Mercurial > octave-nkf
view liboctave/randgamma.c @ 6980:e5d51f9fa1c9
[project @ 2007-10-08 21:52:04 by jwe]
author | jwe |
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date | Mon, 08 Oct 2007 21:52:04 +0000 |
parents | 2cd0af543e7a |
children | 4270ded9ddc6 |
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/* This code is in the public domain */ /* double randg(a) void fill_randg(a,n,x) Generate a series of standard gamma distributions. See: Marsaglia G and Tsang W (2000), "A simple method for generating gamma variables", ACM Transactions on Mathematical Software 26(3) 363-372 Needs the following defines: * NAN: value to return for Not-A-Number * RUNI: uniform generator on (0,1) * RNOR: normal generator * REXP: exponential generator, or -log(RUNI) if one isn't available * INFINITE: function to test whether a value is infinite Test using: mean = a variance = a skewness = 2/sqrt(a) kurtosis = 3 + 6/sqrt(a) Note that randg can be used to generate many distributions: gamma(a,b) for a>0, b>0 (from R) r = b*randg(a) beta(a,b) for a>0, b>0 r1 = randg(a,1) r = r1 / (r1 + randg(b,1)) Erlang(a,n) r = a*randg(n) chisq(df) for df>0 r = 2*randg(df/2) t(df) for 0<df<inf (use randn if df is infinite) r = randn() / sqrt(2*randg(df/2)/df) F(n1,n2) for 0<n1, 0<n2 r1 = 2*randg(n1/2)/n1 or 1 if n1 is infinite r2 = 2*randg(n2/2)/n2 or 1 if n2 is infinite r = r1 / r2 negative binonial (n, p) for n>0, 0<p<=1 r = randp((1-p)/p * randg(n)) (from R, citing Devroye(1986), Non-Uniform Random Variate Generation) non-central chisq(df,L), for df>=0 and L>0 (use chisq if L=0) r = randp(L/2) r(r>0) = 2*randg(r(r>0)) r(df>0) += 2*randg(df(df>0)/2) (from R, citing formula 29.5b-c in Johnson, Kotz, Balkrishnan(1995)) Dirichlet(a1,...,ak) for ai > 0 r = (randg(a1),...,randg(ak)) r = r / sum(r) (from GSL, citing Law & Kelton(1991), Simulation Modeling and Analysis) */ #if defined (HAVE_CONFIG_H) #include <config.h> #endif #include <math.h> #include <stdio.h> #include "lo-ieee.h" #include "randmtzig.h" #include "randgamma.h" #undef NAN #define NAN octave_NaN #define INFINITE lo_ieee_isinf #define RUNI oct_randu() #define RNOR oct_randn() #define REXP oct_rande() void oct_fill_randg (double a, octave_idx_type n, double *r) { octave_idx_type i; /* If a < 1, start by generating gamma(1+a) */ const double d = (a < 1. ? 1.+a : a) - 1./3.; const double c = 1./sqrt(9.*d); /* Handle invalid cases */ if (a <= 0 || INFINITE(a)) { for (i=0; i < n; i++) r[i] = NAN; return; } for (i=0; i < n; i++) { double x, xsq, v, u; restart: x = RNOR; v = (1+c*x); v *= v*v; if (v <= 0) goto restart; /* rare, so don't bother moving up */ u = RUNI; xsq = x*x; if (u >= 1.-0.0331*xsq*xsq && log(u) >= 0.5*xsq + d*(1-v+log(v))) goto restart; r[i] = d*v; } if (a < 1) { /* Use gamma(a) = gamma(1+a)*U^(1/a) */ /* Given REXP = -log(U) then U^(1/a) = exp(-REXP/a) */ for (i = 0; i < n; i++) r[i] *= exp(-REXP/a); } } double oct_randg (double a) { double ret; oct_fill_randg(a,1,&ret); return ret; } /* ;;; Local Variables: *** ;;; mode: C *** ;;; End: *** */