NAG FL Interface
g01ptf (pdf_​landau_​moment1)

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1 Purpose

g01ptf returns the value of the first moment Φ1(x) of the Landau density function.

2 Specification

Fortran Interface
Function g01ptf ( x)
Real (Kind=nag_wp) :: g01ptf
Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#include <nag.h>
double  g01ptf_ (const double *x)
The routine may be called by the names g01ptf or nagf_stat_pdf_landau_moment1.

3 Description

g01ptf evaluates an approximation to the first moment Φ1 (x) of the Landau density function given by
Φ1(x)=1Φ(x) -xλϕ(λ)dλ,  
where ϕ(λ) is described in g01mtf, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of Φ2(x), g01qtf 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 x 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.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g01ptf is not threaded in any implementation.

9 Further Comments


10 Example

This example evaluates Φ1(x) at x=0.5, and prints the results.

10.1 Program Text

Program Text (g01ptfe.f90)

10.2 Program Data

Program Data (g01ptfe.d)

10.3 Program Results

Program Results (g01ptfe.r)