NAG FL Interface
g01ftf (inv_​cdf_​landau)

Settings help

FL Name Style:

FL Specification Language:

1 Purpose

g01ftf returns the value of the inverse Φ-1(x) of the Landau distribution function.

2 Specification

Fortran Interface
Function g01ftf ( x, ifail)
Real (Kind=nag_wp) :: g01ftf
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#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.

3 Description

g01ftf evaluates an approximation to the inverse Φ-1 (x) of the Landau distribution function given by
(where Φ(λ) 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<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 Real (Kind=nag_wp) Input
On entry: the argument x of the function.
Constraint: 0.0<x<1.0.
2: 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 -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry 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:
On entry, x=value.
Constraint: x<1.0.
On entry, x=value.
Constraint: x>0.0.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

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.
g01ftf is not threaded in any implementation.

9 Further Comments


10 Example

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

10.1 Program Text

Program Text (g01ftfe.f90)

10.2 Program Data

Program Data (g01ftfe.d)

10.3 Program Results

Program Results (g01ftfe.r)