naginterfaces.library.blas.zrot2

naginterfaces.library.blas.zrot2(x, y, z, c, s)

zrot2 applies a complex similarity rotation having real cosine and complex sine to a $2\times 2$ complex Hermitian matrix.

For full information please refer to the NAG Library document for f06ch

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06chf.html

Parameters

xcomplex

The value $x$, the $(1,1)$ element of the input matrix.

ycomplex

The value $y$, the $(1,2)$ element of the input matrix.

zcomplex

The value $z$, the $(2,2)$ element of the input matrix.

cfloat

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

scomplex

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

Returns

xcomplex

The transformed value $x$.

ycomplex

The transformed value $y$.

zcomplex

The transformed value $z$.

Notes

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

zrot2 applies a complex similarity rotation, with parameters $c$ (real) and $s$ (complex), to a given $2\times 2$ complex Hermitian matrix; that is, it performs the operation:

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

where $x$ and $z$ are real.

The argument $x$ and $z$ which hold $x$ and $z$ are declared complex for convenience when using the function to operate on submatrices of larger Hermitian matrices.

Note that:

$$\begin{array}{c}\left(\begin{array}{cc}z& \overline{y}\\ y& x\end{array}\right)\leftarrow \left(\begin{array}{cc}c& \overline{w}\\ -w& c\end{array}\right)\left(\begin{array}{cc}z& \overline{y}\\ y& x\end{array}\right)\left(\begin{array}{cc}c& -\overline{w}\\ w& c\end{array}\right)\text{,}\end{array}$$

where $w=-\overline{s}$, so to use zrot2 when $y$ is the $(2,1)$ element of the matrix, you can make the call to zrot2 using $s=w$