naginterfaces.library.rand.init_​repeat

naginterfaces.library.rand.init_repeat(genid, seed, subid=0)

init_repeat initializes the selected base generator, as used by the group of pseudorandom number functions (see init_leapfrog()–init_skipahead(), permute(), sample(), times_garch_asym1()–times_mv_varma(), matrix_orthog()–matrix_2waytable(), copula_students_t(), copula_normal(), multivar_students_t(), multivar_normal() and dist_uniform01()–int_uniform()) and the quasi-random scrambled sequence initialization function, quasi_init_scrambled().

For full information please refer to the NAG Library document for g05kf

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g05/g05kff.html

Parameters

genidint

Must contain the type of base generator to use.

$genid=1$

NAG basic generator.

$genid=2$

Wichmann Hill I generator.

$genid=3$

Mersenne Twister.

$genid=4$

Wichmann Hill II generator.

$genid=5$

ACORN generator.

$genid=6$

L’Ecuyer MRG32k3a generator.

See the G05 Introduction for details of each of the base generators.

seedint, array-like, shape $\left(\text{lseed}\right)$

The initial (seed) values for the selected base generator. The number of initial values required varies with each of the base generators.

If $genid=1$, one seed is required.

If $genid=2$, four seeds are required.

If $genid=3$, $624$ seeds are required.

If $genid=4$, four seeds are required.

If $genid=5$, $(k+1)p$ seeds are required, where $k$ and $p$ are defined by $subid$.

For the ACORN generator it is recommended that an odd value is used for $seed\left[0\right]$.

If $genid=6$, six seeds are required.

If insufficient seeds are provided then the first $\text{lseed}-1$ values supplied in $seed$ are used and the remaining values are randomly generated using the NAG basic generator.

In such cases the NAG basic generator is initialized using the value supplied in $seed[\text{lseed}-1]$.

subidint, optional

If $genid=2$, $subid$ indicates which of the $273$ sub-generators to use. In this case, the $\left((\left|subid\right|+272)mod273\right)+1$ sub-generator is used.

If $genid=5$, $subid$ indicates the values of $k$ and $p$ to use, where $k$ is the order of the generator, and $p$ controls the size of the modulus, $M$, with $M=2^{(p\times 30)}$.

If $subid<1$, the default values of $k=10$ and $p=2$ are used, otherwise values for $k$ and $p$ are calculated from the formula, $subid=k+1000(p-1)$.

If $genid=6$ and $mod(subid,2)=0$ the range of the generator is set to $(0,1]$, otherwise the range is set to $(0,1)$; in this case the sequence is identical to the implementation of MRG32k3a in TestU01 (see L’Ecuyer and Simard (2002)) for identical seeds.

For all other values of $genid$, $subid$ is not referenced.

Returns

statecommdict, RNG communication object

RNG communication structure.

Raises

NagValueError

(errno $1$)

On entry, $genid=⟨value⟩$.

Constraint: $genid=1$, $2$, $3$, $4$, $5$ or $6$.

(errno $3$)

On entry, invalid $seed$.

(errno $4$)

On entry, $\text{lseed}=⟨value⟩$.

Constraint: $\text{lseed}\ge 1$.

Notes

init_repeat selects a base generator through the input value of the arguments $genid$ and $subid$, and then initializes it based on the values given in the array $seed$.

A given base generator will yield different sequences of random numbers if initialized with different values of $seed$. Alternatively, the same sequence of random numbers will be generated if the same value of $seed$ is used. It should be noted that there is no guarantee of statistical properties between sequences, only within sequences.

A definition of some of the terms used in this description, along with details of the various base generators can be found in the G05 Introduction.

References

L’Ecuyer, P and Simard, R, 2002, TestU01: a software library in ANSI C for empirical testing of random number generators, Departement d’Informatique et de Recherche Operationnelle, Universite de Montreal, https://www.iro.umontreal.ca/~lecuyer

Maclaren, N M, 1989, The generation of multiple independent sequences of pseudorandom numbers, Appl. Statist. (38), 351–359

Matsumoto, M and Nishimura, T, 1998, Mersenne twister: a 623-dimensionally equidistributed uniform pseudorandom number generator, ACM Transactions on Modelling and Computer Simulations

Wichmann, B A and Hill, I D, 2006, Generating good pseudo-random numbers, Computational Statistics and Data Analysis (51), 1614–1622

Wikramaratna, R S, 1989, ACORN - a new method for generating sequences of uniformly distributed pseudo-random numbers, Journal of Computational Physics (83), 16–31

See also

naginterfaces.library.examples.correg.glm_binomial_ex.main()

naginterfaces.library.examples.fit.dim2_spline_ts_sctr_ex.main()

naginterfaces.library.examples.rand.bb_inc_ex.main()

naginterfaces.library.examples.rand.copula_students_t_ex.main()