int
gsl_eigen_gensymm (gsl_matrix * A, gsl_matrix * B, gsl_vector * eval,
gsl_eigen_gensymm_workspace * w)
{
const size_t N = A->size1;
/* check matrix and vector sizes */
if (N != A->size2)
{
GSL_ERROR ("matrix must be square to compute eigenvalues", GSL_ENOTSQR);
}
else if ((N != B->size1) || (N != B->size2))
{
GSL_ERROR ("B matrix dimensions must match A", GSL_EBADLEN);
}
else if (eval->size != N)
{
GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN);
}
else if (w->size != N)
{
GSL_ERROR ("matrix size does not match workspace", GSL_EBADLEN);
}
else
{
int s;
/* compute Cholesky factorization of B */
s = gsl_linalg_cholesky_decomp(B);
if (s != GSL_SUCCESS)
return s; /* B is not positive definite */
/* transform to standard symmetric eigenvalue problem */
gsl_eigen_gensymm_standardize(A, B);
s = gsl_eigen_symm(A, eval, w->symm_workspace_p);
return s;
}
} /* gsl_eigen_gensymm() */
int
gsl_eigen_gensymmv (gsl_matrix * A, gsl_matrix * B, gsl_vector * eval,
gsl_matrix * evec, gsl_eigen_gensymmv_workspace * w)
{
const size_t N = A->size1;
/* check matrix and vector sizes */
if (N != A->size2)
{
GSL_ERROR ("matrix must be square to compute eigenvalues", GSL_ENOTSQR);
}
else if ((N != B->size1) || (N != B->size2))
{
GSL_ERROR ("B matrix dimensions must match A", GSL_EBADLEN);
}
else if (eval->size != N)
{
GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN);
}
else if (evec->size1 != evec->size2)
{
GSL_ERROR ("eigenvector matrix must be square", GSL_ENOTSQR);
}
else if (evec->size1 != N)
{
GSL_ERROR ("eigenvector matrix has wrong size", GSL_EBADLEN);
}
else if (w->size != N)
{
GSL_ERROR ("matrix size does not match workspace", GSL_EBADLEN);
}
else
{
int s;
/* compute Cholesky factorization of B */
s = gsl_linalg_cholesky_decomp(B);
if (s != GSL_SUCCESS)
return s; /* B is not positive definite */
/* transform to standard symmetric eigenvalue problem */
gsl_eigen_gensymm_standardize(A, B);
/* compute eigenvalues and eigenvectors */
s = gsl_eigen_symmv(A, eval, evec, w->symmv_workspace_p);
if (s != GSL_SUCCESS)
return s;
/* backtransform eigenvectors: evec -> L^{-T} evec */
gsl_blas_dtrsm(CblasLeft,
CblasLower,
CblasTrans,
CblasNonUnit,
1.0,
B,
evec);
/* the blas call destroyed the normalization - renormalize */
gensymmv_normalize_eigenvectors(evec);
return GSL_SUCCESS;
}
} /* gsl_eigen_gensymmv() */
