# naginterfaces.library.lapackeig.dsterf¶

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

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

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

https://www.nag.com/numeric/nl/nagdoc_29/flhtml/f08/f08jff.html

Parameters
dfloat, array-like, shape

The diagonal elements of the tridiagonal matrix .

efloat, array-like, shape

The off-diagonal elements of the tridiagonal matrix .

Returns
dfloat, ndarray, shape

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

efloat, ndarray, shape

is overwritten.

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

The algorithm has failed to find all the eigenvalues after a total of iterations; elements of 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 algorithm.

The function uses an explicit shift, and, like dsteqr(), switches between the and 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