naginterfaces.library.lapackeig.zungql

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

zungql generates all or part of the complex unitary matrix from a factorization computed by zgeqlf().

For full information please refer to the NAG Library document for f08ct

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f08/f08ctf.html

Parameters
acomplex, array-like, shape

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

taucomplex, array-like, shape

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

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

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

Usually is determined from the factorization of an matrix with . The whole of may be computed by calling zungql with set to or its trailing columns by calling zungql 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 zgeqlf() followed by zungql can be used to orthogonalize the columns of .

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