NAG Library Function Document

1Purpose

nag_prob_density_landau (g01mtc) returns the value of the Landau density function $\varphi \left(\lambda \right)$.

2Specification

 #include #include
 double nag_prob_density_landau (double x)

3Description

nag_prob_density_landau (g01mtc) evaluates an approximation to the Landau density function $\varphi \left(\lambda \right)$ given by
 $ϕλ=12πi ∫c-i∞ c+i∞expλs+sln⁡sds,$
where $c$ is an arbitrary real constant, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of ${\varphi }^{\prime }\left(\lambda \right)$, nag_prob_der_landau (g01rtc) can be used.

4References

Kölbig K S and Schorr B (1984) A program package for the Landau distribution Comp. Phys. Comm. 31 97–111

5Arguments

1:    $\mathbf{x}$doubleInput
On entry: the argument $\lambda$ of the function.

None.

7Accuracy

At least $7$ significant digits are usually correct, but occasionally only $6$. Such accuracy is normally considered to be adequate for applications in experimental physics.
Because of the asymptotic behaviour of $\varphi \left(\lambda \right)$, which is of the order of $\mathrm{exp}\left[-\mathrm{exp}\left(-\lambda \right)\right]$, underflow may occur on some machines when $\lambda$ is moderately large and negative.

8Parallelism and Performance

nag_prob_density_landau (g01mtc) is not threaded in any implementation.

None.

10Example

This example evaluates $\varphi \left(\lambda \right)$ at $\lambda =0.5$, and prints the results.

10.1Program Text

Program Text (g01mtce.c)

10.2Program Data

Program Data (g01mtce.d)

10.3Program Results

Program Results (g01mtce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017