# naginterfaces.library.lapackeig.dorglq¶

naginterfaces.library.lapackeig.dorglq(a, tau)[source]

dorglq generates all or part of the real orthogonal matrix from an factorization computed by dgelqf().

For full information please refer to the NAG Library document for f08aj

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08ajf.html

Parameters
afloat, array-like, shape

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

taufloat, array-like, shape

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

Returns
afloat, ndarray, shape

The matrix .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

dorglq is intended to be used after a call to dgelqf(), which performs an factorization of a real matrix . The orthogonal matrix is represented as a product of elementary reflectors.

This function may be used to generate explicitly as a square matrix, or to form only its leading rows.

Usually is determined from the factorization of a matrix with . The whole of may be computed by calling dorglq with set to and set to or its leading rows by calling dorglq with and set to .

The rows of returned by the last call form an orthonormal basis for the space spanned by the rows of ; thus dgelqf() followed by dorglq can be used to orthogonalize the rows of .

The information returned by the factorization functions also yields the factorization of the leading rows of , where . The orthogonal matrix arising from this factorization can be computed by calling dorglq with set to or its leading rows by calling dorglq with set to .

References

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