NAME
Math::Random::AcceptReject - Acceptance-Rejection PDF transformations
SYNOPSIS
use Math::Random::AcceptReject;
my $pdf = Math::Random::AcceptReject->new(
xmin => 0, # defaults to 0
xmax => 2, # defaults to 1
ymax => 2, # no default!
pdf => 'x', # a triangle from x=0 to x=2 with slope 1
random => 'rand', # use Perl's builtin (default)
);
foreach (1..100) {
my $rnd = $pdf->rand();
# ...
}
# Use Math::Random::MT instead of bultin rand()
# Same target PDF but as Perl code instead of a Math::Symbolic
# function!
use Math::Random::MT;
my $mt = Math::Random::Mt->new($seed);
$pdf = Math::Random::AcceptReject->new(
xmax => 2,
ymax => 2,
pdf => sub { $_[0] },
random => sub { $mt->rand() };
);
DESCRIPTION
This module implements acceptance-rejection transformations of uniformly
distributed random numbers to mostly arbitrary probability density
functions (*PDF*s).
Note that whereas J. von Neumann's algorithm can transform from
arbitrary source PDFs to arbitrary destination PDFs, this module is
currently limited to uniform "[0,1]" source PDFs!
METHODS
new
Creates a new random number generator. Takes named arguments.
Mandatory parameters:
pdf: The probability density function. This can either be a
subroutine reference which takes an argument ('x') and
returns f(x), a Math::Symbolic tree representing f(x) and
using the variable 'x', or a string which can be parsed
as such a Math::Symbolic tree.
ymax: Maximum value of the target PDF f(x) in the x range. This
max theoretically be safely set to a very large value which
is much higher than the real maximum of f(x) within
the range [xmin,xmax]. The efficiency of the algorithm goes
down with
Optional parameters:
random: The random number generator. Defaults to using Perl's
rand() function. May be set to either 'rand' for the
default or a subroutine reference for custom random
number generators. Expected to return one or more(!)
random numbers per call.
xmin: Minimum value for x. Defaults to 0.
xmax: Maximum value for x. Defaults to 1.
rand
Returns the next random number of PDF f(x) as specified by the "pdf"
parameter to "new()".
SEE ALSO
Math::Random::MT, Math::Random, Math::Random::OO, Math::TrulyRandom
Math::Symbolic
The examples in the examples/ subdirectory of this distribution.
AUTHOR
Steffen Mueller,
COPYRIGHT AND LICENSE
Copyright (C) 2007 by Steffen Mueller
This library is free software; you can redistribute it and/or modify it
under the same terms as Perl itself, either Perl version 5.6 or, at your
option, any later version of Perl 5 you may have available.