naginterfaces.library.lapackeig.zunglq

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

zunglq generates all or part of the complex unitary matrix from an factorization computed by zgelqf().

For full information please refer to the NAG Library document for f08aw

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/f08/f08awf.html

Parameters
acomplex, array-like, shape

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

taucomplex, array-like, shape

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

Returns
acomplex, 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

zunglq is intended to be used after a call to zgelqf(), which performs an factorization of a complex matrix . The unitary 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 zunglq with set to and set to or its leading rows by calling zunglq 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 zgelqf() followed by zunglq 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 unitary matrix arising from this factorization can be computed by calling zunglq with set to or its leading rows by calling zunglq with set to .

References

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