## functions in random.i - r

random_ipq

random_ipq(ipq_model, dimlist) returns an array of double values with the given DIMLIST (see array function, nil for a scalar result). The numbers are distributed according to a piecewise linear function (possibly with power law or exponential tails) specified by the IPQ_MODEL. The "IPQ" stands for "inverse piecewise quadratic", which the type of function required to transform a uniform random deviate into the piecewise linear distribution. Use the ipq_setup function to compute IPQ_MODEL. Interpreted function, defined at i/random.i line 179SEE ALSO: random, random_x, random_u, random_n, random_rej, ipq_setup

random_n

random_n(dimlist) returns an array of normally distributed random double values with the given DIMLIST (see array function, nil for a scalar result). The mean is 0.0 and the standard deviation is 1.0. The algorithm follows the Box-Muller method (see Numerical Recipes by Press et al.). Interpreted function, defined at i/random.i line 130SEE ALSO: random, random_x, random_u, random_ipq, random_rej, poisson

random_rej

random_rej(target_dist, ipq_model, dimlist) or random_rej(target_dist, bounding_dist, bounding_rand, dimlist) returns an array of double values with the given DIMLIST (see array function, nil for a scalar result). The numbers are distributed according to the TARGET_DIST function: func target_dist(x) returning u(x)>=0 of same number and dimensionality as x, normalized so that the integral of target_dist(x) from -infinity to +infinity is 1.0. The BOUNDING_DIST function must have the same calling sequence as TARGET_DIST: func bounding_dist(x) returning b(x)>=u(x) everywhere. Since u(x) is normalized, the integral of b(x) must be >=1.0. Finally, BOUNDING_RAND is a function which converts an array of uniformly distributed random numbers on (0,1) -- as returned by random -- into an array distributed according to BOUNDING_DIST: func bounding_rand(uniform_x_01) Mathematically, BOUNDING_RAND is the inverse of the integral of BOUNDING_DIST from -infinity to x, with its input scaled to (0,1). If BOUNDING_DIST is not a function, then it must be an IPQ_MODEL returned by the ipq_setup function. In this case BOUNDING_RAND is omitted -- ipq_compute will be used automatically. Interpreted function, defined at i/random.i line 199SEE ALSO: random, random_x, random_u, random_n, random_ipq, ipq_setup

random_u

random_u(a, b, dimlist) return uniformly distributed random numbers between A and B. (Will never exactly equal A or B.) The DIMLIST is as for the array function. Same as (b-a)*random(dimlist)+a. If A==0, you are better off just writing B*random(dimlist). Interpreted function, defined at i/random.i line 113SEE ALSO: random, random_x, random_n, random_ipq, random_rej

random_x

random_x(dimlist) same as random(DIMLIST), except that random_x calls random twice at each point, to avoid the defect that random only can produce about 2.e9 numbers on the interval (0.,1.) (see random for an explanation of these bins). You may set random=random_x to get these "better" random numbers in every call to random. Unlike random, there is a chance in 1.e15 or so that random_x may return exactly 1.0 or 0.0 (the latter may not be possible with IEEE standard arithmetic, while the former apparently is). Since cosmic rays are far more likely, you may as well not worry about this. Also, because of rounding errors, some bit patterns may still be more likely than others, but the 0.5e-9 wide bins of random will be absent. Interpreted function, defined at i/random.i line 74SEE ALSO: random