naginterfaces.library.blas.dnhousg

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

dnhousg generates a real elementary reflection in the NAG (as opposed to LINPACK) style.

For full information please refer to the NAG Library document for f06fr

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f06/f06frf.html

Parameters
alphafloat

The scalar .

xfloat, array-like, shape

The -element vector .

tolfloat

The value .

Returns
alphafloat

The scalar .

xfloat, ndarray, shape

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

zetafloat

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.

dnhousg generates details of a real elementary reflection (Householder matrix), , such that

where is orthogonal, and are real scalars, and is an -element real vector.

is given in the form

where is an -element real vector and is a real scalar.

If is such that

where is the machine precision and is a user-supplied tolerance, then is set to , and can be taken to be the unit matrix. Otherwise .