[6] | 1 | // |
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| 2 | // C++ Implementation: itpp_ext |
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| 3 | // |
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[145] | 4 | // Description: |
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[6] | 5 | // |
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| 6 | // |
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| 7 | // Author: smidl <smidl@utia.cas.cz>, (C) 2008 |
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| 8 | // |
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| 9 | // Copyright: See COPYING file that comes with this distribution |
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| 10 | // |
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| 11 | // |
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| 12 | |
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[32] | 13 | #include "itpp_ext.h" |
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[6] | 14 | |
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[343] | 15 | #ifndef M_PI |
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| 16 | #define M_PI 3.14159265358979323846 |
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| 17 | #endif |
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[37] | 18 | // from algebra/lapack.h |
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| 19 | |
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[622] | 20 | extern "C" /* QR factorization of a general matrix A */ |
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| 21 | { |
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| 22 | void dgeqrf_ (int *m, int *n, double *a, int *lda, double *tau, double *work, |
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| 23 | int *lwork, int *info); |
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[37] | 24 | }; |
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| 25 | |
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[622] | 26 | namespace itpp |
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| 27 | { |
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[679] | 28 | vec empty_vec = vec(0); |
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| 29 | |
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[622] | 30 | Array<int> to_Arr (const ivec &indices) |
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| 31 | { |
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| 32 | Array<int> a (indices.size()); |
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| 33 | for (int i = 0; i < a.size(); i++) { |
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| 34 | a (i) = indices (i); |
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[145] | 35 | } |
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[477] | 36 | return a; |
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| 37 | } |
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[6] | 38 | |
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[622] | 39 | ivec linspace (int from, int to) |
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| 40 | { |
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[477] | 41 | int n = to - from + 1; |
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| 42 | int i; |
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[622] | 43 | it_assert_debug (n > 0, "wrong linspace"); |
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| 44 | ivec iv (n); |
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| 45 | for (i = 0; i < n; i++) iv (i) = from + i; |
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[477] | 46 | return iv; |
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| 47 | }; |
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[86] | 48 | |
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[622] | 49 | void set_subvector (vec &ov, const ivec &iv, const vec &v) |
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| 50 | { |
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| 51 | it_assert_debug ( (iv.length() <= v.length()), |
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[477] | 52 | "Vec<>::set_subvector(ivec, vec<Num_T>): Indexing out " |
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[622] | 53 | "of range of v"); |
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| 54 | for (int i = 0; i < iv.length(); i++) { |
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| 55 | it_assert_debug (iv (i) < ov.length(), |
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| 56 | "Vec<>::set_subvector(ivec, vec<Num_T>): Indexing out " |
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| 57 | "of range of v"); |
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| 58 | ov (iv (i)) = v (i); |
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[145] | 59 | } |
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[477] | 60 | } |
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[145] | 61 | |
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[622] | 62 | vec get_vec (const vec &v, const ivec &indexlist) |
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| 63 | { |
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[477] | 64 | int size = indexlist.size(); |
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[622] | 65 | vec temp (size); |
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| 66 | for (int i = 0; i < size; ++i) { |
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| 67 | temp (i) = v._data() [indexlist (i) ]; |
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[180] | 68 | } |
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[477] | 69 | return temp; |
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| 70 | } |
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[180] | 71 | |
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[276] | 72 | // Gamma |
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[404] | 73 | #define log std::log |
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| 74 | #define exp std::exp |
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| 75 | #define sqrt std::sqrt |
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| 76 | #define R_FINITE std::isfinite |
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[11] | 77 | |
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[622] | 78 | bvec operator> (const vec &t1, const vec &t2) |
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| 79 | { |
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| 80 | it_assert_debug (t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors"); |
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| 81 | bvec temp (t1.length()); |
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| 82 | for (int i = 0; i < t1.length(); i++) |
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| 83 | temp (i) = (t1[i] > t2[i]); |
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[477] | 84 | return temp; |
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| 85 | } |
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[32] | 86 | |
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[622] | 87 | bvec operator< (const vec &t1, const vec &t2) |
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| 88 | { |
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| 89 | it_assert_debug (t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors"); |
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| 90 | bvec temp (t1.length()); |
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| 91 | for (int i = 0; i < t1.length(); i++) |
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| 92 | temp (i) = (t1[i] < t2[i]); |
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[477] | 93 | return temp; |
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| 94 | } |
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[145] | 95 | |
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| 96 | |
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[622] | 97 | bvec operator& (const bvec &a, const bvec &b) |
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| 98 | { |
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| 99 | it_assert_debug (b.size() == a.size(), "operator&(): Vectors of different lengths"); |
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[477] | 100 | |
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[622] | 101 | bvec temp (a.size()); |
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| 102 | for (int i = 0; i < a.size(); i++) { |
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| 103 | temp (i) = a (i) & b (i); |
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[145] | 104 | } |
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[477] | 105 | return temp; |
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| 106 | } |
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[145] | 107 | |
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[622] | 108 | bvec operator| (const bvec &a, const bvec &b) |
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| 109 | { |
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| 110 | it_assert_debug (b.size() != a.size(), "operator&(): Vectors of different lengths"); |
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[145] | 111 | |
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[622] | 112 | bvec temp (a.size()); |
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| 113 | for (int i = 0; i < a.size(); i++) { |
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| 114 | temp (i) = a (i) | b (i); |
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[145] | 115 | } |
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[477] | 116 | return temp; |
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| 117 | } |
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[32] | 118 | |
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[662] | 119 | //#if 0 |
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[622] | 120 | Gamma_RNG::Gamma_RNG (double a, double b) |
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| 121 | { |
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| 122 | setup (a, b); |
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[404] | 123 | } |
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[622] | 124 | double Gamma_RNG::sample() |
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| 125 | { |
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[477] | 126 | //A copy of rgamma code from the R package!! |
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| 127 | // |
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[32] | 128 | |
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[477] | 129 | /* Constants : */ |
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| 130 | const static double sqrt32 = 5.656854; |
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| 131 | const static double exp_m1 = 0.36787944117144232159;/* exp(-1) = 1/e */ |
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[276] | 132 | |
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[477] | 133 | /* Coefficients q[k] - for q0 = sum(q[k]*a^(-k)) |
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| 134 | * Coefficients a[k] - for q = q0+(t*t/2)*sum(a[k]*v^k) |
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| 135 | * Coefficients e[k] - for exp(q)-1 = sum(e[k]*q^k) |
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| 136 | */ |
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| 137 | const static double q1 = 0.04166669; |
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| 138 | const static double q2 = 0.02083148; |
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| 139 | const static double q3 = 0.00801191; |
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| 140 | const static double q4 = 0.00144121; |
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| 141 | const static double q5 = -7.388e-5; |
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| 142 | const static double q6 = 2.4511e-4; |
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| 143 | const static double q7 = 2.424e-4; |
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[276] | 144 | |
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[477] | 145 | const static double a1 = 0.3333333; |
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| 146 | const static double a2 = -0.250003; |
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| 147 | const static double a3 = 0.2000062; |
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| 148 | const static double a4 = -0.1662921; |
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| 149 | const static double a5 = 0.1423657; |
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| 150 | const static double a6 = -0.1367177; |
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| 151 | const static double a7 = 0.1233795; |
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[276] | 152 | |
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[477] | 153 | /* State variables [FIXME for threading!] :*/ |
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| 154 | static double aa = 0.; |
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| 155 | static double aaa = 0.; |
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| 156 | static double s, s2, d; /* no. 1 (step 1) */ |
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| 157 | static double q0, b, si, c;/* no. 2 (step 4) */ |
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[276] | 158 | |
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[477] | 159 | double e, p, q, r, t, u, v, w, x, ret_val; |
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| 160 | double a = alpha; |
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| 161 | double scale = 1.0 / beta; |
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[276] | 162 | |
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[622] | 163 | if (!R_FINITE (a) || !R_FINITE (scale) || a < 0.0 || scale <= 0.0) { |
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| 164 | it_error ("Gamma_RNG wrong parameters"); |
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[477] | 165 | } |
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[276] | 166 | |
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[622] | 167 | if (a < 1.) { /* GS algorithm for parameters a < 1 */ |
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| 168 | if (a == 0) |
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[477] | 169 | return 0.; |
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| 170 | e = 1.0 + exp_m1 * a; |
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[622] | 171 | for (;;) { //VS repeat |
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[477] | 172 | p = e * unif_rand(); |
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[622] | 173 | if (p >= 1.0) { |
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| 174 | x = -log ( (e - p) / a); |
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| 175 | if (exp_rand() >= (1.0 - a) * log (x)) |
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[477] | 176 | break; |
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| 177 | } else { |
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[622] | 178 | x = exp (log (p) / a); |
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| 179 | if (exp_rand() >= x) |
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[477] | 180 | break; |
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[276] | 181 | } |
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| 182 | } |
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[477] | 183 | return scale * x; |
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| 184 | } |
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[276] | 185 | |
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[477] | 186 | /* --- a >= 1 : GD algorithm --- */ |
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[276] | 187 | |
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[477] | 188 | /* Step 1: Recalculations of s2, s, d if a has changed */ |
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[622] | 189 | if (a != aa) { |
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[477] | 190 | aa = a; |
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| 191 | s2 = a - 0.5; |
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[622] | 192 | s = sqrt (s2); |
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[477] | 193 | d = sqrt32 - s * 12.0; |
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| 194 | } |
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| 195 | /* Step 2: t = standard normal deviate, |
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| 196 | x = (s,1/2) -normal deviate. */ |
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[276] | 197 | |
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[477] | 198 | /* immediate acceptance (i) */ |
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| 199 | t = norm_rand(); |
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| 200 | x = s + 0.5 * t; |
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| 201 | ret_val = x * x; |
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[622] | 202 | if (t >= 0.0) |
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[477] | 203 | return scale * ret_val; |
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[276] | 204 | |
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[477] | 205 | /* Step 3: u = 0,1 - uniform sample. squeeze acceptance (s) */ |
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| 206 | u = unif_rand(); |
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[622] | 207 | if ( (d * u) <= (t * t * t)) |
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[477] | 208 | return scale * ret_val; |
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[276] | 209 | |
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[477] | 210 | /* Step 4: recalculations of q0, b, si, c if necessary */ |
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[276] | 211 | |
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[622] | 212 | if (a != aaa) { |
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[477] | 213 | aaa = a; |
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| 214 | r = 1.0 / a; |
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[622] | 215 | q0 = ( ( ( ( ( (q7 * r + q6) * r + q5) * r + q4) * r + q3) * r |
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| 216 | + q2) * r + q1) * r; |
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[276] | 217 | |
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[477] | 218 | /* Approximation depending on size of parameter a */ |
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| 219 | /* The constants in the expressions for b, si and c */ |
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| 220 | /* were established by numerical experiments */ |
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[276] | 221 | |
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[622] | 222 | if (a <= 3.686) { |
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[477] | 223 | b = 0.463 + s + 0.178 * s2; |
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| 224 | si = 1.235; |
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| 225 | c = 0.195 / s - 0.079 + 0.16 * s; |
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[622] | 226 | } else if (a <= 13.022) { |
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[477] | 227 | b = 1.654 + 0.0076 * s2; |
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| 228 | si = 1.68 / s + 0.275; |
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| 229 | c = 0.062 / s + 0.024; |
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| 230 | } else { |
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| 231 | b = 1.77; |
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| 232 | si = 0.75; |
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| 233 | c = 0.1515 / s; |
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[276] | 234 | } |
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[477] | 235 | } |
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| 236 | /* Step 5: no quotient test if x not positive */ |
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[276] | 237 | |
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[622] | 238 | if (x > 0.0) { |
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[477] | 239 | /* Step 6: calculation of v and quotient q */ |
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[622] | 240 | v = t / (s + s); |
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| 241 | if (fabs (v) <= 0.25) |
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| 242 | q = q0 + 0.5 * t * t * ( ( ( ( ( (a7 * v + a6) * v + a5) * v + a4) * v |
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| 243 | + a3) * v + a2) * v + a1) * v; |
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[477] | 244 | else |
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[622] | 245 | q = q0 - s * t + 0.25 * t * t + (s2 + s2) * log (1.0 + v); |
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[477] | 246 | |
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| 247 | |
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| 248 | /* Step 7: quotient acceptance (q) */ |
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[622] | 249 | if (log (1.0 - u) <= q) |
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[477] | 250 | return scale * ret_val; |
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| 251 | } |
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| 252 | |
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[622] | 253 | for (;;) { //VS repeat |
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[477] | 254 | /* Step 8: e = standard exponential deviate |
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| 255 | * u = 0,1 -uniform deviate |
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| 256 | * t = (b,si)-double exponential (laplace) sample */ |
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| 257 | e = exp_rand(); |
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| 258 | u = unif_rand(); |
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| 259 | u = u + u - 1.0; |
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[622] | 260 | if (u < 0.0) |
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[477] | 261 | t = b - si * e; |
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| 262 | else |
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| 263 | t = b + si * e; |
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| 264 | /* Step 9: rejection if t < tau(1) = -0.71874483771719 */ |
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[622] | 265 | if (t >= -0.71874483771719) { |
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[477] | 266 | /* Step 10: calculation of v and quotient q */ |
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[622] | 267 | v = t / (s + s); |
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| 268 | if (fabs (v) <= 0.25) |
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[477] | 269 | q = q0 + 0.5 * t * t * |
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[622] | 270 | ( ( ( ( ( (a7 * v + a6) * v + a5) * v + a4) * v + a3) * v |
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| 271 | + a2) * v + a1) * v; |
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[276] | 272 | else |
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[622] | 273 | q = q0 - s * t + 0.25 * t * t + (s2 + s2) * log (1.0 + v); |
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[477] | 274 | /* Step 11: hat acceptance (h) */ |
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| 275 | /* (if q not positive go to step 8) */ |
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[622] | 276 | if (q > 0.0) { |
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[477] | 277 | // TODO: w = expm1(q); |
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[622] | 278 | w = exp (q) - 1; |
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[477] | 279 | /* ^^^^^ original code had approximation with rel.err < 2e-7 */ |
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| 280 | /* if t is rejected sample again at step 8 */ |
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[622] | 281 | if ( (c * fabs (u)) <= (w * exp (e - 0.5 * t * t))) |
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[477] | 282 | break; |
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| 283 | } |
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[276] | 284 | } |
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[477] | 285 | } /* repeat .. until `t' is accepted */ |
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| 286 | x = s + 0.5 * t; |
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| 287 | return scale * x * x; |
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| 288 | } |
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[276] | 289 | |
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| 290 | |
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[622] | 291 | bool qr (const mat &A, mat &R) |
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| 292 | { |
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[477] | 293 | int info; |
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| 294 | int m = A.rows(); |
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| 295 | int n = A.cols(); |
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| 296 | int lwork = n; |
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[622] | 297 | int k = std::min (m, n); |
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| 298 | vec tau (k); |
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| 299 | vec work (lwork); |
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[276] | 300 | |
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[477] | 301 | R = A; |
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[37] | 302 | |
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[477] | 303 | // perform workspace query for optimum lwork value |
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| 304 | int lwork_tmp = -1; |
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[622] | 305 | dgeqrf_ (&m, &n, R._data(), &m, tau._data(), work._data(), &lwork_tmp, |
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| 306 | &info); |
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| 307 | if (info == 0) { |
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| 308 | lwork = static_cast<int> (work (0)); |
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| 309 | work.set_size (lwork, false); |
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[477] | 310 | } |
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[622] | 311 | dgeqrf_ (&m, &n, R._data(), &m, tau._data(), work._data(), &lwork, &info); |
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[37] | 312 | |
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[477] | 313 | // construct R |
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[622] | 314 | for (int i = 0; i < m; i++) |
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| 315 | for (int j = 0; j < std::min (i, n); j++) |
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| 316 | R (i, j) = 0; |
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[37] | 317 | |
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[622] | 318 | return (info == 0); |
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[477] | 319 | } |
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[37] | 320 | |
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[662] | 321 | //#endif |
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[622] | 322 | std::string num2str (double d) |
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| 323 | { |
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[477] | 324 | char tmp[20];//that should do |
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[622] | 325 | sprintf (tmp, "%f", d); |
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| 326 | return std::string (tmp); |
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[477] | 327 | }; |
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[622] | 328 | std::string num2str (int i) |
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| 329 | { |
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[477] | 330 | char tmp[10];//that should do |
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[622] | 331 | sprintf (tmp, "%d", i); |
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| 332 | return std::string (tmp); |
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[477] | 333 | }; |
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[328] | 334 | |
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| 335 | // digamma |
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| 336 | // copied from C. Bonds' source |
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| 337 | #include <math.h> |
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| 338 | #define el 0.5772156649015329 |
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| 339 | |
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[622] | 340 | double psi (double x) |
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| 341 | { |
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[477] | 342 | double s, ps, xa, x2; |
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| 343 | int n, k; |
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| 344 | static double a[] = { |
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| 345 | -0.8333333333333e-01, |
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| 346 | 0.83333333333333333e-02, |
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| 347 | -0.39682539682539683e-02, |
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| 348 | 0.41666666666666667e-02, |
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| 349 | -0.75757575757575758e-02, |
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| 350 | 0.21092796092796093e-01, |
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| 351 | -0.83333333333333333e-01, |
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| 352 | 0.4432598039215686 |
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| 353 | }; |
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[328] | 354 | |
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[622] | 355 | xa = fabs (x); |
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[477] | 356 | s = 0.0; |
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[622] | 357 | if ( (x == (int) x) && (x <= 0.0)) { |
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[477] | 358 | ps = 1e308; |
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| 359 | return ps; |
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| 360 | } |
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[622] | 361 | if (xa == (int) xa) { |
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[477] | 362 | n = xa; |
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[622] | 363 | for (k = 1; k < n; k++) { |
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[477] | 364 | s += 1.0 / k; |
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| 365 | } |
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| 366 | ps = s - el; |
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[622] | 367 | } else if ( (xa + 0.5) == ( (int) (xa + 0.5))) { |
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[477] | 368 | n = xa - 0.5; |
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[622] | 369 | for (k = 1; k <= n; k++) { |
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| 370 | s += 1.0 / (2.0 * k - 1.0); |
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[477] | 371 | } |
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| 372 | ps = 2.0 * s - el - 1.386294361119891; |
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| 373 | } else { |
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[622] | 374 | if (xa < 10.0) { |
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| 375 | n = 10 - (int) xa; |
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| 376 | for (k = 0; k < n; k++) { |
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| 377 | s += 1.0 / (xa + k); |
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[477] | 378 | } |
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| 379 | xa += n; |
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| 380 | } |
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[622] | 381 | x2 = 1.0 / (xa * xa); |
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| 382 | ps = log (xa) - 0.5 / xa + x2 * ( ( ( ( ( ( (a[7] * x2 + a[6]) * x2 + a[5]) * x2 + |
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| 383 | a[4]) * x2 + a[3]) * x2 + a[2]) * x2 + a[1]) * x2 + a[0]); |
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[477] | 384 | ps -= s; |
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| 385 | } |
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[622] | 386 | if (x < 0.0) |
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| 387 | ps = ps - M_PI * std::cos (M_PI * x) / std::sin (M_PI * x) - 1.0 / x; |
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[477] | 388 | return ps; |
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[32] | 389 | } |
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[328] | 390 | |
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[622] | 391 | void triu (mat &A) |
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| 392 | { |
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| 393 | for (int i = 1;i < A.rows();i++) { // row cycle |
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| 394 | for (int j = 0; j < i; j++) {A (i, j) = 0;} |
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[508] | 395 | } |
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[328] | 396 | } |
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[579] | 397 | |
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[661] | 398 | //! Storage of randun() internals |
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[622] | 399 | class RandunStorage |
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| 400 | { |
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| 401 | const int A; |
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| 402 | const int M; |
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| 403 | static double seed; |
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| 404 | static int counter; |
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[579] | 405 | public: |
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[622] | 406 | RandunStorage() : A (16807), M (2147483647) {}; |
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[661] | 407 | //!set seed of the randun() generator |
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[622] | 408 | void set_seed (double seed0) {seed = seed0;} |
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[661] | 409 | //! generate randun() sample |
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[622] | 410 | double get() { |
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[581] | 411 | long long tmp = A * seed; |
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| 412 | tmp = tmp % M; |
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| 413 | seed = tmp; |
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[622] | 414 | counter++; |
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| 415 | return seed / M; |
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| 416 | } |
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[579] | 417 | }; |
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| 418 | static RandunStorage randun_global_storage; |
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[622] | 419 | double RandunStorage::seed = 1111111; |
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| 420 | int RandunStorage::counter = 0; |
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| 421 | double randun() {return randun_global_storage.get();}; |
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| 422 | vec randun (int n) {vec res (n); for (int i = 0;i < n;i++) {res (i) = randun();}; return res;}; |
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| 423 | mat randun (int n, int m) {mat res (n, m); for (int i = 0;i < n*m;i++) {res (i) = randun();}; return res;}; |
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| 424 | |
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[584] | 425 | ivec unique (const ivec &in) |
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| 426 | { |
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| 427 | ivec uniq (0); |
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| 428 | int j = 0; |
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| 429 | bool found = false; |
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| 430 | for (int i = 0;i < in.length(); i++) { |
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| 431 | found = false; |
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| 432 | j = 0; |
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| 433 | while ( (!found) && (j < uniq.length())) { |
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| 434 | if (in (i) == uniq (j)) found = true; |
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| 435 | j++; |
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| 436 | } |
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| 437 | if (!found) uniq = concat (uniq, in (i)); |
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| 438 | } |
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| 439 | return uniq; |
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| 440 | } |
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[579] | 441 | |
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[586] | 442 | ivec unique_complement (const ivec &in, const ivec &base) |
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| 443 | { |
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| 444 | // almost a copy of unique |
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| 445 | ivec uniq (0); |
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| 446 | int j = 0; |
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| 447 | bool found = false; |
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| 448 | for (int i = 0;i < in.length(); i++) { |
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| 449 | found = false; |
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| 450 | j = 0; |
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| 451 | while ( (!found) && (j < uniq.length())) { |
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| 452 | if (in (i) == uniq (j)) found = true; |
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| 453 | j++; |
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| 454 | } |
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| 455 | j=0; |
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| 456 | while ( (!found) && (j < base.length())) { |
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[587] | 457 | if (in (i) == base (j)) found = true; |
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[586] | 458 | j++; |
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| 459 | } |
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| 460 | if (!found) uniq = concat (uniq, in (i)); |
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| 461 | } |
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| 462 | return uniq; |
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[508] | 463 | } |
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[586] | 464 | |
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| 465 | } |
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