﻿ g01ft Method
g01ft returns the value of the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function.

# Syntax

C#
```public static double g01ft(
double x,
out int ifail
)```
Visual Basic
```Public Shared Function g01ft ( _
x As Double, _
<OutAttribute> ByRef ifail As Integer _
) As Double```
Visual C++
```public:
static double g01ft(
double x,
[OutAttribute] int% ifail
)```
F#
```static member g01ft :
x : float *
ifail : int byref -> float
```

#### Parameters

x
Type: System..::..Double
On entry: the argument $x$ of the function.
Constraint: $0.0<{\mathbf{x}}<1.0$.
ifail
Type: System..::..Int32%
On exit: ${\mathbf{ifail}}={0}$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

#### Return Value

g01ft returns the value of the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function.

# Description

g01ft 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 g01et and g01mt), 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.

# References

Kölbig K S and Schorr B (1984) A program package for the Landau distribution Comp. Phys. Comm. 31 97–111

# Error Indicators and Warnings

Errors or warnings detected by the method:
${\mathbf{ifail}}=1$
 On entry, ${\mathbf{x}}\le 0.0$, or ${\mathbf{x}}\ge 1.0$.
${\mathbf{ifail}}=-9000$
An error occured, see message report.

# 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.

None.

# Example

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

Example program (C#): g01fte.cs

Example program data: g01fte.d

Example program results: g01fte.r