NAG CL Interface
g01rtc (pdf_​landau_​deriv)

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1 Purpose

g01rtc returns the value of the derivative ϕ(λ) of the Landau density function.

2 Specification

#include <nag.h>
double  g01rtc (double x)
The function may be called by the names: g01rtc, nag_stat_pdf_landau_deriv or nag_prob_der_landau.

3 Description

g01rtc evaluates an approximation to the derivative ϕ(λ) of the Landau density function given by
ϕ(λ)=dϕ(λ) dλ ,  
where ϕ(λ) is described in g01mtc, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of ϕ(λ), g01mtc 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 double 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.
g01rtc 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 (g01rtce.c)

10.2 Program Data

Program Data (g01rtce.d)

10.3 Program Results

Program Results (g01rtce.r)