[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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[737] | 20 | extern "C" { /* QR factorization of a general matrix A */ |
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| 21 | void dgeqrf_ ( int *m, int *n, double *a, int *lda, double *tau, double *work, |
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| 22 | int *lwork, int *info ); |
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[37] | 23 | }; |
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| 24 | |
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[737] | 25 | namespace itpp { |
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| 26 | vec empty_vec = vec ( 0 ); |
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| 27 | |
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| 28 | Array<int> to_Arr ( const ivec &indices ) { |
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| 29 | Array<int> a ( indices.size() ); |
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| 30 | for ( int i = 0; i < a.size(); i++ ) { |
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| 31 | a ( i ) = indices ( i ); |
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[145] | 32 | } |
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[477] | 33 | return a; |
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| 34 | } |
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[6] | 35 | |
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[737] | 36 | ivec linspace ( int from, int to ) { |
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[477] | 37 | int n = to - from + 1; |
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| 38 | int i; |
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[737] | 39 | it_assert_debug ( n > 0, "wrong linspace" ); |
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| 40 | ivec iv ( n ); |
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| 41 | for ( i = 0; i < n; i++ ) iv ( i ) = from + i; |
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[477] | 42 | return iv; |
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| 43 | }; |
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[86] | 44 | |
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[737] | 45 | void set_subvector ( vec &ov, const ivec &iv, const vec &v ) { |
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| 46 | it_assert_debug ( ( iv.length() <= v.length() ), |
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[477] | 47 | "Vec<>::set_subvector(ivec, vec<Num_T>): Indexing out " |
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[737] | 48 | "of range of v" ); |
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| 49 | for ( int i = 0; i < iv.length(); i++ ) { |
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| 50 | it_assert_debug ( iv ( i ) < ov.length(), |
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| 51 | "Vec<>::set_subvector(ivec, vec<Num_T>): Indexing out " |
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| 52 | "of range of v" ); |
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| 53 | ov ( iv ( i ) ) = v ( i ); |
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[145] | 54 | } |
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[477] | 55 | } |
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[145] | 56 | |
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[737] | 57 | vec get_vec ( const vec &v, const ivec &indexlist ) { |
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[477] | 58 | int size = indexlist.size(); |
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[737] | 59 | vec temp ( size ); |
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| 60 | for ( int i = 0; i < size; ++i ) { |
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| 61 | temp ( i ) = v._data() [indexlist ( i ) ]; |
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[180] | 62 | } |
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[477] | 63 | return temp; |
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| 64 | } |
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[180] | 65 | |
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[276] | 66 | // Gamma |
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[404] | 67 | #define log std::log |
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| 68 | #define exp std::exp |
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| 69 | #define sqrt std::sqrt |
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| 70 | #define R_FINITE std::isfinite |
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[11] | 71 | |
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[737] | 72 | bvec operator> ( const vec &t1, const vec &t2 ) { |
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| 73 | it_assert_debug ( t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors" ); |
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| 74 | bvec temp ( t1.length() ); |
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| 75 | for ( int i = 0; i < t1.length(); i++ ) |
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| 76 | temp ( i ) = ( t1[i] > t2[i] ); |
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[477] | 77 | return temp; |
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| 78 | } |
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[32] | 79 | |
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[737] | 80 | bvec operator< ( const vec &t1, const vec &t2 ) { |
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| 81 | it_assert_debug ( t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors" ); |
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| 82 | bvec temp ( t1.length() ); |
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| 83 | for ( int i = 0; i < t1.length(); i++ ) |
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| 84 | temp ( i ) = ( t1[i] < t2[i] ); |
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[477] | 85 | return temp; |
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| 86 | } |
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[145] | 87 | |
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| 88 | |
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[737] | 89 | bvec operator& ( const bvec &a, const bvec &b ) { |
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| 90 | it_assert_debug ( b.size() == a.size(), "operator&(): Vectors of different lengths" ); |
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[477] | 91 | |
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[737] | 92 | bvec temp ( a.size() ); |
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| 93 | for ( int i = 0; i < a.size(); i++ ) { |
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| 94 | temp ( i ) = a ( i ) & b ( i ); |
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[145] | 95 | } |
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[477] | 96 | return temp; |
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| 97 | } |
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[145] | 98 | |
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[737] | 99 | bvec operator| ( const bvec &a, const bvec &b ) { |
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| 100 | it_assert_debug ( b.size() == a.size(), "operator|(): Vectors of different lengths" ); |
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[145] | 101 | |
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[737] | 102 | bvec temp ( a.size() ); |
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| 103 | for ( int i = 0; i < a.size(); i++ ) { |
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| 104 | temp ( i ) = a ( i ) | b ( i ); |
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[145] | 105 | } |
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[477] | 106 | return temp; |
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| 107 | } |
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[32] | 108 | |
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[712] | 109 | //! poor man's operator vec(bvec) - copied for svn version of itpp |
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[737] | 110 | ivec get_from_bvec ( const ivec &v, const bvec &binlist ) { |
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| 111 | int size = binlist.size(); |
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| 112 | it_assert_debug ( v.size() == size, "Vec<>::operator()(bvec &): " |
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| 113 | "Wrong size of binlist vector" ); |
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| 114 | ivec temp ( size ); |
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| 115 | int j = 0; |
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| 116 | for ( int i = 0; i < size; ++i ) |
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| 117 | if ( binlist ( i ) == bin ( 1 ) ) |
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| 118 | temp ( j++ ) = v ( i ); |
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| 119 | temp.set_size ( j, true ); |
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| 120 | return temp; |
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[712] | 121 | } |
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| 122 | |
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| 123 | |
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[662] | 124 | //#if 0 |
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[737] | 125 | Gamma_RNG::Gamma_RNG ( double a, double b ) { |
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| 126 | setup ( a, b ); |
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[404] | 127 | } |
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[737] | 128 | double Gamma_RNG::sample() { |
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[477] | 129 | //A copy of rgamma code from the R package!! |
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| 130 | // |
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[32] | 131 | |
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[477] | 132 | /* Constants : */ |
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| 133 | const static double sqrt32 = 5.656854; |
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| 134 | const static double exp_m1 = 0.36787944117144232159;/* exp(-1) = 1/e */ |
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[276] | 135 | |
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[477] | 136 | /* Coefficients q[k] - for q0 = sum(q[k]*a^(-k)) |
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| 137 | * Coefficients a[k] - for q = q0+(t*t/2)*sum(a[k]*v^k) |
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| 138 | * Coefficients e[k] - for exp(q)-1 = sum(e[k]*q^k) |
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| 139 | */ |
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| 140 | const static double q1 = 0.04166669; |
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| 141 | const static double q2 = 0.02083148; |
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| 142 | const static double q3 = 0.00801191; |
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| 143 | const static double q4 = 0.00144121; |
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| 144 | const static double q5 = -7.388e-5; |
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| 145 | const static double q6 = 2.4511e-4; |
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| 146 | const static double q7 = 2.424e-4; |
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[276] | 147 | |
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[477] | 148 | const static double a1 = 0.3333333; |
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| 149 | const static double a2 = -0.250003; |
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| 150 | const static double a3 = 0.2000062; |
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| 151 | const static double a4 = -0.1662921; |
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| 152 | const static double a5 = 0.1423657; |
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| 153 | const static double a6 = -0.1367177; |
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| 154 | const static double a7 = 0.1233795; |
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[276] | 155 | |
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[477] | 156 | /* State variables [FIXME for threading!] :*/ |
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| 157 | static double aa = 0.; |
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| 158 | static double aaa = 0.; |
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| 159 | static double s, s2, d; /* no. 1 (step 1) */ |
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| 160 | static double q0, b, si, c;/* no. 2 (step 4) */ |
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[276] | 161 | |
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[477] | 162 | double e, p, q, r, t, u, v, w, x, ret_val; |
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| 163 | double a = alpha; |
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| 164 | double scale = 1.0 / beta; |
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[276] | 165 | |
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[737] | 166 | if ( !R_FINITE ( a ) || !R_FINITE ( scale ) || a < 0.0 || scale <= 0.0 ) { |
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| 167 | it_error ( "Gamma_RNG wrong parameters" ); |
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[477] | 168 | } |
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[276] | 169 | |
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[737] | 170 | if ( a < 1. ) { /* GS algorithm for parameters a < 1 */ |
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| 171 | if ( a == 0 ) |
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[477] | 172 | return 0.; |
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| 173 | e = 1.0 + exp_m1 * a; |
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[737] | 174 | for ( ;; ) { //VS repeat |
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[477] | 175 | p = e * unif_rand(); |
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[737] | 176 | if ( p >= 1.0 ) { |
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| 177 | x = -log ( ( e - p ) / a ); |
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| 178 | if ( exp_rand() >= ( 1.0 - a ) * log ( x ) ) |
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[477] | 179 | break; |
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| 180 | } else { |
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[737] | 181 | x = exp ( log ( p ) / a ); |
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| 182 | if ( exp_rand() >= x ) |
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[477] | 183 | break; |
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[276] | 184 | } |
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| 185 | } |
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[477] | 186 | return scale * x; |
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| 187 | } |
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[276] | 188 | |
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[477] | 189 | /* --- a >= 1 : GD algorithm --- */ |
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[276] | 190 | |
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[477] | 191 | /* Step 1: Recalculations of s2, s, d if a has changed */ |
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[737] | 192 | if ( a != aa ) { |
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[477] | 193 | aa = a; |
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| 194 | s2 = a - 0.5; |
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[737] | 195 | s = sqrt ( s2 ); |
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[477] | 196 | d = sqrt32 - s * 12.0; |
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| 197 | } |
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| 198 | /* Step 2: t = standard normal deviate, |
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| 199 | x = (s,1/2) -normal deviate. */ |
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[276] | 200 | |
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[477] | 201 | /* immediate acceptance (i) */ |
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| 202 | t = norm_rand(); |
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| 203 | x = s + 0.5 * t; |
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| 204 | ret_val = x * x; |
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[737] | 205 | if ( t >= 0.0 ) |
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[477] | 206 | return scale * ret_val; |
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[276] | 207 | |
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[477] | 208 | /* Step 3: u = 0,1 - uniform sample. squeeze acceptance (s) */ |
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| 209 | u = unif_rand(); |
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[737] | 210 | if ( ( d * u ) <= ( t * t * t ) ) |
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[477] | 211 | return scale * ret_val; |
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[276] | 212 | |
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[477] | 213 | /* Step 4: recalculations of q0, b, si, c if necessary */ |
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[276] | 214 | |
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[737] | 215 | if ( a != aaa ) { |
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[477] | 216 | aaa = a; |
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| 217 | r = 1.0 / a; |
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[737] | 218 | q0 = ( ( ( ( ( ( q7 * r + q6 ) * r + q5 ) * r + q4 ) * r + q3 ) * r |
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| 219 | + q2 ) * r + q1 ) * r; |
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[276] | 220 | |
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[477] | 221 | /* Approximation depending on size of parameter a */ |
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| 222 | /* The constants in the expressions for b, si and c */ |
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| 223 | /* were established by numerical experiments */ |
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[276] | 224 | |
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[737] | 225 | if ( a <= 3.686 ) { |
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[477] | 226 | b = 0.463 + s + 0.178 * s2; |
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| 227 | si = 1.235; |
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| 228 | c = 0.195 / s - 0.079 + 0.16 * s; |
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[737] | 229 | } else if ( a <= 13.022 ) { |
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[477] | 230 | b = 1.654 + 0.0076 * s2; |
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| 231 | si = 1.68 / s + 0.275; |
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| 232 | c = 0.062 / s + 0.024; |
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| 233 | } else { |
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| 234 | b = 1.77; |
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| 235 | si = 0.75; |
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| 236 | c = 0.1515 / s; |
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[276] | 237 | } |
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[477] | 238 | } |
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| 239 | /* Step 5: no quotient test if x not positive */ |
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[276] | 240 | |
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[737] | 241 | if ( x > 0.0 ) { |
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[477] | 242 | /* Step 6: calculation of v and quotient q */ |
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[737] | 243 | v = t / ( s + s ); |
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| 244 | if ( fabs ( v ) <= 0.25 ) |
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| 245 | q = q0 + 0.5 * t * t * ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v |
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| 246 | + a3 ) * v + a2 ) * v + a1 ) * v; |
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[477] | 247 | else |
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[737] | 248 | q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
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[477] | 249 | |
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| 250 | |
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| 251 | /* Step 7: quotient acceptance (q) */ |
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[737] | 252 | if ( log ( 1.0 - u ) <= q ) |
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[477] | 253 | return scale * ret_val; |
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| 254 | } |
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| 255 | |
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[737] | 256 | for ( ;; ) { //VS repeat |
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[477] | 257 | /* Step 8: e = standard exponential deviate |
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| 258 | * u = 0,1 -uniform deviate |
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| 259 | * t = (b,si)-double exponential (laplace) sample */ |
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| 260 | e = exp_rand(); |
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| 261 | u = unif_rand(); |
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| 262 | u = u + u - 1.0; |
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[737] | 263 | if ( u < 0.0 ) |
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[477] | 264 | t = b - si * e; |
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| 265 | else |
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| 266 | t = b + si * e; |
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| 267 | /* Step 9: rejection if t < tau(1) = -0.71874483771719 */ |
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[737] | 268 | if ( t >= -0.71874483771719 ) { |
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[477] | 269 | /* Step 10: calculation of v and quotient q */ |
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[737] | 270 | v = t / ( s + s ); |
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| 271 | if ( fabs ( v ) <= 0.25 ) |
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[477] | 272 | q = q0 + 0.5 * t * t * |
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[737] | 273 | ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v + a3 ) * v |
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| 274 | + a2 ) * v + a1 ) * v; |
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[276] | 275 | else |
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[737] | 276 | q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
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[477] | 277 | /* Step 11: hat acceptance (h) */ |
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| 278 | /* (if q not positive go to step 8) */ |
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[737] | 279 | if ( q > 0.0 ) { |
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[477] | 280 | // TODO: w = expm1(q); |
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[737] | 281 | w = exp ( q ) - 1; |
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[477] | 282 | /* ^^^^^ original code had approximation with rel.err < 2e-7 */ |
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| 283 | /* if t is rejected sample again at step 8 */ |
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[737] | 284 | if ( ( c * fabs ( u ) ) <= ( w * exp ( e - 0.5 * t * t ) ) ) |
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[477] | 285 | break; |
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| 286 | } |
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[276] | 287 | } |
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[477] | 288 | } /* repeat .. until `t' is accepted */ |
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| 289 | x = s + 0.5 * t; |
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| 290 | return scale * x * x; |
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| 291 | } |
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[276] | 292 | |
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| 293 | |
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[737] | 294 | bool qr ( const mat &A, mat &R ) { |
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[477] | 295 | int info; |
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| 296 | int m = A.rows(); |
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| 297 | int n = A.cols(); |
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| 298 | int lwork = n; |
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[737] | 299 | int k = std::min ( m, n ); |
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| 300 | vec tau ( k ); |
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| 301 | vec work ( lwork ); |
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[276] | 302 | |
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[477] | 303 | R = A; |
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[37] | 304 | |
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[477] | 305 | // perform workspace query for optimum lwork value |
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| 306 | int lwork_tmp = -1; |
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[737] | 307 | dgeqrf_ ( &m, &n, R._data(), &m, tau._data(), work._data(), &lwork_tmp, |
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| 308 | &info ); |
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| 309 | if ( info == 0 ) { |
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| 310 | lwork = static_cast<int> ( work ( 0 ) ); |
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| 311 | work.set_size ( lwork, false ); |
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[477] | 312 | } |
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[737] | 313 | dgeqrf_ ( &m, &n, R._data(), &m, tau._data(), work._data(), &lwork, &info ); |
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[37] | 314 | |
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[477] | 315 | // construct R |
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[737] | 316 | for ( int i = 0; i < m; i++ ) |
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| 317 | for ( int j = 0; j < std::min ( i, n ); j++ ) |
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| 318 | R ( i, j ) = 0; |
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[37] | 319 | |
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[737] | 320 | return ( info == 0 ); |
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[477] | 321 | } |
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[37] | 322 | |
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[662] | 323 | //#endif |
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[737] | 324 | std::string num2str ( double d ) { |
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[477] | 325 | char tmp[20];//that should do |
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[737] | 326 | sprintf ( tmp, "%f", d ); |
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| 327 | return std::string ( tmp ); |
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[477] | 328 | }; |
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[737] | 329 | std::string num2str ( int i ) { |
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[477] | 330 | char tmp[10];//that should do |
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[737] | 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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[737] | 340 | double psi ( double x ) { |
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[477] | 341 | double s, ps, xa, x2; |
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| 342 | int n, k; |
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| 343 | static double a[] = { |
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| 344 | -0.8333333333333e-01, |
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| 345 | 0.83333333333333333e-02, |
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| 346 | -0.39682539682539683e-02, |
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| 347 | 0.41666666666666667e-02, |
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| 348 | -0.75757575757575758e-02, |
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| 349 | 0.21092796092796093e-01, |
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| 350 | -0.83333333333333333e-01, |
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| 351 | 0.4432598039215686 |
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| 352 | }; |
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[328] | 353 | |
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[737] | 354 | xa = fabs ( x ); |
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[477] | 355 | s = 0.0; |
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[737] | 356 | if ( ( x == ( int ) x ) && ( x <= 0.0 ) ) { |
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[477] | 357 | ps = 1e308; |
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| 358 | return ps; |
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| 359 | } |
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[737] | 360 | if ( xa == ( int ) xa ) { |
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[766] | 361 | n = (int) xa; |
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[737] | 362 | for ( k = 1; k < n; k++ ) { |
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[477] | 363 | s += 1.0 / k; |
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| 364 | } |
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| 365 | ps = s - el; |
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[737] | 366 | } else if ( ( xa + 0.5 ) == ( ( int ) ( xa + 0.5 ) ) ) { |
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[766] | 367 | n = (int) (xa - 0.5); |
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[737] | 368 | for ( k = 1; k <= n; k++ ) { |
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| 369 | s += 1.0 / ( 2.0 * k - 1.0 ); |
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[477] | 370 | } |
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| 371 | ps = 2.0 * s - el - 1.386294361119891; |
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| 372 | } else { |
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[737] | 373 | if ( xa < 10.0 ) { |
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| 374 | n = 10 - ( int ) xa; |
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| 375 | for ( k = 0; k < n; k++ ) { |
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| 376 | s += 1.0 / ( xa + k ); |
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[477] | 377 | } |
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| 378 | xa += n; |
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| 379 | } |
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[737] | 380 | x2 = 1.0 / ( xa * xa ); |
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| 381 | ps = log ( xa ) - 0.5 / xa + x2 * ( ( ( ( ( ( ( a[7] * x2 + a[6] ) * x2 + a[5] ) * x2 + |
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| 382 | a[4] ) * x2 + a[3] ) * x2 + a[2] ) * x2 + a[1] ) * x2 + a[0] ); |
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[477] | 383 | ps -= s; |
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| 384 | } |
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[737] | 385 | if ( x < 0.0 ) |
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| 386 | ps = ps - M_PI * std::cos ( M_PI * x ) / std::sin ( M_PI * x ) - 1.0 / x; |
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[477] | 387 | return ps; |
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[32] | 388 | } |
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[328] | 389 | |
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[737] | 390 | void triu ( mat &A ) { |
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| 391 | for ( int i = 1; i < A.rows(); i++ ) { // row cycle |
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[787] | 392 | for ( int j = 0; (j < i) && (j<A.cols()); j++ ) { |
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[737] | 393 | A ( i, j ) = 0; |
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| 394 | } |
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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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[737] | 399 | class RandunStorage { |
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| 400 | const int A; |
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| 401 | const int M; |
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| 402 | static double seed; |
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| 403 | static int counter; |
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| 404 | public: |
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| 405 | RandunStorage() : A ( 16807 ), M ( 2147483647 ) {}; |
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| 406 | //!set seed of the randun() generator |
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| 407 | void set_seed ( double seed0 ) { |
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| 408 | seed = seed0; |
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| 409 | } |
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| 410 | //! generate randun() sample |
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| 411 | double get() { |
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[869] | 412 | long long tmp = (long long) (A * seed); |
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[737] | 413 | tmp = tmp % M; |
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| 414 | seed = tmp; |
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| 415 | counter++; |
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| 416 | return seed / M; |
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| 417 | } |
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[579] | 418 | }; |
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| 419 | static RandunStorage randun_global_storage; |
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[622] | 420 | double RandunStorage::seed = 1111111; |
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| 421 | int RandunStorage::counter = 0; |
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[737] | 422 | double randun() { |
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| 423 | return randun_global_storage.get(); |
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| 424 | }; |
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| 425 | vec randun ( int n ) { |
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| 426 | vec res ( n ); |
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| 427 | for ( int i = 0; i < n; i++ ) { |
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| 428 | res ( i ) = randun(); |
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| 429 | }; |
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| 430 | return res; |
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| 431 | }; |
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| 432 | mat randun ( int n, int m ) { |
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| 433 | mat res ( n, m ); |
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| 434 | for ( int i = 0; i < n*m; i++ ) { |
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| 435 | res ( i ) = randun(); |
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| 436 | }; |
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| 437 | return res; |
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| 438 | }; |
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[622] | 439 | |
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[737] | 440 | ivec unique ( const ivec &in ) { |
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| 441 | ivec uniq ( 0 ); |
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[584] | 442 | int j = 0; |
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| 443 | bool found = false; |
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[737] | 444 | for ( int i = 0; i < in.length(); i++ ) { |
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[584] | 445 | found = false; |
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| 446 | j = 0; |
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[737] | 447 | while ( ( !found ) && ( j < uniq.length() ) ) { |
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| 448 | if ( in ( i ) == uniq ( j ) ) found = true; |
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[584] | 449 | j++; |
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| 450 | } |
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[737] | 451 | if ( !found ) uniq = concat ( uniq, in ( i ) ); |
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[584] | 452 | } |
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| 453 | return uniq; |
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| 454 | } |
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[579] | 455 | |
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[737] | 456 | ivec unique_complement ( const ivec &in, const ivec &base ) { |
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[586] | 457 | // almost a copy of unique |
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[737] | 458 | ivec uniq ( 0 ); |
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[586] | 459 | int j = 0; |
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| 460 | bool found = false; |
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[737] | 461 | for ( int i = 0; i < in.length(); i++ ) { |
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[586] | 462 | found = false; |
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| 463 | j = 0; |
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[737] | 464 | while ( ( !found ) && ( j < uniq.length() ) ) { |
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| 465 | if ( in ( i ) == uniq ( j ) ) found = true; |
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[586] | 466 | j++; |
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| 467 | } |
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[737] | 468 | j = 0; |
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| 469 | while ( ( !found ) && ( j < base.length() ) ) { |
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| 470 | if ( in ( i ) == base ( j ) ) found = true; |
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[586] | 471 | j++; |
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| 472 | } |
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[737] | 473 | if ( !found ) uniq = concat ( uniq, in ( i ) ); |
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[586] | 474 | } |
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| 475 | return uniq; |
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[508] | 476 | } |
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[586] | 477 | |
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| 478 | } |
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