randtoolbox (version 1.11)

quasiRNG: Toolbox for quasi random number generation

Description

the Torus algorithm, the Sobol and Halton sequences.

Usage

halton(n, dim = 1, init = TRUE, normal = FALSE, usetime = FALSE)
sobol(n, dim = 1, init = TRUE, scrambling = 0, seed = 4711, normal = FALSE)
torus(n, dim = 1, prime, init = TRUE, mixed = FALSE, usetime = FALSE, normal=FALSE)

Arguments

n

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

dim

dimension of observations default 1.

init

a logical, if TRUE the sequence is initialized and restarts, otherwise not. By default TRUE.

normal

a logical if normal deviates are needed, default FALSE

scrambling

an integer value, if 1, 2 or 3 the sequence is scrambled otherwise not. If 1, Owen type type of scrambling is applied, if 2, Faure-Tezuka type of scrambling, is applied, and if 3, both Owen+Faure-Tezuka type of scrambling is a

seed

an integer value, the random seed for initialization of the scrambling process. By default 4711. On effective if scrambling>0.

prime

a single prime number or a vector of prime numbers to be used in the Torus sequence. (optional argument).

mixed

a logical to use the mixed Torus algorithm, default FALSE.

usetime

a logical to use the machine time to start the Torus sequence, default TRUE. if FALSE, the Torus sequence start from the first term.

Value

• torus, halton and sobol generates random variables in ]0,1[. It returns a $n$x$dim$ matrix, when dim>1 otherwise a vector of length n.

Details

The currently available generator are given below. [object Object],[object Object],[object Object]See the pdf vignette for details.

References

Bratley P., Fox B.L. (1988); Algorithm 659: Implementing Sobol's Quasirandom Sequence Generator, ACM Transactions on Mathematical Software 14, 88--100.

Joe S., Kuo F.Y. (1998); Remark on Algorithm 659: Implementing Sobol's Quaisrandom Seqence Generator.

Planchet F., Jacquemin J. (2003), L'utilisation de methodes de simulation en assurance. Bulletin Francais d'Actuariat, vol. 6, 11, 3-69. (available online)

See Also

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

Examples

# (1) the Torus algorithm
#
torus(100)

# example of setting the seed
setSeed(1)
torus(5)
setSeed(6)
torus(5)
#the same
setSeed(1)
torus(10)

#no use of the machine time
torus(10, use=FALSE)

#Kolmogorov Smirnov test
#KS statistic should be around 0.0019
ks.test(torus(1000), punif) 
	
#KS statistic should be around 0.0003
ks.test(torus(10000), punif) 

#the mixed Torus sequence
torus(10, mix=TRUE)
par(mfrow = c(1,2))
acf(torus(10^6))
acf(torus(10^6, mix=TRUE))

#usage of the init argument
torus(5)
torus(5, init=FALSE)

#should be equal to the combination of the two
#previous call
torus(10)

# (2) Halton sequences
#

# uniform variate
halton(n = 10, dim = 5)

# normal variate
halton(n = 10, dim = 5, normal = TRUE)

#usage of the init argument
halton(5)
halton(5, init=FALSE)

#should be equal to the combination of the two
#previous call
halton(10)

# some plots
par(mfrow = c(2, 2), cex = 0.75)
hist(halton(n = 5000, dim = 1), main = "Uniform Halton", 
  xlab = "x", col = "steelblue3", border = "white")

hist(halton(n = 5000, dim = 1, norm = TRUE), main = "Normal Halton", 
  xlab = "x", col = "steelblue3", border = "white")
   
# (3) Sobol sequences
#

# uniform variate
sobol(n = 10, dim = 5, scrambling = 3)

# normal variate
sobol(n = 10, dim = 5, scrambling = 3, normal = TRUE)

# some plots
hist(sobol(5000, 1, scrambling = 2), main = "Uniform Sobol", 
  xlab = "x", col = "steelblue3", border = "white")

hist(sobol(5000, 1, scrambling = 2, normal = TRUE), main = "Normal Sobol", 
  xlab = "x", col = "steelblue3", border = "white")

#usage of the init argument
sobol(5)
sobol(5, init=FALSE)

#should be equal to the combination of the two
#previous call
sobol(10)

# (4) computation times on my macbook, mean of 1000 runs
#

# algorithm			time in seconds for n=10^6
# Torus algo					0.058 
# mixed Torus algo 	       			0.087 
# Halton sequence				0.878
# Sobol sequence				0.214
n <- 1e+06
mean( replicate( 1000, system.time( torus(n), gcFirst=TRUE)[3]) )
mean( replicate( 1000, system.time( torus(n, mixed=TRUE), gcFirst=T)[3]) )
mean( replicate( 1000, system.time( halton(n), gcFirst=TRUE)[3]) )
mean( replicate( 1000, system.time( sobol(n), gcFirst=TRUE)[3]) )