naginterfaces.library.blas.dnhous

naginterfaces.library.blas.dnhous(delta, y, zeta, z)

dnhous applies a NAG (as opposed to LINPACK) style real elementary reflection to a real vector.

For full information please refer to the NAG Library document for f06ft

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06ftf.html

Parameters

deltafloat

The original scalar $\delta$.

yfloat, array-like, shape $\left(n\right)$

The original vector $y$.

zetafloat

The scalar $\zeta$, as returned by dnhousg().

If $\zeta =0$, $P$ is assumed to be the unit matrix and the transformation is skipped.

zfloat, array-like, shape $\left(n\right)$

The vector $z$, as returned by dnhousg().

Returns

deltafloat

The transformed scalar $\delta$.

yfloat, ndarray, shape $\left(n\right)$

The transformed vector.

Raises

NagValueError

(errno $5$)

On entry, error in parameter $zeta$.

Constraint: $zeta=0.0$.

Notes

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

dnhous applies a real elementary reflection (Householder matrix) $P$, as generated by dnhousg(), to a given real vector:

$$\begin{array}{c}\left(\begin{array}{c}\delta \\ y\end{array}\right)\leftarrow P\left(\begin{array}{c}\delta \\ y\end{array}\right)\text{,}\end{array}$$

where $y$ is an $n$-element real vector and $\delta$ a real scalar.