naginterfaces.library.blas.dlhousg

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

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

For full information please refer to the NAG Library document for f06fs

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f06/f06fsf.html

Parameters
alphafloat

The scalar .

xfloat, array-like, shape

The -element vector .

tolfloat

The value .

If is not in the range , the value is used for .

Returns
alphafloat

The scalar .

xfloat, ndarray, shape

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

z1float

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.

dlhousg 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. (This form is compatible with that used by LINPACK.)

If the elements of are all zero, or if the elements of are all less than in absolute value, then is set to and can be taken to be the unit matrix. Otherwise always lies in the range .