.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.
RNGversion
can be used to set the random generators as they
were in an earlier R version (for reproducibility).
set.seed
is the recommended way to specify seeds.
.Random.seed <- c(rng.kind, n1, n2, ...)
RNGkind(kind = NULL, normal.kind = NULL)
RNGversion(vstr)
set.seed(seed, kind = NULL, normal.kind = NULL)
NULL
. If kind
is a character
string, set R's RNG to the kind desired. Use "default"
to
return to the R default. See ‘Details’ for the
interpretation of NULL
.NULL
. If it is a character
string, set the method of Normal generation. Use "default"
to return to the R default. NULL
makes no change.NULL
(see ‘Details’)."1.6.2"
0:k
for the above kind
.rng.kind
)..Random.seed
is an integer
vector whose first
element codes the kind of RNG and normal generator. The lowest
two decimal digits are 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, due to
the representation of an unsigned integer by a signed integer.RNGkind
returns a two-element character vector of the RNG and
normal kinds selected before the call, invisibly if either
argument is not NULL
. A type starts a session as the default,
and is selected either by a call to RNGkind
or by setting
.Random.seed
in the workspace.RNGversion
returns the same information as RNGkind
about
the defaults in a specific R version.set.seed
returns NULL
, invisibly.
kind
is
partially matched to this list. The default is
"Mersenne-Twister"
.
"Wichmann-Hill"
.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
$6.9536e12$ (=
prod(p-1)/4
, see Applied Statistics (1984)
33, 123 which corrects the original article).
"Marsaglia-Multicarry"
:
"Super-Duper"
: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"
:
"Knuth-TAOCP-2002"
:
"Knuth-TAOCP"
:The 2002 version was not backwards compatible with the earlier version: the initialization of the GFSR from the seed was altered. R did not allow you to choose consecutive seeds, the reported ‘weakness’, and already scrambled the seeds.
Initialization of this generator is done in interpreted R code and so takes a short but noticeable time.
"L'Ecuyer-CMRG"
: The 6 elements of the seed are internally regarded as 32-bit
unsigned integers. Neither the first three nor the last three
should be all zero, and they are limited to less than
4294967087
and 4294944443
respectively.
This is not particularly interesting of itself, but provides the basis for the multiple streams used in package parallel.
"user-supplied"
:Random.user
for
details.
normal.kind
can be "Kinderman-Ramage"
,
"Buggy Kinderman-Ramage"
(not for set.seed
),
"Ahrens-Dieter"
, "Box-Muller"
, "Inversion"
(the
default), or "user-supplied"
. (For inversion, see the
reference in qnorm
.) The Kinderman-Ramage generator
used in versions prior to 1.7.1 (now called "Buggy"
) had several
approximation errors and should only be used for reproduction of old
results. The "Box-Muller"
generator is stateful as pairs of
normals are generated and returned sequentially. The state is reset
whenever it is selected (even if it is the current normal generator)
and when kind
is changed.
set.seed
uses a 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
"Mersenne-Twister"
and "Knuth-TAOCP"
). There is no
guarantee that different values of seed
will seed the RNG
differently, although any exceptions would be extremely rare. If
called with seed = NULL
it re-initializes (see ‘Note’)
as if no seed had yet been set.
The use of kind = NULL
or normal.kind = NULL
in
RNGkind
or set.seed
selects the currently-used
generator (including that used in the previous session if the
workspace has been restored): if no generator has been used it selects
"default"
.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
The New S Language.
Wadsworth & Brooks/Cole. (set.seed
, storing in .Random.seed
.)
Box, G. E. P. and Muller, M. E. (1958) A note on the generation of normal random deviates. Annals of Mathematical Statistics 29, 610--611.
De Matteis, A. and Pagnutti, S. (1993) Long-range Correlation Analysis of the Wichmann-Hill Random Number Generator, Statist. Comput., 3, 67--70.
Kinderman, A. J. and Ramage, J. G. (1976) Computer generation of normal random variables. Journal of the American Statistical Association 71, 893-896.
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.
Knuth, D. E. (2002) The Art of Computer Programming. Volume 2, third edition, ninth printing. See http://Sunburn.Stanford.EDU/~knuth/news02.html.
L'Ecuyer, P. (1999) Good parameters and implementations for combined multiple recursive random number generators. Operations Research 47, 159--164.
Marsaglia, G. (1997) A random number generator for C. Discussion
paper, posting on Usenet newsgroup sci.stat.math
on
September 29, 1997.
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.
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.)
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.
sample
for random sampling with and without replacement.Distributions for functions for random-variate generation from standard distributions.