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