naginterfaces.library.blas.drotj

naginterfaces.library.blas.drotj(job, x, y, z)

drotj generates a real Jacobi plane rotation.

For full information please refer to the NAG Library document for f06be

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f06/f06bef.html

Parameters

jobstr, length 1

Specifies the property which determines the precise form of the rotation.

$job=\text{'B'}$

$c\ge 1/\sqrt{2}$.

$job=\text{'S'}$

$0\le c\le 1/\sqrt{2}$.

$job=\text{'M'}$

$\left|a\right|\ge \left|b\right|$.

xfloat

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

yfloat

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

zfloat

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

Returns

xfloat

The value $a$.

yfloat

The value $t$, the tangent of the rotation.

zfloat

The value $b$.

cfloat

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

sfloat

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

Raises

NagValueError

(errno $1$)

On entry, error in parameter $job$.

Constraint: $job=\text{'B'}$, $\text{'S'}$ or $\text{'M'}$.

Notes

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

drotj generates a real Jacobi plane rotation with parameters $c$ and $s$, which diagonalizes a given $2\times 2$ real symmetric matrix:

$$\begin{array}{c}\left(\begin{array}{cc}c& s\\ -s& c\end{array}\right)\left(\begin{array}{cc}x& y\\ y& z\end{array}\right)\left(\begin{array}{cc}c& -s\\ s& c\end{array}\right)=\left(\begin{array}{cc}a& 0\\ 0& b\end{array}\right)\text{.}\end{array}$$