naginterfaces.library.lapackeig.zhpev

naginterfaces.library.lapackeig.zhpev(jobz, uplo, n, ap)[source]

zhpev computes all the eigenvalues and, optionally, all the eigenvectors of a complex Hermitian matrix in packed storage.

For full information please refer to the NAG Library document for f08gn

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f08/f08gnf.html

Parameters
jobzstr, length 1

Indicates whether eigenvectors are computed.

Only eigenvalues are computed.

Eigenvalues and eigenvectors are computed.

uplostr, length 1

If , the upper triangular part of is stored.

If , the lower triangular part of is stored.

nint

, the order of the matrix .

apcomplex, array-like, shape

The upper or lower triangle of the Hermitian matrix , packed by columns.

Returns
apcomplex, ndarray, shape

is overwritten by the values generated during the reduction to tridiagonal form. The elements of the diagonal and the off-diagonal of the tridiagonal matrix overwrite the corresponding elements of .

wfloat, ndarray, shape

The eigenvalues in ascending order.

zcomplex, ndarray, shape

If , contains the orthonormal eigenvectors of the matrix , with the th column of holding the eigenvector associated with .

If , is not referenced.

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

The algorithm failed to converge; off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

Notes

The Hermitian matrix is first reduced to real tridiagonal form, using unitary similarity transformations, and then the algorithm is applied to the tridiagonal matrix to compute the eigenvalues and (optionally) the eigenvectors.

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore