# NAG FL Interfaceg01ftf (inv_​cdf_​landau)

## 1Purpose

g01ftf returns the value of the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function.

## 2Specification

Fortran Interface
 Function g01ftf ( x,
 Real (Kind=nag_wp) :: g01ftf Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: x
#include <nag.h>
 double g01ftf_ (const double *x, Integer *ifail)
The routine may be called by the names g01ftf or nagf_stat_inv_cdf_landau.

## 3Description

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.

## 4References

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

## 5Arguments

1: $\mathbf{x}$Real (Kind=nag_wp) Input
On entry: the argument $x$ of the function.
Constraint: $0.0<{\mathbf{x}}<1.0$.
2: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, 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, ${\mathbf{x}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{x}}<1.0$.
On entry, ${\mathbf{x}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{x}}>0.0$.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

## 7Accuracy

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

## 8Parallelism and Performance

g01ftf is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (g01ftfe.f90)

### 10.2Program Data

Program Data (g01ftfe.d)

### 10.3Program Results

Program Results (g01ftfe.r)