NAG Library Routine Document

g05sgf (dist_expmix)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of pseudorandom numbers to be generated.

Constraint: $\mathbf{n}\ge 0$.

2:     $\mathbf{nmix}$ – IntegerInput

On entry: $m$, the number of exponential distributions in the mix.

Constraint: $\mathbf{nmix}\ge 1$.

3:     $\mathbf{a}\left(\mathbf{nmix}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the $m$ parameters $a_i$ for the $m$ exponential distributions in the mix.

Constraint: $\mathbf{a}\left(\mathit{i}\right)>0.0$, for $\mathit{i}=1,2,\dots ,\mathbf{nmix}$.

4:     $\mathbf{wgt}\left(\mathbf{nmix}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: the $m$ weights $w_i$ for the $m$ exponential distributions in the mix.

Constraints:

• ${\displaystyle \sum _{\mathit{i}=1}^m}\mathbf{wgt}\left(\mathit{i}\right)=1.0$;
• $\mathbf{wgt}\left(\mathit{i}\right)\ge 0.0$, for $\mathit{i}=1,2,\dots ,m$.

5:     $\mathbf{state}\left(*\right)$ – Integer arrayCommunication Array

Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.

6:     $\mathbf{x}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the $n$ pseudorandom numbers from the specified exponential mix distribution.

7:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. 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 $-1\text{ or }1$ 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 $-\mathbf{1}\text{ or }\mathbf{1}$ 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).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

$\mathbf{ifail}=2$

On entry, $\mathbf{nmix}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nmix}\ge 1$.

$\mathbf{ifail}=3$

On entry, $\mathbf{a}\left(〈\mathit{\text{value}}〉\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{a}\left(i\right)>0.0$.

$\mathbf{ifail}=4$

On entry, sum of $\mathbf{wgt}=〈\mathit{\text{value}}〉$.
Constraint: sum of $\mathbf{wgt}=1.0$.

On entry, $\mathbf{wgt}\left(〈\mathit{\text{value}}〉\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{wgt}\left(i\right)\ge 0.0$.

$\mathbf{ifail}=5$

On entry, state vector has been corrupted or not initialized.

$\mathbf{ifail}=-99$

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.

$\mathbf{ifail}=-399$

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.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g05sgfe.f90)

10.2

Program Data

Program Data (g05sgfe.d)

10.3

Program Results

Program Results (g05sgfe.r)