nag_prob_der_landau (g01rtc) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_prob_der_landau (g01rtc)

+− Contents

    1  Purpose
    2  Specification
    3  Description
    4  References
    5  Arguments
    6  Error Indicators and Warnings
    7  Accuracy
    8  Parallelism and Performance
    9  Further Comments
+− 10  Example

1  Purpose

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

2  Specification

#include <nag.h>
#include <nagg01.h>
double  nag_prob_der_landau (double x)

3  Description

nag_prob_der_landau (g01rtc) evaluates an approximation to the derivative ϕ′λ of the Landau density function given by
ϕ′λ=dϕλ dλ ,
where ϕλ is described in nag_prob_density_landau (g01mtc), using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of ϕλ, nag_prob_density_landau (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 – doubleInput
On entry: the argument λ of the function.

6  Error Indicators and Warnings

None.

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

Not applicable.

9  Further Comments

None.

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)

nag_prob_der_landau (g01rtc) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual
© The Numerical Algorithms Group Ltd, Oxford, UK. 2014