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  1. #include <random>
  2. #include <cmath>
  3.  
  4. const double pi = 3.14159265358979323846;
  5.  
  6. void rejection_sampling(int count)
  7. {
  8. 	std::mt19937 rnd;
  9. 	std::uniform_real_distribution<double> dist(-1.0, 1.0);
  10.  
  11. 	for(int i=0; i<count; ++i)
  12. 	{
  13. 		bool rejected = false;
  14. 		do
  15. 		{
  16. 			double x = dist(rnd);
  17. 			double y = dist(rnd);
  18. 			double z = dist(rnd);
  19. 			double r2 = x*x + y*y + z*z;
  20. 			if(r2 > 1.0 || r2 == 0)
  21. 				rejected = true;
  22. 			else
  23. 			{
  24. 				rejected = false;
  25. 				double r = sqrt(r2);
  26. 				printf("%f %f %f\n", x/r, y/r, z/r);
  27. 			}
  28. 		}
  29. 		while(rejected);
  30. 	}
  31. }
  32.  
  33. void normal_deviate(int count)
  34. {
  35. 	std::mt19937 rnd;
  36. 	std::normal_distribution<double> dist(0.0, 1.0);
  37.  
  38. 	for(int i=0; i<count; ++i)
  39. 	{
  40. 		bool bad_luck = false;
  41. 		do
  42. 		{
  43. 			double x = dist(rnd);
  44. 			double y = dist(rnd);
  45. 			double z = dist(rnd);
  46. 			double r2 = x*x + y*y + z*z;
  47. 			if(r2 == 0)
  48. 				bad_luck = true;
  49. 			else
  50. 			{
  51. 				bad_luck = false;
  52. 				double r = sqrt(r2);
  53. 				printf("%f %f %f\n", x/r, y/r, z/r);
  54. 			}
  55. 		}
  56. 		while(bad_luck);
  57. 	}
  58. }
  59.  
  60. void trig_method(int count)
  61. {
  62. 	std::mt19937 rnd;
  63. 	std::uniform_real_distribution<double> dist(0.0, 1.0);
  64.  
  65. 	for(int i=0; i<count; ++i)
  66. 	{
  67. 		double z = 2.0*dist(rnd) - 1.0;
  68. 		double t = 2.0*pi*dist(rnd);
  69. 		double r = sqrt(1.0-z*z);
  70. 		printf("%f %f %f\n", r*cos(t), r*sin(t), z);
  71. 	}
  72. }
  73.  
  74. void coordinate_approach(int count)
  75. {
  76. 	std::mt19937 rnd;
  77. 	std::uniform_real_distribution<double> dist(-1.0, 1.0);
  78.  
  79. 	for(int i=0; i<count; ++i)
  80. 	{
  81. 		bool rejected = false;
  82. 		do
  83. 		{
  84. 			double u = dist(rnd);
  85. 			double v = dist(rnd);
  86. 			double s = u*u + v*v;
  87. 			if(s > 1.0)
  88. 				rejected = true;
  89. 			else
  90. 			{
  91. 				rejected = false;
  92. 				double a = 2.0*sqrt(1.0-s);
  93. 				printf("%f %f %f\n", a*u, a*v, 2.0*s-1.0);
  94. 			}
  95. 		}
  96. 		while(rejected);
  97. 	}
  98. }
  99.  
  100. int main(int argc, char* argv[])
  101. {
  102. 	printf("[rejection sampling]\n\n");
  103. 	rejection_sampling(500);
  104.  
  105. 	printf("\n[normal deviate]\n\n");
  106. 	normal_deviate(500);
  107.  
  108. 	printf("\n[trig method]\n\n");
  109. 	trig_method(500);
  110.  
  111. 	printf("\n[coordinate approach]\n\n");
  112. 	coordinate_approach(500);
  113.  
  114. 	return 0;
  115. }
Success #stdin #stdout 0s 2832KB
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Standard input is empty
stdout
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[rejection sampling]

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-0.561888 -0.745138 -0.359236
-0.950519 -0.302902 0.069024
0.728761 0.607207 0.316556
-0.856095 -0.264396 -0.444068
0.473700 0.832340 0.287783
0.679042 0.248906 -0.690614
0.421240 0.326525 0.846131
0.380502 -0.131117 0.915438
-0.208362 -0.798420 -0.564899
-0.513153 0.791506 -0.331953
-0.774736 0.373171 -0.510420
-0.206522 0.545383 0.812346
0.884395 -0.307062 0.351509
-0.944378 0.233032 -0.232049
0.555948 -0.437200 0.706950
0.562725 0.397570 0.724761
0.422337 0.139351 -0.895664
0.669168 -0.486734 -0.561519
-0.196091 -0.276215 0.940879
0.277895 -0.959957 -0.035461
-0.484954 -0.667839 -0.564633
-0.153386 -0.078134 0.985072
-0.761240 -0.556446 -0.332988
-0.641411 -0.685029 -0.345438
-0.615542 0.382167 0.689244
-0.002352 -0.985363 0.170452
0.790413 -0.222283 -0.570822
-0.810116 -0.241153 -0.534376
0.237969 -0.350973 -0.905642
0.213063 -0.250941 0.944263
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-0.767627 -0.117105 0.630107
0.655009 -0.406650 -0.636866
0.264830 0.056490 -0.962639
0.313078 0.174788 -0.933505
0.646129 0.754698 0.113789
-0.179719 0.749433 0.637222
0.045989 -0.947127 -0.317547
-0.436731 -0.157731 0.885656
-0.510668 0.576546 0.637819
0.891265 -0.450089 -0.055375
-0.726291 -0.110455 0.678455
-0.812250 -0.560014 -0.163201
0.863182 0.497903 0.083724
-0.272337 0.961005 0.047984
0.895390 0.232427 0.379808
-0.963360 0.083837 0.254771
0.587565 -0.752492 0.297529
-0.471265 -0.866583 -0.164146
0.214233 -0.851187 -0.479150
0.695550 -0.682129 -0.225631
-0.956560 -0.127501 -0.262176
-0.898588 0.185751 0.397538
-0.332343 0.935234 -0.122006
-0.274351 0.920951 0.276731
0.811386 -0.577636 -0.089385
0.634168 0.484857 -0.602283
-0.763109 0.102971 -0.638014
-0.162510 -0.967369 0.194392
-0.238747 0.936825 0.255652
0.588849 -0.269374 -0.762033
0.619882 0.302516 -0.724038
-0.264985 -0.963209 0.044859
0.654200 0.453747 0.605092
-0.676909 -0.531162 0.509569
0.189551 -0.755138 0.627564
-0.569102 0.386328 -0.725861
0.264356 -0.679728 -0.684168
0.266887 0.002227 -0.963725
0.186775 0.840940 0.507873
-0.969194 0.135527 0.205657
-0.430552 -0.889639 0.152209
0.106481 0.880702 -0.461548
-0.980499 -0.195400 -0.021011
0.529525 0.838286 0.129919
-0.775476 0.104201 0.622719
0.360163 -0.638533 -0.680116
-0.654563 -0.646684 -0.391596
0.498219 0.547932 -0.671974
0.880762 0.020950 -0.473096
-0.943272 -0.111112 0.312878
0.829457 -0.451894 0.328317
0.272601 -0.301108 0.913796
0.640825 0.360624 0.677712
-0.731736 -0.091322 0.675442
0.066442 -0.398378 -0.914812
0.345809 -0.038548 0.937513
-0.080000 -0.833403 -0.546845
0.430606 -0.057842 -0.900684
0.195661 -0.848300 -0.492040
-0.877601 0.473578 0.074434
-0.284027 -0.854269 -0.435377
-0.842782 -0.510697 -0.170018
0.739690 0.654844 -0.155041
0.990805 -0.088518 -0.102319
-0.135548 0.164086 0.977089
-0.747972 0.481524 0.456806
-0.024584 -0.458771 0.888214
-0.754178 -0.612569 0.236589
0.017791 -0.349204 0.936878
-0.381820 -0.871327 0.308227
-0.303358 -0.199192 -0.931824
0.045049 -0.229250 -0.972325
-0.268220 0.957843 0.102929
0.985265 -0.130129 -0.110993
-0.401881 -0.341484 0.849635
-0.462961 0.735619 -0.494502
-0.225450 -0.808394 -0.543756
0.483489 -0.854520 -0.189828
-0.882613 0.262163 0.390211
-0.104843 -0.449585 -0.887063
0.944406 -0.302268 -0.129347
0.876483 -0.170662 0.450168
-0.939761 0.307220 0.149882
0.209207 -0.107969 0.971893
0.993958 0.108067 0.019183
0.600636 -0.636493 0.483852
0.863719 0.388651 0.320841
0.697277 -0.705546 -0.126531

[normal deviate]

0.268136 -0.291759 0.918139
-0.989778 0.086587 -0.113319
0.339235 -0.940630 0.011606
0.631591 -0.327230 0.702861
0.341361 -0.542225 0.767766
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0.865420 0.288342 -0.409765
0.989236 -0.056903 -0.134810
-0.144891 -0.413717 -0.898802
0.843282 -0.035659 0.536288
0.661596 0.740383 -0.118841
0.902542 0.176683 0.392685
0.555233 -0.161894 0.815786
0.712340 -0.676072 0.188412
-0.569243 0.619908 -0.540070
0.096503 -0.066985 0.993076
0.365040 0.630725 0.684787
0.495473 -0.866707 0.057664
-0.579552 -0.683093 -0.444414
-0.666745 0.430823 -0.608146
-0.667317 -0.328240 0.668541
-0.135874 0.909251 0.393447
0.687274 -0.053398 -0.724433
0.179505 -0.961108 0.209879
0.082745 0.992163 0.093625
-0.834898 0.070974 -0.545809
0.860986 0.143494 0.487968
0.274412 -0.000832 0.961612
-0.731133 0.626274 -0.270601
0.184168 -0.523267 -0.832030
0.336142 0.764544 -0.549982
0.079977 -0.265228 -0.960863
0.939744 -0.263074 -0.218344
0.681648 -0.305644 0.664784
0.085815 -0.912482 -0.400015
0.168986 -0.967183 -0.189738
0.869509 -0.300767 0.391782
-0.033225 -0.998987 -0.030348
-0.966592 0.081210 0.243116
-0.226016 0.898783 -0.375641
0.039978 -0.471594 -0.880909
-0.237358 -0.154991 -0.958978
-0.092198 -0.693762 0.714278
0.744840 0.294798 -0.598588
-0.794578 0.544307 -0.269026
-0.410728 0.576625 -0.706262
-0.406867 -0.025315 0.913136
-0.388511 0.253553 0.885872
-0.366309 0.882680 -0.294438
-0.992070 0.120765 -0.034814
-0.112121 -0.082713 0.990246
-0.923609 0.076985 -0.375525
0.803921 -0.353679 -0.478144
-0.088361 0.981197 0.171592
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0.992957 -0.087105 -0.080305
-0.745984 -0.082172 -0.660875
0.386718 -0.430885 0.815345
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0.203431 -0.651035 0.731280
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-0.181985 0.552432 -0.813449
0.609925 -0.789300 0.070698
-0.213155 -0.529751 0.820932
-0.428951 -0.764819 -0.480680
0.980814 -0.194944 0.000772
-0.147879 -0.514939 0.844375
-0.762083 0.020639 -0.647151
0.885908 -0.354835 -0.298761
-0.989162 0.129065 -0.070001
0.631625 -0.156458 0.759322
-0.849429 -0.289120 -0.441452
0.958228 0.023566 0.285032
-0.449358 -0.639212 -0.624088
0.034465 0.449132 -0.892801
0.661797 -0.622393 0.417913
0.864544 -0.154214 0.478311
-0.318752 -0.870002 -0.376156
0.020725 -0.895180 0.445223
0.752450 -0.207160 -0.625223
0.820587 -0.509484 0.258966
0.500005 0.040718 -0.865065
-0.356653 0.823036 -0.442053
0.563923 -0.018156 -0.825628
0.519763 -0.434685 0.735456
-0.787306 -0.168681 0.593039
0.054087 0.399009 -0.915350
0.100476 0.628261 0.771487
-0.608065 -0.303767 -0.733472
0.782555 -0.434438 0.445951
0.508661 -0.249614 0.823988
0.354362 0.889629 -0.288076
-0.067216 0.938977 -0.337348
-0.695459 -0.557047 -0.453912
0.899306 0.380427 0.215693
0.392350 -0.076048 -0.916667
-0.915331 0.335654 0.222498
-0.008690 0.996749 0.080096
-0.712999 0.656825 -0.245382
0.606756 -0.354268 0.711577
0.642602 -0.699321 -0.313070
0.069984 -0.030462 0.997083
-0.887131 -0.147902 0.437177
-0.615863 -0.751585 0.236290
0.193239 0.891092 -0.410627
-0.556743 0.828570 0.059240
-0.474964 -0.720757 0.504894
0.884963 -0.427725 0.184098
0.729159 -0.151110 -0.667453
0.173546 -0.983829 -0.044302
0.604097 -0.622677 -0.497333
-0.974124 0.056023 -0.218960
0.681183 -0.015798 0.731942
-0.400402 -0.167967 -0.900814
-0.775857 0.029117 -0.630237
0.989418 -0.144811 -0.009028
0.415896 -0.047314 -0.908180
-0.582221 0.627559 -0.516903
-0.986121 -0.145298 0.080331
-0.730213 -0.475666 0.490439
0.824598 0.138103 0.548603
-0.522533 0.200404 0.828733
0.811994 0.476401 -0.337206
-0.152958 0.968149 0.198220
-0.718126 0.346785 -0.603354
-0.634391 -0.593124 -0.495733
-0.314871 0.778658 0.542723
0.451368 -0.680815 0.576852
-0.830458 -0.403090 0.384523
0.184031 -0.950129 -0.251770
0.154883 0.964683 -0.213069
-0.134002 -0.986355 -0.095646
-0.474247 0.861034 0.183601
0.481066 -0.840738 -0.248467
0.114473 -0.469847 0.875294
0.962310 0.255848 0.092204
0.653833 -0.364987 -0.662787
-0.772649 -0.369503 0.516218
0.180494 0.983567 0.004223
0.560156 -0.746944 0.358190
0.046211 0.163482 0.985463
-0.025631 0.995448 -0.091793
0.613821 0.224328 -0.756902
0.117147 0.744695 -0.657043
-0.359545 -0.842966 0.400170
0.205545 0.360340 -0.909894
-0.982676 -0.126023 0.135887
-0.606659 0.511014 0.608957
-0.287847 -0.374461 -0.881432
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-0.775564 -0.414339 -0.476261
-0.397644 -0.455400 -0.796549
-0.160506 -0.825312 -0.541385
0.936924 -0.170103 -0.305350
0.604277 -0.712949 0.355744
0.450230 0.892426 -0.029483
-0.822105 0.179592 0.540268
-0.280471 0.471430 0.836116
-0.269346 -0.059483 -0.961205
0.853538 0.146990 -0.499867
-0.298049 -0.953401 0.046831
0.022637 0.919721 -0.391919
-0.821915 0.569537 -0.009084
0.062034 -0.552264 0.831358
0.539917 0.360063 0.760818
-0.155383 -0.603709 -0.781915
0.903382 -0.414817 0.108751
-0.381743 -0.342273 -0.858558
-0.274426 -0.912517 -0.303320
-0.085593 -0.988701 -0.123060
-0.057210 0.706598 0.705299
0.520576 0.471546 0.711790
-0.131652 -0.739225 -0.660466
0.711727 -0.161762 0.683577
0.341756 -0.839990 -0.421449
-0.406931 0.836307 -0.367420
-0.428259 -0.885053 -0.182419
0.905801 -0.097164 0.412413
-0.237676 -0.822757 -0.516315
0.668632 -0.159140 -0.726365
-0.945173 0.302041 -0.124174
-0.260403 -0.644148 0.719210
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-0.361547 -0.823213 0.437726
0.616323 -0.407640 -0.673777
-0.283326 0.528440 0.800299
0.702252 0.199981 0.683264
0.946687 0.096209 -0.307453
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0.497344 -0.867516 0.008069
0.775980 0.389040 0.496490
0.393061 0.661457 -0.638732
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0.844678 -0.259858 0.467967
0.586463 0.800208 0.125411
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0.595938 -0.608104 -0.524469
0.384291 -0.420913 0.821676
0.209547 -0.977785 -0.005146
-0.738282 0.656303 0.155580
-0.820863 -0.441588 0.362193
-0.257406 0.916253 0.306956
0.363269 -0.603602 0.709719
0.950726 -0.217306 0.221129
-0.696006 0.316843 -0.644349
0.688332 -0.703739 -0.175929
-0.877037 0.480037 0.019245
0.376028 -0.907644 -0.186508
0.629394 -0.258978 -0.732662
0.389882 -0.352926 -0.850550
-0.795625 0.581977 0.168174
-0.603944 -0.770578 -0.203619
-0.728071 0.164733 -0.665414
-0.950458 0.278538 0.138005
-0.543657 0.725491 0.422019
0.343084 0.529873 0.775582
0.192471 -0.039792 0.980496
0.532680 0.106906 -0.839537
-0.135720 -0.079508 0.987552
-0.593832 -0.161510 -0.788212
0.285820 0.239491 -0.927874
-0.050435 -0.756645 -0.651878
-0.215773 -0.775292 0.593603
0.785969 0.236270 0.571339
0.325973 0.653844 0.682810
0.552470 0.693689 0.462139
0.893979 0.443213 0.066059
-0.505617 0.133465 0.852372
0.428060 -0.592287 -0.682614
0.856582 0.448064 0.255940
0.821242 0.570536 0.007087
-0.538898 0.699186 0.469817
0.784753 -0.195206 0.588267
0.013331 -0.986476 0.163364
-0.543419 0.824867 0.155853
-0.892884 -0.145514 -0.426127
-0.220385 -0.582314 0.782522
-0.867008 0.318988 -0.382811
-0.368971 -0.024685 0.929113
-0.843969 -0.109935 -0.525006
-0.203779 -0.978647 -0.026923
-0.674865 -0.455851 -0.580308
-0.742023 -0.666707 0.070033
0.373065 0.610488 0.698661
0.358586 -0.493095 0.792637
-0.059112 0.417946 -0.906547
0.847418 0.072407 -0.525966
0.746959 -0.420075 0.515354
0.274075 -0.393624 0.877464
0.739418 0.656880 -0.147543
-0.071694 0.953975 0.291191
0.609553 0.655925 -0.445205
0.170980 -0.484138 0.858124
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0.075080 -0.653294 0.753372
0.849201 -0.367823 0.378898
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0.451376 0.869325 -0.201330
0.760494 -0.409080 0.504285
0.247977 0.931440 -0.266320
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0.081733 -0.682512 -0.726290
0.159739 -0.856467 -0.490865
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0.213903 0.381323 0.899354
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0.712046 0.676673 0.187360
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0.267874 -0.212862 0.939645
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0.415644 0.498178 0.760959
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0.162634 -0.704275 0.691048
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0.588780 0.755874 -0.286342
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0.757693 0.354396 0.548000
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0.209989 -0.106375 0.971900
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0.731658 0.363402 -0.576729
0.047181 0.878667 0.475098
0.441438 -0.050641 -0.895862
0.264664 0.175839 -0.948174
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0.289994 0.064805 0.954832
0.815857 -0.403251 -0.414448
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0.964212 0.093534 0.248087
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0.866661 -0.217176 -0.449147
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0.404712 -0.637252 0.655834
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0.625436 -0.405822 -0.666437
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0.186501 -0.462742 -0.866653
0.828316 0.230836 0.510497
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0.529068 -0.489322 0.693290
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0.852146 -0.105462 0.512567
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0.422813 -0.179905 0.888180
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https://ideone.com/oYEVR
language:
C++14 (gcc 8.3)
created:
12 years ago
visibility:
secret

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