NAG Library Function Document

nag_quasi_random_normal (g05ybc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     state – Nag_QuasiRandom_StateInput

On entry: the type of operation to perform.

$\mathbf{state}=\mathrm{Nag\_QuasiRandom\_Init}$

The first call for initialization and there is no output via array quasi.

$\mathbf{state}=\mathrm{Nag\_QuasiRandom\_Cont}$

The sequence has already been initialized by a prior call to nag_quasi_random_normal (g05ybc) with $\mathbf{state}=\mathrm{Nag\_QuasiRandom\_Init}$. Random numbers are output via array quasi.

$\mathbf{state}=\mathrm{Nag\_QuasiRandom\_Finish}$

The final call to release memory and no further random numbers are required for output via array quasi.

Constraint: $\mathbf{state}=\mathrm{Nag\_QuasiRandom\_Init}$, $\mathrm{Nag\_QuasiRandom\_Cont}$ or $\mathrm{Nag\_QuasiRandom\_Finish}$.

2:     seq – Nag_QuasiRandom_SequenceInput

On entry: the type of sequence to generate.

$\mathbf{seq}=\mathrm{Nag\_QuasiRandom\_Sobol}$

A Sobol sequence.

$\mathbf{seq}=\mathrm{Nag\_QuasiRandom\_Nied}$

A Niederreiter sequence.

$\mathbf{seq}=\mathrm{Nag\_QuasiRandom\_Faure}$

A Faure sequence.

Constraint: $\mathbf{seq}=\mathrm{Nag\_QuasiRandom\_Sobol}$, $\mathrm{Nag\_QuasiRandom\_Nied}$ or $\mathrm{Nag\_QuasiRandom\_Faure}$.

3:     lnorm – Nag_DistributionsInput

On entry: indicates whether to create Gaussian or log-normal variates.

$\mathbf{lnorm}=\mathrm{Nag\_LogNormal}$

The variates are log-normal.

$\mathbf{lnorm}=\mathrm{Nag\_Normal}$

The variates are Gaussian.

Constraint: $\mathbf{lnorm}=\mathrm{Nag\_LogNormal}$ or $\mathrm{Nag\_Normal}$.

4:     mean[idim] – const doubleInput

On entry: $\mathbf{mean}\left[k-1\right]$ is the mean of distribution for the $k$th dimension.

5:     std[idim] – const doubleInput

On entry: $\mathbf{std}\left[k-1\right]$ is the standard deviation of the distribution for the $k$th dimension.

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

6:     iskip – IntegerInput

On entry: the number of terms in the sequence to skip on initialization.

If $\mathbf{seq}=\mathrm{Nag\_QuasiRandom\_Faure}$, iskip is not referenced.

Constraint: if $\mathbf{seq}=\mathrm{Nag\_QuasiRandom\_Nied}$ or $\mathrm{Nag\_QuasiRandom\_Sobol}$ and $\mathbf{state}=\mathrm{Nag\_QuasiRandom\_Init}$, $\mathbf{iskip}\ge 0$.

7:     idim – IntegerInput

On entry: the number of dimensions required.

Constraint: $2\le \mathbf{idim}\le 40$ and $\mathbf{idim}\text{ must be even}$.

8:     quasi[idim] – doubleOutput

On exit: the random numbers, generated in pairs. That is, on the first call with $\mathbf{state}=\mathrm{Nag\_QuasiRandom\_Cont}$, $\mathbf{quasi}\left[k-1\right]$ contains the first quasi-random number for the $k$th dimension. On the next call $\mathbf{quasi}\left[k-1\right]$ contains the second quasi-random number for the $k$th dimension, etc..

9:     gf – Nag_QuasiRandom *Communication Structure

Workspace used to communicate information between calls to nag_quasi_random_normal (g05ybc). The contents of this structure should not be changed between calls.

10:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM

On entry, seq is not valid: .

NE_INITIALIZATION

Incorrect initialization.

NE_INT

On entry, $\mathbf{idim}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{idim}\le 40$.

On entry, $\mathbf{idim}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{idim}\ge 2$.

On entry, idim is not even: $\mathbf{idim}=〈\mathit{\text{value}}〉$.

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

On entry, value of skip too large: $\mathbf{iskip}=〈\mathit{\text{value}}〉$.

NE_INT_ARRAY_ELEM_CONS

On entry, element $〈\mathit{\text{value}}〉$ of $\mathbf{std}\le 0.0$.

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.

NE_TOO_MANY_CALLS

Too many calls to generator.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g05ybce.c)

9.2  Program Data

9.3  Program Results

Program Results (g05ybce.r)