naginterfaces.library.lapackeig.zheev

naginterfaces.library.lapackeig.zheev(jobz, uplo, a)[source]

zheev computes all the eigenvalues and, optionally, all the eigenvectors of a complex Hermitian matrix .

For full information please refer to the NAG Library document for f08fn

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/f08/f08fnf.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.

acomplex, array-like, shape

The Hermitian matrix .

Returns
aNone or complex, ndarray, shape

If , contains the orthonormal eigenvectors of the matrix .

wfloat, ndarray, shape

The eigenvalues in ascending order.

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: .

Warns
NagAlgorithmicWarning
(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