Mercurial > hg > octave-nkf
annotate liboctave/randgamma.c @ 15283:a95432e7309c stable release-3-6-3
Version 3.6.3 released.
* configure.ac (AC_INIT): Version is now 3.6.3.
(OCTAVE_RELEASE_DATE): Now 2012-09-04.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Tue, 04 Sep 2012 13:17:13 -0400 |
| parents | 72c96de7a403 |
| children | 43db83eff9db |
| rev | line source |
|---|---|
| 7019 | 1 /* |
| 2 | |
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3 Copyright (C) 2006-2012 John W. Eaton |
| 7019 | 4 |
| 5 This file is part of Octave. | |
| 6 | |
| 7 Octave is free software; you can redistribute it and/or modify it | |
| 8 under the terms of the GNU General Public License as published by the | |
| 9 Free Software Foundation; either version 3 of the License, or (at your | |
| 10 option) any later version. | |
| 11 | |
| 12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 15 for more details. | |
| 16 | |
| 17 You should have received a copy of the GNU General Public License | |
| 18 along with Octave; see the file COPYING. If not, see | |
| 19 <http://www.gnu.org/licenses/>. | |
| 20 | |
| 21 */ | |
| 22 | |
| 23 /* Original version written by Paul Kienzle distributed as free | |
| 24 software in the in the public domain. */ | |
| 5742 | 25 |
| 26 /* | |
| 27 | |
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28 double randg(a) |
| 5742 | 29 void fill_randg(a,n,x) |
| 30 | |
| 31 Generate a series of standard gamma distributions. | |
| 32 | |
| 33 See: Marsaglia G and Tsang W (2000), "A simple method for generating | |
| 34 gamma variables", ACM Transactions on Mathematical Software 26(3) 363-372 | |
| 35 | |
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36 Needs the following defines: |
| 5742 | 37 * NAN: value to return for Not-A-Number |
| 38 * RUNI: uniform generator on (0,1) | |
| 39 * RNOR: normal generator | |
| 40 * REXP: exponential generator, or -log(RUNI) if one isn't available | |
| 41 * INFINITE: function to test whether a value is infinite | |
| 42 | |
| 43 Test using: | |
| 44 mean = a | |
| 45 variance = a | |
| 46 skewness = 2/sqrt(a) | |
| 47 kurtosis = 3 + 6/sqrt(a) | |
| 48 | |
| 49 Note that randg can be used to generate many distributions: | |
| 50 | |
| 51 gamma(a,b) for a>0, b>0 (from R) | |
| 52 r = b*randg(a) | |
| 53 beta(a,b) for a>0, b>0 | |
| 54 r1 = randg(a,1) | |
| 55 r = r1 / (r1 + randg(b,1)) | |
| 56 Erlang(a,n) | |
| 57 r = a*randg(n) | |
| 58 chisq(df) for df>0 | |
| 59 r = 2*randg(df/2) | |
| 60 t(df) for 0<df<inf (use randn if df is infinite) | |
| 61 r = randn() / sqrt(2*randg(df/2)/df) | |
| 62 F(n1,n2) for 0<n1, 0<n2 | |
| 63 r1 = 2*randg(n1/2)/n1 or 1 if n1 is infinite | |
| 64 r2 = 2*randg(n2/2)/n2 or 1 if n2 is infinite | |
| 65 r = r1 / r2 | |
| 66 negative binonial (n, p) for n>0, 0<p<=1 | |
| 67 r = randp((1-p)/p * randg(n)) | |
| 68 (from R, citing Devroye(1986), Non-Uniform Random Variate Generation) | |
| 69 non-central chisq(df,L), for df>=0 and L>0 (use chisq if L=0) | |
| 70 r = randp(L/2) | |
| 71 r(r>0) = 2*randg(r(r>0)) | |
| 72 r(df>0) += 2*randg(df(df>0)/2) | |
| 73 (from R, citing formula 29.5b-c in Johnson, Kotz, Balkrishnan(1995)) | |
| 74 Dirichlet(a1,...,ak) for ai > 0 | |
| 75 r = (randg(a1),...,randg(ak)) | |
| 76 r = r / sum(r) | |
| 77 (from GSL, citing Law & Kelton(1991), Simulation Modeling and Analysis) | |
| 78 */ | |
| 79 | |
| 80 #if defined (HAVE_CONFIG_H) | |
| 81 #include <config.h> | |
| 82 #endif | |
| 83 | |
| 84 #include <stdio.h> | |
| 85 | |
| 86 #include "lo-ieee.h" | |
| 7231 | 87 #include "lo-math.h" |
| 5742 | 88 #include "randmtzig.h" |
| 89 #include "randgamma.h" | |
| 90 | |
| 91 #undef NAN | |
| 92 #define NAN octave_NaN | |
| 93 #define INFINITE lo_ieee_isinf | |
| 94 #define RUNI oct_randu() | |
| 95 #define RNOR oct_randn() | |
| 96 #define REXP oct_rande() | |
| 97 | |
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98 void |
| 5742 | 99 oct_fill_randg (double a, octave_idx_type n, double *r) |
| 100 { | |
| 101 octave_idx_type i; | |
| 102 /* If a < 1, start by generating gamma(1+a) */ | |
| 103 const double d = (a < 1. ? 1.+a : a) - 1./3.; | |
| 104 const double c = 1./sqrt(9.*d); | |
| 105 | |
| 106 /* Handle invalid cases */ | |
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107 if (a <= 0 || INFINITE(a)) |
| 5742 | 108 { |
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109 for (i=0; i < n; i++) |
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110 r[i] = NAN; |
| 5742 | 111 return; |
| 112 } | |
| 113 | |
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114 for (i=0; i < n; i++) |
| 5742 | 115 { |
| 116 double x, xsq, v, u; | |
| 117 restart: | |
| 118 x = RNOR; | |
| 119 v = (1+c*x); | |
| 120 v *= v*v; | |
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121 if (v <= 0) |
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122 goto restart; /* rare, so don't bother moving up */ |
| 5742 | 123 u = RUNI; |
| 124 xsq = x*x; | |
| 125 if (u >= 1.-0.0331*xsq*xsq && log(u) >= 0.5*xsq + d*(1-v+log(v))) | |
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126 goto restart; |
| 5742 | 127 r[i] = d*v; |
| 128 } | |
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129 if (a < 1) |
| 5742 | 130 { /* Use gamma(a) = gamma(1+a)*U^(1/a) */ |
| 131 /* Given REXP = -log(U) then U^(1/a) = exp(-REXP/a) */ | |
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132 for (i = 0; i < n; i++) |
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133 r[i] *= exp(-REXP/a); |
| 5742 | 134 } |
| 135 } | |
| 136 | |
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137 double |
| 5742 | 138 oct_randg (double a) |
| 139 { | |
| 140 double ret; | |
| 141 oct_fill_randg(a,1,&ret); | |
| 142 return ret; | |
| 143 } |