naginterfaces.library.lapackeig.dstev

naginterfaces.library.lapackeig.dstev(jobz, d, e)

dstev computes all the eigenvalues and, optionally, all the eigenvectors of a real $n\times n$ symmetric tridiagonal matrix $A$.

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

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f08/f08jaf.html

Parameters

jobzstr, length 1

Indicates whether eigenvectors are computed.

$jobz=\text{'N'}$

Only eigenvalues are computed.

$jobz=\text{'V'}$

Eigenvalues and eigenvectors are computed.

dfloat, array-like, shape $\left(n\right)$

The $n$ diagonal elements of the tridiagonal matrix $A$.

efloat, array-like, shape $(n-1)$

The $(n-1)$ subdiagonal elements of the tridiagonal matrix $A$.

Returns

dfloat, ndarray, shape $\left(n\right)$

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

efloat, ndarray, shape $(n-1)$

The contents of $e$ are destroyed.

zfloat, ndarray, shape $(:,:)$

If $jobz=\text{'V'}$, then if no exception or warning is raised, $z$ contains the orthonormal eigenvectors of the matrix $A$, with the $i$th column of $Z$ holding the eigenvector associated with $d[i-1]$.

If $jobz=\text{'N'}$, $z$ is not referenced.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $jobz$.

Constraint: $jobz=\text{'N'}$ or $\text{'V'}$.

(errno $-2$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

(errno $i>0$)

The algorithm failed to converge; $⟨value⟩$ off-diagonal elements of $e$ did not converge to zero.

Notes

dstev computes all the eigenvalues and, optionally, all the eigenvectors of $A$ using a combination of the $QR$ and $QL$ 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