g01et: FL CL CPP AD PY MB

NAG FL Interface
g01etf (prob_landau)

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NAG Library Manual, Mark 28.6

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction

g01et: FL CL CPP AD PY MB

▸▿ 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

10.1 Program Text

10.2 Program Data

10.3 Program Results

1 Purpose

g01etf returns the value of the Landau distribution function

Φ (λ)

2 Specification

Fortran Interface

Function g01etf (

Real (Kind=nag_wp)	::	g01etf
Real (Kind=nag_wp), Intent (In)	::	x

C Header Interface

#include <nag.h>

double

g01etf_ (const double *x)

The routine may be called by the names g01etf or nagf_stat_prob_landau.

3 Description

g01etf evaluates an approximation to the Landau distribution function

Φ (λ)

given by

Φ (λ) = \int_{- \infty}^{λ} 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).

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

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

Background information to multithreading can be found in the Multithreading documentation.

g01etf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example evaluates

Φ (λ)

λ = 0.5

, and prints the results.

g01et: FL CL CPP AD PY MB

NAG FL Interfaceg01etf (prob_​landau)

▸▿ 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

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g01etf (prob_landau)