naginterfaces.library.lapackeig.dsyev

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

dsyev computes all the eigenvalues and, optionally, all the eigenvectors of a real symmetric matrix .

For full information please refer to the NAG Library document for f08fa

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f08/f08faf.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.

afloat, array-like, shape

The symmetric matrix .

Returns
aNone or float, 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: .

(errno )

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

Notes

The symmetric matrix is first reduced to tridiagonal form, using orthogonal 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