NAG Library Routine Document

G01RTF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

G01RTF returns the value of the derivative

ϕ^{'} (λ)

of the Landau density function, via the routine name.

2 Specification

FUNCTION G01RTF (

REAL (KIND=nag_wp) G01RTF

REAL (KIND=nag_wp)

3 Description

G01RTF evaluates an approximation to the derivative

ϕ^{'} (λ)

of the Landau density function given by

ϕ^{'} (λ) = \frac{d ϕ (λ)}{d λ},

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

ϕ (λ)

, 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

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 Further Comments

None.

9 Example

This example evaluates

ϕ^{'} (λ)

λ = 0.5

, and prints the results.

NAG Library Routine DocumentG01RTF