# naginterfaces.library.lapackeig.dorgrq¶

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

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

For full information please refer to the NAG Library document for f08cj

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f08/f08cjf.html

Parameters
afloat, array-like, shape

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

taufloat, array-like, shape

must contain the scalar factor of the elementary reflector , as returned by dgerqf().

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

dorgrq is intended to be used following a call to dgerqf(), which performs an factorization of a real matrix and represents the orthogonal matrix as a product of elementary reflectors of order .

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

Usually is determined from the factorization of a matrix with . The whole of may be computed by calling dorgrq with set to and set to or its trailing rows by calling dorgrq 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 dgerqf() followed by dorgrq can be used to orthogonalize the rows of .

The information returned by dgerqf() also yields the factorization of the trailing rows of , where . The orthogonal matrix arising from this factorization can be computed by calling dorgrq with set to or its leading columns by calling dorgrq with set to .

References

Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug

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