NAG FL Interface
g05yrf (quasi_​lognormal_​bydim)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{sorder}$ – Integer Input

On entry: the order in which the generated values are returned.

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

2: $\mathbf{n}$ – Integer Input

On entry: the number of quasi-random numbers required.

Constraint: $\mathbf{n}\ge 0$ and $\mathbf{n}+\text{previous number of generated values}\le 2^{31}-1$.

3: $\mathbf{xmean}(*)$ – Real (Kind=nag_wp) array Input

Note: the dimension of the array xmean must be at least $\mathit{idim}$.

On entry: specifies, for each dimension, the mean of the underlying Normal distribution.

Constraint: $\left|\mathbf{xmean}\left(\mathit{i}\right)\right|\le |-\log \left(\mathbf{x02amf}\right)-10.0\times \mathbf{std}\left(\mathit{i}\right)|$, for $\mathit{i}=1,2,\dots ,\mathit{idim}$.

4: $\mathbf{std}(*)$ – Real (Kind=nag_wp) array Input

Note: the dimension of the array std must be at least $\mathit{idim}$.

On entry: specifies, for each dimension, the standard deviation of the underlying Normal distribution.

Constraint: $\mathbf{std}\left(\mathit{i}\right)\ge 0.0$, for $\mathit{i}=1,2,\dots ,\mathit{idim}$.

5: $\mathbf{fdim}$ – Integer Input

On entry: the first dimension to return.

Constraint: $1\le \mathbf{fdim}\le \mathbf{ldim}$.

6: $\mathbf{ldim}$ – Integer Input

On entry: the last dimension to return.

Constraint: $\mathbf{ldim}\le \mathit{idim}$.

7: $\mathbf{quas}(\mathbf{ldquas},*)$ – Real (Kind=nag_wp) array Output

Note: the second dimension of the array quas must be at least $\mathbf{ldim}-\mathbf{fdim}+1$ if $\mathbf{sorder}=1$ and at least $\mathbf{n}$ if $\mathbf{sorder}=2$.

On exit: contains the n quasi-random numbers for the required dimensions of a sequence with idim dimensions.

For $i=1,2,\dots ,\mathbf{n}$, $j=\mathbf{fdim},\mathbf{fdim}+1,\dots ,\mathbf{ldim}$ and $k=\mathit{j}-\mathbf{fdim}+1$, the $\mathit{i}$th value for the $\mathit{j}$th dimension is held in

• $\mathbf{quas}(\mathit{i},k)$, if $\mathbf{sorder}=1$,
• $\mathbf{quas}(k,\mathit{i})$, if $\mathbf{sorder}=2$.

8: $\mathbf{ldquas}$ – Integer Input

On entry: the first dimension of the array quas as declared in the (sub)program from which g05yrf is called.

Constraints:

• if $\mathbf{sorder}=1$, $\mathbf{ldquas}\ge \mathbf{n}$;
• if $\mathbf{sorder}=2$, $\mathbf{ldquas}\ge \mathbf{ldim}-\mathbf{fdim}+1$.

9: $\mathbf{iref}(*)$ – Integer array Communication Array

Note: the dimension of the array iref must be at least $\mathit{liref}$.

On entry: contains information on the current state of the sequence.

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

10: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $\mathrm{-1}$ 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 $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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

$\mathbf{ifail}=11$

On entry, $\mathbf{sorder}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{sorder}=1$ or $2$.

$\mathbf{ifail}=21$

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

$\mathbf{ifail}=22$

On entry, value of n would result in too many calls to the generator: $\mathbf{n}=⟨\mathit{\text{value}}⟩$, generator has previously been called $⟨\mathit{\text{value}}⟩$ times.

$\mathbf{ifail}=31$

On entry, $i=⟨\mathit{\text{value}}⟩$ and $\mathbf{xmean}\left(i\right)=⟨\mathit{\text{value}}⟩$.
Constraint: $\left|\mathbf{xmean}\left(i\right)\right|\le ⟨\mathit{\text{value}}⟩$.

$\mathbf{ifail}=41$

On entry, $i=⟨\mathit{\text{value}}⟩$ and $\mathbf{std}\left(i\right)=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{std}\left(i\right)\ge 0$.

$\mathbf{ifail}=61$

On entry, $\mathbf{fdim}=⟨\mathit{\text{value}}⟩$ and $\mathbf{ldim}=⟨\mathit{\text{value}}⟩$.
Constraint: $1\le \mathbf{fdim}\le \mathbf{ldim}$

$\mathbf{ifail}=71$

On entry, $\mathbf{ldim}=⟨\mathit{\text{value}}⟩$ and $\mathit{idim}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldim}\le \mathit{idim}$

$\mathbf{ifail}=91$

On entry, $\mathbf{ldquas}=⟨\mathit{\text{value}}⟩$ and $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldquas}\ge \mathbf{n}$.

$\mathbf{ifail}=92$

On entry, $\mathbf{ldquas}=⟨\mathit{\text{value}}⟩$ and $\mathbf{ldim}-\mathbf{fdim}+1=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldquas}\ge \mathbf{ldim}-\mathbf{fdim}+1$.

$\mathbf{ifail}=111$

On entry, iref has either not been initialized or has been corrupted.

$\mathbf{ifail}=113$

On entry, iref is too short to use with g05yrf.

$\mathbf{ifail}=114$

On entry, the specified dimensions are out of sync.
A different number of values have been generated from at least one of the specified dimensions.

$\mathbf{ifail}=115$

g05yrf can not be used with the Faure generator.

$\mathbf{ifail}=-99$

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.

$\mathbf{ifail}=-399$

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.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results