G01 Chapter Contents
G01 Chapter Introduction
NAG Library Manual

NAG Library Routine DocumentG01FTF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

1  Purpose

G01FTF returns the value of the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function, via the routine name.

2  Specification

 FUNCTION G01FTF ( X, IFAIL)
 REAL (KIND=nag_wp) G01FTF
 INTEGER IFAIL REAL (KIND=nag_wp) X

3  Description

G01FTF evaluates an approximation to the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function given by
 $Ψx=Φ-1x$
(where $\Phi \left(\lambda \right)$ is described in G01ETF and G01MTF), 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.

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 $x$ of the function.
Constraint: $0.0<{\mathbf{X}}<1.0$.
2:     IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{​ or ​}1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{​ or ​}\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.
On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=1$
 On entry, ${\mathbf{X}}\le 0.0$, or ${\mathbf{X}}\ge 1.0$.

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.

None.

9  Example

This example evaluates ${\Phi }^{-1}\left(x\right)$ at $x=0.5$, and prints the results.

9.1  Program Text

Program Text (g01ftfe.f90)

9.2  Program Data

Program Data (g01ftfe.d)

9.3  Program Results

Program Results (g01ftfe.r)