naginterfaces.library.lapackeig.dstev

naginterfaces.library.lapackeig.dstev(jobz, d, e)[source]

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

For full information please refer to the NAG Library document for f08ja

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f08/f08jaf.html

Parameters
jobzstr, length 1

Indicates whether eigenvectors are computed.

Only eigenvalues are computed.

Eigenvalues and eigenvectors are computed.

dfloat, array-like, shape

The diagonal elements of the tridiagonal matrix .

efloat, array-like, shape

The subdiagonal elements of the tridiagonal matrix .

Returns
dfloat, ndarray, shape

If no exception or warning is raised, the eigenvalues in ascending order.

efloat, ndarray, shape

The contents of are destroyed.

zfloat, ndarray, shape

If , then if no exception or warning is raised, 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: .

(errno )

The algorithm failed to converge; off-diagonal elements of did not converge to zero.

Notes

dstev computes all the eigenvalues and, optionally, all the eigenvectors of using a combination of the and algorithms, with an implicit shift.

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