naginterfaces.library.blas.dlhous

naginterfaces.library.blas.dlhous(z, z1, alpha, x)

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

For full information please refer to the NAG Library document for f06fu

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06fuf.html

Parameters

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

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

z1float

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

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

alphafloat

The original scalar $\alpha$.

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

The original vector $x$.

Returns

alphafloat

The transformed scalar $\alpha$.

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

The transformed vector $x$.

Notes

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

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

$$\begin{array}{c}\left(\begin{array}{c}\alpha \\ x\end{array}\right)\leftarrow P\left(\begin{array}{c}\alpha \\ x\end{array}\right)\end{array}$$

where $x$ is an $n$-element real vector and $\alpha$ a real scalar.