Random Number Generation

Description

.Random.seed is an integer vector, containing the random number generator (RNG) state for random number generation in R. It can be saved and restored, but should not be altered by the user.

RNGkind is a more friendly interface to query or set the kind of RNG in use.

set.seed is the recommended way to specify seeds.

Usage

.Random.seed <- c(rng.kind, n1, n2, ...)
save.seed <- .Random.seed

RNGkind(kind = NULL, normal.kind = NULL)
set.seed(seed, kind = NULL)

Arguments

Details

The currently available RNG kinds are given below. kind is partially matched to this list. The default is "Marsaglia-Multicarry".

"Wichmann-Hill"

The seed, .Random.seed[-1] == r[1:3] is an integer vector of length 3, where each r[i] is in 1:(p[i] - 1), where p is the length 3 vector of primes, p = (30269, 30307, 30323). The Wichmann–Hill generator has a cycle length of 6.9536 \times 10^{12} (= prod(p-1)/4, see Applied Statistics (1984) 33, 123 which corrects the original article).

"Marsaglia-Multicarry":

A multiply-with-carry RNG is used, as recommended by George Marsaglia in his post to the mailing list ‘sci.stat.math’. It has a period of more than 2^{60} and has passed all tests (according to Marsaglia). The seed is two integers (all values allowed).

"Super-Duper":

Marsaglia's famous Super-Duper from the 70's. This is the original version which does not pass the MTUPLE test of the Diehard battery. It has a period of \approx 4.6\times 10^{18} for most initial seeds. The seed is two integers (all values allowed for the first seed: the second must be odd).

We use the implementation by Reeds et al.\ (1982–84).

The two seeds are the Tausworthe and congruence long integers, respectively. A one-to-one mapping to S's .Random.seed[1:12] is possible but we will not publish one, not least as this generator is not exactly the same as that in recent versions of S-PLUS.

"Mersenne-Twister":

From Matsumoto and Nishimura (1998). A twisted GFSR with period 2^{19937} - 1 and equidistribution in 623 consecutive dimensions (over the whole period). The “seed” is a 624-dimensional set of 32-bit integers plus a current position in that set.

"Knuth-TAOCP":

From Knuth (1997). A GFSR using lagged Fibonacci sequences with subtraction. That is, the recurrence used is

X_j = (X_{j-100} - X_{j-37}) \bmod 2^{30}%

and the “seed” is the set of the 100 last numbers (actually recorded as 101 numbers, the last being a cyclic shift of the buffer). The period is around 2^{129}.

"user-supplied":

Use a user-supplied generator. See Random.user for details.

normal.kind can be "Kinderman-Ramage" (the default) or "Ahrens-Dieter" or "Box-Muller" or "user-supplied".

set.seed uses its single integer argument to set as many seeds as are required. It is intended as a simple way to get quite different seeds by specifying small integer arguments, and also as a way to get valid seed sets for the more complicated methods (especially "Knuth-TAOCP").

Value

.Random.seed is an integer vector whose first element codes the kind of RNG and normal generator. The lowest two decimal digits are in in 0:(k-1) where k is the number of available RNGs. The hundreds represent the type of normal generator (starting at 0).

In the underlying C, .Random.seed[-1] is unsigned; therefore in R .Random.seed[-1] can be negative.

RNGkind returns a two-element character vector of the RNG and normal kinds in use before the call, invisibly if either argument is not NULL.

set.seed returns NULL, invisibly.

Note

.Random.seed saves the seed set for the uniform random-number generator, at least for the system generators. It does not necessarily save the state of other generators, and in particular does not save the state of the Box–Muller normal generator. If you want to reproduce work later, call set.seed rather than set .Random.seed.

Note

Initially, there is no seed; a new one is created from the current time when one is required. Hence, different sessions will give different simulation results, by default.

Author(s)

of RNGkind: Martin Maechler. Current implementation, B. D. Ripley

References

Wichmann, B. A. and Hill, I. D. (1982) Algorithm AS 183: An Efficient and Portable Pseudo-random Number Generator, Applied Statistics, 31, 188–190; Remarks: 34, 198 and 35, 89.

De Matteis, A. and Pagnutti, S. (1993) Long-range Correlation Analysis of the Wichmann-Hill Random Number Generator, Statist. Comput., 3, 67–70.

Marsaglia, G. (1997) A random number generator for C. Discussion paper, posting on Usenet newsgroup sci.stat.math on September 29, 1997.

Reeds, J., Hubert, S. and Abrahams, M. (1982–4) C implementation of SuperDuper, University of California at Berkeley. (Personal communication from Jim Reeds to Ross Ihaka.)

Marsaglia, G. and Zaman, A. (1994) Some portable very-long-period random number generators. Computers in Physics, 8, 117–121.

Matsumoto, M. and Nishimura, T. (1998) Mersenne Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator, ACM Transactions on Modeling and Computer Simulation, 8, 3–30.
Source code at http://www.math.keio.ac.jp/~matumoto/emt.html.

Knuth, D. E. (1997) The Art of Computer Programming. Volume 2, third edition.
Source code at http://www-cs-faculty.stanford.edu/~knuth/taocp.html.

See Also

runif, rnorm, ....

Examples

runif(1); .Random.seed; runif(1); .Random.seed
## If there is no seed,  a ``random'' new one is created:
rm(.Random.seed); runif(1); .Random.seed

RNGkind("Wich")# (partial string matching on 'kind')
p.WH <- c(30269, 30307, 30323)
a.WH <- c(  171,   172,   170)
next.WHseed <- function(i.seed = .Random.seed[-1]) (a.WH * i.seed) %% p.WH
my.runif1 <- function(i.seed = .Random.seed)
  { ns <- next.WHseed(i.seed[-1]); sum(ns / p.WH) %% 1 }

## This shows how `runif(.)' works for Wichmann-Hill, using only R functions:
rs <- .Random.seed
(WHs <- next.WHseed(rs[-1]))
u <- runif(1)
stopifnot(
 next.WHseed(rs[-1]) == .Random.seed[-1],
 all.equal(u, my.runif1(rs))
)

## ----
.Random.seed
ok <- RNGkind()
RNGkind("Super")#matches  "Super-Duper"
RNGkind()
.Random.seed # new, corresponding to  Super-Duper

## Reset:
RNGkind(ok[1])