naginterfaces.library.lapackeig.dorgql

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

dorgql generates all or part of the real orthogonal matrix from a factorization computed by dgeqlf().

For full information please refer to the NAG Library document for f08cf

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f08/f08cff.html

Parameters
afloat, array-like, shape

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

taufloat, array-like, shape

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

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

dorgql is intended to be used after a call to dgeqlf(), which performs a 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 trailing columns.

Usually is determined from the factorization of an matrix with . The whole of may be computed by calling dorgql with set to and set to or its trailing columns by calling dorgql with and set to .

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

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