G01RTF (PDF version)
G01 Chapter Contents
G01 Chapter Introduction
NAG Library Manual

NAG Library Routine Document


Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

G01RTF returns the value of the derivative ϕλ of the Landau density function, via the routine name.

2  Specification

REAL (KIND=nag_wp) G01RTF
REAL (KIND=nag_wp)  X

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  Parameters

1:     X – REAL (KIND=nag_wp)Input
On entry: the argument λ of the function.

6  Error Indicators and Warnings

There are no failure exits from this routine.

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  Further Comments


9  Example

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

9.1  Program Text

Program Text (g01rtfe.f90)

9.2  Program Data

Program Data (g01rtfe.d)

9.3  Program Results

Program Results (g01rtfe.r)

G01RTF (PDF version)
G01 Chapter Contents
G01 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012