naginterfaces.library.blas.zutupd

naginterfaces.library.blas.zutupd(alpha, x, a)[source]

zutupd performs a factorization (as a sequence of plane rotations) of a complex upper triangular matrix that has been augmented by a full row.

For full information please refer to the NAG Library document for f06tq

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f06/f06tqf.html

Parameters
alphacomplex

The scalar .

xcomplex, array-like, shape

The -element vector .

acomplex, array-like, shape

The upper triangular matrix .

Returns
xcomplex, ndarray, shape

The referenced elements are overwritten by details of the sequence of plane rotations.

acomplex, ndarray, shape

The upper triangular matrix .

cfloat, ndarray, shape

The values , the cosines of the rotations , for .

scomplex, ndarray, shape

The values , the sines of the rotations , for .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

(errno )

On entry, error in parameter .

Constraint: .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

zutupd performs the factorization

where and are complex upper triangular matrices, is an -element complex vector, is a complex scalar, and is a complex unitary matrix. If has real diagonal elements, then so does .

is formed as a sequence of plane rotations

where is a rotation in the plane, chosen to annihilate .

The plane rotation part of has the form

with real.