naginterfaces.library.blas.zrot

naginterfaces.library.blas.zrot(cx, cy, c, s)

zrot applies a plane rotation with a real cosine and complex sine to two complex vectors.

For full information please refer to the NAG Library document for f06hm

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06hmf.html

Parameters

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

The $n$-element vector $x$.

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

The $n$-element vector $y$.

cfloat

The value $c$, the cosine of the rotation.

scomplex

The value $s$, the sine of the rotation.

Returns

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

The transformed vector $x$.

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

The transformed vector $y$.

Notes

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

zrot applies a plane rotation, where the cosine is real and the sine is complex, to two $n$-element complex vectors $x$ and $y$:

$$\begin{array}{c}\left(\begin{array}{c}{x}^T\\ y^T\end{array}\right)\leftarrow \left(\begin{array}{cc}c& s\\ -\overline{s}& c\end{array}\right)\left(\begin{array}{c}{x}^T\\ y^T\end{array}\right)\text{.}\end{array}$$