naginterfaces.library.blas.zcsgs

naginterfaces.library.blas.zcsgs(t)

zcsgs reconstructs the parameters $c$ (complex) and $s$ (real) of a complex plane rotation from the tangent of that rotation.

For full information please refer to the NAG Library document for f06cd

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f06/f06cdf.html

Parameters

tcomplex

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

Returns

ccomplex

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

sfloat

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

Notes

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

zcsgs reconstructs the parameters $c$ (complex) and $s$ (real) of a complex plane rotation, from the value of the tangent $t$, as returned by zrotgs():

$$c=\frac{sign\left(Re\left(t\right)\right)\left|t\right|}{t\sqrt{1+{\left|t\right|}^2}}\text{,}s=ct\text{.}$$

If $\left|t\right|<\sqrt{ϵ}$, where $ϵ$ is the machine precision, the function sets:

$$c=\frac{sign\left(Re\left(t\right)\right)\left|t\right|}{t}\text{,}s=sign\left(Re\left(t\right)\right)\left|t\right|\text{.}$$