naginterfaces.library.blas.drotgc

naginterfaces.library.blas.drotgc(a, b)

drotgc generates a real Givens plane rotation and the tangent of that rotation.

For full information please refer to the NAG Library document for f06ba

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f06/f06baf.html

Parameters

afloat

The value $a$, the first element of the vector which determines the rotation.

bfloat

The value $b$, the second element of the vector which determines the rotation.

Returns

afloat

The value $d$.

bfloat

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

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.

drotgc generates a real Givens plane rotation with parameters $c$ ($\ge 0$) and $s$, such that, given real $a$ and $b$:

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

On exit, $b$ is overwritten by $t$, the tangent of the rotation; $c$ and $s$ can be reconstructed from the single stored value $t$, by a subsequent call to dcsg().

If $\left|b\right|<\sqrt{ϵ}\left|a\right|$, where $ϵ$ is the machine precision, the function sets $c=1$ and $s=0$; if $\left|a\right|<\sqrt{ϵ}\left|b\right|$, the function sets $c=0$ and $s=sign\left(b\right)/a$.

Note that $t$ is always set to $b/a$, unless this would overflow, in which case the value $\text{flmax}\times sign\left(b\right)/a$ is returned, where $\text{flmax}$ is the value given by $1/\left(\text{machine.real\_safe}\right)$.

To apply the plane rotation to a pair of real vectors, call drot(); to apply it to a pair of complex vectors, call zdrot().