g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_quasi_init (g05ylc)

## 1  Purpose

nag_quasi_init (g05ylc) initializes a quasi-random generator prior to calling nag_quasi_rand_normal (g05yjc), nag_quasi_rand_lognormal (g05ykc) or nag_quasi_rand_uniform (g05ymc).

## 2  Specification

 #include #include
 void nag_quasi_init (Nag_QuasiRandom_Sequence genid, Integer idim, Integer iref[], Integer liref, Integer iskip, NagError *fail)

## 3  Description

nag_quasi_init (g05ylc) selects a quasi-random number generator through the input value of genid and initializes the iref communication array for use by the functions nag_quasi_rand_normal (g05yjc), nag_quasi_rand_lognormal (g05ykc) or nag_quasi_rand_uniform (g05ymc).
One of three types of quasi-random generator may be chosen, allowing the low-discrepancy sequences proposed by Sobol, Faure or Niederreiter to be generated.
Two sets of Sobol sequences are supplied, the first, is based on the work of Joe and Kuo (2008). The second, referred to in the documentation as "Sobol (A659)", is based on Algorithm 659 of Bratley and Fox (1988) with the extension to 1111 dimensions proposed by Joe and Kuo (2003). Both sets of Sobol sequences should satisfy the so-called Property A, up to $1111$ dimensions, but the first set should have better two-dimensional projections than those produced using Algorithm 659.

## 4  References

Bratley P and Fox B L (1988) Algorithm 659: implementing Sobol's quasirandom sequence generator ACM Trans. Math. Software 14(1) 88–100
Fox B L (1986) Algorithm 647: implementation and relative efficiency of quasirandom sequence generators ACM Trans. Math. Software 12(4) 362–376
Joe S and Kuo F Y (2003) Remark on Algorithm 659: implementing Sobol's quasirandom sequence generator ACM Trans. Math. Software (TOMS) 29 49–57
Joe S and Kuo F Y (2008) Constructing Sobol sequences with better two-dimensional projections SIAM J. Sci. Comput. 30 2635–2654

## 5  Arguments

1:     genidNag_QuasiRandom_SequenceInput
On entry: must identify the quasi-random generator to use.
${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Sobol}$
Sobol generator.
${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_SobolA659}$
Sobol (A659) generator.
${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Nied}$
Niederreiter generator.
${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Faure}$
Faure generator.
Constraint: ${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Sobol}$, $\mathrm{Nag_QuasiRandom_SobolA659}$, $\mathrm{Nag_QuasiRandom_Nied}$ or $\mathrm{Nag_QuasiRandom_Faure}$.
2:     idimIntegerInput
On entry: the number of dimensions required.
Constraints:
• if ${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Sobol}$, $1\le {\mathbf{idim}}\le 10000$;
• if ${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_SobolA659}$, $1\le {\mathbf{idim}}\le 1111$;
• if ${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Nied}$, $1\le {\mathbf{idim}}\le 318$;
• if ${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Faure}$, $1\le {\mathbf{idim}}\le 40$.
3:     iref[liref]IntegerCommunication Array
On exit: contains initialization information for use by the generator functions nag_quasi_rand_normal (g05yjc), nag_quasi_rand_lognormal (g05ykc) and nag_quasi_rand_uniform (g05ymc). iref must not be altered in any way between initialization and calls of the generator functions.
4:     lirefIntegerInput
On entry: the dimension of the array iref.
Constraints:
• if ${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Sobol}$, $\mathrm{Nag_QuasiRandom_SobolA659}$ or $\mathrm{Nag_QuasiRandom_Nied}$, ${\mathbf{liref}}\ge 32×{\mathbf{idim}}+7$;
• if ${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Faure}$, ${\mathbf{liref}}\ge 407$.
5:     iskipIntegerInput
On entry: the number of terms of the sequence to skip on initialization for the Sobol and Niederreiter generators. If ${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Faure}$, iskip is ignored.
Constraint: if ${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Sobol}$, $\mathrm{Nag_QuasiRandom_SobolA659}$ or $\mathrm{Nag_QuasiRandom_Nied}$, $0\le {\mathbf{iskip}}\le {2}^{30}$.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{idim}}=〈\mathit{\text{value}}〉$.
Constraint: $1\le {\mathbf{idim}}\le 〈\mathit{\text{value}}〉$.
On entry, ${\mathbf{iskip}}<0$ or iskip is too large: ${\mathbf{iskip}}=〈\mathit{\text{value}}〉$, maximum value is $〈\mathit{\text{value}}〉$.
On entry, liref is too small: ${\mathbf{liref}}=〈\mathit{\text{value}}〉$, minimum length is $〈\mathit{\text{value}}〉$.
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.

## 7  Accuracy

Not applicable.

The primitive polynomials and direction numbers used for the Sobol generator (${\mathbf{genid}}=\mathrm{Nag_QuasiRandom_Sobol}$) were calculated by Joe and Kuo (2008) using the search critera ${D}^{\left(6\right)}$.