The rand module provides a number of random number functions.
It may be loaded using require("rand").
Generate exponentially distributed random numbers
X = rand_exp([Rand_Type g,] beta [,num])
This function generates random numbers that are distributed according to an exponential distribution with parameter beta > 0. The distribution's probability density is given by
P(x,beta) = (1/beta) exp(-x/beta)
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
The exponential generator is commonly used to simulate waiting times between events.
rand_new, rand_uniform
Generate random integers
X = rand_int ([Rand_Type g,] imin, imax [,num])
This function may be used to generate a random integer X such
that imin <= X <= imax.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_uniform, rand, rand_new
Generate random numbers from the Student t distribution
X = rand_tdist ([Rand_Type g,] nu [,num])
This function generates random numbers that are distributed according to the Student-t distribution with nu>0.0 degrees of freedom.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_uniform, rand_new, rand_chisq, rand_fdist
Generate random numbers from the F distribution
X = rand_fdist ([Rand_Type g,], nu1, nu2 [,num])
This function generates random numbers that are distributed according
to the F-distribution, which is the ratio of two chi-squared
distributed variates whose degrees of freedom are given by
nu1 (numerator) and nu2 (denominator).
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_uniform, rand_chisq, rand_tdist, rand_gauss, rand_new
Generate Chi-Square distributed random numbers
X = rand_fdist ([Rand_Type g,] nu, [,num])
This function generates random numbers that are distributed according
to the Chi-squared distribution with nu > 0 degrees of freedom.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_uniform, rand_fdist, rand_tdist, rand_gauss, rand_new
Generate uniformly distributed random numbers
X = rand_fdist ([Rand_Type g,] xmin, xmax [,num])
This function generates random double-precision floating point
numbers that are uniformly distributed in the range
xmin<=X<xmax.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_uniform, rand_uniform_pos, rand_int, rand, rand_new
Generate Gamma distributed random numbers
X = rand_gamma ([Rand_Type g,], k, theta [,num])
This function returns random deviates that are Gamma-distributed according to the probability density
P(x; k,theta) = x^(k-1)*exp(-x/theta)/(theta^k * Gamma(k))
k,theta>0.0.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_beta, rand_uniform, rand_binomial, rand_new
Generate random numbers from the binomial distribution
X = rand_binomial ([Rand_Type g,], p, n, [,num])
This function generates binomial distributed random numbers according to the probability density
P(x;p,n) = n!/(k!*(n-k)!) * p^k * (1-p)^(n-k)
n is a non-negative integer and 0<=p<=1.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_gamma, rand_poisson, rand_uniform, rand_new
Generate Poisson distributed random numbers
k = rand_poisson ([Rand_Type g,] mu [,num])
This function generates random unsigned integers that are poisson-distributed according to the probability distribution
P(k;mu) = mu^k/k! * exp(-mu)
mu>0.0.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_gauss, rand_uniform, rand_binomial, rand_new
Generate random numbers from the geometric distribution
k = rand_geometric ([Rand_Type g,] p [,num])
This function generates random numbers that are distributed according to a geometric distribution with a probability density
P(k; p) = p*(1-p)^(k-1)
0<=p<=1
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_poisson, rand_exp, rand_gauss, rand_uniform, rand_new
Generate random numbers from the Cauchy distribution
X = rand_cauchy ([Rand_Type g,] gamma [,num])
This function generates random numbers that are distributed according to a cauchy-distribution with a probability density
P(x; gamma) = 1/(PI*gamma)/(1+(x/gamma)^2)
gamma>=0.0.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_gauss, rand_poisson, rand_exp, rand_new
Generate random numbers from the beta distribution
X = rand_fdist ([Rand_Type g,] a, b [,num])
This function generates random numbers that are distributed according to a Beta-distribution with a probability density
P(x; a,b) = x^(a-1)*(1-x)^(b-1)/B(a,b)
a, b > 0.
rand_gamma, rand_binomial, rand_chisq
Generate gaussian-distributed random numbers
X = rand_gauss ([Rand_Type g,] sigma [,num])
This function generates gaussian random numbers with the specified sigma and mean of 0 according to the probability density
P(x; sigma) = 1/sqrt(2*PI*sigma^2) * exp(-0.5*x^2/sigma^2)
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
This implementation utilizes the Box-Muller algorithm.
rand_uniform, rand_poisson, rand_chisq, rand_gauss, rand_new
Generate random integers numbers
X = rand ([Rand_Type g,] [,num])
This function generates unsigned 32 bit randomly distributed integers on the closed interval 0<=X<=0xFFFFFFFFUL.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_new, rand_int, rand_uniform, rand_flat
Generate uniform positive random numbers
X = rand_uniform_pos ([Rand_Type] [num])
This function generates uniformly distributed random numbers in open
interval 0<X<1.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_uniform, rand_new
Generate uniform random numbers
X = rand_uniform ([Rand_Type g] [num])
This function generates uniformly distributed double precision
numbers on the semi-closed interval 0<=r<1.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
rand_uniform_pos, rand_int, rand_flat, rand_new
Seed the random number generator
srand ([Rand_Type g,] Array_Type seeds)
This function may be used to seed an instance of a rand number
generator using the values of an array of an unsigned long integers.
If a generator (created by rand_new) is specified as the first
argument, then is will be seeded; otherwise, the seeds will
get applied to the default generator.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
The num parameter indicates that num random values are to
be generated and returned as an array.
gen = rand_new ();
srand (gen, [_time(), _pid(), 0xFF80743]);
rand_new, rand, rand_uniform
Instantiate a new random number generator
Rand_Type rand_new ([array-of-seeds])
This function creates a new instance of the basic random number
generator. An optional array of 32 bit unsigned integers may be used
to seed the generator. By default, the generator is seeding using
the current time and process id. The srand function may also
be used to seed the generator. The generator created by the
rand_new function may be passed as the first argument to most
of the other functions in the module to indicate that this instance
should be used as the basic generator.
The following example shows how to create an array of 512 uniform random numbers derived from the default instance of the basic generator:
x = rand_uniform (512);
rand_new function and used by rand_uniform as follows:
g = rand_new ([0x1234, 0x5678912, 0xEFAB1234]);
x = rand_uniform (g, 512);
The generator is a hybrid one that sums the results of 3 separate generators: George Marsaglia's MZRAN13 generator, a multiply with carry generator (also by Marsaglia), and a product generator. The combined generator has a 192 bit state and a period exceeding 10^46.
The resulting random sequences were tested using version 2.24.4 of
the dieharder random number testing program. The tests showed that
this generator performed better than the famous Marsenne
Twister (mt19937) both in terms of randomness and speed. More
information about the test results may be found at
http://www.jedsoft.org/slang/modules/rand.html.
The mt19937 generator is separately available via the GSL
module.
srand, rand_int, rand_uniform
Randomly sample from one or more arrays
(b1 [,b2,...]) = rand_sample ([Rand_Type g,] a1 [,a2,...], num);
This function may be used to randomly sample num elements from
one or more arrays (a1,...). The arrays must be consistent in
the sense that they must have the same leading dimension, which is
the one to be sampled.
The optional first argument may be used to specify a different instance of a random number generator. Otherwise, the default generator will be used.
Suppose A is a 1-d array with 20 elements, and B is a 2d array with dimensions [20,30]. Then
(A1, B1) = rand_sample (A, B, 5);
The indices used to sample the arrays are created using the first
num elements of a random permutation of the integers
[0:dim0-1] where dim0 is the size of the leading
dimension. The same set of indices are used for all the arrays.
Hence any correspondence between a0[i,..] and a1[i,...
will be preserved in the samples.
rand_permutation, rand_new
Generate a random permutation of integers
p = rand_permutation ([Rand_Type g,] Int_Type n)
This function may be used to generate a random permutation of the
sequence of integers 0,1,..,n-1.
The optional parameter g may be used to
specify the underlying random number generator. See the
documentation for the rand_new function for more information.
rand_sample