Mercurial > octave
annotate liboctave/numeric/randpoisson.cc @ 29228:5c14f81e0937
Set API tags in files in liboctave/numeric (patch #8919).
Add API tag to template class definitions. Add API tag to (un-defined) functions
and member functions in headers. Export template class instantiations and
template functions from .cc files.
author | Markus Mützel <markus.muetzel@gmx.de> |
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date | Tue, 29 Dec 2020 17:51:23 +0100 |
parents | bd51beb6205e |
children | 7854d5752dd2 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 2006-2020 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
7019 | 25 |
26 /* Original version written by Paul Kienzle distributed as free | |
27 software in the in the public domain. */ | |
5742 | 28 |
29 #if defined (HAVE_CONFIG_H) | |
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30 # include "config.h" |
5742 | 31 #endif |
32 | |
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33 #include <cmath> |
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34 #include <cstddef> |
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35 |
5742 | 36 #include "f77-fcn.h" |
7231 | 37 #include "lo-error.h" |
5742 | 38 #include "lo-ieee.h" |
39 #include "randmtzig.h" | |
40 #include "randpoisson.h" | |
41 | |
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42 namespace octave |
5742 | 43 { |
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44 static double xlgamma (double x) |
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45 { |
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46 return std::lgamma (x); |
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47 } |
5742 | 48 |
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49 /* ---- pprsc.c from Stadloeber's winrand --- */ |
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50 |
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51 /* flogfak(k) = ln(k!) */ |
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52 static double flogfak (double k) |
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53 { |
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54 #define C0 9.18938533204672742e-01 |
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55 #define C1 8.33333333333333333e-02 |
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56 #define C3 -2.77777777777777778e-03 |
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57 #define C5 7.93650793650793651e-04 |
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58 #define C7 -5.95238095238095238e-04 |
5742 | 59 |
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60 static double logfak[30L] = |
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61 { |
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62 0.00000000000000000, 0.00000000000000000, 0.69314718055994531, |
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63 1.79175946922805500, 3.17805383034794562, 4.78749174278204599, |
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64 6.57925121201010100, 8.52516136106541430, 10.60460290274525023, |
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65 12.80182748008146961, 15.10441257307551530, 17.50230784587388584, |
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66 19.98721449566188615, 22.55216385312342289, 25.19122118273868150, |
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67 27.89927138384089157, 30.67186010608067280, 33.50507345013688888, |
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68 36.39544520803305358, 39.33988418719949404, 42.33561646075348503, |
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69 45.38013889847690803, 48.47118135183522388, 51.60667556776437357, |
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70 54.78472939811231919, 58.00360522298051994, 61.26170176100200198, |
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71 64.55753862700633106, 67.88974313718153498, 71.25703896716800901 |
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72 }; |
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73 |
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74 double r, rr; |
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75 |
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76 if (k >= 30.0) |
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77 { |
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78 r = 1.0 / k; |
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79 rr = r * r; |
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80 return ((k + 0.5)*std::log (k) - k + C0 |
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81 + r*(C1 + rr*(C3 + rr*(C5 + rr*C7)))); |
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82 } |
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83 else |
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84 return (logfak[static_cast<int> (k)]); |
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85 } |
5742 | 86 |
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87 /****************************************************************** |
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88 * * |
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89 * Poisson Distribution - Patchwork Rejection/Inversion * |
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90 * * |
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91 ****************************************************************** |
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92 * * |
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93 * For parameter my < 10, Tabulated Inversion is applied. * |
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94 * For my >= 10, Patchwork Rejection is employed: * |
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95 * The area below the histogram function f(x) is rearranged in * |
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96 * its body by certain point reflections. Within a large center * |
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97 * interval variates are sampled efficiently by rejection from * |
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98 * uniform hats. Rectangular immediate acceptance regions speed * |
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99 * up the generation. The remaining tails are covered by * |
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100 * exponential functions. * |
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101 * * |
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102 ****************************************************************** |
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103 * * |
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104 * FUNCTION : - pprsc samples a random number from the Poisson * |
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105 * distribution with parameter my > 0. * |
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106 * REFERENCE : - H. Zechner (1994): Efficient sampling from * |
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107 * continuous and discrete unimodal distributions, * |
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108 * Doctoral Dissertation, 156 pp., Technical * |
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109 * University Graz, Austria. * |
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110 * SUBPROGRAM : - drand(seed) ... (0,1)-Uniform generator with * |
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111 * unsigned long integer *seed. * |
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112 * * |
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113 * Implemented by H. Zechner, January 1994 * |
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114 * Revised by F. Niederl, July 1994 * |
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115 * * |
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116 ******************************************************************/ |
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118 static double f (double k, double l_nu, double c_pm) |
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119 { |
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120 return exp (k * l_nu - flogfak (k) - c_pm); |
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121 } |
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123 static double pprsc (double my) |
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124 { |
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125 static double my_last = -1.0; |
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126 static double m, k2, k4, k1, k5; |
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127 static double dl, dr, r1, r2, r4, r5, ll, lr, l_my, c_pm, |
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128 f1, f2, f4, f5, p1, p2, p3, p4, p5, p6; |
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129 double Dk, X, Y; |
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130 double Ds, U, V, W; |
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131 |
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132 if (my != my_last) |
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133 { /* set-up */ |
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134 my_last = my; |
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135 /* approximate deviation of reflection points k2, k4 from my - 1/2 */ |
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136 Ds = std::sqrt (my + 0.25); |
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137 |
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138 /* mode m, reflection points k2 and k4, and points k1 and k5, */ |
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139 /* which delimit the centre region of h(x) */ |
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140 m = std::floor (my); |
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141 k2 = ceil (my - 0.5 - Ds); |
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142 k4 = std::floor (my - 0.5 + Ds); |
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143 k1 = k2 + k2 - m + 1L; |
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144 k5 = k4 + k4 - m; |
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145 |
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146 /* range width of the critical left and right centre region */ |
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147 dl = (k2 - k1); |
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148 dr = (k5 - k4); |
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149 |
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150 /* recurrence constants r(k)=p(k)/p(k-1) at k = k1, k2, k4+1, k5+1 */ |
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151 r1 = my / k1; |
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152 r2 = my / k2; |
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153 r4 = my / (k4 + 1.0); |
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154 r5 = my / (k5 + 1.0); |
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156 /* reciprocal values of the scale parameters of exp. tail envelope */ |
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157 ll = std::log (r1); /* expon. tail left */ |
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158 lr = -std::log (r5); /* expon. tail right*/ |
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159 |
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160 /* Poisson constants, necessary for computing function values f(k) */ |
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161 l_my = std::log (my); |
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162 c_pm = m * l_my - flogfak (m); |
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163 |
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164 /* function values f(k) = p(k)/p(m) at k = k2, k4, k1, k5 */ |
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165 f2 = f (k2, l_my, c_pm); |
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166 f4 = f (k4, l_my, c_pm); |
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167 f1 = f (k1, l_my, c_pm); |
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168 f5 = f (k5, l_my, c_pm); |
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169 |
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170 /* area of the two centre and the two exponential tail regions */ |
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171 /* area of the two immediate acceptance regions between k2, k4 */ |
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172 p1 = f2 * (dl + 1.0); /* immed. left */ |
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173 p2 = f2 * dl + p1; /* centre left */ |
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174 p3 = f4 * (dr + 1.0) + p2; /* immed. right */ |
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175 p4 = f4 * dr + p3; /* centre right */ |
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176 p5 = f1 / ll + p4; /* exp. tail left */ |
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177 p6 = f5 / lr + p5; /* exp. tail right*/ |
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178 } |
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179 |
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180 for (;;) |
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181 { |
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182 /* generate uniform number U -- U(0, p6) */ |
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183 /* case distinction corresponding to U */ |
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184 if ((U = rand_uniform<double> () * p6) < p2) |
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185 { /* centre left */ |
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186 |
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187 /* immediate acceptance region |
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188 R2 = [k2, m) *[0, f2), X = k2, ... m -1 */ |
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189 if ((V = U - p1) < 0.0) return (k2 + std::floor (U/f2)); |
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190 /* immediate acceptance region |
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191 R1 = [k1, k2)*[0, f1), X = k1, ... k2-1 */ |
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192 if ((W = V / dl) < f1 ) return (k1 + std::floor (V/f1)); |
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193 |
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194 /* computation of candidate X < k2, and its counterpart Y > k2 */ |
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195 /* either squeeze-acceptance of X or acceptance-rejection of Y */ |
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196 Dk = std::floor (dl * rand_uniform<double> ()) + 1.0; |
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197 if (W <= f2 - Dk * (f2 - f2/r2)) |
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198 { /* quick accept of */ |
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199 return (k2 - Dk); /* X = k2 - Dk */ |
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200 } |
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201 if ((V = f2 + f2 - W) < 1.0) |
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202 { /* quick reject of Y*/ |
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203 Y = k2 + Dk; |
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204 if (V <= f2 + Dk * (1.0 - f2)/(dl + 1.0)) |
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205 { /* quick accept of */ |
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206 return (Y); /* Y = k2 + Dk */ |
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207 } |
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208 if (V <= f (Y, l_my, c_pm)) return (Y); /* final accept of Y*/ |
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209 } |
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210 X = k2 - Dk; |
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211 } |
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212 else if (U < p4) |
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213 { /* centre right */ |
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214 /* immediate acceptance region |
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215 R3 = [m, k4+1)*[0, f4), X = m, ... k4 */ |
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216 if ((V = U - p3) < 0.0) return (k4 - std::floor ((U - p2)/f4)); |
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217 /* immediate acceptance region |
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218 R4 = [k4+1, k5+1)*[0, f5) */ |
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219 if ((W = V / dr) < f5 ) return (k5 - std::floor (V/f5)); |
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220 |
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221 /* computation of candidate X > k4, and its counterpart Y < k4 */ |
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222 /* either squeeze-acceptance of X or acceptance-rejection of Y */ |
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223 Dk = std::floor (dr * rand_uniform<double> ()) + 1.0; |
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224 if (W <= f4 - Dk * (f4 - f4*r4)) |
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225 { /* quick accept of */ |
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226 return (k4 + Dk); /* X = k4 + Dk */ |
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227 } |
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228 if ((V = f4 + f4 - W) < 1.0) |
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229 { /* quick reject of Y*/ |
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230 Y = k4 - Dk; |
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231 if (V <= f4 + Dk * (1.0 - f4)/ dr) |
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232 { /* quick accept of */ |
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233 return (Y); /* Y = k4 - Dk */ |
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234 } |
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235 if (V <= f (Y, l_my, c_pm)) return (Y); /* final accept of Y*/ |
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236 } |
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237 X = k4 + Dk; |
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238 } |
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239 else |
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240 { |
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241 W = rand_uniform<double> (); |
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242 if (U < p5) |
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243 { /* expon. tail left */ |
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244 Dk = std::floor (1.0 - std::log (W)/ll); |
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245 if ((X = k1 - Dk) < 0L) continue; /* 0 <= X <= k1 - 1 */ |
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246 W *= (U - p4) * ll; /* W -- U(0, h(x)) */ |
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247 if (W <= f1 - Dk * (f1 - f1/r1)) |
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248 return (X); /* quick accept of X*/ |
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249 } |
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250 else |
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251 { /* expon. tail right*/ |
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252 Dk = std::floor (1.0 - std::log (W)/lr); |
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253 X = k5 + Dk; /* X >= k5 + 1 */ |
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254 W *= (U - p5) * lr; /* W -- U(0, h(x)) */ |
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255 if (W <= f5 - Dk * (f5 - f5*r5)) |
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256 return (X); /* quick accept of X*/ |
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257 } |
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258 } |
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259 |
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260 /* acceptance-rejection test of candidate X from the original area */ |
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261 /* test, whether W <= f(k), with W = U*h(x) and U -- U(0, 1)*/ |
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262 /* log f(X) = (X - m)*log(my) - log X! + log m! */ |
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263 if (std::log (W) <= X * l_my - flogfak (X) - c_pm) return (X); |
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264 } |
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265 } |
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266 /* ---- pprsc.c end ------ */ |
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268 /* The remainder of the file is by Paul Kienzle */ |
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270 /* Table size is predicated on the maximum value of lambda |
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271 * we want to store in the table, and the maximum value of |
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272 * returned by the uniform random number generator on [0,1). |
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273 * With lambda==10 and u_max = 1 - 1/(2^32+1), we |
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274 * have poisson_pdf(lambda,36) < 1-u_max. If instead our |
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275 * generator uses more bits of mantissa or returns a value |
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276 * in the range [0,1], then for lambda==10 we need a table |
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277 * size of 46 instead. For long doubles, the table size |
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278 * will need to be longer still. */ |
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279 #define TABLESIZE 46 |
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280 |
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281 /* Given uniform u, find x such that CDF(L,x)==u. Return x. */ |
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282 |
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283 template <typename T> |
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284 static void |
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285 poisson_cdf_lookup (double lambda, T *p, size_t n) |
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286 { |
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287 double t[TABLESIZE]; |
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288 |
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289 /* Precompute the table for the u up to and including 0.458. |
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290 * We will almost certainly need it. */ |
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291 int intlambda = static_cast<int> (std::floor (lambda)); |
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292 double P; |
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293 int tableidx; |
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294 size_t i = n; |
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295 |
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296 t[0] = P = exp (-lambda); |
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297 for (tableidx = 1; tableidx <= intlambda; tableidx++) |
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298 { |
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299 P = P*lambda/static_cast<double> (tableidx); |
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300 t[tableidx] = t[tableidx-1] + P; |
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301 } |
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302 |
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303 while (i-- > 0) |
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304 { |
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305 double u = rand_uniform<double> (); |
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306 |
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307 /* If u > 0.458 we know we can jump to floor(lambda) before |
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308 * comparing (this observation is based on Stadlober's winrand |
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309 * code). For lambda >= 1, this will be a win. Lambda < 1 |
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310 * is already fast, so adding an extra comparison is not a |
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311 * problem. */ |
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312 int k = (u > 0.458 ? intlambda : 0); |
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313 |
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314 /* We aren't using a for loop here because when we find the |
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315 * right k we want to jump to the next iteration of the |
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316 * outer loop, and the continue statement will only work for |
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317 * the inner loop. */ |
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318 nextk: |
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319 if (u <= t[k]) |
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320 { |
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321 p[i] = static_cast<T> (k); |
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322 continue; |
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323 } |
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324 if (++k < tableidx) |
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325 goto nextk; |
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326 |
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327 /* We only need high values of the table very rarely so we |
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328 * don't automatically compute the entire table. */ |
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329 while (tableidx < TABLESIZE) |
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330 { |
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331 P = P*lambda/static_cast<double> (tableidx); |
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332 t[tableidx] = t[tableidx-1] + P; |
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333 /* Make sure we converge to 1.0 just in case u is uniform |
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334 * on [0,1] rather than [0,1). */ |
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335 if (t[tableidx] == t[tableidx-1]) t[tableidx] = 1.0; |
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336 tableidx++; |
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337 if (u <= t[tableidx-1]) break; |
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338 } |
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339 |
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340 /* We are assuming that the table size is big enough here. |
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341 * This should be true even if rand_uniform is returning values in |
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342 * the range [0,1] rather than [0,1). */ |
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343 p[i] = static_cast<T> (tableidx-1); |
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344 } |
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345 } |
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346 |
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347 /* From Press, et al., Numerical Recipes */ |
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348 template <typename T> |
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349 static void |
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350 poisson_rejection (double lambda, T *p, size_t n) |
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351 { |
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352 double sq = std::sqrt (2.0*lambda); |
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353 double alxm = std::log (lambda); |
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354 double g = lambda*alxm - xlgamma (lambda+1.0); |
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355 size_t i; |
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356 |
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357 for (i = 0; i < n; i++) |
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358 { |
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359 double y, em, t; |
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360 do |
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361 { |
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362 do |
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363 { |
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364 y = tan (M_PI*rand_uniform<double> ()); |
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365 em = sq * y + lambda; |
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366 } while (em < 0.0); |
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367 em = std::floor (em); |
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368 t = 0.9*(1.0+y*y)*exp (em*alxm-flogfak (em)-g); |
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369 } while (rand_uniform<double> () > t); |
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370 p[i] = em; |
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371 } |
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372 } |
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373 |
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374 /* The cutoff of L <= 1e8 in the following two functions before using |
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375 * the normal approximation is based on: |
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376 * > L=1e8; x=floor(linspace(0,2*L,1000)); |
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377 * > max(abs(normal_pdf(x,L,L)-poisson_pdf(x,L))) |
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378 * ans = 1.1376e-28 |
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379 * For L=1e7, the max is around 1e-9, which is within the step size of |
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380 * rand_uniform. For L>1e10 the pprsc function breaks down, as I saw |
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381 * from the histogram of a large sample, so 1e8 is both small enough |
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382 * and large enough. */ |
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384 /* Generate a set of poisson numbers with the same distribution */ |
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385 template <typename T> void rand_poisson (T L_arg, octave_idx_type n, T *p) |
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386 { |
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387 double L = L_arg; |
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388 octave_idx_type i; |
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389 if (L < 0.0 || lo_ieee_isinf (L)) |
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390 { |
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391 for (i=0; i<n; i++) |
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392 p[i] = numeric_limits<T>::NaN (); |
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393 } |
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394 else if (L <= 10.0) |
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395 { |
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396 poisson_cdf_lookup<T> (L, p, n); |
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397 } |
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398 else if (L <= 1e8) |
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399 { |
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400 for (i=0; i<n; i++) |
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401 p[i] = pprsc (L); |
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402 } |
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403 else |
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404 { |
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405 /* normal approximation: from Phys. Rev. D (1994) v50 p1284 */ |
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406 const double sqrtL = std::sqrt (L); |
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407 for (i = 0; i < n; i++) |
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408 { |
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409 p[i] = std::floor (rand_normal<T> () * sqrtL + L + 0.5); |
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410 if (p[i] < 0.0) |
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411 p[i] = 0.0; /* will probably never happen */ |
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412 } |
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413 } |
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414 } |
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416 template void rand_poisson<double> (double, octave_idx_type, double *); |
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417 template void rand_poisson<float> (float, octave_idx_type, float *); |
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418 |
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419 /* Generate one poisson variate */ |
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420 template <typename T> T rand_poisson (T L_arg) |
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421 { |
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422 double L = L_arg; |
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423 T ret; |
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424 if (L < 0.0) ret = numeric_limits<T>::NaN (); |
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425 else if (L <= 12.0) |
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426 { |
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427 /* From Press, et al. Numerical recipes */ |
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428 double g = exp (-L); |
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429 int em = -1; |
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430 double t = 1.0; |
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431 do |
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432 { |
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433 ++em; |
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434 t *= rand_uniform<T> (); |
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435 } while (t > g); |
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436 ret = em; |
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437 } |
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438 else if (L <= 1e8) |
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439 { |
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440 /* numerical recipes */ |
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441 poisson_rejection<T> (L, &ret, 1); |
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442 } |
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443 else if (lo_ieee_isinf (L)) |
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444 { |
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445 /* FIXME: R uses NaN, but the normal approximation suggests that |
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446 * limit should be Inf. Which is correct? */ |
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447 ret = numeric_limits<T>::NaN (); |
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448 } |
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449 else |
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450 { |
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451 /* normal approximation: from Phys. Rev. D (1994) v50 p1284 */ |
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452 ret = std::floor (rand_normal<T> () * std::sqrt (L) + L + 0.5); |
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453 if (ret < 0.0) ret = 0.0; /* will probably never happen */ |
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454 } |
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455 return ret; |
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456 } |
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457 |
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458 template OCTAVE_API double rand_poisson<double> (double); |
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459 template OCTAVE_API float rand_poisson<float> (float); |
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460 } |