naginterfaces.library.lapackeig.dsbev¶

naginterfaces.library.lapackeig.dsbev(jobz, uplo, kd, ab)[source]

dsbev computes all the eigenvalues and, optionally, all the eigenvectors of a real symmetric band matrix of bandwidth .

For full information please refer to the NAG Library document for f08ha

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08haf.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.

kdint

If , the number of superdiagonals, , of the matrix .

If , the number of subdiagonals, , of the matrix .

abfloat, array-like, shape

The upper or lower triangle of the symmetric band matrix .

Returns
abfloat, ndarray, shape

is overwritten by values generated during the reduction to tridiagonal form.

The first superdiagonal or subdiagonal and the diagonal of the tridiagonal matrix are returned in using the same storage format as described above.

wfloat, ndarray, shape

The eigenvalues in ascending order.

zfloat, 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 )

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 band 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