naginterfaces.library.blas.dcsg

naginterfaces.library.blas.dcsg(t)

dcsg reconstructs the parameters $c$ and $s$ of a real plane rotation from the tangent of that rotation.

For full information please refer to the NAG Library document for f06bc

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f06/f06bcf.html

Parameters

tfloat

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

Returns

cfloat

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.

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

$$c=\frac{1}{\sqrt{1+t^2}}\text{,}s=ct\text{,}$$

so that $c\ge 0$ and $s$ has the same sign as $t$.

If $\left|t\right|<\sqrt{ϵ}$, where $ϵ$ is the machine precision, the function sets $c=1$ and $s=t$; if $\left|t\right|>1/\sqrt{ϵ}$, the function sets $c=\frac{1}{\left|t\right|}$ and $s=sign\left(t\right)$.