NAG FL Interface
g01etf (prob_​landau)

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1 Purpose

g01etf returns the value of the Landau distribution function Φ(λ).

2 Specification

Fortran Interface
Function g01etf ( x)
Real (Kind=nag_wp) :: g01etf
Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#include <nag.h>
double  g01etf_ (const double *x)
The routine may be called by the names g01etf or nagf_stat_prob_landau.

3 Description

g01etf evaluates an approximation to the Landau distribution function Φ(λ) given by
where ϕ(λ) is described in g01mtf, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).

4 References

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

5 Arguments

1: x Real (Kind=nag_wp) Input
On entry: the argument λ of the function.

6 Error Indicators and Warnings


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 Φ(λ), which is of the order of exp[-exp(-λ)], underflow may occur on some machines when λ is moderately large and negative.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g01etf is not threaded in any implementation.

9 Further Comments


10 Example

This example evaluates Φ(λ) at λ=0.5, and prints the results.

10.1 Program Text

Program Text (g01etfe.f90)

10.2 Program Data

Program Data (g01etfe.d)

10.3 Program Results

Program Results (g01etfe.r)