NAG FL Interface
g01rtf (pdf_​landau_​deriv)

1 Purpose

g01rtf returns the value of the derivative ϕλ of the Landau density function.

2 Specification

Fortran Interface
Function g01rtf ( x)
Real (Kind=nag_wp) :: g01rtf
Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#include <nag.h>
double  g01rtf_ (const double *x)
The routine may be called by the names g01rtf or nagf_stat_pdf_landau_deriv.

3 Description

g01rtf evaluates an approximation to the derivative ϕλ of the Landau density function given by
ϕλ=dϕλ dλ ,  
where ϕλ 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 ϕλ, g01mtf 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 ϕλ, 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

g01rtf is not threaded in any implementation.

9 Further Comments


10 Example

This example evaluates ϕλ at λ=0.5, and prints the results.

10.1 Program Text

Program Text (g01rtfe.f90)

10.2 Program Data

Program Data (g01rtfe.d)

10.3 Program Results

Program Results (g01rtfe.r)