1 | // -*- C++ -*- |
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2 | // $Id$ |
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3 | |
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4 | /* |
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5 | * This is a modification of the Kinderman + Monahan algorithm for |
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6 | * generating normal random numbers, due to Leva: |
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7 | * |
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8 | * J.L. Leva, Algorithm 712. A normal random number generator, ACM Trans. |
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9 | * Math. Softw. 18 (1992) 454--455. |
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10 | * |
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11 | * http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p449-leva/ |
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12 | * |
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13 | * Note: Some of the constants used below look like they have dubious |
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14 | * precision. These constants are used for an approximate bounding |
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15 | * region test (see the paper). If the approximate test fails, |
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16 | * then an exact region test is performed. |
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17 | * |
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18 | * Only 0.012 logarithm evaluations are required per random number |
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19 | * generated, making this method comparatively fast. |
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20 | * |
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21 | * Adapted to C++ by T. Veldhuizen. |
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22 | */ |
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23 | |
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24 | #ifndef BZ_RANDOM_NORMAL |
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25 | #define BZ_RANDOM_NORMAL |
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26 | |
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27 | #ifndef BZ_RANDOM_UNIFORM |
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28 | #include <random/uniform.h> |
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29 | #endif |
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30 | |
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31 | BZ_NAMESPACE(ranlib) |
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32 | |
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33 | template<typename T = double, typename IRNG = defaultIRNG, |
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34 | typename stateTag = defaultState> |
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35 | class NormalUnit : public UniformOpen<T,IRNG,stateTag> |
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36 | { |
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37 | public: |
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38 | typedef T T_numtype; |
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39 | |
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40 | NormalUnit() {} |
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41 | |
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42 | explicit NormalUnit(unsigned int i) : |
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43 | UniformOpen<T,IRNG,stateTag>(i) {}; |
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44 | |
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45 | T random() |
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46 | { |
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47 | const T s = 0.449871, t = -0.386595, a = 0.19600, b = 0.25472; |
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48 | const T r1 = 0.27597, r2 = 0.27846; |
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49 | |
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50 | T u, v; |
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51 | |
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52 | for (;;) { |
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53 | // Generate P = (u,v) uniform in rectangle enclosing |
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54 | // acceptance region: |
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55 | // 0 < u < 1 |
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56 | // - sqrt(2/e) < v < sqrt(2/e) |
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57 | // The constant below is 2*sqrt(2/e). |
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58 | |
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59 | u = this->getUniform(); |
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60 | v = 1.715527769921413592960379282557544956242L |
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61 | * (this->getUniform() - 0.5); |
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62 | |
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63 | // Evaluate the quadratic form |
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64 | T x = u - s; |
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65 | T y = fabs(v) - t; |
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66 | T q = x*x + y*(a*y - b*x); |
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67 | |
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68 | // Accept P if inside inner ellipse |
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69 | if (q < r1) |
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70 | break; |
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71 | |
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72 | // Reject P if outside outer ellipse |
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73 | if (q > r2) |
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74 | continue; |
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75 | |
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76 | // Between ellipses: perform exact test |
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77 | if (v*v <= -4.0 * log(u)*u*u) |
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78 | break; |
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79 | } |
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80 | |
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81 | return v/u; |
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82 | } |
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83 | |
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84 | }; |
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85 | |
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86 | |
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87 | template<typename T = double, typename IRNG = defaultIRNG, |
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88 | typename stateTag = defaultState> |
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89 | class Normal : public NormalUnit<T,IRNG,stateTag> { |
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90 | |
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91 | public: |
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92 | typedef T T_numtype; |
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93 | |
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94 | Normal(T mean, T standardDeviation) |
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95 | { |
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96 | mean_ = mean; |
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97 | standardDeviation_ = standardDeviation; |
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98 | } |
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99 | |
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100 | Normal(T mean, T standardDeviation, unsigned int i) : |
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101 | NormalUnit<T,IRNG,stateTag>(i) |
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102 | { |
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103 | mean_ = mean; |
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104 | standardDeviation_ = standardDeviation; |
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105 | }; |
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106 | |
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107 | T random() |
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108 | { |
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109 | return mean_ + standardDeviation_ |
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110 | * NormalUnit<T,IRNG,stateTag>::random(); |
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111 | } |
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112 | |
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113 | private: |
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114 | T mean_; |
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115 | T standardDeviation_; |
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116 | }; |
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117 | |
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118 | BZ_NAMESPACE_END |
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119 | |
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120 | #endif // BZ_RANDOM_NORMAL |
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