naginterfaces.library.complex.sqrt

naginterfaces.library.complex.sqrt(xr, xi)

sqrt evaluates the square root of the complex number $x=(x_r,x_i)$.

For full information please refer to the NAG Library document for a02aa

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/a02/a02aaf.html

Parameters

xrfloat

$x_r$, the real part of $x$.

xifloat

$x_i$, the imaginary part of $x$.

Returns

yrfloat

$y_r$, the real part of $y$.

yifloat

$y_i$, the imaginary part of $y$.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

The method of evaluating $y=\sqrt{x}$ depends on the value of $x_r$.

For $x_r\ge 0$,

$$y_r=\sqrt{\frac{x_r+\sqrt{x_r^2+x_i^2}}{2}}\text{,}{y}_i=\frac{x_i}{2y_r}\text{.}$$

For $x_r<0$,

$$y_i=sign\left(x_i\right)\times \sqrt{\frac{\left|x_r\right|+\sqrt{x_r^2+x_i^2}}{2}}\text{,}{y}_r=\frac{x_i}{2y_i}\text{.}$$

Overflow is avoided when squaring $x_i$ and $x_r$ by calling abs() to evaluate $\sqrt{x_r^2+x_i^2}$.

References

Wilkinson, J H and Reinsch, C, 1971, Handbook for Automatic Computation II, Linear Algebra, Springer–Verlag