NAG FL Interface
g01euf (prob_​vavilov)

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1 Purpose

g01euf returns the value of the Vavilov distribution function ΦV(λ;κ,β2).
It is intended to be used after a call to g01zuf.

2 Specification

Fortran Interface
Function g01euf ( x, rcomm, ifail)
Real (Kind=nag_wp) :: g01euf
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x, rcomm(322)
C Header Interface
#include <nag.h>
double  g01euf_ (const double *x, const double rcomm[], Integer *ifail)
The routine may be called by the names g01euf or nagf_stat_prob_vavilov.

3 Description

g01euf evaluates an approximation to the Vavilov distribution function ΦV(λ;κ,β2) given by
where ϕ(λ) is described in g01muf. The method used is based on Fourier expansions. Further details can be found in Schorr (1974).

4 References

Schorr B (1974) Programs for the Landau and the Vavilov distributions and the corresponding random numbers Comp. Phys. Comm. 7 215–224

5 Arguments

1: x Real (Kind=nag_wp) Input
On entry: the argument λ of the function.
2: rcomm(322) Real (Kind=nag_wp) array Communication Array
On entry: this must be the same argument rcomm as returned by a previous call to g01zuf.
3: 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:
Either the initialization routine has not been called prior to the first call of this routine or a communication array has become corrupted.
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 five significant digits are usually correct.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g01euf is not threaded in any implementation.

9 Further Comments

g01euf can be called repeatedly with different values of λ provided that the values of κ and β2 remain unchanged between calls. Otherwise, g01zuf must be called again.

10 Example

This example evaluates ΦV(λ;κ,β2) at λ=0.1, κ=2.5 and β2=0.7, and prints the results.

10.1 Program Text

Program Text (g01eufe.f90)

10.2 Program Data

Program Data (g01eufe.d)

10.3 Program Results

Program Results (g01eufe.r)