naginterfaces.library.lapackeig.dsptrd

naginterfaces.library.lapackeig.dsptrd(uplo, n, ap)[source]

dsptrd reduces a real symmetric matrix to tridiagonal form, using packed storage.

For full information please refer to the NAG Library document for f08ge

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/f08/f08gef.html

Parameters
uplostr, length 1

Indicates whether the upper or lower triangular part of is stored.

The upper triangular part of is stored.

The lower triangular part of is stored.

nint

, the order of the matrix .

apfloat, array-like, shape

The upper or lower triangle of the symmetric matrix , packed by columns.

Returns
apfloat, ndarray, shape

is overwritten by the tridiagonal matrix and details of the orthogonal matrix .

dfloat, ndarray, shape

The diagonal elements of the tridiagonal matrix .

efloat, ndarray, shape

The off-diagonal elements of the tridiagonal matrix .

taufloat, ndarray, shape

Further details of the orthogonal matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dsptrd reduces a real symmetric matrix , held in packed storage, to symmetric tridiagonal form by an orthogonal similarity transformation: .

The matrix is not formed explicitly but is represented as a product of elementary reflectors (see the F08 Introduction for details). Functions are provided to work with in this representation (see Further Comments).

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore