# naginterfaces.library.lapackeig.dopgtr¶

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

dopgtr generates the real orthogonal matrix , which was determined by dsptrd() when reducing a symmetric matrix to tridiagonal form.

For full information please refer to the NAG Library document for f08gf

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/f08/f08gff.html

Parameters
uplostr, length 1

This must be the same argument as supplied to dsptrd().

nint

, the order of the matrix .

apfloat, array-like, shape

Details of the vectors which define the elementary reflectors, as returned by dsptrd().

taufloat, array-like, shape

Further details of the elementary reflectors, as returned by dsptrd().

Returns
qfloat, ndarray, shape

The orthogonal matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: or .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dopgtr is intended to be used after a call to dsptrd(), which reduces a real symmetric matrix to symmetric tridiagonal form by an orthogonal similarity transformation: . dsptrd() represents the orthogonal matrix as a product of elementary reflectors.

This function may be used to generate explicitly as a square matrix.

References

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