(const Array2 < doublevar > & Ain, const Array2 < doublevar> & Bin, Array1 < doublevar> & evals, Array2 < doublevar> & evecs){
//solves generalized eigensystem problem A.x=labda*B.x
//returns eigenvalues from largest to lowest and
//eigenvectors, where for i-th eigenvalue, the eigenvector components are evecs(*,i)
//eigenvectors are normalized such that: evecs**T*B*evecs = I;
#ifdef USE_LAPACK //if LAPACK
int N=Ain.dim[0];
/* allocate and initialise the matrix */
Array2 <doublevar> A_temp(N,N), B_temp(N,N);
Array1 <doublevar> W,WORK;
/* allocate space for the output parameters and workspace arrays */
W.Resize(N);
A_temp=Ain;
B_temp=Bin;
int info;
int NB=64;
int NMAX=N;
int lda=NMAX;
int ldb=NMAX;
int LWORK=(NB+2)*NMAX;
WORK.Resize(LWORK);
/* get the eigenvalues and eigenvectors */
info=dsygv(1, 'V', 'U' , N, A_temp.v, lda, B_temp.v, ldb, W.v, WORK.v, LWORK);
if(info>0)
error("Internal error in the LAPACK routine dsyevr");
if(info<0)
error("Problem with the input parameter of LAPACK routine dsyevr in position "-info);
for (int i=0; i<N; i++)
evals(i)=W[N-1-i];
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) {
evecs(j,i)=A_temp(N-1-i,j);
}
}
//END OF LAPACK
#else //IF NO LAPACK
//for now we will solve it only approximatively
int N=Ain.dim[0];
Array2 <doublevar> B_inverse(N,N),A_renorm(N,N);
InvertMatrix(Bin,B_inverse,N);
MultiplyMatrices(B_inverse,Ain,A_renorm,N);
//note A_renorm is not explicitly symmetric
EigenSystemSolverRealSymmetricMatrix(A_renorm,evals,evecs);
#endif //END OF NO LAPACK
}
static HYPRE_Int dsygv_interface (HYPRE_Int *itype, char *jobz, char *uplo, HYPRE_Int *
n, double *a, HYPRE_Int *lda, double *b, HYPRE_Int *ldb,
double *w, double *work, HYPRE_Int *lwork, HYPRE_Int *info)
{
#ifdef HYPRE_USING_ESSL
dsygv(*itype, a, *lda, b, *ldb, w, a, *lda, *n, work, *lwork );
#else
hypre_F90_NAME_LAPACK( dsygv, DSYGV )( itype, jobz, uplo, n,
a, lda, b, ldb,
w, work, lwork, info );
#endif
return 0;
}