A hermitian matrix A can be factorized by similarity transformations into the form,
A = U T U^T
where U is a unitary matrix and T is a real symmetric tridiagonal matrix.
This function factorizes the hermitian matrix A into the symmetric tridiagonal decomposition U T U^T. On output the real parts of the diagonal and subdiagonal part of the input matrix A contain the tridiagonal matrix T. The remaining lower triangular part of the input matrix contains the Householder vectors which, together with the Householder coefficients tau, encode the unitary matrix U. This storage scheme is the same as used by LAPACK. The upper triangular part of A and imaginary parts of the diagonal are not referenced.
This function unpacks the encoded tridiagonal decomposition (A,
tau) obtained from
gsl_linalg_hermtd_decomp into the
unitary matrix U, the real vector of diagonal elements diag and
the real vector of subdiagonal elements subdiag.
This function unpacks the diagonal and subdiagonal of the encoded
tridiagonal decomposition (A, tau) obtained from the
gsl_linalg_hermtd_decomp into the real vectors
diag and subdiag.