g01qt: FL CL CPP AD

NAG FL Interface
g01qtf (pdf_landau_moment2)

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NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG FL Interface Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction

g01qt: FL CL CPP AD

▸▿ 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

g01qtf returns the value of the second moment

Φ_{2} (x)

of the Landau density function.

2 Specification

Fortran Interface

Function g01qtf (

Real (Kind=nag_wp)	::	g01qtf
Real (Kind=nag_wp), Intent (In)	::	x

C Header Interface

#include <nag.h>

double

g01qtf_ (const double *x)

The routine may be called by the names g01qtf or nagf_stat_pdf_landau_moment2.

3 Description

g01qtf evaluates an approximation to the second moment

Φ_{2} (x)

of the Landau density function given by

Φ_{2} (x) = \frac{1}{Φ (x)} \int_{- \infty}^{x} λ^{2} 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_{1} (x)

, g01ptf 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 $x$ 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.

8 Parallelism and Performance

g01qtf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example evaluates

Φ_{2} (x)

x = 0.5

, and prints the results.

g01qt: FL CL CPP AD

NAG FL Interfaceg01qtf (pdf_​landau_​moment2)

▸▿ 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
g01qtf (pdf_landau_moment2)