naginterfaces.library.complex.abs

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

abs returns the value of the modulus of the complex number $x=(x_r,x_i)$.

For full information please refer to the NAG Library document for a02ab

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/a02/a02abf.html

Parameters

xrfloat

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

xifloat

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

Returns

xafloat

The modulus of the complex number $x=(x_r,x_i)$.

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 function evaluates $\sqrt{x_r^2+x_i^2}$ by using $a\sqrt{1+{\left(\frac{b}{a}\right)}^2}$ where $a$ is the larger of $\left|x_r\right|$ and $\left|x_i\right|$, and $b$ is the smaller of $\left|x_r\right|$ and $\left|x_i\right|$. This ensures against unnecessary overflow and loss of accuracy when calculating $(x_r^2+x_i^2)$.

References

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