NAG Library Routine Document

g05ryf (multivar_students_t)

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 g05ryf.

$\mathbf{mode}=2$

Set up reference vector and generate variates.

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

2:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of random variates required.

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

3:     $\mathbf{df}$ – IntegerInput

On entry: $\nu$, the number of degrees of freedom of the distribution.

Constraint: $\mathbf{df}\ge 3$.

4:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of dimensions of the distribution.

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

5:     $\mathbf{xmu}\left(\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $a$, the vector of means of the distribution.

6:     $\mathbf{c}\left(\mathbf{ldc},\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: matrix which, along with df, defines the covariance of the distribution. Only the upper triangle need be set.

Constraint: c must be positive semidefinite to machine precision.

7:     $\mathbf{ldc}$ – IntegerInput

On entry: the first dimension of the array c as declared in the (sub)program from which g05ryf is called.

Constraint: $\mathbf{ldc}\ge \mathbf{m}$.

8:     $\mathbf{r}\left(\mathbf{lr}\right)$ – Real (Kind=nag_wp) arrayInput/Output

On entry: if $\mathbf{mode}=1$, the reference vector as set up by g05ryf in a previous call with $\mathbf{mode}=0$ or $2$.

On exit: if $\mathbf{mode}=0$ or $2$, the reference vector that can be used in subsequent calls to g05ryf with $\mathbf{mode}=1$.

9:     $\mathbf{lr}$ – IntegerInput

On entry: the dimension of the array r as declared in the (sub)program from which g05ryf is called. If $\mathbf{mode}=1$, it must be the same as the value of lr specified in the prior call to g05ryf with $\mathbf{mode}=0$ or $2$.

Constraint: $\mathbf{lr}\ge \mathbf{m}\times \left(\mathbf{m}+1\right)+2$.

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

11:   $\mathbf{x}\left(\mathbf{ldx},*\right)$ – Real (Kind=nag_wp) arrayOutput

Note: the second dimension of the array x must be at least $\mathbf{m}$.

On exit: the array of pseudorandom multivariate Student's $t$ vectors generated by the routine, with $\mathbf{x}\left(i,j\right)$ holding the $j$th dimension for the $i$th variate.

12:   $\mathbf{ldx}$ – IntegerInput

On entry: the first dimension of the array x as declared in the (sub)program from which g05ryf is called.

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

13:   $\mathbf{ifail}$ – 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, $\mathbf{df}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{df}\ge 3$.

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=6$

On entry, the covariance matrix $C$ is not positive semidefinite to machine precision.

$\mathbf{ifail}=7$

On entry, $\mathbf{ldc}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldc}\ge \mathbf{m}$.

$\mathbf{ifail}=8$

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

$\mathbf{ifail}=9$

On entry, lr is not large enough, $\mathbf{lr}=〈\mathit{\text{value}}〉$: minimum length required $=〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=10$

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

$\mathbf{ifail}=12$

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

$\mathbf{ifail}=-99$

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 (g05ryfe.f90)

10.2

Program Data

Program Data (g05ryfe.d)

10.3

Program Results

Program Results (g05ryfe.r)