Mercurial > octave
annotate libinterp/corefcn/rand.cc @ 33617:ec2635a02328 bytecode-interpreter tip
maint: Merge default to bytecode-interpreter.
author | Markus Mützel <markus.muetzel@gmx.de> |
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date | Tue, 21 May 2024 18:29:03 +0200 |
parents | f53ac65ffba6 |
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1 /////////////////////////////////////////////////////////////////////////* |
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2 // |
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3 // Copyright (C) 1996-2024 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
2928 | 28 #endif |
29 | |
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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 |
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46 OCTAVE_BEGIN_NAMESPACE(octave) |
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47 |
6437 | 48 /* |
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49 %% Restore all rand* "seed" and "state" values in order, so that the |
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50 %% new "state" algorithm remains active after these tests complete. |
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51 %!function restore_rand_states (seed, state) |
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52 %! rand ("seed", seed.rand); |
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53 %! rande ("seed", seed.rande); |
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54 %! randg ("seed", seed.randg); |
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55 %! randn ("seed", seed.randn); |
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56 %! randp ("seed", seed.randp); |
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57 %! rand ("state", state.rand); |
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58 %! rande ("state", state.rande); |
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59 %! randg ("state", state.randg); |
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60 %! randn ("state", state.randn); |
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61 %! randp ("state", state.randp); |
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62 %!endfunction |
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63 |
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64 %!shared __random_statistical_tests__, old_seed, old_state, restore_state |
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65 %! ## Flag whether the statistical tests should be run in "make check" or not |
6437 | 66 %! __random_statistical_tests__ = 0; |
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67 %! ## Save and restore the states of each of the random number generators |
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68 %! ## that are tested by the unit tests in this file. |
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69 %! old_seed.rand = rand ("seed"); |
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70 %! old_seed.rande = rande ("seed"); |
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71 %! old_seed.randg = randg ("seed"); |
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72 %! old_seed.randn = randn ("seed"); |
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73 %! old_seed.randp = randp ("seed"); |
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74 %! old_state.rand = rand ("state"); |
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75 %! old_state.rande = rande ("state"); |
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76 %! old_state.randg = randg ("state"); |
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77 %! old_state.randn = randn ("state"); |
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78 %! old_state.randp = randp ("state"); |
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79 %! restore_state = onCleanup (@() restore_rand_states (old_seed, old_state)); |
6437 | 80 */ |
81 | |
4307 | 82 static octave_value |
5730 | 83 do_rand (const octave_value_list& args, int nargin, const char *fcn, |
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84 const std::string& distribution, bool additional_arg = false) |
2928 | 85 { |
5730 | 86 NDArray a; |
87 int idx = 0; | |
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88 bool is_single = false; |
2928 | 89 |
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90 if (nargin > 0 && args(nargin-1).is_string ()) |
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91 { |
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92 std::string s_arg = args(nargin-1).string_value (); |
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93 |
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94 if (s_arg == "single") |
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95 { |
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96 is_single = true; |
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97 nargin--; |
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98 } |
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99 else if (s_arg == "double") |
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100 nargin--; |
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101 } |
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102 |
5730 | 103 if (additional_arg) |
104 { | |
105 if (nargin == 0) | |
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106 error ("%s: at least one argument is required", fcn); |
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107 else if (args(0).is_string ()) |
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108 additional_arg = false; |
5730 | 109 else |
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110 { |
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111 a = args(0).xarray_value ("%s: dimension must be a scalar integer", fcn); |
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112 |
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113 idx++; |
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114 nargin--; |
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115 } |
5730 | 116 } |
2928 | 117 |
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118 octave_value retval; |
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119 dim_vector dims; |
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120 |
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121 // Restore current distribution on any exit. |
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122 unwind_action restore_distribution |
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123 ([] (const std::string& old_distribution) |
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124 { |
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125 rand::distribution (old_distribution); |
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126 }, rand::distribution ()); |
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127 |
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128 rand::distribution (distribution); |
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129 |
4543 | 130 switch (nargin) |
2928 | 131 { |
4543 | 132 case 0: |
133 { | |
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134 if (additional_arg) |
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135 dims = a.dims (); |
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136 else |
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137 { |
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138 dims.resize (2); |
4543 | 139 |
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140 dims(0) = 1; |
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141 dims(1) = 1; |
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142 } |
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143 |
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144 goto gen_matrix; |
4543 | 145 } |
146 break; | |
2928 | 147 |
4543 | 148 case 1: |
149 { | |
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150 octave_value tmp = args(idx); |
4543 | 151 |
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152 if (tmp.is_string ()) |
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153 { |
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154 std::string s_arg = tmp.string_value (); |
2928 | 155 |
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156 if (s_arg == "dist") |
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157 retval = rand::distribution (); |
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158 else if (s_arg == "seed") |
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159 retval = rand::seed (); |
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160 else if (s_arg == "state" || s_arg == "twister") |
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161 retval = rand::state (fcn); |
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162 else if (s_arg == "uniform") |
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163 rand::uniform_distribution (); |
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164 else if (s_arg == "normal") |
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165 rand::normal_distribution (); |
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166 else if (s_arg == "exponential") |
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167 rand::exponential_distribution (); |
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168 else if (s_arg == "poisson") |
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169 rand::poisson_distribution (); |
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170 else if (s_arg == "gamma") |
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171 rand::gamma_distribution (); |
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172 else |
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173 error ("%s: unrecognized string argument", fcn); |
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174 } |
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175 else if (tmp.is_scalar_type ()) |
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176 { |
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177 octave_idx_type n = tmp.idx_type_value (true); |
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178 |
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179 dims.resize (2); |
4543 | 180 |
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181 dims(0) = dims(1) = n; |
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<double> 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 = math::nint_big (r.base ()); |
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197 octave_idx_type incr = math::nint_big (r.increment ()); |
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 { |
25927
d6581134daaa
Emit an error when utility matrices (zeros, ones, rand, etc.) are given a fractional dimension in a dimension vector (bug #54781).
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25926
diff
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210 Array<octave_idx_type> iv; |
4543 | 211 |
20743
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212 try |
10154
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|
213 { |
25927
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Emit an error when utility matrices (zeros, ones, rand, etc.) are given a fractional dimension in a dimension vector (bug #54781).
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25926
diff
changeset
|
214 iv = tmp.octave_idx_type_vector_value (true); |
20743
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215 } |
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216 catch (execution_exception& ee) |
20743
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|
217 { |
29163
8f67ad8b3103
maint: Updating naming conventions for exceptions and use const where possible.
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28850
diff
changeset
|
218 error (ee, "%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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|
229 dims(i) = (elt >=0 ? elt : 0); |
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|
230 } |
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|
231 |
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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") |
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248 { |
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249 if (args(idx+1).is_real_scalar ()) |
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250 { |
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251 double d = args(idx+1).double_value (); |
2928 | 252 |
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253 rand::seed (d); |
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|
254 } |
11586
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|
255 else if (args(idx+1).is_string () |
14846
460a3c6d8bf1
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") |
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257 rand::reset (); |
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258 else |
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|
259 error ("%s: seed must be a real scalar", fcn); |
40dfc0c99116
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260 } |
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261 else if (ts == "state" || ts == "twister") |
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262 { |
10709
92a85ed5b86e
Don't special case color_property type when emitting factory default (bug #30118)
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|
263 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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|
264 && args(idx+1).string_value () == "reset") |
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|
265 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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|
267 { |
27277
db687716fed6
style fixes: generally aim to break long lines before operators, not after
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27249
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changeset
|
268 ColumnVector s |
db687716fed6
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|
269 = ColumnVector (args(idx+1).vector_value (false, true)); |
25946
85f499b88c43
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diff
changeset
|
270 |
25651
c759aa39c23a
Produce same random number stream for "state" initialized to Inf (bug #54342).
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|
271 // Backwards compatibility with previous versions of |
c759aa39c23a
Produce same random number stream for "state" initialized to Inf (bug #54342).
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|
272 // Octave which mapped Inf to 0. |
c759aa39c23a
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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274 if (math::isinf (s.xelem (i))) |
25651
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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 |
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277 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 } |
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279 } |
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280 else |
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281 error ("%s: unrecognized string argument", fcn); |
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282 } |
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283 else |
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284 { |
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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 { |
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Emit an error when utility matrices (zeros, ones, rand, etc.) are given a fractional dimension (bug #54781).
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289 octave_idx_type elt = args(idx+i).idx_type_value (true); |
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290 |
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291 // Negative dimensions treated as zero for Matlab compatibility |
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292 dims(i) = (elt >= 0 ? elt : 0); |
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293 } |
4543 | 294 |
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295 goto gen_matrix; |
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296 } |
4543 | 297 } |
298 break; | |
2928 | 299 } |
300 | |
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301 // No "goto gen_matrix" in code path. Must be done processing. |
2928 | 302 return retval; |
303 | |
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304 gen_matrix: |
2928 | 305 |
5355 | 306 dims.chop_trailing_singletons (); |
307 | |
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308 if (is_single) |
5730 | 309 { |
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310 if (additional_arg) |
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311 { |
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312 if (a.numel () == 1) |
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313 return rand::float_nd_array (dims, a(0)); |
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314 else |
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315 { |
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316 if (a.dims () != dims) |
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317 error ("%s: mismatch in argument size", fcn); |
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318 |
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319 octave_idx_type len = a.numel (); |
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320 FloatNDArray m (dims); |
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321 float *v = m.rwdata (); |
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322 |
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323 for (octave_idx_type i = 0; i < len; i++) |
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324 v[i] = rand::float_scalar (a(i)); |
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325 |
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326 return m; |
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327 } |
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328 } |
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329 else |
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330 return rand::float_nd_array (dims); |
5730 | 331 } |
332 else | |
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333 { |
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334 if (additional_arg) |
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335 { |
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336 if (a.numel () == 1) |
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337 return rand::nd_array (dims, a(0)); |
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338 else |
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339 { |
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340 if (a.dims () != dims) |
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341 error ("%s: mismatch in argument size", fcn); |
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342 |
20232
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|
343 octave_idx_type len = a.numel (); |
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344 NDArray m (dims); |
32660
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345 double *v = m.rwdata (); |
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346 |
14655
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347 for (octave_idx_type i = 0; i < len; i++) |
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348 v[i] = rand::scalar (a(i)); |
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349 |
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350 return m; |
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|
351 } |
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352 } |
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353 else |
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354 return rand::nd_array (dims); |
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355 } |
2928 | 356 } |
357 | |
15039
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maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
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diff
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|
358 DEFUN (rand, args, , |
21966
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359 doc: /* -*- texinfo -*- |
30888
32d2b6604a9f
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|
360 @deftypefn {} {@var{x} =} rand (@var{n}) |
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361 @deftypefnx {} {@var{x} =} rand (@var{m}, @var{n}, @dots{}) |
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362 @deftypefnx {} {@var{x} =} rand ([@var{m} @var{n} @dots{}]) |
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363 @deftypefnx {} {@var{x} =} rand (@dots{}, "single") |
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|
364 @deftypefnx {} {@var{x} =} rand (@dots{}, "double") |
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365 @deftypefnx {} {@var{v} =} rand ("state") |
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366 @deftypefnx {} {} rand ("state", @var{v}) |
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|
367 @deftypefnx {} {} rand ("state", "reset") |
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368 @deftypefnx {} {@var{v} =} rand ("seed") |
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|
369 @deftypefnx {} {} rand ("seed", @var{v}) |
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370 @deftypefnx {} {} rand ("seed", "reset") |
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371 Return a matrix with random elements uniformly distributed on the |
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|
372 interval (0, 1). |
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|
373 |
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|
374 The arguments are handled the same as the arguments for @code{eye}. |
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|
375 |
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|
376 You can query the state of the random number generator using the form |
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|
377 |
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|
378 @example |
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|
379 v = rand ("state") |
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|
380 @end example |
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|
381 |
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|
382 This returns a column vector @var{v} of length 625. Later, you can restore |
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383 the random number generator to the state @var{v} using the form |
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|
384 |
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|
385 @example |
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|
386 rand ("state", v) |
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|
387 @end example |
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|
388 |
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|
389 @noindent |
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390 You may also initialize the state vector from an arbitrary vector of length |
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|
391 @leq{} 625 for @var{v}. This new state will be a hash based on the value of |
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392 @var{v}, not @var{v} itself. |
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|
393 |
28598
43c285a20829
Update documentation of the random number generator (bug #58800).
Markus Meisinger <chloros2@gmx.de>
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|
394 By default, the generator is initialized by contributing entropy from the |
43c285a20829
Update documentation of the random number generator (bug #58800).
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|
395 wall clock time, the CPU time, the current fraction of a second, the process |
43c285a20829
Update documentation of the random number generator (bug #58800).
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|
396 ID and---if available---up to 1024 bits from the C++ random numbers source |
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397 @code{random_device}, which might be non-deterministic (implementation |
43c285a20829
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398 specific). Note that this differs from @sc{matlab}, which always initializes |
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Update documentation of the random number generator (bug #58800).
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|
399 the state to the same state at startup. To obtain behavior comparable to |
43c285a20829
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|
400 @sc{matlab}, initialize with a deterministic state vector in Octave's startup |
43c285a20829
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|
401 files (@pxref{Startup Files}). |
21966
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402 |
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403 To compute the pseudo-random sequence, @code{rand} uses the Mersenne |
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404 Twister with a period of @math{2^{19937}-1} |
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405 (See @nospell{M. Matsumoto and T. Nishimura}, |
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406 @cite{Mersenne Twister: A 623-dimensionally equidistributed uniform |
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407 pseudorandom number generator}, |
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408 @nospell{ACM} Trans.@: on Modeling and Computer Simulation Vol.@: 8, No.@: 1, |
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409 pp.@: 3--30, January 1998, |
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410 @url{http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html}). |
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411 Do @strong{not} use for cryptography without securely hashing several |
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412 returned values together, otherwise the generator state can be learned after |
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413 reading 624 consecutive values. |
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414 |
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415 Older versions of Octave used a different random number generator. |
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416 The new generator is used by default as it is significantly faster than the |
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417 old generator, and produces random numbers with a significantly longer cycle |
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418 time. However, in some circumstances it might be desirable to obtain the |
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419 same random sequences as produced by the old generators. To do this the |
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420 keyword @qcode{"seed"} is used to specify that the old generators should |
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421 be used, as in |
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422 |
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423 @example |
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424 rand ("seed", val) |
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425 @end example |
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426 |
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427 @noindent |
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428 which sets the seed of the generator to @var{val}. The seed of the |
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429 generator can be queried with |
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430 |
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431 @example |
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432 s = rand ("seed") |
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433 @end example |
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434 |
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435 However, it should be noted that querying the seed will not cause |
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436 @code{rand} to use the old generators, only setting the seed will. To cause |
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437 @code{rand} to once again use the new generators, the keyword |
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438 @qcode{"state"} should be used to reset the state of the @code{rand}. |
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439 |
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440 The state or seed of the generator can be reset to a new random value using |
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441 the @qcode{"reset"} keyword. |
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442 |
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443 The class of the value returned can be controlled by a trailing |
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444 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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445 classes. |
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446 @seealso{randn, rande, randg, randp} |
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447 @end deftypefn */) |
2928 | 448 { |
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449 return do_rand (args, args.length (), "rand", "uniform"); |
2928 | 450 } |
451 | |
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452 // FIXME: The old generator (selected when "seed" is set) will not |
8871 | 453 // work properly if compiled to use 64-bit integers. |
454 | |
5730 | 455 /* |
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456 %!test # "state" can be a scalar |
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457 %! rand ("state", 12); x = rand (1,4); |
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458 %! rand ("state", 12); y = rand (1,4); |
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459 %! assert (x, y); |
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460 %!test # "state" can be a vector |
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461 %! rand ("state", [12,13]); x = rand (1,4); |
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462 %! rand ("state", [12;13]); y = rand (1,4); |
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463 %! assert (x, y); |
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464 %!test # querying "state" returns a value which can be used later |
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465 %! s = rand ("state"); x = rand (1,2); |
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466 %! rand ("state", s); y = rand (1,2); |
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467 %! assert (x, y); |
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468 %!test # querying "state" doesn't disturb sequence |
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469 %! rand ("state", 12); rand (1,2); x = rand (1,2); |
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470 %! rand ("state", 12); rand (1,2); s = rand ("state"); y = rand (1,2); |
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471 %! assert (x, y); |
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472 %! rand ("state", s); z = rand (1,2); |
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473 %! assert (x, z); |
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474 %!test # "seed" must be a scalar |
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475 %! rand ("seed", 12); x = rand (1,4); |
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476 %! rand ("seed", 12); y = rand (1,4); |
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477 %! assert (x, y); |
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478 %!error <seed must be a real scalar> rand ("seed", [12,13]) |
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479 %!test # querying "seed" returns a value which can be used later |
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480 %! s = rand ("seed"); x = rand (1,2); |
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481 %! rand ("seed", s); y = rand (1,2); |
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482 %! assert (x, y); |
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483 %!test # querying "seed" doesn't disturb sequence |
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484 %! rand ("seed", 12); rand (1,2); x = rand (1,2); |
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485 %! rand ("seed", 12); rand (1,2); s = rand ("seed"); y = rand (1,2); |
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486 %! assert (x, y); |
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487 %! rand ("seed", s); z = rand (1,2); |
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488 %! assert (x, z); |
5730 | 489 */ |
490 | |
491 /* | |
492 %!test | |
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493 %! ## Test a known fixed state |
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494 %! rand ("state", 1); |
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495 %! assert (rand (1,6), [0.1343642441124013 0.8474337369372327 0.763774618976614 0.2550690257394218 0.495435087091941 0.4494910647887382], eps); |
6437 | 496 %!test |
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497 %! ## Test a known fixed seed |
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498 %! rand ("seed", 1); |
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499 %! assert (rand (1,6), [0.8668024251237512 0.9126510815694928 0.09366085007786751 0.1664607301354408 0.7408077004365623 0.7615650338120759], 1e-6); |
5730 | 500 %!test |
6437 | 501 %! if (__random_statistical_tests__) |
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502 %! ## statistical tests may fail occasionally. |
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503 %! rand ("state", 12); |
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504 %! x = rand (100_000, 1); |
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505 %! assert (min (x) > 0); #*** Please report this!!! *** |
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506 %! assert (max (x) < 1); #*** Please report this!!! *** |
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507 %! assert (mean (x), 0.5, 0.0024); |
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508 %! assert (var (x), 1/48, 0.0632); |
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509 %! assert (skewness (x), 0, 0.012); |
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510 %! assert (kurtosis (x), -6/5, 0.0094); |
6437 | 511 %! endif |
512 %!test | |
513 %! if (__random_statistical_tests__) | |
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514 %! ## statistical tests may fail occasionally. |
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515 %! rand ("seed", 12); |
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516 %! x = rand (100_000, 1); |
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517 %! assert (max (x) < 1); #*** Please report this!!! *** |
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518 %! assert (min (x) > 0); #*** Please report this!!! *** |
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519 %! assert (mean (x), 0.5, 0.0024); |
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520 %! assert (var (x), 1/48, 0.0632); |
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521 %! assert (skewness (x), 0, 0.012); |
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522 %! assert (kurtosis (x), -6/5, 0.0094); |
6437 | 523 %! endif |
5730 | 524 */ |
525 | |
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526 /* |
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527 ## Test out-of-range values as rand() seeds. |
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528 %!function v = __rand_sample__ (initval) |
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529 %! rand ("state", initval); |
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530 %! v = rand (1, 6); |
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531 %!endfunction |
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532 %! |
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533 %!assert (__rand_sample__ (-1), __rand_sample__ (0)) |
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534 %!assert (__rand_sample__ (-Inf), __rand_sample__ (0)) |
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535 %!assert (__rand_sample__ (2^33), __rand_sample__ (intmax ("uint32"))) |
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536 %!assert (__rand_sample__ (Inf), __rand_sample__ (0)) |
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537 %!assert (__rand_sample__ (NaN), __rand_sample__ (0)) |
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538 */ |
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539 |
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540 /* |
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541 ## Note: Matlab compatibility requires using 0 for negative dimensions. |
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542 %!assert (size (rand (1, -1, 2)), [1, 0, 2]) |
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543 |
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544 ## Test input validation |
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545 %!error <conversion of 1.1 to.* failed> rand (1, 1.1) |
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546 %!error <dimensions must be .* array of integers> rand ([1, 1.1]) |
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547 */ |
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548 |
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549 static std::string current_distribution = rand::distribution (); |
4307 | 550 |
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551 DEFUN (randn, args, , |
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552 doc: /* -*- texinfo -*- |
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553 @deftypefn {} {@var{x} =} randn (@var{n}) |
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554 @deftypefnx {} {@var{x} =} randn (@var{m}, @var{n}, @dots{}) |
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555 @deftypefnx {} {@var{x} =} randn ([@var{m} @var{n} @dots{}]) |
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556 @deftypefnx {} {@var{x} =} randn (@dots{}, "single") |
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557 @deftypefnx {} {@var{x} =} randn (@dots{}, "double") |
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558 @deftypefnx {} {@var{v} =} randn ("state") |
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559 @deftypefnx {} {} randn ("state", @var{v}) |
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560 @deftypefnx {} {} randn ("state", "reset") |
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561 @deftypefnx {} {@var{v} =} randn ("seed") |
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562 @deftypefnx {} {} randn ("seed", @var{v}) |
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563 @deftypefnx {} {} randn ("seed", "reset") |
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564 Return a matrix with normally distributed random elements having zero mean |
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565 and variance one. |
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566 |
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567 The arguments are handled the same as the arguments for @code{rand}. |
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568 |
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569 By default, @code{randn} uses the @nospell{Marsaglia and Tsang} |
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570 ``Ziggurat technique'' to transform from a uniform to a normal distribution. |
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571 |
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572 The class of the value returned can be controlled by a trailing |
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573 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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574 classes. |
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575 |
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576 Reference: @nospell{G. Marsaglia and W.W. Tsang}, |
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577 @cite{Ziggurat Method for Generating Random Variables}, |
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578 J. Statistical Software, vol 5, 2000, |
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579 @url{https://www.jstatsoft.org/v05/i08/} |
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580 |
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581 @seealso{rand, rande, randg, randp} |
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582 @end deftypefn */) |
2928 | 583 { |
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584 return do_rand (args, args.length (), "randn", "normal"); |
2928 | 585 } |
586 | |
587 /* | |
5730 | 588 %!test |
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589 %! ## Test a known fixed state |
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590 %! randn ("state", 1); |
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591 %! assert (randn (1, 6), [-2.666521678978671 -0.7381719971724564 1.507903992673601 0.6019427189162239 -0.450661261143348 -0.7054431351574116], 14*eps); |
6437 | 592 %!test |
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593 %! ## Test a known fixed seed |
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594 %! randn ("seed", 1); |
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595 %! assert (randn (1, 6), [-1.039402365684509 -1.25938892364502 0.1968704611063004 0.3874166905879974 -0.5976632833480835 -0.6615074276924133], 1e-6); |
5730 | 596 %!test |
6437 | 597 %! if (__random_statistical_tests__) |
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598 %! ## statistical tests may fail occasionally. |
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599 %! randn ("state", 12); |
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600 %! x = randn (100_000, 1); |
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601 %! assert (mean (x), 0, 0.01); |
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602 %! assert (var (x), 1, 0.02); |
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603 %! assert (skewness (x), 0, 0.02); |
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604 %! assert (kurtosis (x), 0, 0.04); |
6437 | 605 %! endif |
606 %!test | |
607 %! if (__random_statistical_tests__) | |
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608 %! ## statistical tests may fail occasionally. |
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609 %! randn ("seed", 12); |
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610 %! x = randn (100_000, 1); |
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611 %! assert (mean (x), 0, 0.01); |
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612 %! assert (var (x), 1, 0.02); |
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613 %! assert (skewness (x), 0, 0.02); |
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614 %! assert (kurtosis (x), 0, 0.04); |
6437 | 615 %! endif |
5730 | 616 */ |
617 | |
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618 DEFUN (rande, args, , |
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619 doc: /* -*- texinfo -*- |
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620 @deftypefn {} {@var{x} =} rande (@var{n}) |
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621 @deftypefnx {} {@var{x} =} rande (@var{m}, @var{n}, @dots{}) |
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622 @deftypefnx {} {@var{x} =} rande ([@var{m} @var{n} @dots{}]) |
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623 @deftypefnx {} {@var{x} =} rande (@dots{}, "single") |
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624 @deftypefnx {} {@var{x} =} rande (@dots{}, "double") |
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625 @deftypefnx {} {@var{v} =} rande ("state") |
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626 @deftypefnx {} {} rande ("state", @var{v}) |
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627 @deftypefnx {} {} rande ("state", "reset") |
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628 @deftypefnx {} {@var{v} =} rande ("seed") |
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629 @deftypefnx {} {} rande ("seed", @var{v}) |
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630 @deftypefnx {} {} rande ("seed", "reset") |
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631 Return a matrix with exponentially distributed random elements. |
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632 |
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633 The arguments are handled the same as the arguments for @code{rand}. |
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634 |
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635 By default, @code{rande} uses the @nospell{Marsaglia and Tsang} |
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636 ``Ziggurat technique'' to transform from a uniform to an exponential |
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637 distribution. |
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638 |
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639 The class of the value returned can be controlled by a trailing |
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640 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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641 classes. |
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642 |
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643 Reference: @nospell{G. Marsaglia and W.W. Tsang}, |
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644 @cite{Ziggurat Method for Generating Random Variables}, |
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645 J. Statistical Software, vol 5, 2000, |
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646 @url{https://www.jstatsoft.org/v05/i08/} |
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647 |
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648 @seealso{rand, randn, randg, randp} |
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649 @end deftypefn */) |
5730 | 650 { |
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651 return do_rand (args, args.length (), "rande", "exponential"); |
5730 | 652 } |
653 | |
654 /* | |
655 %!test | |
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656 %! ## Test a known fixed state |
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657 %! rande ("state", 1); |
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658 %! assert (rande (1, 6), [3.602973885835625 0.1386190677555021 0.6743112889616958 0.4512830847258422 0.7255744741233175 0.3415969205292291], 2*eps); |
6437 | 659 %!test |
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660 %! ## Test a known fixed seed |
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661 %! rande ("seed", 1); |
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662 %! assert (rande (1, 6), [0.06492075175653866 1.717980206012726 0.4816154008731246 0.5231300676241517 0.103910739364359 1.668931916356087], 1e-6); |
5730 | 663 %!test |
6437 | 664 %! if (__random_statistical_tests__) |
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665 %! ## statistical tests may fail occasionally |
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666 %! rande ("state", 1); |
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667 %! x = rande (100_000, 1); |
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668 %! assert (min (x) > 0); # *** Please report this!!! *** |
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669 %! assert (mean (x), 1, 0.01); |
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670 %! assert (var (x), 1, 0.03); |
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671 %! assert (skewness (x), 2, 0.06); |
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672 %! assert (kurtosis (x), 6, 0.7); |
6437 | 673 %! endif |
674 %!test | |
675 %! if (__random_statistical_tests__) | |
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676 %! ## statistical tests may fail occasionally |
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677 %! rande ("seed", 1); |
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678 %! x = rande (100_000, 1); |
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679 %! assert (min (x)>0); # *** Please report this!!! *** |
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680 %! assert (mean (x), 1, 0.01); |
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681 %! assert (var (x), 1, 0.03); |
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682 %! assert (skewness (x), 2, 0.06); |
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683 %! assert (kurtosis (x), 6, 0.7); |
6437 | 684 %! endif |
5730 | 685 */ |
686 | |
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687 DEFUN (randg, args, , |
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688 doc: /* -*- texinfo -*- |
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689 @deftypefn {} {@var{x} =} randg (@var{a}, @var{n}) |
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690 @deftypefnx {} {@var{x} =} randg (@var{a}, @var{m}, @var{n}, @dots{}) |
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691 @deftypefnx {} {@var{x} =} randg (@var{a}, [@var{m} @var{n} @dots{}]) |
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692 @deftypefnx {} {@var{x} =} randg (@dots{}, "single") |
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693 @deftypefnx {} {@var{x} =} randg (@dots{}, "double") |
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694 @deftypefnx {} {@var{v} =} randg ("state") |
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695 @deftypefnx {} {} randg ("state", @var{v}) |
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696 @deftypefnx {} {} randg ("state", "reset") |
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697 @deftypefnx {} {@var{v} =} randg ("seed") |
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698 @deftypefnx {} {} randg ("seed", @var{v}) |
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699 @deftypefnx {} {} randg ("seed", "reset") |
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700 |
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701 Return a matrix with @code{gamma (@var{a},1)} distributed random elements. |
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702 |
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703 The arguments are handled the same as the arguments for @code{rand}, except |
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704 for the argument @var{a}. |
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705 |
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706 This can be used to generate many distributions: |
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707 |
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708 @table @asis |
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709 @item @code{gamma (a, b)} for @code{a > -1}, @code{b > 0} |
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710 |
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711 @example |
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712 r = b * randg (a) |
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713 @end example |
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714 |
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715 @item @code{beta (a, b)} for @code{a > -1}, @code{b > -1} |
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716 |
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717 @example |
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718 @group |
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719 r1 = randg (a, 1) |
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720 r = r1 / (r1 + randg (b, 1)) |
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721 @end group |
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722 @end example |
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723 |
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724 @item @code{Erlang (a, n)} |
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725 |
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726 @example |
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727 r = a * randg (n) |
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728 @end example |
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729 |
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730 @item @code{chisq (df)} for @code{df > 0} |
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731 |
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732 @example |
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733 r = 2 * randg (df / 2) |
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734 @end example |
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735 |
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736 @item @code{t (df)} for @code{0 < df < inf} (use randn if df is infinite) |
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737 |
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738 @example |
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739 r = randn () / sqrt (2 * randg (df / 2) / df) |
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740 @end example |
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741 |
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742 @item @code{F (n1, n2)} for @code{0 < n1}, @code{0 < n2} |
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743 |
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744 @example |
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745 @group |
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746 ## r1 equals 1 if n1 is infinite |
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747 r1 = 2 * randg (n1 / 2) / n1 |
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748 ## r2 equals 1 if n2 is infinite |
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749 r2 = 2 * randg (n2 / 2) / n2 |
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750 r = r1 / r2 |
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751 @end group |
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752 @end example |
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753 |
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754 @item negative @code{binomial (n, p)} for @code{n > 0}, @code{0 < p <= 1} |
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755 |
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756 @example |
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757 r = randp ((1 - p) / p * randg (n)) |
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758 @end example |
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759 |
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760 @item non-central @code{chisq (df, L)}, for @code{df >= 0} and @code{L > 0} |
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761 (use chisq if @code{L = 0}) |
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762 |
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763 @example |
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764 @group |
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765 r = randp (L / 2) |
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766 r(r > 0) = 2 * randg (r(r > 0)) |
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767 r(df > 0) += 2 * randg (df(df > 0)/2) |
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768 @end group |
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769 @end example |
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770 |
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771 @item @code{Dirichlet (a1, @dots{} ak)} |
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772 |
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773 @example |
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774 @group |
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775 r = (randg (a1), @dots{}, randg (ak)) |
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776 r = r / sum (r) |
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777 @end group |
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778 @end example |
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779 |
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780 @end table |
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781 |
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782 The class of the value returned can be controlled by a trailing |
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783 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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784 classes. |
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785 @seealso{rand, randn, rande, randp} |
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786 @end deftypefn */) |
5730 | 787 { |
788 int nargin = args.length (); | |
789 | |
790 if (nargin < 1) | |
791 error ("randg: insufficient arguments"); | |
792 | |
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793 return do_rand (args, nargin, "randg", "gamma", true); |
5730 | 794 } |
795 | |
796 /* | |
797 %!test | |
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798 %! randg ("state", 12); |
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799 %! assert (randg ([-inf, -1, 0, inf, nan]), [nan, nan, nan, nan, nan]); |
6437 | 800 |
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 (0.1, 1, 6), [0.0103951513331241 8.335671459898252e-05 0.00138691397249762 0.000587308416993855 0.495590518784736 2.3921917414795e-12], 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 (0.95, 1, 6), [3.099382433255327 0.3974529788871218 0.644367450750855 1.143261091802246 1.964111762696822 0.04011915547957939], 12*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 (1, 1, 6), [0.2273389379645993 1.288822625058359 0.2406335209340746 1.218869553370733 1.024649860162554 0.09631230343599533], 40*eps); |
6437 | 813 %!test |
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814 %! ## Test a known fixed state |
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815 %! randg ("state", 1); |
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816 %! assert (randg (10, 1, 6), [3.520369644331133 15.15369864472106 8.332112081991205 8.406211067432674 11.81193475187611 10.88792728177059], 56*eps); |
6437 | 817 %!test |
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818 %! ## Test a known fixed state |
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819 %! randg ("state", 1); |
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820 %! assert (randg (100, 1, 6), [75.34570255262264 115.4911985594699 95.23493031356388 95.48926019250911 106.2397448229803 103.4813150404118], 256*eps); |
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 (0.1, 1, 6), [0.07144210487604141 0.460641473531723 0.4749028384685516 0.06823389977216721 0.000293838675133884 1.802567535340305e-12], 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 (0.95, 1, 6), [1.664905071258545 1.879976987838745 1.905677795410156 0.9948706030845642 0.5606933236122131 0.0766092911362648], 1e-6); |
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 (1, 1, 6), [0.03512085229158401 0.6488978862762451 0.8114678859710693 0.1666885763406754 1.60791552066803 1.90356981754303], 1e-6); |
6437 | 833 %!test |
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834 %! ## Test a known fixed seed |
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835 %! randg ("seed", 1); |
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836 %! assert (randg (10, 1, 6), [6.566435813903809 10.11648464202881 10.73162078857422 7.747178077697754 6.278522491455078 6.240195751190186], 1e-5); |
6437 | 837 %!test |
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838 %! ## Test a known fixed seed |
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839 %! randg ("seed", 1); |
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840 %! assert (randg (100, 1, 6), [89.40208435058594 101.4734725952148 103.4020004272461 93.62763214111328 88.33104705810547 88.1871337890625], 1e-4); |
18573
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841 %!test |
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842 %! ## Test out-of-bounds values produce NaN w/old-style generators & floats |
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843 %! randg ("seed", 1); |
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844 %! result = randg ([-2 Inf], "single"); |
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845 %! assert (result, single ([NaN NaN])); |
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846 |
6437 | 847 %!test |
848 %! if (__random_statistical_tests__) | |
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849 %! ## statistical tests may fail occasionally. |
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850 %! randg ("state", 12); |
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851 %! a = 0.1; |
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852 %! x = randg (a, 100_000, 1); |
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853 %! assert (mean (x), a, 0.01); |
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854 %! assert (var (x), a, 0.01); |
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855 %! assert (skewness (x), 2/sqrt (a), 1); |
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856 %! assert (kurtosis (x), 6/a, 50); |
6437 | 857 %! endif |
858 %!test | |
859 %! if (__random_statistical_tests__) | |
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860 %! ## statistical tests may fail occasionally. |
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861 %! randg ("state", 12); |
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862 %! a = 0.95; |
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863 %! x = randg (a, 100_000, 1); |
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864 %! assert (mean (x), a, 0.01); |
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865 %! assert (var (x), a, 0.04); |
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866 %! assert (skewness (x), 2/sqrt (a), 0.2); |
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867 %! assert (kurtosis (x), 6/a, 2); |
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868 %! endif |
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869 %!test |
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870 %! if (__random_statistical_tests__) |
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871 %! ## statistical tests may fail occasionally. |
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872 %! randg ("state", 12); |
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873 %! a = 1; |
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874 %! x = randg (a, 100_000, 1); |
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875 %! assert (mean (x), a, 0.01); |
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876 %! assert (var (x), a, 0.04); |
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877 %! assert (skewness (x), 2/sqrt (a), 0.2); |
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878 %! assert (kurtosis (x), 6/a, 2); |
6437 | 879 %! endif |
880 %!test | |
881 %! if (__random_statistical_tests__) | |
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882 %! ## statistical tests may fail occasionally. |
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883 %! randg ("state", 12); |
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884 %! a = 10; |
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885 %! x = randg (a, 100_000, 1); |
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886 %! assert (mean (x), a, 0.1); |
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887 %! assert (var (x), a, 0.5); |
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888 %! assert (skewness (x), 2/sqrt (a), 0.1); |
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889 %! assert (kurtosis (x), 6/a, 0.5); |
6437 | 890 %! endif |
891 %!test | |
892 %! if (__random_statistical_tests__) | |
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893 %! ## statistical tests may fail occasionally. |
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894 %! randg ("state", 12); |
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895 %! a = 100; |
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896 %! x = randg (a, 100_000, 1); |
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897 %! assert (mean (x), a, 0.2); |
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898 %! assert (var (x), a, 2); |
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899 %! assert (skewness (x), 2/sqrt (a), 0.05); |
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900 %! assert (kurtosis (x), 6/a, 0.2); |
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901 %! endif |
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902 %!test |
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903 %! randg ("seed", 12); |
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904 %! assert (randg ([-inf, -1, 0, inf, nan]), [nan, nan, nan, nan, nan]); |
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905 %!test |
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906 %! if (__random_statistical_tests__) |
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907 %! ## statistical tests may fail occasionally. |
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908 %! randg ("seed", 12); |
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909 %! a = 0.1; |
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910 %! x = randg (a, 100_000, 1); |
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911 %! assert (mean (x), a, 0.01); |
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912 %! assert (var (x), a, 0.01); |
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913 %! assert (skewness (x), 2/sqrt (a), 1); |
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914 %! assert (kurtosis (x), 6/a, 50); |
6437 | 915 %! endif |
916 %!test | |
917 %! if (__random_statistical_tests__) | |
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918 %! ## statistical tests may fail occasionally. |
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919 %! randg ("seed", 12); |
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920 %! a = 0.95; |
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921 %! x = randg (a, 100_000, 1); |
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922 %! assert (mean (x), a, 0.01); |
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923 %! assert (var (x), a, 0.04); |
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924 %! assert (skewness (x), 2/sqrt (a), 0.2); |
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925 %! assert (kurtosis (x), 6/a, 2); |
6437 | 926 %! endif |
927 %!test | |
928 %! if (__random_statistical_tests__) | |
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929 %! ## statistical tests may fail occasionally. |
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930 %! randg ("seed", 12); |
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931 %! a = 1; |
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932 %! x = randg (a, 100_000, 1); |
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933 %! assert (mean (x), a, 0.01); |
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934 %! assert (var (x), a, 0.04); |
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935 %! assert (skewness (x), 2/sqrt (a), 0.2); |
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936 %! assert (kurtosis (x), 6/a, 2); |
6437 | 937 %! endif |
5730 | 938 %!test |
6437 | 939 %! if (__random_statistical_tests__) |
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940 %! ## statistical tests may fail occasionally. |
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941 %! randg ("seed", 12); |
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942 %! a = 10; |
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943 %! x = randg (a, 100_000, 1); |
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944 %! assert (mean (x), a, 0.1); |
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945 %! assert (var (x), a, 0.5); |
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946 %! assert (skewness (x), 2/sqrt (a), 0.1); |
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947 %! assert (kurtosis (x), 6/a, 0.5); |
6437 | 948 %! endif |
5730 | 949 %!test |
6437 | 950 %! if (__random_statistical_tests__) |
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951 %! ## statistical tests may fail occasionally. |
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952 %! randg ("seed", 12); |
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953 %! a = 100; |
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954 %! x = randg (a, 100_000, 1); |
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955 %! assert (mean (x), a, 0.2); |
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956 %! assert (var (x), a, 2); |
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957 %! assert (skewness (x), 2/sqrt (a), 0.05); |
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958 %! assert (kurtosis (x), 6/a, 0.2); |
6437 | 959 %! endif |
5730 | 960 */ |
961 | |
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962 DEFUN (randp, args, , |
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963 doc: /* -*- texinfo -*- |
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964 @deftypefn {} {@var{x} =} randp (@var{l}, @var{n}) |
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965 @deftypefnx {} {@var{x} =} randp (@var{l}, @var{m}, @var{n}, @dots{}) |
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966 @deftypefnx {} {@var{x} =} randp (@var{l}, [@var{m} @var{n} @dots{}]) |
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967 @deftypefnx {} {@var{x} =} randp (@dots{}, "single") |
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968 @deftypefnx {} {@var{x} =} randp (@dots{}, "double") |
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969 @deftypefnx {} {@var{v} =} randp ("state") |
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970 @deftypefnx {} {} randp ("state", @var{v}) |
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971 @deftypefnx {} {} randp ("state", "reset") |
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972 @deftypefnx {} {@var{v} =} randp ("seed") |
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973 @deftypefnx {} {} randp ("seed", @var{v}) |
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974 @deftypefnx {} {} randp ("seed", "reset") |
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975 Return a matrix with Poisson distributed random elements with mean value |
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976 parameter given by the first argument, @var{l}. |
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977 |
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978 The arguments are handled the same as the arguments for @code{rand}, except |
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979 for the argument @var{l}. |
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980 |
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981 Five different algorithms are used depending on the range of @var{l} and |
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982 whether or not @var{l} is a scalar or a matrix. |
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983 |
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984 @table @asis |
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985 @item For scalar @var{l} @leq{} 12, use direct method. |
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986 W.H. Press, et al., @cite{Numerical Recipes in C}, |
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987 Cambridge University Press, 1992. |
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988 |
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989 @item For scalar @var{l} > 12, use rejection method.[1] |
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990 W.H. Press, et al., @cite{Numerical Recipes in C}, |
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991 Cambridge University Press, 1992. |
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992 |
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993 @item For matrix @var{l} @leq{} 10, use inversion method.[2] |
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994 @nospell{E. Stadlober, et al., WinRand source code}, available via FTP. |
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995 |
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996 @item For matrix @var{l} > 10, use patchwork rejection method. |
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997 @nospell{E. Stadlober, et al., WinRand source code}, available via FTP, or |
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998 @nospell{H. Zechner}, @cite{Efficient sampling from continuous and discrete |
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999 unimodal distributions}, Doctoral Dissertation, 156pp., Technical |
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1000 University @nospell{Graz}, Austria, 1994. |
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1001 |
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1002 @item For @var{l} > 1e8, use normal approximation. |
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1003 @nospell{L. Montanet}, et al., @cite{Review of Particle Properties}, |
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1004 Physical Review D 50 p1284, 1994. |
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1005 @end table |
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1006 |
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1007 The class of the value returned can be controlled by a trailing |
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1008 @qcode{"double"} or @qcode{"single"} argument. These are the only valid |
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1009 classes. |
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1010 @seealso{rand, randn, rande, randg} |
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1011 @end deftypefn */) |
5730 | 1012 { |
1013 int nargin = args.length (); | |
1014 | |
1015 if (nargin < 1) | |
1016 error ("randp: insufficient arguments"); | |
1017 | |
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1018 return do_rand (args, nargin, "randp", "poisson", true); |
5730 | 1019 } |
1020 | |
1021 /* | |
1022 %!test | |
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1023 %! randp ("state", 12); |
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1024 %! assert (randp ([-inf, -1, 0, inf, nan]), [nan, nan, 0, nan, nan]); |
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 (5, 1, 6), [5 5 3 7 7 3]); |
6437 | 1029 %!test |
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1030 %! ## Test a known fixed state |
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1031 %! randp ("state", 1); |
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1032 %! assert (randp (15, 1, 6), [13 15 8 18 18 15]); |
6437 | 1033 %!test |
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1034 %! ## Test a known fixed state |
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1035 %! randp ("state", 1); |
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1036 %! assert (randp (1e9, 1, 6), |
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1037 %! [999915677 999976657 1000047684 1000019035 999985749 999977692], |
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1038 %! -1e-6); |
6437 | 1039 %!test |
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1040 %! ## Test a known fixed seed |
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1041 %! randp ("seed", 1); |
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1042 %! %%assert (randp (5, 1, 6), [8 2 3 6 6 8]) |
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1043 %! assert (randp (5, 1, 5), [8 2 3 6 6]); |
6437 | 1044 %!test |
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1045 %! ## Test a known fixed seed |
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1046 %! randp ("seed", 1); |
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1047 %! assert (randp (15, 1, 6), [15 16 12 10 10 12]); |
6437 | 1048 %!test |
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1049 %! ## Test a known fixed seed |
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1050 %! randp ("seed", 1); |
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1051 %! assert (randp (1e9, 1, 6), |
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1052 %! [1000006208 1000012224 999981120 999963520 999963072 999981440], |
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1053 %! -1e-6); |
6437 | 1054 %!test |
1055 %! if (__random_statistical_tests__) | |
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1056 %! ## statistical tests may fail occasionally. |
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1057 %! randp ("state", 12); |
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1058 %! for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03] |
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1059 %! x = randp (a (1), 100_000, 1); |
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1060 %! assert (min (x) >= 0); # *** Please report this!!! *** |
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1061 %! assert (mean (x), a(1), a(2)); |
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1062 %! assert (var (x), a(1), 0.02*a(1)); |
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1063 %! assert (skewness (x), 1/sqrt (a(1)), a(3)); |
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1064 %! assert (kurtosis (x), 1/a(1), 3*a(3)); |
6437 | 1065 %! endfor |
1066 %! endif | |
1067 %!test | |
1068 %! if (__random_statistical_tests__) | |
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1069 %! ## statistical tests may fail occasionally. |
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1070 %! randp ("state", 12); |
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1071 %! for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03] |
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1072 %! x = randp (a(1)* ones (100_000, 1), 100_000, 1); |
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1073 %! assert (min (x) >= 0); # *** Please report this!!! *** |
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1074 %! assert (mean (x), a(1), a(2)); |
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1075 %! assert (var (x), a(1), 0.02*a(1)); |
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1076 %! assert (skewness (x), 1/sqrt (a(1)), a(3)); |
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1077 %! assert (kurtosis (x), 1/a(1), 3*a(3)); |
6437 | 1078 %! endfor |
1079 %! endif | |
1080 %!test | |
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1081 %! randp ("seed", 12); |
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1082 %! assert (randp ([-inf, -1, 0, inf, nan]), [nan, nan, 0, nan, nan]); |
5730 | 1083 %!test |
6449 | 1084 %! if (__random_statistical_tests__) |
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1085 %! ## statistical tests may fail occasionally. |
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1086 %! randp ("seed", 12); |
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1087 %! for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03] |
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1088 %! x = randp (a(1), 100_000, 1); |
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1089 %! assert (min (x) >= 0); # *** Please report this!!! *** |
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1090 %! assert (mean (x), a(1), a(2)); |
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1091 %! assert (var (x), a(1), 0.02*a(1)); |
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1092 %! assert (skewness (x), 1/sqrt (a(1)), a(3)); |
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1093 %! assert (kurtosis (x), 1/a(1), 3*a(3)); |
6449 | 1094 %! endfor |
1095 %! endif | |
5730 | 1096 %!test |
6449 | 1097 %! if (__random_statistical_tests__) |
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1098 %! ## statistical tests may fail occasionally. |
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1099 %! randp ("seed", 12); |
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1100 %! for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03] |
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1101 %! x = randp (a(1)* ones (100_000, 1), 100_000, 1); |
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1102 %! assert (min (x) >= 0); # *** Please report this!!! *** |
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1103 %! assert (mean (x), a(1), a(2)); |
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1104 %! assert (var (x), a(1), 0.02*a(1)); |
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1105 %! assert (skewness (x), 1/sqrt (a(1)), a(3)); |
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1106 %! assert (kurtosis (x), 1/a(1), 3*a(3)); |
6449 | 1107 %! endfor |
1108 %! endif | |
5730 | 1109 */ |
1110 | |
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1111 DEFUN (randperm, args, , |
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1112 doc: /* -*- texinfo -*- |
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1113 @deftypefn {} {@var{v} =} randperm (@var{n}) |
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1114 @deftypefnx {} {@var{v} =} randperm (@var{n}, @var{m}) |
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1115 Return a row vector containing a random permutation of @code{1:@var{n}}. |
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1116 |
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1117 If @var{m} is supplied, return @var{m} unique entries, sampled without |
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1118 replacement from @code{1:@var{n}}. |
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1119 |
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1120 The complexity is O(@var{n}) in memory and O(@var{m}) in time, unless |
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1121 @var{m} < @var{n}/5, in which case O(@var{m}) memory is used as well. The |
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1122 randomization is performed using rand(). All permutations are equally |
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1123 likely. |
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1124 @seealso{perms} |
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1125 @end deftypefn */) |
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1126 { |
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1127 int nargin = args.length (); |
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1128 |
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1129 if (nargin < 1 || nargin > 2) |
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1130 print_usage (); |
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1131 |
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1132 octave_idx_type n = args(0).idx_type_value (true); |
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1133 octave_idx_type m = (nargin == 2) ? args(1).idx_type_value (true) : n; |
11586
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1134 |
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1135 if (m < 0 || n < 0) |
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1136 error ("randperm: M and N must be non-negative"); |
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1137 |
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1138 if (m > n) |
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1139 error ("randperm: M must be less than or equal to N"); |
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1140 |
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1141 // Quick and dirty heuristic to decide if we allocate or not the |
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1142 // whole vector for tracking the truncated shuffle. |
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1143 bool short_shuffle = m < n/5; |
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1144 |
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1145 // Generate random numbers. |
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1146 NDArray r = rand::nd_array (dim_vector (1, m)); |
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1147 double *rvec = r.rwdata (); |
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1148 |
23450
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1149 octave_idx_type idx_len = (short_shuffle ? m : n); |
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1150 Array<octave_idx_type> idx; |
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1151 try |
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1152 { |
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1153 idx = Array<octave_idx_type> (dim_vector (1, idx_len)); |
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1154 } |
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1155 catch (const std::bad_alloc&) |
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1156 { |
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1157 // Looks like n is too big and short_shuffle is false. |
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1158 // Let's try again, but this time with the alternative. |
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1159 idx_len = m; |
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1160 short_shuffle = true; |
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1161 idx = Array<octave_idx_type> (dim_vector (1, idx_len)); |
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1162 } |
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1163 |
32660
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1164 octave_idx_type *ivec = idx.rwdata (); |
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1165 |
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1166 for (octave_idx_type i = 0; i < idx_len; i++) |
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1167 ivec[i] = i; |
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1168 |
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1169 if (short_shuffle) |
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1170 { |
22150
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1171 std::unordered_map<octave_idx_type, octave_idx_type> map (m); |
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1172 |
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1173 // Perform the Knuth shuffle only keeping track of moved |
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1174 // entries in the map |
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1175 for (octave_idx_type i = 0; i < m; i++) |
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1176 { |
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1177 octave_idx_type k = i + std::floor (rvec[i] * (n - i)); |
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1178 |
22407
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1179 // For shuffling first m entries, no need to use extra storage |
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1180 if (k < m) |
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1181 { |
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1182 std::swap (ivec[i], ivec[k]); |
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1183 } |
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1184 else |
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1185 { |
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1186 if (map.find (k) == map.end ()) |
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1187 map[k] = k; |
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1188 |
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1189 std::swap (ivec[i], map[k]); |
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1190 } |
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1191 } |
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1192 } |
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1193 else |
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1194 { |
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1195 // Perform the Knuth shuffle of the first m entries |
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1196 for (octave_idx_type i = 0; i < m; i++) |
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1197 { |
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1198 octave_idx_type k = i + std::floor (rvec[i] * (n - i)); |
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1199 std::swap (ivec[i], ivec[k]); |
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1200 } |
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1201 } |
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1202 |
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1203 // Convert to doubles, reusing r. |
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1204 for (octave_idx_type i = 0; i < m; i++) |
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1205 rvec[i] = ivec[i] + 1; |
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1206 |
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1207 if (m < n) |
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1208 idx.resize (dim_vector (1, m)); |
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1209 |
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1210 // Now create an array object with a cached idx_vector. |
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1211 return ovl (new octave_matrix (r, idx_vector (idx))); |
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1212 } |
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1213 |
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1214 /* |
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1215 %!assert (sort (randperm (20)), 1:20) |
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1216 %!assert (length (randperm (20,10)), 10) |
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1217 |
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|
1218 ## Test biggish N |
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|
1219 %!assert <*39378> (length (randperm (30_000^2, 100_000)), 100_000) |
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1220 |
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1221 %!test |
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|
1222 %! rand ("seed", 0); |
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1223 %! for i = 1:100 |
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1224 %! p = randperm (305, 30); |
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1225 %! assert (length (unique (p)), 30); |
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1226 %! endfor |
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1227 */ |
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1228 |
31605
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|
1229 OCTAVE_END_NAMESPACE(octave) |