naginterfaces.library.lapackeig.ztzrzf¶

naginterfaces.library.lapackeig.ztzrzf(a)[source]

ztzrzf reduces the () complex upper trapezoidal matrix to upper triangular form by means of unitary transformations.

For full information please refer to the NAG Library document for f08bv

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f08/f08bvf.html

Parameters
acomplex, array-like, shape

The leading upper trapezoidal part of the array must contain the matrix to be factorized.

Returns
acomplex, ndarray, shape

The leading upper triangular part of contains the upper triangular matrix , and elements to of the first rows of , with the array , represent the unitary matrix as a product of elementary reflectors (see the F08 Introduction).

taucomplex, ndarray, shape

The scalar factors of the elementary reflectors.

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

The () complex upper trapezoidal matrix given by

where is an upper triangular matrix and is an matrix, is factorized as

where is also an upper triangular matrix and is an unitary matrix.

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