naginterfaces.library.lapackeig.zungqr

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

zungqr generates all or part of the complex unitary matrix from a factorization computed by zgeqrf() or zgeqp3().

For full information please refer to the NAG Library document for f08at

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f08/f08atf.html

Parameters
acomplex, array-like, shape

Details of the vectors which define the elementary reflectors, as returned by zgeqrf() or zgeqp3().

taucomplex, array-like, shape

Further details of the elementary reflectors, as returned by zgeqrf() or zgeqp3().

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

zungqr is intended to be used after a call to zgeqrf() or zgeqp3(), which perform 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 leading columns.

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

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

References

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