NAG Library Function Document

nag_quasi_rand_lognormal (g05ykc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{xmean}\left[\mathit{idim}\right]$ – const doubleInput

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

Constraint: $\left|\mathbf{xmean}\left[\mathit{i}-1\right]\right|\le \left|-\log \left(\mathbf{nag\_real\_safe\_small\_number}\right)-10.0\times \mathbf{std}\left[\mathit{i}-1\right]\right|$, for $\mathit{i}=1,2,\dots ,\mathit{idim}$.

3:    $\mathbf{std}\left[\mathit{idim}\right]$ – const doubleInput

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

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

4:    $\mathbf{n}$ – IntegerInput

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

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

5:    $\mathbf{quas}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, of the array quas must be at least $\mathbf{pdquas}\times \mathit{idim}$.

The dimension, dim, of the array quas must be at least

• $\max \left(1,\mathbf{pdquas}\times \mathit{idim}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdquas}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

Where $\mathbf{QUAS}\left(i,j\right)$ appears in this document, it refers to the array element

• $\mathbf{quas}\left[\left(j-1\right)\times \mathbf{pdquas}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{quas}\left[\left(i-1\right)\times \mathbf{pdquas}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On exit: $\mathbf{QUAS}\left(i,j\right)$ holds the $i$th value for the $j$th dimension.

6:    $\mathbf{pdquas}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array quas.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdquas}\ge \mathbf{n}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdquas}\ge \mathit{idim}$.

7:    $\mathbf{iref}\left[\mathit{liref}\right]$ – IntegerCommunication Array

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

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

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INITIALIZATION

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

NE_INT

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

NE_INT_2

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

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_REAL_ARRAY

On entry, at least one element of xmean is too large, $\mathbf{xmean}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.
Constraint: $\left|\mathbf{xmean}\left[i\right]\right|\le 〈\mathit{\text{value}}〉$.

On entry, $\mathbf{std}\left[〈\mathit{\text{value}}〉\right]=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{std}\left[i\right]\ge 0$.

NE_TOO_MANY_CALLS

There have been too many calls to the generator.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g05ykce.c)

10.2

Program Data

10.3

Program Results

Program Results (g05ykce.r)