naginterfaces.library.blas.zhousg

naginterfaces.library.blas.zhousg(alpha, x, tol)[source]

zhousg generates a complex elementary reflection.

For full information please refer to the NAG Library document for f06hr

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f06/f06hrf.html

Parameters
alphacomplex

The scalar .

xcomplex, array-like, shape

The -element vector .

tolfloat

The value .

Returns
alphacomplex

The scalar .

xcomplex, ndarray, shape

The referenced elements are overwritten by details of the complex elementary reflection.

thetacomplex

The scalar .

Raises
NagValueError
(errno )

On entry, error in parameter .

Constraint: .

Notes

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

zhousg generates details of a complex elementary reflection (Householder matrix), , such that

where is unitary, is a complex scalar, is a real scalar, and is an -element complex vector.

is given in the form

where is an -element complex vector, is a complex scalar such that , and is a real scalar. and are returned in a single complex value . Thus and .

If is such that

where is the machine precision and is a user-supplied tolerance, then:

either is set to , in which case can be taken to be the unit matrix;

or is set so that and , in which case

Otherwise .