NAG Library Routine Document

g05tdf  (int_general)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{mode}$ – IntegerInput

On entry: a code for selecting the operation to be performed by the routine.

$\mathbf{mode}=0$

Set up reference vector only.

$\mathbf{mode}=1$

Generate variates using reference vector set up in a prior call to g05tdf.

$\mathbf{mode}=2$

Set up reference vector and generate variates.

$\mathbf{mode}=3$

Generate variates without using the reference vector.

Constraint: $\mathbf{mode}=0$, $1$, $2$ or $3$.

2:     $\mathbf{n}$ – IntegerInput

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

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

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

On entry: the PDF or CDF of the distribution.

Constraints:

• $0.0\le \mathbf{p}\left(\mathit{i}\right)\le 1.0$, for $\mathit{i}=1,2,\dots ,\mathbf{np}$;
• if $\mathbf{itype}=1$, ${\displaystyle \sum _{\mathit{i}=1}^{\mathbf{np}}}\mathbf{p}\left(\mathit{i}\right)=1.0$;
• if $\mathbf{itype}=2$, $\mathbf{p}\left(\mathit{i}\right)<\mathbf{p}\left(j\right)\text{, }\mathit{i}<j\text{ and }\mathbf{p}\left(\mathbf{np}\right)=1.0$.

4:     $\mathbf{np}$ – IntegerInput

On entry: the number of values supplied in p defining the PDF or CDF of the discrete distribution.

Constraint: $\mathbf{np}>0$.

5:     $\mathbf{ip1}$ – IntegerInput

On entry: the value of the variate, a whole number, to which the probability in $\mathbf{p}\left(1\right)$ corresponds.

6:     $\mathbf{itype}$ – IntegerInput

On entry: indicates the type of information contained in p.

$\mathbf{itype}=1$

p contains a probability distribution function (PDF).

$\mathbf{itype}=2$

p contains a cumulative distribution function (CDF).

Constraint: $\mathbf{itype}=1$ or $2$.

7:     $\mathbf{r}\left(\mathbf{lr}\right)$ – Real (Kind=nag_wp) arrayCommunication Array

On entry: if $\mathbf{mode}=1$, the reference vector from the previous call to g05tdf.

On exit: the reference vector.

8:     $\mathbf{lr}$ – IntegerInput

On entry: the dimension of the array r as declared in the (sub)program from which g05tdf is called.

Suggested values:

• if $\mathbf{mode}\ne 3$, $\mathbf{lr}=10+1.4\times \mathbf{np}$ approximately (for optimum efficiency in generating variates);
• otherwise $\mathbf{lr}=1$.

Constraints:

• if $\mathbf{mode}=0$ or $2$, $\mathbf{lr}\ge \mathbf{np}+8$;
• if $\mathbf{mode}=1$, lr should remain unchanged from the previous call to g05tdf.

9:     $\mathbf{state}\left(*\right)$ – 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.

10:   $\mathbf{x}\left(\mathbf{n}\right)$ – Integer arrayOutput

On exit: contains $n$ pseudorandom numbers from the specified discrete distribution.

11:   $\mathbf{ifail}$ – 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, $\mathbf{mode}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{mode}=0$, $1$ or $2$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

On entry, at least one element of the vector p is less than $0.0$ or greater than $1.0$.

On entry, $\mathbf{itype}=1$ and the sum of the elements of p do not equal one.

On entry, $\mathbf{itype}=2$ and the values of p are not all in stricly ascending order.

On entry, $\mathbf{p}\left(\mathbf{np}\right)=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{itype}=2$, $\mathbf{p}\left(\mathbf{np}\right)=1.0$.

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=6$

On entry, $\mathbf{itype}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{itype}=1$ or $2$.

$\mathbf{ifail}=7$

On entry, some of the elements of the array r have been corrupted or have not been initialized.

The value of np or ip1 is not the same as when r was set up in a previous call.
Previous value of $\mathbf{np}=〈\mathit{\text{value}}〉$ and $\mathbf{np}=〈\mathit{\text{value}}〉$.
Previous value of $\mathbf{ip1}=〈\mathit{\text{value}}〉$ and $\mathbf{ip1}=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=8$

On entry, lr is too small when $\mathbf{mode}=0$ or $2$: $\mathbf{lr}=〈\mathit{\text{value}}〉$, minimum length required $=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=9$

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 (g05tdfe.f90)

10.2

Program Data

Program Data (g05tdfe.d)

10.3

Program Results

Program Results (g05tdfe.r)