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Code Editor : randfuns.hlp
rand_exp SYNOPSIS Generate exponentially distributed random numbers USAGE X = rand_exp([Rand_Type g,] beta [,num]) DESCRIPTION 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. NOTES The exponential generator is commonly used to simulate waiting times between events. SEE ALSO rand_new, rand_uniform -------------------------------------------------------------- rand_int SYNOPSIS Generate random integers USAGE X = rand_int ([Rand_Type g,] imin, imax [,num]) DESCRIPTION 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. SEE ALSO rand_uniform, rand, rand_new -------------------------------------------------------------- rand_tdist SYNOPSIS Generate random numbers from the Student t distribution USAGE X = rand_tdist ([Rand_Type g,] nu [,num]) DESCRIPTION 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. SEE ALSO rand_uniform, rand_new, rand_chisq, rand_fdist -------------------------------------------------------------- rand_fdist SYNOPSIS Generate random numbers from the F distribution USAGE X = rand_fdist ([Rand_Type g,], nu1, nu2 [,num]) DESCRIPTION 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. SEE ALSO rand_uniform, rand_chisq, rand_tdist, rand_gauss, rand_new -------------------------------------------------------------- rand_chisq SYNOPSIS Generate Chi-Square distributed random numbers USAGE X = rand_fdist ([Rand_Type g,] nu, [,num]) DESCRIPTION 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. SEE ALSO rand_uniform, rand_fdist, rand_tdist, rand_gauss, rand_new -------------------------------------------------------------- rand_flat SYNOPSIS Generate uniformly distributed random numbers USAGE X = rand_fdist ([Rand_Type g,] xmin, xmax [,num]) DESCRIPTION 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. SEE ALSO rand_uniform, rand_uniform_pos, rand_int, rand, rand_new -------------------------------------------------------------- rand_gamma SYNOPSIS Generate Gamma distributed random numbers USAGE X = rand_gamma ([Rand_Type g,], k, theta [,num]) DESCRIPTION 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)) where `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. SEE ALSO rand_beta, rand_uniform, rand_binomial, rand_new -------------------------------------------------------------- rand_binomial SYNOPSIS Generate random numbers from the binomial distribution USAGE X = rand_binomial ([Rand_Type g,], p, n, [,num]) DESCRIPTION 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) where `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. SEE ALSO rand_gamma, rand_poisson, rand_uniform, rand_new -------------------------------------------------------------- rand_poisson SYNOPSIS Generate Poisson distributed random numbers USAGE k = rand_poisson ([Rand_Type g,] mu [,num]) DESCRIPTION This function generates random unsigned integers that are poisson-distributed according to the probability distribution P(k;mu) = mu^k/k! * exp(-mu) where `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. SEE ALSO rand_gauss, rand_uniform, rand_binomial, rand_new -------------------------------------------------------------- rand_geometric SYNOPSIS Generate random numbers from the geometric distribution USAGE k = rand_geometric ([Rand_Type g,] p [,num]) DESCRIPTION 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) where `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. SEE ALSO rand_poisson, rand_exp, rand_gauss, rand_uniform, rand_new -------------------------------------------------------------- rand_cauchy SYNOPSIS Generate random numbers from the Cauchy distribution USAGE X = rand_cauchy ([Rand_Type g,] gamma [,num]) DESCRIPTION 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) where `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. SEE ALSO rand_gauss, rand_poisson, rand_exp, rand_new -------------------------------------------------------------- rand_beta SYNOPSIS Generate random numbers from the beta distribution USAGE X = rand_fdist ([Rand_Type g,] a, b [,num]) DESCRIPTION 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) where `a, b > 0'. SEE ALSO rand_gamma, rand_binomial, rand_chisq -------------------------------------------------------------- rand_gauss SYNOPSIS Generate gaussian-distributed random numbers USAGE X = rand_gauss ([Rand_Type g,] sigma [,num]) DESCRIPTION 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. NOTES This implementation utilizes the Box-Muller algorithm. SEE ALSO rand_uniform, rand_poisson, rand_chisq, rand_gauss, rand_new -------------------------------------------------------------- rand SYNOPSIS Generate random integers numbers USAGE X = rand ([Rand_Type g,] [,num]) DESCRIPTION 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. SEE ALSO rand_new, rand_int, rand_uniform, rand_flat -------------------------------------------------------------- rand_uniform_pos SYNOPSIS Generate uniform positive random numbers USAGE X = rand_uniform_pos ([Rand_Type] [num]) DESCRIPTION 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. SEE ALSO rand_uniform, rand_new -------------------------------------------------------------- rand_uniform SYNOPSIS Generate uniform random numbers USAGE X = rand_uniform ([Rand_Type g] [num]) DESCRIPTION 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. SEE ALSO rand_uniform_pos, rand_int, rand_flat, rand_new -------------------------------------------------------------- srand SYNOPSIS Seed the random number generator USAGE srand ([Rand_Type g,] Array_Type seeds) DESCRIPTION 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. EXAMPLE gen = rand_new (); srand (gen, [_time(), _pid(), 0xFF80743]); SEE ALSO rand_new, rand, rand_uniform -------------------------------------------------------------- rand_new SYNOPSIS Instantiate a new random number generator USAGE Rand_Type rand_new ([array-of-seeds]) DESCRIPTION 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. EXAMPLE 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); A specific instance of the generator may be created using the `rand_new' function and used by `rand_uniform' as follows: g = rand_new ([0x1234, 0x5678912, 0xEFAB1234]); x = rand_uniform (g, 512); NOTES 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. SEE ALSO srand, rand_int, rand_uniform -------------------------------------------------------------- rand_sample SYNOPSIS Randomly sample from one or more arrays USAGE (b1 [,b2,...]) = rand_sample ([Rand_Type g,] a1 [,a2,...], num); DESCRIPTION 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. EXAMPLE 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); will produce a 1d array A1 with 5 elements and a 2d array B1 with dimensions [5,30]. NOTES 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. SEE ALSO rand_permutation, rand_new -------------------------------------------------------------- rand_permutation SYNOPSIS Generate a random permutation of integers USAGE p = rand_permutation ([Rand_Type g,] Int_Type n) DESCRIPTION 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. SEE ALSO rand_sample --------------------------------------------------------------
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