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NAG CL Interface
g01ftc (inv_​cdf_​landau)

NAG Library Manual, Mark 29.2
Interfaces:  FL   CL   CPP   AD   PY   MB 
NAG CL Interface Introduction
G01 (Stat) Chapter Contents
G01 (Stat) Chapter Introduction
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▸▿ Contents

© The Numerical Algorithms Group Ltd. 2023
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1 Purpose

g01ftc returns the value of the inverse Φ-1(x) of the Landau distribution function.

2 Specification

#include <nag.h>
double  g01ftc (double x, NagError *fail)
The function may be called by the names: g01ftc, nag_stat_inv_cdf_landau or nag_deviates_landau.

3 Description

g01ftc evaluates an approximation to the inverse Φ-1 (x) of the Landau distribution function given by
Ψ(x)=Φ-1(x)  
(where Φ(λ) is described in g01etc and g01mtc), using either linear or quadratic interpolation or rational approximations which mimic the asymptotic behaviour. Further details can be found in Kölbig and Schorr (1984).
It can also be used to generate Landau distributed random numbers in the range 0<x<1.

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 – double Input
On entry: the argument x of the function.
Constraint: 0.0<x<1.0.
2: fail – NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL
On entry, x=⟨value⟩.
Constraint: x<1.0.
On entry, x=⟨value⟩.
Constraint: x>0.0.

7 Accuracy

At least 5-6 significant digits are correct. Such accuracy is normally considered to be adequate for applications in large scale Monte Carlo simulations.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g01ftc is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example evaluates Φ-1(x) at x=0.5, and prints the results.

10.1 Program Text

Program Text (g01ftce.c)

10.2 Program Data

Program Data (g01ftce.d)

10.3 Program Results

Program Results (g01ftce.r)
NAG Library Manual, Mark 29.2
Interfaces:  FL   CL   CPP   AD   PY   MB 
NAG CL Interface Introduction
G01 (Stat) Chapter Contents
G01 (Stat) Chapter Introduction
g01ft:  FL   CL   CPP   AD   PY   MB 
© The Numerical Algorithms Group Ltd. 2023