NAG FL Interface
g01mtf (pdf_​landau)

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1 Purpose

g01mtf returns the value of the Landau density function ϕ(λ).

2 Specification

Fortran Interface
Function g01mtf ( x)
Real (Kind=nag_wp) :: g01mtf
Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#include <nag.h>
double  g01mtf_ (const double *x)
The routine may be called by the names g01mtf or nagf_stat_pdf_landau.

3 Description

g01mtf evaluates an approximation to the Landau density function ϕ(λ) given by
ϕ(λ)=12πi c-i c+iexp(λs+slns)ds,  
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 ϕ(λ), 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 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.
g01mtf 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 (g01mtfe.f90)

10.2 Program Data

Program Data (g01mtfe.d)

10.3 Program Results

Program Results (g01mtfe.r)