g01mt: FL CL CPP AD PY MB

NAG FL Interface
g01mtf (pdf_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

g01mt: 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

g01mtf returns the value of the Landau density function

ϕ (λ)

2 Specification

Fortran Interface

Function g01mtf (

Real (Kind=nag_wp)	::	g01mtf
Real (Kind=nag_wp), Intent (In)	::	x

C Header Interface

#include <nag.h>

double

g01mtf_ (const double *x)

The routine may be called by the names g01mtf or nagf_stat_pdf_landau.

3 Description

g01mtf evaluates an approximation to the Landau density function

ϕ (λ)

given by

ϕ (λ) = \frac{1}{2 π i} \int_{c - i \infty}^{c + i \infty} \exp (λ s + s \ln s) d s,

where

c

is an arbitrary real constant, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).

To obtain the value of

ϕ^{'} (λ)

, g01rtf 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: $x$ – 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.

g01mtf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example evaluates

ϕ (λ)

λ = 0.5

, and prints the results.

g01mt: FL CL CPP AD PY MB

NAG FL Interfaceg01mtf (pdf_​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
g01mtf (pdf_landau)