Provided by: libmath-random-perl_0.72-2build5_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.)