Mercurial > octave
annotate libinterp/corefcn/rand.cc @ 25828:8b548f2f8086
maint: Strip trailing whitespace from source files.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 28 Aug 2018 00:09:59 -0400 |
parents | b400ad33d92d |
children | 373fe1608f7c |
rev | line source |
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1 |
2928 | 2 /* |
3 | |
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4 Copyright (C) 1996-2018 John W. Eaton |
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5 Copyright (C) 2009 VZLU Prague |
2928 | 6 |
7 This file is part of Octave. | |
8 | |
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9 Octave is free software: you can redistribute it and/or modify it |
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10 under the terms of the GNU General Public License as published by |
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11 the Free Software Foundation, either version 3 of the License, or |
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12 (at your option) any later version. |
2928 | 13 |
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14 Octave is distributed in the hope that it will be useful, but |
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15 WITHOUT ANY WARRANTY; without even the implied warranty of |
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16 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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17 GNU General Public License for more details. |
2928 | 18 |
19 You should have received a copy of the GNU General Public License | |
7016 | 20 along with Octave; see the file COPYING. If not, see |
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21 <https://www.gnu.org/licenses/>. |
2928 | 22 |
23 */ | |
24 | |
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25 #if defined (HAVE_CONFIG_H) |
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26 # include "config.h" |
2928 | 27 #endif |
28 | |
29 #include <ctime> | |
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30 #include <unordered_map> |
2928 | 31 #include <string> |
32 | |
33 #include "f77-fcn.h" | |
34 #include "lo-mappers.h" | |
4307 | 35 #include "oct-rand.h" |
4153 | 36 #include "quit.h" |
2928 | 37 |
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38 #include "defun.h" |
2928 | 39 #include "error.h" |
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40 #include "errwarn.h" |
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41 #include "ovl.h" |
2928 | 42 #include "unwind-prot.h" |
43 #include "utils.h" | |
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44 #include "ov-re-mat.h" |
2928 | 45 |
6437 | 46 /* |
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47 %% Restore all rand* "seed" and "state" values in order, so that the |
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48 %% new "state" algorithm remains active after these tests complete. |
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49 %!function restore_rand_states (seed, state) |
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50 %! rand ("seed", seed.rand); |
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51 %! rande ("seed", seed.rande); |
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52 %! randg ("seed", seed.randg); |
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53 %! randn ("seed", seed.randn); |
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54 %! randp ("seed", seed.randp); |
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55 %! rand ("state", state.rand); |
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56 %! rande ("state", state.rande); |
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57 %! randg ("state", state.randg); |
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58 %! randn ("state", state.randn); |
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59 %! randp ("state", state.randp); |
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60 %!endfunction |
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61 |
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62 %!shared __random_statistical_tests__, old_seed, old_state, restore_state |
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63 %! ## Flag whether the statistical tests should be run in "make check" or not |
6437 | 64 %! __random_statistical_tests__ = 0; |
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65 %! ## Save and restore the states of each of the random number generators |
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66 %! ## that are tested by the unit tests in this file. |
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67 %! old_seed.rand = rand ("seed"); |
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68 %! old_seed.rande = rande ("seed"); |
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69 %! old_seed.randg = randg ("seed"); |
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70 %! old_seed.randn = randn ("seed"); |
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71 %! old_seed.randp = randp ("seed"); |
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72 %! old_state.rand = rand ("state"); |
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73 %! old_state.rande = rande ("state"); |
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74 %! old_state.randg = randg ("state"); |
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75 %! old_state.randn = randn ("state"); |
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76 %! old_state.randp = randp ("state"); |
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77 %! restore_state = onCleanup (@() restore_rand_states (old_seed, old_state)); |
6437 | 78 */ |
79 | |
4307 | 80 static octave_value |
5730 | 81 do_rand (const octave_value_list& args, int nargin, const char *fcn, |
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82 const std::string& distribution, bool additional_arg = false) |
2928 | 83 { |
5730 | 84 NDArray a; |
85 int idx = 0; | |
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86 bool is_single = false; |
2928 | 87 |
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88 if (nargin > 0 && args(nargin-1).is_string ()) |
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89 { |
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90 std::string s_arg = args(nargin-1).string_value (); |
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91 |
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92 if (s_arg == "single") |
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93 { |
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94 is_single = true; |
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95 nargin--; |
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96 } |
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97 else if (s_arg == "double") |
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98 nargin--; |
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99 } |
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100 |
5730 | 101 if (additional_arg) |
102 { | |
103 if (nargin == 0) | |
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104 error ("%s: at least one argument is required", fcn); |
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105 else if (args(0).is_string ()) |
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106 additional_arg = false; |
5730 | 107 else |
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108 { |
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109 a = args(0).xarray_value ("%s: dimension must be a scalar integer", fcn); |
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110 |
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111 idx++; |
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112 nargin--; |
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113 } |
5730 | 114 } |
2928 | 115 |
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116 octave_value retval; |
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117 dim_vector dims; |
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118 |
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119 octave::unwind_protect frame; |
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120 // Restore current distribution on any exit. |
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121 frame.add_fcn (octave::rand::distribution, |
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122 octave::rand::distribution ()); |
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123 |
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124 octave::rand::distribution (distribution); |
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125 |
4543 | 126 switch (nargin) |
2928 | 127 { |
4543 | 128 case 0: |
129 { | |
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130 if (additional_arg) |
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131 dims = a.dims (); |
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132 else |
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133 { |
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134 dims.resize (2); |
4543 | 135 |
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136 dims(0) = 1; |
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137 dims(1) = 1; |
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138 } |
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139 |
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140 goto gen_matrix; |
4543 | 141 } |
142 break; | |
2928 | 143 |
4543 | 144 case 1: |
145 { | |
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146 octave_value tmp = args(idx); |
4543 | 147 |
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148 if (tmp.is_string ()) |
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149 { |
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150 std::string s_arg = tmp.string_value (); |
2928 | 151 |
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152 if (s_arg == "dist") |
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153 retval = octave::rand::distribution (); |
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154 else if (s_arg == "seed") |
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155 retval = octave::rand::seed (); |
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156 else if (s_arg == "state" || s_arg == "twister") |
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157 retval = octave::rand::state (fcn); |
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158 else if (s_arg == "uniform") |
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159 octave::rand::uniform_distribution (); |
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160 else if (s_arg == "normal") |
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161 octave::rand::normal_distribution (); |
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162 else if (s_arg == "exponential") |
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163 octave::rand::exponential_distribution (); |
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164 else if (s_arg == "poisson") |
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165 octave::rand::poisson_distribution (); |
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166 else if (s_arg == "gamma") |
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167 octave::rand::gamma_distribution (); |
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168 else |
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169 error ("%s: unrecognized string argument", fcn); |
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170 } |
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171 else if (tmp.is_scalar_type ()) |
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172 { |
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173 double dval = tmp.double_value (); |
2928 | 174 |
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175 if (octave::math::isnan (dval)) |
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176 error ("%s: NaN is invalid matrix dimension", fcn); |
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177 |
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178 dims.resize (2); |
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180 dims(0) = octave::math::nint_big (tmp.double_value ()); |
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181 dims(1) = octave::math::nint_big (tmp.double_value ()); |
2928 | 182 |
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183 goto gen_matrix; |
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184 } |
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185 else if (tmp.is_range ()) |
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186 { |
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187 Range r = tmp.range_value (); |
4543 | 188 |
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189 if (! r.all_elements_are_ints ()) |
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190 error ("%s: all elements of range must be integers", fcn); |
4543 | 191 |
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192 octave_idx_type n = r.numel (); |
4543 | 193 |
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194 dims.resize (n); |
2928 | 195 |
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196 octave_idx_type base = octave::math::nint_big (r.base ()); |
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197 octave_idx_type incr = octave::math::nint_big (r.inc ()); |
2928 | 198 |
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199 for (octave_idx_type i = 0; i < n; i++) |
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200 { |
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201 // Negative dimensions treated as zero for Matlab compatibility |
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202 dims(i) = (base >= 0 ? base : 0); |
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203 base += incr; |
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204 } |
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205 |
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206 goto gen_matrix; |
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207 } |
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208 else if (tmp.is_matrix_type ()) |
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209 { |
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|
210 Array<int> iv; |
4543 | 211 |
20743
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|
212 try |
10154
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213 { |
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|
214 iv = tmp.int_vector_value (true); |
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|
215 } |
22327
d0562b3159c7
move more classes inside octave namespace
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diff
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|
216 catch (octave::execution_exception& e) |
20743
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|
217 { |
20756
200ae1d650b7
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|
218 error (e, "%s: dimensions must be a scalar or array of integers", fcn); |
20743
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|
219 } |
4543 | 220 |
20743
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|
221 octave_idx_type len = iv.numel (); |
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|
222 |
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|
223 dims.resize (len); |
2928 | 224 |
20743
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|
225 for (octave_idx_type i = 0; i < len; i++) |
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|
226 { |
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|
227 // Negative dimensions treated as zero for Matlab compatibility |
20743
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|
228 octave_idx_type elt = iv(i); |
23450
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maint: Wrap tertiary operator in parentheses "(COND ? x : y)".
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diff
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|
229 dims(i) = (elt >=0 ? elt : 0); |
10154
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|
230 } |
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|
231 |
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eliminate more uses of error_state
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|
232 goto gen_matrix; |
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|
233 } |
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|
234 else |
21129
228b65504557
maint: Eliminate useless statements after err_XXX.
Rik <rik@octave.org>
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21127
diff
changeset
|
235 err_wrong_type_arg ("rand", tmp); |
4543 | 236 } |
237 break; | |
238 | |
239 default: | |
240 { | |
10154
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|
241 octave_value tmp = args(idx); |
4543 | 242 |
10154
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|
243 if (nargin == 2 && tmp.is_string ()) |
40dfc0c99116
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|
244 { |
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|
245 std::string ts = tmp.string_value (); |
5164 | 246 |
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247 if (ts == "seed") |
40dfc0c99116
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|
248 { |
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|
249 if (args(idx+1).is_real_scalar ()) |
40dfc0c99116
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|
250 { |
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changeset
|
251 double d = args(idx+1).double_value (); |
2928 | 252 |
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|
253 octave::rand::seed (d); |
10154
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|
254 } |
11586
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|
255 else if (args(idx+1).is_string () |
14846
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maint: Use Octave coding convention for cuddled parenthis in function calls with empty argument lists.
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|
256 && args(idx+1).string_value () == "reset") |
25433
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changeset
|
257 octave::rand::reset (); |
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|
258 else |
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|
259 error ("%s: seed must be a real scalar", fcn); |
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|
260 } |
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|
261 else if (ts == "state" || ts == "twister") |
40dfc0c99116
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|
262 { |
10709
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Don't special case color_property type when emitting factory default (bug #30118)
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|
263 if (args(idx+1).is_string () |
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|
264 && args(idx+1).string_value () == "reset") |
25433
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|
265 octave::rand::reset (fcn); |
10709
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Don't special case color_property type when emitting factory default (bug #30118)
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|
266 else |
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Don't special case color_property type when emitting factory default (bug #30118)
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diff
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|
267 { |
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|
268 ColumnVector s = |
25651
c759aa39c23a
Produce same random number stream for "state" initialized to Inf (bug #54342).
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|
269 ColumnVector (args(idx+1).vector_value (false, true)); |
25828
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|
270 |
25651
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Produce same random number stream for "state" initialized to Inf (bug #54342).
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|
271 // Backwards compatibility with previous versions of |
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Produce same random number stream for "state" initialized to Inf (bug #54342).
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|
272 // Octave which mapped Inf to 0. |
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Produce same random number stream for "state" initialized to Inf (bug #54342).
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|
273 for (octave_idx_type i = 0; i < s.numel (); i++) |
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Produce same random number stream for "state" initialized to Inf (bug #54342).
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|
274 if (octave::math::isinf (s.xelem (i))) |
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Produce same random number stream for "state" initialized to Inf (bug #54342).
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|
275 s.xelem (i) = 0.0; |
5730 | 276 |
25433
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|
277 octave::rand::state (s, fcn); |
10709
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Don't special case color_property type when emitting factory default (bug #30118)
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|
278 } |
10154
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|
279 } |
40dfc0c99116
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|
280 else |
40dfc0c99116
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|
281 error ("%s: unrecognized string argument", fcn); |
40dfc0c99116
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|
282 } |
40dfc0c99116
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|
283 else |
40dfc0c99116
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|
284 { |
40dfc0c99116
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|
285 dims.resize (nargin); |
4543 | 286 |
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|
287 for (int i = 0; i < nargin; i++) |
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|
288 { |
21041
63374982750b
Usage of corresponding value extractor for octave_idx_type. Improves support
Kai T. Ohlhus <k.ohlhus@gmail.com>
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20940
diff
changeset
|
289 octave_idx_type elt = |
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Usage of corresponding value extractor for octave_idx_type. Improves support
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changeset
|
290 args(idx+i).xidx_type_value ( |
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291 "%s: dimension must be a scalar or array of integers", |
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292 fcn); |
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293 |
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294 // Negative dimensions treated as zero for Matlab compatibility |
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295 dims(i) = (elt >= 0 ? elt : 0); |
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296 } |
4543 | 297 |
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298 goto gen_matrix; |
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299 } |
4543 | 300 } |
301 break; | |
2928 | 302 } |
303 | |
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304 // No "goto gen_matrix" in code path. Must be done processing. |
2928 | 305 return retval; |
306 | |
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307 gen_matrix: |
2928 | 308 |
5355 | 309 dims.chop_trailing_singletons (); |
310 | |
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311 if (is_single) |
5730 | 312 { |
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313 if (additional_arg) |
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314 { |
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315 if (a.numel () == 1) |
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316 return octave::rand::float_nd_array (dims, a(0)); |
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317 else |
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318 { |
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319 if (a.dims () != dims) |
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320 error ("%s: mismatch in argument size", fcn); |
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321 |
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322 octave_idx_type len = a.numel (); |
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323 FloatNDArray m (dims); |
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324 float *v = m.fortran_vec (); |
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325 |
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326 for (octave_idx_type i = 0; i < len; i++) |
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327 v[i] = octave::rand::float_scalar (a(i)); |
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328 |
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329 return m; |
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330 } |
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331 } |
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332 else |
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333 return octave::rand::float_nd_array (dims); |
5730 | 334 } |
335 else | |
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336 { |
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337 if (additional_arg) |
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338 { |
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339 if (a.numel () == 1) |
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340 return octave::rand::nd_array (dims, a(0)); |
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341 else |
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342 { |
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343 if (a.dims () != dims) |
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344 error ("%s: mismatch in argument size", fcn); |
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345 |
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346 octave_idx_type len = a.numel (); |
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347 NDArray m (dims); |
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348 double *v = m.fortran_vec (); |
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349 |
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350 for (octave_idx_type i = 0; i < len; i++) |
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351 v[i] = octave::rand::scalar (a(i)); |
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352 |
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353 return m; |
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354 } |
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355 } |
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356 else |
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357 return octave::rand::nd_array (dims); |
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358 } |
2928 | 359 } |
360 | |
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361 DEFUN (rand, args, , |
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362 doc: /* -*- texinfo -*- |
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363 @deftypefn {} {} rand (@var{n}) |
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364 @deftypefnx {} {} rand (@var{m}, @var{n}, @dots{}) |
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365 @deftypefnx {} {} rand ([@var{m} @var{n} @dots{}]) |
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366 @deftypefnx {} {@var{v} =} rand ("state") |
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367 @deftypefnx {} {} rand ("state", @var{v}) |
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368 @deftypefnx {} {} rand ("state", "reset") |
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369 @deftypefnx {} {@var{v} =} rand ("seed") |
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370 @deftypefnx {} {} rand ("seed", @var{v}) |
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371 @deftypefnx {} {} rand ("seed", "reset") |
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372 @deftypefnx {} {} rand (@dots{}, "single") |
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373 @deftypefnx {} {} rand (@dots{}, "double") |
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374 Return a matrix with random elements uniformly distributed on the |
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375 interval (0, 1). |
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376 |
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377 The arguments are handled the same as the arguments for @code{eye}. |
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378 |
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379 You can query the state of the random number generator using the form |
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380 |
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381 @example |
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382 v = rand ("state") |
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383 @end example |
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384 |
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385 This returns a column vector @var{v} of length 625. Later, you can restore |
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386 the random number generator to the state @var{v} using the form |
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387 |
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388 @example |
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389 rand ("state", v) |
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390 @end example |
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391 |
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392 @noindent |
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393 You may also initialize the state vector from an arbitrary vector of length |
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394 @leq{} 625 for @var{v}. This new state will be a hash based on the value of |
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395 @var{v}, not @var{v} itself. |
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396 |
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397 By default, the generator is initialized from @code{/dev/urandom} if it is |
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398 available, otherwise from CPU time, wall clock time, and the current |
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399 fraction of a second. Note that this differs from @sc{matlab}, which |
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400 always initializes the state to the same state at startup. To obtain |
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401 behavior comparable to @sc{matlab}, initialize with a deterministic state |
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402 vector in Octave's startup files (@pxref{Startup Files}). |
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403 |
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404 To compute the pseudo-random sequence, @code{rand} uses the Mersenne |
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405 Twister with a period of @math{2^{19937}-1} |
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406 (See @nospell{M. Matsumoto and T. Nishimura}, |
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407 @cite{Mersenne Twister: A 623-dimensionally equidistributed uniform |
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408 pseudorandom number generator}, |
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409 @nospell{ACM} Trans. on Modeling and Computer Simulation Vol. 8, No. 1, |
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410 pp. 3--30, January 1998, |
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411 @url{http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html}). |
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412 Do @strong{not} use for cryptography without securely hashing several |
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413 returned values together, otherwise the generator state can be learned after |
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414 reading 624 consecutive values. |
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415 |
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416 Older versions of Octave used a different random number generator. |
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417 The new generator is used by default as it is significantly faster than the |
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418 old generator, and produces random numbers with a significantly longer cycle |
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419 time. However, in some circumstances it might be desirable to obtain the |
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420 same random sequences as produced by the old generators. To do this the |
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421 keyword @qcode{"seed"} is used to specify that the old generators should |
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422 be used, as in |
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423 |
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424 @example |
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425 rand ("seed", val) |
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426 @end example |
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427 |
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428 @noindent |
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429 which sets the seed of the generator to @var{val}. The seed of the |
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430 generator can be queried with |
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431 |
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432 @example |
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433 s = rand ("seed") |
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434 @end example |
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435 |
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436 However, it should be noted that querying the seed will not cause |
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437 @code{rand} to use the old generators, only setting the seed will. To cause |
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438 @code{rand} to once again use the new generators, the keyword |
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439 @qcode{"state"} should be used to reset the state of the @code{rand}. |
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440 |
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441 The state or seed of the generator can be reset to a new random value using |
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442 the @qcode{"reset"} keyword. |
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443 |
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444 The class of the value returned can be controlled by a trailing |
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445 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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446 classes. |
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447 @seealso{randn, rande, randg, randp} |
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448 @end deftypefn */) |
2928 | 449 { |
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450 return do_rand (args, args.length (), "rand", "uniform"); |
2928 | 451 } |
452 | |
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453 // FIXME: The old generator (selected when "seed" is set) will not |
8871 | 454 // work properly if compiled to use 64-bit integers. |
455 | |
5730 | 456 /* |
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457 %!test # "state" can be a scalar |
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458 %! rand ("state", 12); x = rand (1,4); |
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459 %! rand ("state", 12); y = rand (1,4); |
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460 %! assert (x, y); |
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461 %!test # "state" can be a vector |
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462 %! rand ("state", [12,13]); x = rand (1,4); |
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463 %! rand ("state", [12;13]); y = rand (1,4); |
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464 %! assert (x, y); |
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465 %!test # querying "state" returns a value which can be used later |
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466 %! s = rand ("state"); x = rand (1,2); |
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467 %! rand ("state", s); y = rand (1,2); |
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468 %! assert (x, y); |
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469 %!test # querying "state" doesn't disturb sequence |
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470 %! rand ("state", 12); rand (1,2); x = rand (1,2); |
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471 %! rand ("state", 12); rand (1,2); s = rand ("state"); y = rand (1,2); |
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472 %! assert (x, y); |
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473 %! rand ("state", s); z = rand (1,2); |
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474 %! assert (x, z); |
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475 %!test # "seed" must be a scalar |
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476 %! rand ("seed", 12); x = rand (1,4); |
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477 %! rand ("seed", 12); y = rand (1,4); |
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478 %! assert (x, y); |
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479 %!error <seed must be a real scalar> rand ("seed", [12,13]) |
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480 %!test # querying "seed" returns a value which can be used later |
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481 %! s = rand ("seed"); x = rand (1,2); |
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482 %! rand ("seed", s); y = rand (1,2); |
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483 %! assert (x, y); |
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484 %!test # querying "seed" doesn't disturb sequence |
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485 %! rand ("seed", 12); rand (1,2); x = rand (1,2); |
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486 %! rand ("seed", 12); rand (1,2); s = rand ("seed"); y = rand (1,2); |
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487 %! assert (x, y); |
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488 %! rand ("seed", s); z = rand (1,2); |
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489 %! assert (x, z); |
5730 | 490 */ |
491 | |
492 /* | |
493 %!test | |
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494 %! ## Test a known fixed state |
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495 %! rand ("state", 1); |
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496 %! assert (rand (1,6), [0.1343642441124013 0.8474337369372327 0.763774618976614 0.2550690257394218 0.495435087091941 0.4494910647887382], eps); |
6437 | 497 %!test |
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498 %! ## Test a known fixed seed |
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499 %! rand ("seed", 1); |
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500 %! assert (rand (1,6), [0.8668024251237512 0.9126510815694928 0.09366085007786751 0.1664607301354408 0.7408077004365623 0.7615650338120759], 1e-6); |
5730 | 501 %!test |
6437 | 502 %! if (__random_statistical_tests__) |
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503 %! ## statistical tests may fail occasionally. |
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504 %! rand ("state", 12); |
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505 %! x = rand (100_000, 1); |
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506 %! assert (min (x) > 0); #*** Please report this!!! *** |
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507 %! assert (max (x) < 1); #*** Please report this!!! *** |
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508 %! assert (mean (x), 0.5, 0.0024); |
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509 %! assert (var (x), 1/48, 0.0632); |
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510 %! assert (skewness (x), 0, 0.012); |
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511 %! assert (kurtosis (x), -6/5, 0.0094); |
6437 | 512 %! endif |
513 %!test | |
514 %! if (__random_statistical_tests__) | |
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515 %! ## statistical tests may fail occasionally. |
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516 %! rand ("seed", 12); |
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517 %! x = rand (100_000, 1); |
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518 %! assert (max (x) < 1); #*** Please report this!!! *** |
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519 %! assert (min (x) > 0); #*** Please report this!!! *** |
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520 %! assert (mean (x), 0.5, 0.0024); |
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521 %! assert (var (x), 1/48, 0.0632); |
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522 %! assert (skewness (x), 0, 0.012); |
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523 %! assert (kurtosis (x), -6/5, 0.0094); |
6437 | 524 %! endif |
5730 | 525 */ |
526 | |
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527 /* |
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528 ## Test out-of-range values as rand() seeds. |
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529 %!function v = __rand_sample__ (initval) |
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530 %! rand ("state", initval); |
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531 %! v = rand (1, 6); |
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532 %!endfunction |
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533 %! |
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534 %!assert (__rand_sample__ (-1), __rand_sample__ (0)) |
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535 %!assert (__rand_sample__ (-Inf), __rand_sample__ (0)) |
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536 %!assert (__rand_sample__ (2^33), __rand_sample__ (intmax ("uint32"))) |
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537 %!assert (__rand_sample__ (Inf), __rand_sample__ (0)) |
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538 %!assert (__rand_sample__ (NaN), __rand_sample__ (0)) |
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539 */ |
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540 |
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541 static std::string current_distribution = octave::rand::distribution (); |
4307 | 542 |
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543 DEFUN (randn, args, , |
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544 doc: /* -*- texinfo -*- |
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545 @deftypefn {} {} randn (@var{n}) |
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546 @deftypefnx {} {} randn (@var{m}, @var{n}, @dots{}) |
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547 @deftypefnx {} {} randn ([@var{m} @var{n} @dots{}]) |
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548 @deftypefnx {} {@var{v} =} randn ("state") |
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549 @deftypefnx {} {} randn ("state", @var{v}) |
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550 @deftypefnx {} {} randn ("state", "reset") |
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551 @deftypefnx {} {@var{v} =} randn ("seed") |
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552 @deftypefnx {} {} randn ("seed", @var{v}) |
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553 @deftypefnx {} {} randn ("seed", "reset") |
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554 @deftypefnx {} {} randn (@dots{}, "single") |
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555 @deftypefnx {} {} randn (@dots{}, "double") |
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556 Return a matrix with normally distributed random elements having zero mean |
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557 and variance one. |
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558 |
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559 The arguments are handled the same as the arguments for @code{rand}. |
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560 |
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561 By default, @code{randn} uses the @nospell{Marsaglia and Tsang} |
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562 ``Ziggurat technique'' to transform from a uniform to a normal distribution. |
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563 |
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564 The class of the value returned can be controlled by a trailing |
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565 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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566 classes. |
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567 |
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568 Reference: @nospell{G. Marsaglia and W.W. Tsang}, |
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569 @cite{Ziggurat Method for Generating Random Variables}, |
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570 J. Statistical Software, vol 5, 2000, |
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571 @url{https://www.jstatsoft.org/v05/i08/} |
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572 |
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573 @seealso{rand, rande, randg, randp} |
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574 @end deftypefn */) |
2928 | 575 { |
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576 return do_rand (args, args.length (), "randn", "normal"); |
2928 | 577 } |
578 | |
579 /* | |
5730 | 580 %!test |
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581 %! ## Test a known fixed state |
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582 %! randn ("state", 1); |
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583 %! assert (randn (1, 6), [-2.666521678978671 -0.7381719971724564 1.507903992673601 0.6019427189162239 -0.450661261143348 -0.7054431351574116], 14*eps); |
6437 | 584 %!test |
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585 %! ## Test a known fixed seed |
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586 %! randn ("seed", 1); |
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587 %! assert (randn (1, 6), [-1.039402365684509 -1.25938892364502 0.1968704611063004 0.3874166905879974 -0.5976632833480835 -0.6615074276924133], 1e-6); |
5730 | 588 %!test |
6437 | 589 %! if (__random_statistical_tests__) |
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590 %! ## statistical tests may fail occasionally. |
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591 %! randn ("state", 12); |
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592 %! x = randn (100_000, 1); |
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593 %! assert (mean (x), 0, 0.01); |
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594 %! assert (var (x), 1, 0.02); |
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595 %! assert (skewness (x), 0, 0.02); |
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596 %! assert (kurtosis (x), 0, 0.04); |
6437 | 597 %! endif |
598 %!test | |
599 %! if (__random_statistical_tests__) | |
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600 %! ## statistical tests may fail occasionally. |
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601 %! randn ("seed", 12); |
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602 %! x = randn (100_000, 1); |
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603 %! assert (mean (x), 0, 0.01); |
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604 %! assert (var (x), 1, 0.02); |
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605 %! assert (skewness (x), 0, 0.02); |
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606 %! assert (kurtosis (x), 0, 0.04); |
6437 | 607 %! endif |
5730 | 608 */ |
609 | |
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610 DEFUN (rande, args, , |
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611 doc: /* -*- texinfo -*- |
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612 @deftypefn {} {} rande (@var{n}) |
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613 @deftypefnx {} {} rande (@var{m}, @var{n}, @dots{}) |
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614 @deftypefnx {} {} rande ([@var{m} @var{n} @dots{}]) |
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615 @deftypefnx {} {@var{v} =} rande ("state") |
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616 @deftypefnx {} {} rande ("state", @var{v}) |
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617 @deftypefnx {} {} rande ("state", "reset") |
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618 @deftypefnx {} {@var{v} =} rande ("seed") |
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619 @deftypefnx {} {} rande ("seed", @var{v}) |
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620 @deftypefnx {} {} rande ("seed", "reset") |
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621 @deftypefnx {} {} rande (@dots{}, "single") |
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622 @deftypefnx {} {} rande (@dots{}, "double") |
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623 Return a matrix with exponentially distributed random elements. |
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624 |
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625 The arguments are handled the same as the arguments for @code{rand}. |
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626 |
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627 By default, @code{rande} uses the @nospell{Marsaglia and Tsang} |
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628 ``Ziggurat technique'' to transform from a uniform to an exponential |
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629 distribution. |
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630 |
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631 The class of the value returned can be controlled by a trailing |
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632 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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633 classes. |
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634 |
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635 Reference: @nospell{G. Marsaglia and W.W. Tsang}, |
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636 @cite{Ziggurat Method for Generating Random Variables}, |
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637 J. Statistical Software, vol 5, 2000, |
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638 @url{https://www.jstatsoft.org/v05/i08/} |
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639 |
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640 @seealso{rand, randn, randg, randp} |
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641 @end deftypefn */) |
5730 | 642 { |
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643 return do_rand (args, args.length (), "rande", "exponential"); |
5730 | 644 } |
645 | |
646 /* | |
647 %!test | |
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648 %! ## Test a known fixed state |
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649 %! rande ("state", 1); |
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650 %! assert (rande (1, 6), [3.602973885835625 0.1386190677555021 0.6743112889616958 0.4512830847258422 0.7255744741233175 0.3415969205292291], 2*eps); |
6437 | 651 %!test |
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652 %! ## Test a known fixed seed |
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653 %! rande ("seed", 1); |
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654 %! assert (rande (1, 6), [0.06492075175653866 1.717980206012726 0.4816154008731246 0.5231300676241517 0.103910739364359 1.668931916356087], 1e-6); |
5730 | 655 %!test |
6437 | 656 %! if (__random_statistical_tests__) |
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657 %! ## statistical tests may fail occasionally |
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658 %! rande ("state", 1); |
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659 %! x = rande (100_000, 1); |
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660 %! assert (min (x) > 0); # *** Please report this!!! *** |
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661 %! assert (mean (x), 1, 0.01); |
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662 %! assert (var (x), 1, 0.03); |
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663 %! assert (skewness (x), 2, 0.06); |
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664 %! assert (kurtosis (x), 6, 0.7); |
6437 | 665 %! endif |
666 %!test | |
667 %! if (__random_statistical_tests__) | |
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668 %! ## statistical tests may fail occasionally |
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669 %! rande ("seed", 1); |
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670 %! x = rande (100_000, 1); |
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671 %! assert (min (x)>0); # *** Please report this!!! *** |
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672 %! assert (mean (x), 1, 0.01); |
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673 %! assert (var (x), 1, 0.03); |
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674 %! assert (skewness (x), 2, 0.06); |
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675 %! assert (kurtosis (x), 6, 0.7); |
6437 | 676 %! endif |
5730 | 677 */ |
678 | |
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679 DEFUN (randg, args, , |
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680 doc: /* -*- texinfo -*- |
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681 @deftypefn {} {} randg (@var{a}, @var{n}) |
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682 @deftypefnx {} {} randg (@var{a}, @var{m}, @var{n}, @dots{}) |
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683 @deftypefnx {} {} randg (@var{a}, [@var{m} @var{n} @dots{}]) |
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684 @deftypefnx {} {@var{v} =} randg ("state") |
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685 @deftypefnx {} {} randg ("state", @var{v}) |
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686 @deftypefnx {} {} randg ("state", "reset") |
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687 @deftypefnx {} {@var{v} =} randg ("seed") |
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688 @deftypefnx {} {} randg ("seed", @var{v}) |
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689 @deftypefnx {} {} randg ("seed", "reset") |
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690 @deftypefnx {} {} randg (@dots{}, "single") |
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691 @deftypefnx {} {} randg (@dots{}, "double") |
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692 |
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693 Return a matrix with @code{gamma (@var{a},1)} distributed random elements. |
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694 |
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695 The arguments are handled the same as the arguments for @code{rand}, except |
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696 for the argument @var{a}. |
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697 |
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698 This can be used to generate many distributions: |
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699 |
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700 @table @asis |
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701 @item @code{gamma (a, b)} for @code{a > -1}, @code{b > 0} |
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702 |
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703 @example |
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704 r = b * randg (a) |
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705 @end example |
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706 |
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707 @item @code{beta (a, b)} for @code{a > -1}, @code{b > -1} |
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708 |
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709 @example |
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710 @group |
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711 r1 = randg (a, 1) |
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712 r = r1 / (r1 + randg (b, 1)) |
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713 @end group |
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714 @end example |
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715 |
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716 @item @code{Erlang (a, n)} |
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717 |
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718 @example |
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719 r = a * randg (n) |
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720 @end example |
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721 |
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722 @item @code{chisq (df)} for @code{df > 0} |
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723 |
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724 @example |
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725 r = 2 * randg (df / 2) |
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726 @end example |
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727 |
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728 @item @code{t (df)} for @code{0 < df < inf} (use randn if df is infinite) |
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729 |
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730 @example |
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731 r = randn () / sqrt (2 * randg (df / 2) / df) |
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732 @end example |
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733 |
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734 @item @code{F (n1, n2)} for @code{0 < n1}, @code{0 < n2} |
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735 |
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736 @example |
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737 @group |
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738 ## r1 equals 1 if n1 is infinite |
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739 r1 = 2 * randg (n1 / 2) / n1 |
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740 ## r2 equals 1 if n2 is infinite |
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741 r2 = 2 * randg (n2 / 2) / n2 |
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742 r = r1 / r2 |
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743 @end group |
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744 @end example |
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745 |
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746 @item negative @code{binomial (n, p)} for @code{n > 0}, @code{0 < p <= 1} |
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747 |
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748 @example |
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749 r = randp ((1 - p) / p * randg (n)) |
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750 @end example |
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751 |
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752 @item non-central @code{chisq (df, L)}, for @code{df >= 0} and @code{L > 0} |
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753 (use chisq if @code{L = 0}) |
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754 |
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755 @example |
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756 @group |
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757 r = randp (L / 2) |
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758 r(r > 0) = 2 * randg (r(r > 0)) |
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759 r(df > 0) += 2 * randg (df(df > 0)/2) |
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760 @end group |
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761 @end example |
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762 |
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763 @item @code{Dirichlet (a1, @dots{} ak)} |
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764 |
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765 @example |
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766 @group |
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767 r = (randg (a1), @dots{}, randg (ak)) |
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768 r = r / sum (r) |
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769 @end group |
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770 @end example |
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771 |
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772 @end table |
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773 |
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774 The class of the value returned can be controlled by a trailing |
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775 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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776 classes. |
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777 @seealso{rand, randn, rande, randp} |
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778 @end deftypefn */) |
5730 | 779 { |
780 int nargin = args.length (); | |
781 | |
782 if (nargin < 1) | |
783 error ("randg: insufficient arguments"); | |
784 | |
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785 return do_rand (args, nargin, "randg", "gamma", true); |
5730 | 786 } |
787 | |
788 /* | |
789 %!test | |
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790 %! randg ("state", 12); |
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791 %! assert (randg ([-inf, -1, 0, inf, nan]), [nan, nan, nan, nan, nan]); # *** Please report |
6437 | 792 |
793 %!test | |
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794 %! ## Test a known fixed state |
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795 %! randg ("state", 1); |
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796 %! assert (randg (0.1, 1, 6), [0.0103951513331241 8.335671459898252e-05 0.00138691397249762 0.000587308416993855 0.495590518784736 2.3921917414795e-12], eps); |
6437 | 797 %!test |
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798 %! ## Test a known fixed state |
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799 %! randg ("state", 1); |
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800 %! assert (randg (0.95, 1, 6), [3.099382433255327 0.3974529788871218 0.644367450750855 1.143261091802246 1.964111762696822 0.04011915547957939], 12*eps); |
6437 | 801 %!test |
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802 %! ## Test a known fixed state |
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803 %! randg ("state", 1); |
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804 %! assert (randg (1, 1, 6), [0.2273389379645993 1.288822625058359 0.2406335209340746 1.218869553370733 1.024649860162554 0.09631230343599533], 40*eps); |
6437 | 805 %!test |
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806 %! ## Test a known fixed state |
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807 %! randg ("state", 1); |
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808 %! assert (randg (10, 1, 6), [3.520369644331133 15.15369864472106 8.332112081991205 8.406211067432674 11.81193475187611 10.88792728177059], 56*eps); |
6437 | 809 %!test |
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810 %! ## Test a known fixed state |
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811 %! randg ("state", 1); |
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812 %! assert (randg (100, 1, 6), [75.34570255262264 115.4911985594699 95.23493031356388 95.48926019250911 106.2397448229803 103.4813150404118], 256*eps); |
6437 | 813 %!test |
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814 %! ## Test a known fixed seed |
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815 %! randg ("seed", 1); |
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816 %! assert (randg (0.1, 1, 6), [0.07144210487604141 0.460641473531723 0.4749028384685516 0.06823389977216721 0.000293838675133884 1.802567535340305e-12], 1e-6); |
6437 | 817 %!test |
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818 %! ## Test a known fixed seed |
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819 %! randg ("seed", 1); |
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820 %! assert (randg (0.95, 1, 6), [1.664905071258545 1.879976987838745 1.905677795410156 0.9948706030845642 0.5606933236122131 0.0766092911362648], 1e-6); |
6437 | 821 %!test |
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822 %! ## Test a known fixed seed |
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823 %! randg ("seed", 1); |
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824 %! assert (randg (1, 1, 6), [0.03512085229158401 0.6488978862762451 0.8114678859710693 0.1666885763406754 1.60791552066803 1.90356981754303], 1e-6); |
6437 | 825 %!test |
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826 %! ## Test a known fixed seed |
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827 %! randg ("seed", 1); |
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828 %! assert (randg (10, 1, 6), [6.566435813903809 10.11648464202881 10.73162078857422 7.747178077697754 6.278522491455078 6.240195751190186], 1e-5); |
6437 | 829 %!test |
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830 %! ## Test a known fixed seed |
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831 %! randg ("seed", 1); |
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832 %! assert (randg (100, 1, 6), [89.40208435058594 101.4734725952148 103.4020004272461 93.62763214111328 88.33104705810547 88.1871337890625], 1e-4); |
18573
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833 %!test |
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834 %! ## Test out-of-bounds values produce NaN w/old-style generators & floats |
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835 %! randg ("seed", 1); |
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836 %! result = randg ([-2 Inf], "single"); |
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837 %! assert (result, single ([NaN NaN])); |
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838 |
6437 | 839 %!test |
840 %! if (__random_statistical_tests__) | |
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841 %! ## statistical tests may fail occasionally. |
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842 %! randg ("state", 12); |
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843 %! a = 0.1; |
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844 %! x = randg (a, 100_000, 1); |
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845 %! assert (mean (x), a, 0.01); |
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846 %! assert (var (x), a, 0.01); |
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847 %! assert (skewness (x), 2/sqrt (a), 1); |
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848 %! assert (kurtosis (x), 6/a, 50); |
6437 | 849 %! endif |
850 %!test | |
851 %! if (__random_statistical_tests__) | |
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852 %! ## statistical tests may fail occasionally. |
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853 %! randg ("state", 12); |
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854 %! a = 0.95; |
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855 %! x = randg (a, 100_000, 1); |
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856 %! assert (mean (x), a, 0.01); |
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857 %! assert (var (x), a, 0.04); |
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858 %! assert (skewness (x), 2/sqrt (a), 0.2); |
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859 %! assert (kurtosis (x), 6/a, 2); |
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860 %! endif |
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861 %!test |
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862 %! if (__random_statistical_tests__) |
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863 %! ## statistical tests may fail occasionally. |
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864 %! randg ("state", 12); |
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865 %! a = 1; |
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866 %! x = randg (a, 100_000, 1); |
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867 %! assert (mean (x), a, 0.01); |
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868 %! assert (var (x), a, 0.04); |
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869 %! assert (skewness (x), 2/sqrt (a), 0.2); |
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870 %! assert (kurtosis (x), 6/a, 2); |
6437 | 871 %! endif |
872 %!test | |
873 %! if (__random_statistical_tests__) | |
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874 %! ## statistical tests may fail occasionally. |
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875 %! randg ("state", 12); |
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876 %! a = 10; |
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877 %! x = randg (a, 100_000, 1); |
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878 %! assert (mean (x), a, 0.1); |
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879 %! assert (var (x), a, 0.5); |
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880 %! assert (skewness (x), 2/sqrt (a), 0.1); |
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881 %! assert (kurtosis (x), 6/a, 0.5); |
6437 | 882 %! endif |
883 %!test | |
884 %! if (__random_statistical_tests__) | |
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885 %! ## statistical tests may fail occasionally. |
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886 %! randg ("state", 12); |
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887 %! a = 100; |
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888 %! x = randg (a, 100_000, 1); |
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889 %! assert (mean (x), a, 0.2); |
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890 %! assert (var (x), a, 2); |
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891 %! assert (skewness (x), 2/sqrt (a), 0.05); |
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892 %! assert (kurtosis (x), 6/a, 0.2); |
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893 %! endif |
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894 %!test |
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895 %! randg ("seed", 12); |
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896 %!assert (randg ([-inf, -1, 0, inf, nan]), [nan, nan, nan, nan, nan]) # *** Please report |
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897 %!test |
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898 %! if (__random_statistical_tests__) |
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899 %! ## statistical tests may fail occasionally. |
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900 %! randg ("seed", 12); |
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901 %! a = 0.1; |
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902 %! x = randg (a, 100_000, 1); |
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903 %! assert (mean (x), a, 0.01); |
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904 %! assert (var (x), a, 0.01); |
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905 %! assert (skewness (x), 2/sqrt (a), 1); |
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906 %! assert (kurtosis (x), 6/a, 50); |
6437 | 907 %! endif |
908 %!test | |
909 %! if (__random_statistical_tests__) | |
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910 %! ## statistical tests may fail occasionally. |
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911 %! randg ("seed", 12); |
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912 %! a = 0.95; |
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913 %! x = randg (a, 100_000, 1); |
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914 %! assert (mean (x), a, 0.01); |
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915 %! assert (var (x), a, 0.04); |
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916 %! assert (skewness (x), 2/sqrt (a), 0.2); |
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917 %! assert (kurtosis (x), 6/a, 2); |
6437 | 918 %! endif |
919 %!test | |
920 %! if (__random_statistical_tests__) | |
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921 %! ## statistical tests may fail occasionally. |
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922 %! randg ("seed", 12); |
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923 %! a = 1; |
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924 %! x = randg (a, 100_000, 1); |
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925 %! assert (mean (x), a, 0.01); |
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926 %! assert (var (x), a, 0.04); |
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927 %! assert (skewness (x), 2/sqrt (a), 0.2); |
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928 %! assert (kurtosis (x), 6/a, 2); |
6437 | 929 %! endif |
5730 | 930 %!test |
6437 | 931 %! if (__random_statistical_tests__) |
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932 %! ## statistical tests may fail occasionally. |
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933 %! randg ("seed", 12); |
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934 %! a = 10; |
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935 %! x = randg (a, 100_000, 1); |
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936 %! assert (mean (x), a, 0.1); |
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937 %! assert (var (x), a, 0.5); |
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938 %! assert (skewness (x), 2/sqrt (a), 0.1); |
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939 %! assert (kurtosis (x), 6/a, 0.5); |
6437 | 940 %! endif |
5730 | 941 %!test |
6437 | 942 %! if (__random_statistical_tests__) |
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943 %! ## statistical tests may fail occasionally. |
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944 %! randg ("seed", 12); |
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945 %! a = 100; |
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946 %! x = randg (a, 100_000, 1); |
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947 %! assert (mean (x), a, 0.2); |
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948 %! assert (var (x), a, 2); |
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949 %! assert (skewness (x), 2/sqrt (a), 0.05); |
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950 %! assert (kurtosis (x), 6/a, 0.2); |
6437 | 951 %! endif |
5730 | 952 */ |
953 | |
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954 DEFUN (randp, args, , |
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955 doc: /* -*- texinfo -*- |
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956 @deftypefn {} {} randp (@var{l}, @var{n}) |
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957 @deftypefnx {} {} randp (@var{l}, @var{m}, @var{n}, @dots{}) |
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958 @deftypefnx {} {} randp (@var{l}, [@var{m} @var{n} @dots{}]) |
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959 @deftypefnx {} {@var{v} =} randp ("state") |
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960 @deftypefnx {} {} randp ("state", @var{v}) |
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961 @deftypefnx {} {} randp ("state", "reset") |
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962 @deftypefnx {} {@var{v} =} randp ("seed") |
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963 @deftypefnx {} {} randp ("seed", @var{v}) |
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964 @deftypefnx {} {} randp ("seed", "reset") |
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965 @deftypefnx {} {} randp (@dots{}, "single") |
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966 @deftypefnx {} {} randp (@dots{}, "double") |
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967 Return a matrix with Poisson distributed random elements with mean value |
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968 parameter given by the first argument, @var{l}. |
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969 |
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970 The arguments are handled the same as the arguments for @code{rand}, except |
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971 for the argument @var{l}. |
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972 |
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973 Five different algorithms are used depending on the range of @var{l} and |
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974 whether or not @var{l} is a scalar or a matrix. |
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975 |
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976 @table @asis |
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977 @item For scalar @var{l} @leq{} 12, use direct method. |
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978 W.H. Press, et al., @cite{Numerical Recipes in C}, |
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979 Cambridge University Press, 1992. |
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980 |
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981 @item For scalar @var{l} > 12, use rejection method.[1] |
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982 W.H. Press, et al., @cite{Numerical Recipes in C}, |
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983 Cambridge University Press, 1992. |
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984 |
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985 @item For matrix @var{l} @leq{} 10, use inversion method.[2] |
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986 @nospell{E. Stadlober, et al., WinRand source code}, available via FTP. |
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987 |
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988 @item For matrix @var{l} > 10, use patchwork rejection method. |
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989 @nospell{E. Stadlober, et al., WinRand source code}, available via FTP, or |
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990 @nospell{H. Zechner}, @cite{Efficient sampling from continuous and discrete |
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991 unimodal distributions}, Doctoral Dissertation, 156pp., Technical |
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992 University @nospell{Graz}, Austria, 1994. |
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993 |
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994 @item For @var{l} > 1e8, use normal approximation. |
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995 @nospell{L. Montanet}, et al., @cite{Review of Particle Properties}, |
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996 Physical Review D 50 p1284, 1994. |
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997 @end table |
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998 |
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999 The class of the value returned can be controlled by a trailing |
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1000 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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1001 classes. |
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1002 @seealso{rand, randn, rande, randg} |
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1003 @end deftypefn */) |
5730 | 1004 { |
1005 int nargin = args.length (); | |
1006 | |
1007 if (nargin < 1) | |
1008 error ("randp: insufficient arguments"); | |
1009 | |
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1010 return do_rand (args, nargin, "randp", "poisson", true); |
5730 | 1011 } |
1012 | |
1013 /* | |
1014 %!test | |
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1015 %! randp ("state", 12); |
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1016 %! assert (randp ([-inf, -1, 0, inf, nan]), [nan, nan, 0, nan, nan]); # *** Please report |
6437 | 1017 %!test |
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1018 %! ## Test a known fixed state |
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1019 %! randp ("state", 1); |
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1020 %! assert (randp (5, 1, 6), [5 5 3 7 7 3]); |
6437 | 1021 %!test |
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1022 %! ## Test a known fixed state |
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1023 %! randp ("state", 1); |
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1024 %! assert (randp (15, 1, 6), [13 15 8 18 18 15]); |
6437 | 1025 %!test |
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1026 %! ## Test a known fixed state |
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1027 %! randp ("state", 1); |
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1028 %! assert (randp (1e9, 1, 6), [999915677 999976657 1000047684 1000019035 999985749 999977692], -1e-6); |
6437 | 1029 %!test |
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1030 %! ## Test a known fixed seed |
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1031 %! randp ("seed", 1); |
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1032 %! %%assert (randp (5, 1, 6), [8 2 3 6 6 8]) |
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1033 %! assert (randp (5, 1, 5), [8 2 3 6 6]); |
6437 | 1034 %!test |
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1035 %! ## Test a known fixed seed |
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1036 %! randp ("seed", 1); |
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1037 %! assert (randp (15, 1, 6), [15 16 12 10 10 12]); |
6437 | 1038 %!test |
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1039 %! ## Test a known fixed seed |
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1040 %! randp ("seed", 1); |
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1041 %! assert (randp (1e9, 1, 6), [1000006208 1000012224 999981120 999963520 999963072 999981440], -1e-6); |
6437 | 1042 %!test |
1043 %! if (__random_statistical_tests__) | |
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1044 %! ## statistical tests may fail occasionally. |
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1045 %! randp ("state", 12); |
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1046 %! for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03] |
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1047 %! x = randp (a (1), 100_000, 1); |
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1048 %! assert (min (x) >= 0); # *** Please report this!!! *** |
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1049 %! assert (mean (x), a(1), a(2)); |
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1050 %! assert (var (x), a(1), 0.02*a(1)); |
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1051 %! assert (skewness (x), 1/sqrt (a(1)), a(3)); |
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1052 %! assert (kurtosis (x), 1/a(1), 3*a(3)); |
6437 | 1053 %! endfor |
1054 %! endif | |
1055 %!test | |
1056 %! if (__random_statistical_tests__) | |
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1057 %! ## statistical tests may fail occasionally. |
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1058 %! randp ("state", 12); |
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1059 %! for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03] |
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1060 %! x = randp (a(1)*ones (100_000, 1), 100_000, 1); |
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1061 %! assert (min (x) >= 0); # *** Please report this!!! *** |
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1062 %! assert (mean (x), a(1), a(2)); |
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1063 %! assert (var (x), a(1), 0.02*a(1)); |
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1064 %! assert (skewness (x), 1/sqrt (a(1)), a(3)); |
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1065 %! assert (kurtosis (x), 1/a(1), 3*a(3)); |
6437 | 1066 %! endfor |
1067 %! endif | |
1068 %!test | |
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1069 %! randp ("seed", 12); |
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1070 %! assert (randp ([-inf, -1, 0, inf, nan]), [nan, nan, 0, nan, nan]); # *** Please report |
5730 | 1071 %!test |
6449 | 1072 %! if (__random_statistical_tests__) |
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1073 %! ## statistical tests may fail occasionally. |
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1074 %! randp ("seed", 12); |
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1075 %! for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03] |
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1076 %! x = randp (a(1), 100_000, 1); |
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1077 %! assert (min (x) >= 0); # *** Please report this!!! *** |
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1078 %! assert (mean (x), a(1), a(2)); |
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1079 %! assert (var (x), a(1), 0.02*a(1)); |
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1080 %! assert (skewness (x), 1/sqrt (a(1)), a(3)); |
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1081 %! assert (kurtosis (x), 1/a(1), 3*a(3)); |
6449 | 1082 %! endfor |
1083 %! endif | |
5730 | 1084 %!test |
6449 | 1085 %! if (__random_statistical_tests__) |
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1086 %! ## statistical tests may fail occasionally. |
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1087 %! randp ("seed", 12); |
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1088 %! for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03] |
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1089 %! x = randp (a(1)*ones (100_000, 1), 100_000, 1); |
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1090 %! assert (min (x) >= 0); # *** Please report this!!! *** |
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1091 %! assert (mean (x), a(1), a(2)); |
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1092 %! assert (var (x), a(1), 0.02*a(1)); |
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1093 %! assert (skewness (x), 1/sqrt (a(1)), a(3)); |
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1094 %! assert (kurtosis (x), 1/a(1), 3*a(3)); |
6449 | 1095 %! endfor |
1096 %! endif | |
5730 | 1097 */ |
1098 | |
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1099 DEFUN (randperm, args, , |
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1100 doc: /* -*- texinfo -*- |
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1101 @deftypefn {} {} randperm (@var{n}) |
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1102 @deftypefnx {} {} randperm (@var{n}, @var{m}) |
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1103 Return a row vector containing a random permutation of @code{1:@var{n}}. |
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1104 |
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1105 If @var{m} is supplied, return @var{m} unique entries, sampled without |
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1106 replacement from @code{1:@var{n}}. |
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1107 |
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1108 The complexity is O(@var{n}) in memory and O(@var{m}) in time, unless |
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1109 @var{m} < @var{n}/5, in which case O(@var{m}) memory is used as well. The |
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1110 randomization is performed using rand(). All permutations are equally |
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1111 likely. |
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1112 @seealso{perms} |
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1113 @end deftypefn */) |
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1114 { |
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1115 int nargin = args.length (); |
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1116 |
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1117 if (nargin < 1 || nargin > 2) |
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1118 print_usage (); |
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1119 |
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1120 octave_idx_type n = args(0).idx_type_value (true); |
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1121 octave_idx_type m = (nargin == 2) ? args(1).idx_type_value (true) : n; |
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1122 |
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1123 if (m < 0 || n < 0) |
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1124 error ("randperm: M and N must be non-negative"); |
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1125 |
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1126 if (m > n) |
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1127 error ("randperm: M must be less than or equal to N"); |
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1128 |
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1129 // Quick and dirty heuristic to decide if we allocate or not the |
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1130 // whole vector for tracking the truncated shuffle. |
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1131 bool short_shuffle = m < n/5; |
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1132 |
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1133 // Generate random numbers. |
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1134 NDArray r = octave::rand::nd_array (dim_vector (1, m)); |
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1135 double *rvec = r.fortran_vec (); |
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1136 |
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1137 octave_idx_type idx_len = (short_shuffle ? m : n); |
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1138 Array<octave_idx_type> idx; |
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1139 try |
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1140 { |
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1141 idx = Array<octave_idx_type> (dim_vector (1, idx_len)); |
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1142 } |
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1143 catch (const std::bad_alloc&) |
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1144 { |
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1145 // Looks like n is too big and short_shuffle is false. |
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1146 // Let's try again, but this time with the alternative. |
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1147 idx_len = m; |
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1148 short_shuffle = true; |
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1149 idx = Array<octave_idx_type> (dim_vector (1, idx_len)); |
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1150 } |
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1151 |
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1152 octave_idx_type *ivec = idx.fortran_vec (); |
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1153 |
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1154 for (octave_idx_type i = 0; i < idx_len; i++) |
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1155 ivec[i] = i; |
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1156 |
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1157 if (short_shuffle) |
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1158 { |
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1159 std::unordered_map<octave_idx_type, octave_idx_type> map (m); |
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1160 |
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1161 // Perform the Knuth shuffle only keeping track of moved |
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1162 // entries in the map |
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1163 for (octave_idx_type i = 0; i < m; i++) |
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1164 { |
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1165 octave_idx_type k = i + std::floor (rvec[i] * (n - i)); |
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1166 |
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1167 // For shuffling first m entries, no need to use extra storage |
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1168 if (k < m) |
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1169 { |
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1170 std::swap (ivec[i], ivec[k]); |
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1171 } |
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1172 else |
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1173 { |
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1174 if (map.find (k) == map.end ()) |
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1175 map[k] = k; |
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1176 |
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1177 std::swap (ivec[i], map[k]); |
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1178 } |
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1179 } |
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1180 } |
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1181 else |
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1182 { |
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1183 // Perform the Knuth shuffle of the first m entries |
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1184 for (octave_idx_type i = 0; i < m; i++) |
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1185 { |
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1186 octave_idx_type k = i + std::floor (rvec[i] * (n - i)); |
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1187 std::swap (ivec[i], ivec[k]); |
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1188 } |
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1189 } |
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1190 |
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1191 // Convert to doubles, reusing r. |
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1192 for (octave_idx_type i = 0; i < m; i++) |
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1193 rvec[i] = ivec[i] + 1; |
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1194 |
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1195 if (m < n) |
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1196 idx.resize (dim_vector (1, m)); |
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1197 |
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1198 // Now create an array object with a cached idx_vector. |
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1199 return ovl (new octave_matrix (r, idx_vector (idx))); |
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1200 } |
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1201 |
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1202 /* |
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1203 %!assert (sort (randperm (20)), 1:20) |
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1204 %!assert (length (randperm (20,10)), 10) |
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1205 |
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1206 ## Test biggish N |
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1207 %!assert <*39378> (length (randperm (30_000^2, 100_000)), 100_000) |
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1208 |
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1209 %!test |
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1210 %! rand ("seed", 0); |
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1211 %! for i = 1:100 |
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1212 %! p = randperm (305, 30); |
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1213 %! assert (length (unique (p)), 30); |
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1214 %! endfor |
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1215 */ |