Provided by: libmath-random-perl_0.71-3build2_amd64 
NAME
Math::Random - Random Number Generators
SYNOPSIS
•
use Math::Random;
Exports the following routines by default (see "Default Routines"):
random_set_seed_from_phrase
random_get_seed
random_seed_from_phrase
random_set_seed
random_uniform
random_uniform_integer
random_permutation
random_permuted_index
random_normal
In this case the extended routines (see "Extended Routines") can be used by
qualifying them explicitly with "Math::Random::", for example: "$stdexp =
Math::Random::random_exponential();"
•
use Math::Random qw(random_beta
random_chi_square
random_exponential
random_f
random_gamma
random_multivariate_normal
random_multinomial
random_noncentral_chi_square
random_noncentral_f
random_normal
random_permutation
random_permuted_index
random_uniform
random_poisson
random_uniform_integer
random_negative_binomial
random_binomial
random_seed_from_phrase
random_get_seed
random_set_seed_from_phrase
random_set_seed );
Exports all the routines explicitly. Use a subset of the list for the routines you
want.
•
use Math::Random qw(:all);
Exports all the routines, as well.
DESCRIPTION
Math::Random is a Perl port of the C version of randlib, which is a suite of routines
for generating random deviates. See "RANDLIB" for more information.
This port supports all of the distributions from which the Fortran and C versions
generate deviates. The major functionalities that are excluded are the multiple
generators/splitting facility and antithetic random number generation. These
facilities, along with some of the distributions which are included, are probably not
of interest except to the very sophisticated user. If there is sufficient
interest, the excluded facilities will be included in a future release. The code
to perform the excluded facilities is available as randlib in Fortran and C source.
Default Routines
The routines which are exported by default are the only ones that the average Perl
programmer is likely to need.
"random_set_seed_from_phrase($phrase)"
Sets the seed of the base generator to a value determined by $phrase. If
the module is installed with the default option, the value depends on the machine
collating sequence. It should, however, be the same for 7-bit ASCII character
strings on all ASCII machines. In the original randlib, the value generated for a
given $phrase was consistent from implementation to implementation (it did not rely
on the machine collating sequence). Check with your Perl administrator to see if the
module was installed with the original seed generator. Note: When the Perl processor
loads package Math::Random the seed is set to a value based on the current
time. The seed changes each time Math::Random generates something random.
The ability to set the seed is useful for debugging, or for those who like
reproducible runs.
"random_get_seed()"
Returns an array of length two which contains the two integers constituting
the seed (assuming a call in array context). An invocation in a scalar
context returns the integer 2, which is probably not useful.
"random_seed_from_phrase($phrase)"
Returns an array of length two which contains the two integers constituting
the seed (assuming a call in array context). An invocation in a scalar
context returns the integer 2, which is probably not useful. The seed generated
is the seed used to set the seed in a call to "random_set_seed_from_phrase".
Note: the following two calls (for the same $phrase) are equivalent:
random_set_seed(random_seed_from_phrase($phrase));
and
random_set_seed_from_phrase($phrase);
"random_set_seed(@seed)"
Sets the seed of the base generator to the value @seed[0,1]. Usually, the
argument @seed should be the result of a call to "random_get_seed" or
"random_seed_from_phrase". @seed[0,1] must be two integers in the range (1, 1) to
(2147483562, 2147483398), inclusive.
"random_uniform($n, $low, $high)"
"random_uniform($n)"
"random_uniform()"
When called in an array context, returns an array of $n deviates generated from a
uniform($low, $high) distribution. When called in a scalar context, generates
and returns only one such deviate as a scalar, regardless of the value of $n.
Argument restrictions: $low must be less than or equal to $high.
Defaults are (1, 0, 1). Note: $high must be specified if $low is specified.
"random_uniform_integer($n, $low, $high)"
When called in an array context, returns an array of $n integer deviates generated
from a uniform($low, $high) distribution on the integers. When called in a
scalar context, generates and returns only one such deviate as a scalar, regardless
of the value of $n.
Argument restrictions: $low and $high are first rounded using "int()"; the
resulting $low must be less than or equal to $high, and the resulting range ($high -
$low) must not be greater than 2147483561.
There are no defaults; all three arguments must be provided.
"random_permutation(@array)"
Returns @array, randomly permuted.
"random_permuted_index($n)"
Returns an array of array indices, randomly permuted. The indices used are (0,
... , $n-1). This produces the indices used by "random_permutation" for a given seed,
without passing arrays.
Note: the following are equivalent:
random_set_seed_from_phrase('jjv');
random_permutation(@array);
and
random_set_seed_from_phrase('jjv');
@array[(random_permuted_index(scalar(@array)))];
"random_normal($n, $av, $sd)"
"random_normal($n, $av)"
"random_normal($n)"
"random_normal()"
When called in an array context, returns an array of $n deviates generated from a
normal($av, $sd^2) distribution. When called in a scalar context, generates and
returns only one such deviate as a scalar, regardless of the value of $n.
Argument restrictions: $sd must be non-negative.
Defaults are (1, 0, 1).
Extended Routines
These routines generate deviates from many other distributions.
Note: The parameterizations of these deviates are standard (insofar as there is a
standard ... ) but particular attention should be paid to the distributions of the beta
and gamma deviates (noted in "random_beta" and "random_gamma" below).
"random_beta($n, $aa, $bb)"
When called in an array context, returns an array of $n deviates generated from
the beta distribution with parameters $aa and $bb. The density of the beta is:
X^($aa - 1) * (1 - X)^($bb - 1) / B($aa , $bb) for 0 < X < 1.
When called in a scalar context, generates and returns only one such deviate as a
scalar, regardless of the value of $n.
Argument restrictions: Both $aa and $bb must not be less than "1.0E-37".
There are no defaults; all three arguments must be provided.
"random_binomial($n, $nt, $p)"
When called in an array context, returns an array of $n outcomes generated from
the binomial distribution with number of trials $nt and probability of an event
in each trial $p. When called in a scalar context, generates and returns only one
such outcome as a scalar, regardless of the value of $n.
Argument restrictions: $nt is rounded using "int()"; the result must be non-
negative. $p must be between 0 and 1 inclusive.
There are no defaults; both arguments must be provided.
"random_chi_square($n, $df)"
When called in an array context, returns an array of $n deviates generated from the
chi-square distribution with $df degrees of freedom. When called in a scalar
context, generates and returns only one such deviate as a scalar, regardless of the
value of $n.
Argument restrictions: $df must be positive.
There are no defaults; both arguments must be provided.
"random_exponential($n, $av)"
"random_exponential($n)"
"random_exponential()"
When called in an array context, returns an array of $n deviates generated from the
exponential distribution with mean $av. When called in a scalar context,
generates and returns only one such deviate as a scalar, regardless of the value of
$n.
Argument restrictions: $av must be non-negative.
Defaults are (1, 1).
"random_f($n, $dfn, $dfd)"
When called in an array context, returns an array of $n deviates generated from the
F (variance ratio) distribution with degrees of freedom $dfn (numerator) and $dfd
(denominator). When called in a scalar context, generates and returns only one
such deviate as a scalar, regardless of the value of $n.
Argument restrictions: Both $dfn and $dfd must be positive.
There are no defaults; all three arguments must be provided.
"random_gamma($n, $a, $r)"
When called in an array context, returns an array of $n deviates generated from
the gamma distribution with parameters $a and $r. The density of the gamma is:
($a**$r) / Gamma($r) * X**($r - 1) * Exp(-$a*X)
When called in a scalar context, generates and returns only one such deviate as a
scalar, regardless of the value of $n.
Argument restrictions: Both $a and $r must be positive.
There are no defaults; all three arguments must be provided.
"random_multinomial($n, @p)"
When called in an array context, returns single observation from the multinomial
distribution, with $n events classified into as many categories as the length of @p.
The probability of an event being classified into category i is given by the ith
element of @p. The observation is an array with length equal to @p, so when called in
a scalar context it returns the length of @p. The sum of the elements of the
observation is equal to $n.
Argument restrictions: $n is rounded with "int()" before it is used; the result
must be non-negative. @p must have length at least 2. All elements of @p except
the last must be between 0 and 1 inclusive, and sum to no more than 0.99999.
Note: The last element of @p is a dummy to indicate the number of categories, and it
is adjusted to bring the sum of the elements of @p to 1.
There are no defaults; both arguments must be provided.
"random_multivariate_normal($n, @mean, @covar)"
When called in an array context, returns an array of $n deviates (each deviate
being an array reference) generated from the multivariate normal
distribution with mean vector @mean and variance-covariance matrix @covar.
When called in a scalar context, generates and returns only one such deviate
as an array reference, regardless of the value of $n.
Argument restrictions: If the dimension of the deviate to be generated is p, @mean
should be a length p array of real numbers. @covar should be a length p array of
references to length p arrays of real numbers (i.e. a p by p matrix).
Further, @covar should be a symmetric positive-definite matrix, although the Perl code
does not check positive-definiteness, and the underlying C code assumes the
matrix is symmetric. Given that the variance-covariance matrix is symmetric,
it doesn't matter if the references refer to rows or columns. If a non-
positive definite matrix is passed to the function, it will abort with the
following message:
COVM not positive definite in SETGMN
Also, a non-symmetric @covar may produce deviates without complaint,
although they may not be from the expected distribution. For these reasons, you
are encouraged to verify the arguments passed.
The Perl code does check the dimensionality of @mean and @covar for consistency.
It does so by checking that the length of the argument vector passed is odd, that
what should be the last element of @mean and the first element of @covar look like
they are a number followed by an array reference respectively, and that the arrays
referred to in @covar are as long as @mean.
There are no defaults; all three arguments must be provided.
"random_negative_binomial($n, $ne, $p)"
When called in an array context, returns an array of $n outcomes generated from the
negative binomial distribution with number of events $ne and probability of an
event in each trial $p. When called in a scalar context, generates and returns
only one such outcome as a scalar, regardless of the value of $n.
Argument restrictions: $ne is rounded using "int()", the result must be positive.
$p must be between 0 and 1 exclusive.
There are no defaults; both arguments must be provided.
"random_noncentral_chi_square($n, $df, $nonc)"
When called in an array context, returns an array of $n deviates generated from
the noncentral chi-square distribution with $df degrees of freedom and noncentrality
parameter $nonc. When called in a scalar context, generates and returns only one
such deviate as a scalar, regardless of the value of $n.
Argument restrictions: $df must be at least 1, $nonc must be non-negative.
There are no defaults; all three arguments must be provided.
"random_noncentral_f($n, $dfn, $dfd, $nonc)"
When called in an array context, returns an array of $n deviates generated from the
noncentral F (variance ratio) distribution with degrees of freedom $dfn (numerator)
and $dfd (denominator); and noncentrality parameter $nonc. When called in a scalar
context, generates and returns only one such deviate as a scalar, regardless of the
value of $n.
Argument restrictions: $dfn must be at least 1, $dfd must be positive, and $nonc
must be non-negative.
There are no defaults; all four arguments must be provided.
"random_poisson($n, $mu)"
When called in an array context, returns an array of $n outcomes generated from
the Poisson distribution with mean $mu. When called in a scalar context,
generates and returns only one such outcome as a scalar, regardless of the value of
$n.
Argument restrictions: $mu must be non-negative.
There are no defaults; both arguments must be provided.
ERROR HANDLING
The Perl code should "croak" if bad arguments are passed or if the underlying C code
cannot allocate the necessary memory. The only error which should kill the job without
"croak"ing is a non-positive definite variance-covariance matrix passed
to "random_multivarite_normal" (see "Extended Routines").
RANDLIB
randlib is available in Fortran and C source form, and will soon be available in
Fortran90 source as well. randlib.c can be obtained from statlib. Send mail whose
message is 'send randlib.c.shar from general' to:
statlib@lib.stat.cmu.edu
randlib.c can also be obtained by anonymous ftp to:
odin.mdacc.tmc.edu (143.111.62.32)
where it is available as
/pub/source/randlib.c-1.3.tar.gz
For obvious reasons, the original randlib (in Fortran) has been renamed to
/pub/source/randlib.f-1.3.tar.gz
on the same machine.
Our FTP index is on file "./pub/index".
If you have Internet access and a browser you might note the following web site addresses:
University of Texas M. D. Anderson Cancer Center Home Page:
http://www.mdanderson.org/
Department of Biomathematics Home Page:
http://odin.mdacc.tmc.edu/
Available software:
http://biostatistics.mdanderson.org/SoftwareDownload/
SUPPORT
This work was supported in part by grant CA-16672 from the National Cancer Institute.
We are grateful to Larry and Pat McNeil of Corpus Cristi for their generous support.
Some equipment used in this effort was provided by IBM as part of a cooperative study
agreement; we thank them.
CODE MANIPULATION
The C version of randlib was obtained by translating the original Fortran
randlib using PROMULA.FORTRAN, and performing some hand crafting of the result.
Information on PROMULA.FORTRAN can be obtained from:
PROMULA Development Corporation
3620 N. High Street, Suite 301
Columbus, Ohio 43214
(614) 263-5454
wrapper.c (now obsolete) was created by using SWIG, and performing some
modification of the result. SWIG also produced the skeleton of Random.pm.
Information on SWIG can be obtained from:
http://www.swig.org
SOURCES
The following routines, which were written by others and lightly modified for
consistency in packaging, are included in randlib.
Bottom Level Routines
These routines are a transliteration of the Pascal in the reference to Fortran, and
thence to C.
L'Ecuyer, P., and Cote, S. "Implementing a Random Number Package with Splitting
Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991).
Exponential
This code was obtained from Netlib.
Ahrens, J. H., and Dieter, U. "Computer Methods for Sampling from the Exponential and
Normal Distributions." Comm. ACM, 15,10 (Oct. 1972), 873-882.
Gamma
(Case R >= 1.0)
Ahrens, J. H., and Dieter, U. "Generating Gamma Variates by a Modified Rejection
Technique." Comm. ACM, 25,1 (Jan. 1982), 47-54. Algorithm GD
(Case 0.0 <= R <= 1.0)
Ahrens, J. H., and Dieter, U. "Computer Methods for Sampling from Gamma, Beta,
Poisson and Binomial Distributions." Computing, 12 (1974), 223-246. Adaptation of
algorithm GS.
Normal
This code was obtained from netlib.
Ahrens, J. H., and Dieter, U. "Extensions of Forsythe's Method for Random Sampling
from the Normal Distribution." Math. Comput., 27,124 (Oct. 1973), 927-937.
Binomial
This code was kindly sent to Dr. Brown by Dr. Kachitvichyanukul.
Kachitvichyanukul, V., and Schmeiser, B. W. "Binomial Random Variate Generation."
Comm. ACM, 31, 2 (Feb. 1988), 216.
Poisson
This code was obtained from netlib.
Ahrens, J. H., and Dieter, U. "Computer Generation of Poisson Deviates from Modified
Normal Distributions." ACM Trans. Math. Software, 8, 2 (June 1982), 163-179.
Beta
This code was written by us following the recipe in the following.
Cheng, R. C. H. "Generating Beta Variables with Nonintegral Shape Parameters."
Comm. ACM, 21:317-322 (1978). (Algorithms BB and BC)
Linpack
Routines "SPOFA" and "SDOT" are used to perform the Cholesky decomposition of
the covariance matrix in "SETGMN" (used for the generation of multivariate normal
deviates).
Dongarra, J. J., Moler, C. B., Bunch, J. R., and Stewart, G. W. Linpack User's
Guide. SIAM Press, Philadelphia. (1979)
Multinomial
The algorithm is from page 559 of Devroye, Luc Non-Uniform Random Variate
Generation. New York: Springer-Verlag, 1986.
Negative Binomial
The algorithm is from page 480 of Devroye, Luc Non-Uniform Random Variate
Generation. New York: Springer-Verlag, 1986.
VERSION
This POD documents Math::Random version 0.71.
AUTHORS
• Math::Random (the Perl port of Randlib) was put together by John Venier and Barry
W. Brown with help from SWIG. For version 0.61, Geoffrey Rommel made various
cosmetic changes. Version 0.64 uses plain vanilla XS rather than SWIG.
• randlib was compiled and written by Barry W. Brown, James Lovato, Kathy Russell, and
John Venier.
• Correspondence regarding Math::Random or randlib should be addressed to John
Venier by email to
jvenier@mdanderson.org
• Our address is:
Department of Biomathematics, Box 237
The University of Texas, M.D. Anderson Cancer Center
1515 Holcombe Boulevard
Houston, TX 77030
• Geoffrey Rommel may be reached at grommel [at] cpan [dot] org.
LEGALITIES
• The programs in the Perl code distributed with Math::Random and in the C code
helper.c, as well as the documentation, are copyright by John Venier and Barry
W. Brown for the University of Texas M. D. Anderson Cancer Center in 1997. They
may be distributed and used under the same conditions as Perl.
• randlib.c, com.c, and randlib.h are from randlib (See "RANDLIB") and are
distributed with the following legalities.
Code that appeared in an ACM publication is subject to their algorithms
policy:
Submittal of an algorithm for publication in one of the ACM Transactions
implies that unrestricted use of the algorithm within a computer is permissible.
General permission to copy and distribute the algorithm without fee is granted
provided that the copies are not made or distributed for direct commercial
advantage. The ACM copyright notice and the title of the publication and its date
appear, and notice is given that copying is by permission of the Association for
Computing Machinery. To copy otherwise, or to republish, requires a fee and/or
specific permission.
Krogh, F. "Algorithms Policy." ACM Tran. Math. Softw. 13 (1987), 183-186.
Note, however, that only the particular expression of an algorithm can be copyrighted,
not the algorithm per se; see 17 USC 102(b).
We place the Randlib code that we have written in the public domain.
• Math::Randlib and randlib are distributed with NO WARRANTY. See "NO WARRANTY".
NO WARRANTY
WE PROVIDE ABSOLUTELY NO WARRANTY OF ANY KIND EITHER EXPRESS OR IMPLIED, INCLUDING
BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS
WITH YOU. SHOULD THIS PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY
SERVICING, REPAIR OR CORRECTION.
IN NO EVENT SHALL THE UNIVERSITY OF TEXAS OR ANY OF ITS COMPONENT INSTITUTIONS
INCLUDING M. D. ANDERSON HOSPITAL BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY LOST
PROFITS, LOST MONIES, OR OTHER SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
OUT OF THE USE OR INABILITY TO USE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA OR
ITS ANALYSIS BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY THIRD PARTIES FROM) THE
PROGRAM.
(Above NO WARRANTY modified from the GNU NO WARRANTY statement.)