pseudo.rngWELL {rngWELL}

Toolbox for pseudo and quasi random number generation

Description

General linear congruential generators such as Park Miller sequence, generalized feedback shift register such as SF-Mersenne Twister algorithm and WELL generator; and a quasi random generator (pseudo random generators) and the Torus algorithm (quasi random generation).

Usage

WELL2test(n, dim = 1, order = 512, temper = FALSE, version = "a")
setSeed4WELL(seed)

doinitMT2002(seed, n, state)
doputRngWELL(order, version, state)
dogetRngWELL(order, version, state)

Arguments

n

number of observations. If length(n) > 1, the length is taken to be the required number.

dim

dimension of observations (must be <=100 000, default 1).

seed

a single value, interpreted as a positive integer for the seed. e.g. append your day, your month and your year of birth.

order

a positive integer for the order of the characteristic polynomial. see details

temper

a logical if you want to do a tempering stage. see details

version

a character either "a","b" or "c". see details

state

the state as output of putRngWELL, getRngWELL.

Details

The currently available generator are given below.

WELL generator:

The WELL (which stands for Well Equidistributed Long-period Linear) is in a sentence a generator with better equidistribution than Mersenne Twister algorithm but this gain of quality has to be paid by a slight higher cost of time. See Panneton et al. (2006) for details.

The order argument of WELL generator is the order of the characteristic polynomial, which is denoted by k in Paneton F., L'Ecuyer P. and Matsumoto M. (2006). Possible values for order are 512, 521, 607, 1024 where no tempering are needed (thus possible). Order can also be 800, 19937, 21071, 23209, 44497 where a tempering stage is possible through the temper argument. Furthermore a possible 'b' version of WELL RNGs are possible for the following order 521, 607, 1024, 800, 19937, 23209 with the version argument.

All the C code for WELL generator used in this package is the code of P. L'Ecuyer (cf. http://www.iro.umontreal.ca/~lecuyer/), except some C code, we add, to interface with R.

See the pdf vignette for details.

Value

WELL2test generates random variables in [0,1[. It returns a nxdim matrix, when dim>1 otherwise a vector of length n.

setSeed4WELL set the seed of the rngWELL package (i.e. for the WELL2test functions).

Author(s)

Christophe Dutang and Petr Savicky

References

Paneton F., L'Ecuyer P. and Matsumoto M. (2006), Improved Long-Period Generators Based on Linear Recurrences Modulo 2, ACM Transactions on Mathematical Software. (preprint available online)

See Also

.Random.seed for what is done in R about random number generation.

Examples

# (1) WELL generator
#

# 'basic' calls
# WELL512
WELL2test(10, order = 512)
# WELL1024
WELL2test(10, order = 1024)
# WELL19937
WELL2test(10, order = 19937)
# WELL44497
WELL2test(10, order = 44497)
# WELL19937 with tempering 
WELL2test(10, order = 19937, temper = TRUE)
# WELL44497 with tempering
WELL2test(10, order = 44497, temper = TRUE)

# tempering vs no tempering
setSeed4WELL(08082008)
WELL2test(10, order =19937)
setSeed4WELL(08082008)
WELL2test(10, order =19937, temper=TRUE)


# (2) other tests
#
doinitMT2002(1, 10, 10)