naginterfaces.library.blas.zhous

naginterfaces.library.blas.zhous(delta, y, theta, z)

zhous applies a complex elementary reflection to a complex vector.

For full information please refer to the NAG Library document for f06ht

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06htf.html

Parameters

deltacomplex

The original scalar $\delta$.

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

The original vector $y$.

thetacomplex

The value $\theta$, as returned by zhousg().

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

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

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

Returns

deltacomplex

The transformed scalar $\delta$.

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

The transformed vector.

Raises

NagValueError

(errno $5$)

On entry, error in parameter $theta$.

Constraint: $Re\left(theta\right)\le 0.0$.

Notes

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

zhous applies a complex elementary reflection (Householder matrix) $P$, as generated by zhousg(), to a given complex vector:

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

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

To apply the conjugate transpose matrix $P^H$, call zhous with $\overline{\theta }$ in place of $\theta$.