naginterfaces.library.lapackeig.dsterf

naginterfaces.library.lapackeig.dsterf(d, e)

dsterf computes all the eigenvalues of a real symmetric tridiagonal matrix.

For full information please refer to the NAG Library document for f08jf

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f08/f08jff.html

Parameters

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

The diagonal elements of the tridiagonal matrix $T$.

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

The off-diagonal elements of the tridiagonal matrix $T$.

Returns

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

The $n$ eigenvalues in ascending order, unless $errno$ > 0 (in which case see Exceptions).

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

$e$ is overwritten.

Raises

NagValueError

(errno $-1$)

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

Constraint: $n\ge 0$.

Warns

NagAlgorithmicWarning

(errno $i>0$)

The algorithm has failed to find all the eigenvalues after a total of $30\times n$ iterations; $⟨value⟩$ elements of $e$ have not converged to zero.

Notes

dsterf computes all the eigenvalues of a real symmetric tridiagonal matrix, using a square-root-free variant of the $QR$ algorithm.

The function uses an explicit shift, and, like dsteqr(), switches between the $QR$ and $QL$ variants in order to handle graded matrices effectively (see Greenbaum and Dongarra (1980)).

References

Greenbaum, A and Dongarra, J J, 1980, Experiments with QR/QL methods for the symmetric triangular eigenproblem, LAPACK Working Note No. 17 (Technical Report CS-89-92), University of Tennessee, Knoxville, https://www.netlib.org/lapack/lawnspdf/lawn17.pdf

Parlett, B N, 1998, The Symmetric Eigenvalue Problem, SIAM, Philadelphia