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NAG Library Routine Document

g01euf (prob_vavilov)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1

Purpose

g01euf returns the value of the Vavilov distribution function

Φ_{V} (λ; κ, β^{2})

, via the routine name.

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 nagmk26.h

double

g01euf_ ( const double *x, const double rcomm[], Integer *ifail)

3

Description

g01euf evaluates an approximation to the Vavilov distribution function

Φ_{V} (λ; κ, β^{2})

given by

Φ_{V} (λ; κ, β^{2}) = \int_{- \infty}^{λ} ϕ_{V} (λ; κ, β^{2}) d λ,

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) arrayCommunication Array: On entry: this must be the same argument rcomm as returned by a previous call to g01zuf.
3: $ifail$ – IntegerInput/Output: On entry: ifail must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$ . 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

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: Either the initialization routine has not been called prior to the first call of this routine or a communication array has become corrupted.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

At least five significant digits are usually correct.

8

Parallelism and Performance

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

β^{2}

remain unchanged between calls. Otherwise, g01zuf must be called again. This is illustrated in Section 10.

10

Example

This example evaluates

Φ_{V} (λ; κ, β^{2})

λ = 0.1

κ = 2.5

and

β^{2} = 0.7

, and prints the results.

NAG Library Routine Document

g01euf (prob_vavilov)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results