G01 Chapter Contents
G01 Chapter Introduction
NAG Library Manual

NAG Library Routine DocumentG01MTF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

1  Purpose

G01MTF returns the value of the Landau density function $\varphi \left(\lambda \right)$, via the routine name.

2  Specification

 FUNCTION G01MTF ( X)
 REAL (KIND=nag_wp) G01MTF
 REAL (KIND=nag_wp) X

3  Description

G01MTF 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 ${\varphi }^{\prime }\left(\lambda \right)$, G01RTF can be used.

4  References

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

5  Parameters

1:     X – REAL (KIND=nag_wp)Input
On entry: the argument $\lambda$ of the function.

6  Error Indicators and Warnings

There are no failure exits from this routine.

7  Accuracy

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.

None.

9  Example

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

9.1  Program Text

Program Text (g01mtfe.f90)

9.2  Program Data

Program Data (g01mtfe.d)

9.3  Program Results

Program Results (g01mtfe.r)