1 | // |
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2 | // C++ Implementation: itpp_ext |
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3 | // |
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4 | // Description: |
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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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13 | #include "itpp_ext.h" |
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14 | |
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15 | #ifndef M_PI |
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16 | #define M_PI 3.14159265358979323846 |
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17 | #endif |
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18 | // from algebra/lapack.h |
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19 | |
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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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23 | }; |
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24 | |
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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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32 | } |
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33 | return a; |
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34 | } |
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35 | |
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36 | ivec linspace ( int from, int to ) { |
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37 | int n = to - from + 1; |
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38 | int i; |
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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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42 | return iv; |
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43 | }; |
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44 | |
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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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47 | "Vec<>::set_subvector(ivec, vec<Num_T>): Indexing out " |
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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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54 | } |
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55 | } |
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56 | |
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57 | //! return vector of elements at positions given by indexlist |
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58 | vec get_vec ( const vec &v, const ivec &indexlist ) { |
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59 | int size = indexlist.size(); |
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60 | vec temp ( size ); |
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61 | for ( int i = 0; i < size; ++i ) { |
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62 | temp ( i ) = v._data() [indexlist ( i ) ]; |
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63 | } |
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64 | return temp; |
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65 | } |
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66 | |
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67 | // Gamma |
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68 | #define log std::log |
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69 | #define exp std::exp |
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70 | #define sqrt std::sqrt |
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71 | #define R_FINITE std::isfinite |
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72 | |
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73 | bvec operator> ( const vec &t1, const vec &t2 ) { |
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74 | it_assert_debug ( t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors" ); |
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75 | bvec temp ( t1.length() ); |
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76 | for ( int i = 0; i < t1.length(); i++ ) |
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77 | temp ( i ) = ( t1[i] > t2[i] ); |
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78 | return temp; |
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79 | } |
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80 | |
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81 | bvec operator< ( const vec &t1, const vec &t2 ) { |
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82 | it_assert_debug ( t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors" ); |
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83 | bvec temp ( t1.length() ); |
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84 | for ( int i = 0; i < t1.length(); i++ ) |
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85 | temp ( i ) = ( t1[i] < t2[i] ); |
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86 | return temp; |
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87 | } |
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88 | |
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89 | |
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90 | bvec operator& ( const bvec &a, const bvec &b ) { |
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91 | it_assert_debug ( b.size() == a.size(), "operator&(): Vectors of different lengths" ); |
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92 | |
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93 | bvec temp ( a.size() ); |
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94 | for ( int i = 0; i < a.size(); i++ ) { |
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95 | temp ( i ) = a ( i ) & b ( i ); |
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96 | } |
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97 | return temp; |
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98 | } |
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99 | |
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100 | bvec operator| ( const bvec &a, const bvec &b ) { |
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101 | it_assert_debug ( b.size() == a.size(), "operator|(): Vectors of different lengths" ); |
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102 | |
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103 | bvec temp ( a.size() ); |
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104 | for ( int i = 0; i < a.size(); i++ ) { |
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105 | temp ( i ) = a ( i ) | b ( i ); |
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106 | } |
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107 | return temp; |
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108 | } |
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109 | |
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110 | //! poor man's operator vec(bvec) - copied for svn version of itpp |
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111 | ivec get_from_bvec ( const ivec &v, const bvec &binlist ) { |
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112 | int size = binlist.size(); |
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113 | it_assert_debug ( v.size() == size, "Vec<>::operator()(bvec &): " |
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114 | "Wrong size of binlist vector" ); |
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115 | ivec temp ( size ); |
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116 | int j = 0; |
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117 | for ( int i = 0; i < size; ++i ) |
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118 | if ( binlist ( i ) == bin ( 1 ) ) |
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119 | temp ( j++ ) = v ( i ); |
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120 | temp.set_size ( j, true ); |
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121 | return temp; |
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122 | } |
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123 | |
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124 | |
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125 | //#if 0 |
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126 | Gamma_RNG::Gamma_RNG ( double a, double b ) { |
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127 | setup ( a, b ); |
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128 | } |
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129 | double Gamma_RNG::sample() { |
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130 | //A copy of rgamma code from the R package!! |
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131 | // |
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132 | |
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133 | /* Constants : */ |
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134 | const static double sqrt32 = 5.656854; |
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135 | const static double exp_m1 = 0.36787944117144232159;/* exp(-1) = 1/e */ |
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136 | |
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137 | /* Coefficients q[k] - for q0 = sum(q[k]*a^(-k)) |
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138 | * Coefficients a[k] - for q = q0+(t*t/2)*sum(a[k]*v^k) |
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139 | * Coefficients e[k] - for exp(q)-1 = sum(e[k]*q^k) |
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140 | */ |
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141 | const static double q1 = 0.04166669; |
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142 | const static double q2 = 0.02083148; |
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143 | const static double q3 = 0.00801191; |
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144 | const static double q4 = 0.00144121; |
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145 | const static double q5 = -7.388e-5; |
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146 | const static double q6 = 2.4511e-4; |
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147 | const static double q7 = 2.424e-4; |
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148 | |
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149 | const static double a1 = 0.3333333; |
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150 | const static double a2 = -0.250003; |
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151 | const static double a3 = 0.2000062; |
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152 | const static double a4 = -0.1662921; |
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153 | const static double a5 = 0.1423657; |
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154 | const static double a6 = -0.1367177; |
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155 | const static double a7 = 0.1233795; |
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156 | |
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157 | /* State variables [FIXME for threading!] :*/ |
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158 | static double aa = 0.; |
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159 | static double aaa = 0.; |
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160 | static double s, s2, d; /* no. 1 (step 1) */ |
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161 | static double q0, b, si, c;/* no. 2 (step 4) */ |
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162 | |
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163 | double e, p, q, r, t, u, v, w, x, ret_val; |
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164 | double a = alpha; |
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165 | double scale = 1.0 / beta; |
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166 | |
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167 | if ( !R_FINITE ( a ) || !R_FINITE ( scale ) || a < 0.0 || scale <= 0.0 ) { |
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168 | it_error ( "Gamma_RNG wrong parameters" ); |
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169 | } |
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170 | |
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171 | if ( a < 1. ) { /* GS algorithm for parameters a < 1 */ |
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172 | if ( a == 0 ) |
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173 | return 0.; |
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174 | e = 1.0 + exp_m1 * a; |
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175 | for ( ;; ) { //VS repeat |
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176 | p = e * unif_rand(); |
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177 | if ( p >= 1.0 ) { |
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178 | x = -log ( ( e - p ) / a ); |
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179 | if ( exp_rand() >= ( 1.0 - a ) * log ( x ) ) |
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180 | break; |
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181 | } else { |
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182 | x = exp ( log ( p ) / a ); |
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183 | if ( exp_rand() >= x ) |
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184 | break; |
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185 | } |
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186 | } |
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187 | return scale * x; |
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188 | } |
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189 | |
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190 | /* --- a >= 1 : GD algorithm --- */ |
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191 | |
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192 | /* Step 1: Recalculations of s2, s, d if a has changed */ |
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193 | if ( a != aa ) { |
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194 | aa = a; |
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195 | s2 = a - 0.5; |
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196 | s = sqrt ( s2 ); |
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197 | d = sqrt32 - s * 12.0; |
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198 | } |
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199 | /* Step 2: t = standard normal deviate, |
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200 | x = (s,1/2) -normal deviate. */ |
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201 | |
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202 | /* immediate acceptance (i) */ |
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203 | t = norm_rand(); |
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204 | x = s + 0.5 * t; |
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205 | ret_val = x * x; |
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206 | if ( t >= 0.0 ) |
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207 | return scale * ret_val; |
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208 | |
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209 | /* Step 3: u = 0,1 - uniform sample. squeeze acceptance (s) */ |
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210 | u = unif_rand(); |
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211 | if ( ( d * u ) <= ( t * t * t ) ) |
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212 | return scale * ret_val; |
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213 | |
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214 | /* Step 4: recalculations of q0, b, si, c if necessary */ |
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215 | |
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216 | if ( a != aaa ) { |
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217 | aaa = a; |
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218 | r = 1.0 / a; |
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219 | q0 = ( ( ( ( ( ( q7 * r + q6 ) * r + q5 ) * r + q4 ) * r + q3 ) * r |
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220 | + q2 ) * r + q1 ) * r; |
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221 | |
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222 | /* Approximation depending on size of parameter a */ |
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223 | /* The constants in the expressions for b, si and c */ |
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224 | /* were established by numerical experiments */ |
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225 | |
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226 | if ( a <= 3.686 ) { |
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227 | b = 0.463 + s + 0.178 * s2; |
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228 | si = 1.235; |
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229 | c = 0.195 / s - 0.079 + 0.16 * s; |
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230 | } else if ( a <= 13.022 ) { |
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231 | b = 1.654 + 0.0076 * s2; |
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232 | si = 1.68 / s + 0.275; |
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233 | c = 0.062 / s + 0.024; |
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234 | } else { |
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235 | b = 1.77; |
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236 | si = 0.75; |
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237 | c = 0.1515 / s; |
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238 | } |
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239 | } |
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240 | /* Step 5: no quotient test if x not positive */ |
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241 | |
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242 | if ( x > 0.0 ) { |
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243 | /* Step 6: calculation of v and quotient q */ |
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244 | v = t / ( s + s ); |
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245 | if ( fabs ( v ) <= 0.25 ) |
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246 | q = q0 + 0.5 * t * t * ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v |
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247 | + a3 ) * v + a2 ) * v + a1 ) * v; |
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248 | else |
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249 | q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
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250 | |
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251 | |
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252 | /* Step 7: quotient acceptance (q) */ |
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253 | if ( log ( 1.0 - u ) <= q ) |
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254 | return scale * ret_val; |
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255 | } |
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256 | |
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257 | for ( ;; ) { //VS repeat |
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258 | /* Step 8: e = standard exponential deviate |
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259 | * u = 0,1 -uniform deviate |
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260 | * t = (b,si)-double exponential (laplace) sample */ |
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261 | e = exp_rand(); |
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262 | u = unif_rand(); |
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263 | u = u + u - 1.0; |
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264 | if ( u < 0.0 ) |
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265 | t = b - si * e; |
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266 | else |
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267 | t = b + si * e; |
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268 | /* Step 9: rejection if t < tau(1) = -0.71874483771719 */ |
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269 | if ( t >= -0.71874483771719 ) { |
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270 | /* Step 10: calculation of v and quotient q */ |
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271 | v = t / ( s + s ); |
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272 | if ( fabs ( v ) <= 0.25 ) |
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273 | q = q0 + 0.5 * t * t * |
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274 | ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v + a3 ) * v |
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275 | + a2 ) * v + a1 ) * v; |
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276 | else |
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277 | q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
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278 | /* Step 11: hat acceptance (h) */ |
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279 | /* (if q not positive go to step 8) */ |
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280 | if ( q > 0.0 ) { |
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281 | // TODO: w = expm1(q); |
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282 | w = exp ( q ) - 1; |
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283 | /* ^^^^^ original code had approximation with rel.err < 2e-7 */ |
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284 | /* if t is rejected sample again at step 8 */ |
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285 | if ( ( c * fabs ( u ) ) <= ( w * exp ( e - 0.5 * t * t ) ) ) |
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286 | break; |
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287 | } |
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288 | } |
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289 | } /* repeat .. until `t' is accepted */ |
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290 | x = s + 0.5 * t; |
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291 | return scale * x * x; |
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292 | } |
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293 | |
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294 | |
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295 | bool qr ( const mat &A, mat &R ) { |
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296 | int info; |
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297 | int m = A.rows(); |
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298 | int n = A.cols(); |
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299 | int lwork = n; |
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300 | int k = std::min ( m, n ); |
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301 | vec tau ( k ); |
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302 | vec work ( lwork ); |
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303 | |
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304 | R = A; |
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305 | |
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306 | // perform workspace query for optimum lwork value |
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307 | int lwork_tmp = -1; |
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308 | dgeqrf_ ( &m, &n, R._data(), &m, tau._data(), work._data(), &lwork_tmp, |
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309 | &info ); |
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310 | if ( info == 0 ) { |
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311 | lwork = static_cast<int> ( work ( 0 ) ); |
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312 | work.set_size ( lwork, false ); |
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313 | } |
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314 | dgeqrf_ ( &m, &n, R._data(), &m, tau._data(), work._data(), &lwork, &info ); |
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315 | |
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316 | // construct R |
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317 | for ( int i = 0; i < m; i++ ) |
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318 | for ( int j = 0; j < std::min ( i, n ); j++ ) |
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319 | R ( i, j ) = 0; |
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320 | |
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321 | return ( info == 0 ); |
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322 | } |
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323 | |
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324 | //#endif |
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325 | std::string num2str ( double d ) { |
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326 | char tmp[20];//that should do |
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327 | sprintf ( tmp, "%f", d ); |
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328 | return std::string ( tmp ); |
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329 | }; |
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330 | std::string num2str ( int i ) { |
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331 | char tmp[10];//that should do |
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332 | sprintf ( tmp, "%d", i ); |
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333 | return std::string ( tmp ); |
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334 | }; |
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335 | |
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336 | // digamma |
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337 | // copied from C. Bonds' source |
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338 | #include <math.h> |
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339 | #define el 0.5772156649015329 |
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340 | |
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341 | double psi ( double x ) { |
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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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354 | |
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355 | xa = fabs ( x ); |
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356 | s = 0.0; |
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357 | if ( ( x == ( int ) x ) && ( x <= 0.0 ) ) { |
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358 | ps = 1e308; |
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359 | return ps; |
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360 | } |
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361 | if ( xa == ( int ) xa ) { |
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362 | n = (int) xa; |
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363 | for ( k = 1; k < n; k++ ) { |
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364 | s += 1.0 / k; |
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365 | } |
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366 | ps = s - el; |
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367 | } else if ( ( xa + 0.5 ) == ( ( int ) ( xa + 0.5 ) ) ) { |
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368 | n = (int) (xa - 0.5); |
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369 | for ( k = 1; k <= n; k++ ) { |
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370 | s += 1.0 / ( 2.0 * k - 1.0 ); |
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371 | } |
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372 | ps = 2.0 * s - el - 1.386294361119891; |
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373 | } else { |
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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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378 | } |
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379 | xa += n; |
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380 | } |
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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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384 | ps -= s; |
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385 | } |
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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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388 | return ps; |
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389 | } |
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390 | |
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391 | void triu ( mat &A ) { |
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392 | for ( int i = 1; i < A.rows(); i++ ) { // row cycle |
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393 | for ( int j = 0; (j < i) && (j<A.cols()); j++ ) { |
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394 | A ( i, j ) = 0; |
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395 | } |
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396 | } |
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397 | } |
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398 | |
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399 | //! Storage of randun() internals |
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400 | class RandunStorage { |
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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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405 | public: |
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406 | RandunStorage() : A ( 16807 ), M ( 2147483647 ) {}; |
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407 | //!set seed of the randun() generator |
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408 | void set_seed ( double seed0 ) { |
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409 | seed = seed0; |
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410 | } |
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411 | //! generate randun() sample |
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412 | double get() { |
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413 | long long tmp = (long long) (A * seed); |
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414 | tmp = tmp % M; |
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415 | seed = (double) tmp; |
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416 | counter++; |
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417 | return seed / M; |
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418 | } |
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419 | }; |
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420 | static RandunStorage randun_global_storage; |
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421 | double RandunStorage::seed = 1111111; |
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422 | int RandunStorage::counter = 0; |
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423 | double randun() { |
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424 | return randun_global_storage.get(); |
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425 | }; |
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426 | vec randun ( int n ) { |
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427 | vec res ( n ); |
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428 | for ( int i = 0; i < n; i++ ) { |
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429 | res ( i ) = randun(); |
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430 | }; |
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431 | return res; |
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432 | }; |
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433 | mat randun ( int n, int m ) { |
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434 | mat res ( n, m ); |
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435 | for ( int i = 0; i < n*m; i++ ) { |
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436 | res ( i ) = randun(); |
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437 | }; |
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438 | return res; |
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439 | }; |
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440 | |
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441 | ivec unique ( const ivec &in ) { |
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442 | ivec uniq ( 0 ); |
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443 | int j = 0; |
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444 | bool found = false; |
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445 | for ( int i = 0; i < in.length(); i++ ) { |
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446 | found = false; |
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447 | j = 0; |
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448 | while ( ( !found ) && ( j < uniq.length() ) ) { |
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449 | if ( in ( i ) == uniq ( j ) ) found = true; |
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450 | j++; |
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451 | } |
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452 | if ( !found ) uniq = concat ( uniq, in ( i ) ); |
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453 | } |
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454 | return uniq; |
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455 | } |
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456 | |
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457 | ivec unique_complement ( const ivec &in, const ivec &base ) { |
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458 | // almost a copy of unique |
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459 | ivec uniq ( 0 ); |
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460 | int j = 0; |
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461 | bool found = false; |
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462 | for ( int i = 0; i < in.length(); i++ ) { |
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463 | found = false; |
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464 | j = 0; |
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465 | while ( ( !found ) && ( j < uniq.length() ) ) { |
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466 | if ( in ( i ) == uniq ( j ) ) found = true; |
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467 | j++; |
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468 | } |
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469 | j = 0; |
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470 | while ( ( !found ) && ( j < base.length() ) ) { |
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471 | if ( in ( i ) == base ( j ) ) found = true; |
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472 | j++; |
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473 | } |
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474 | if ( !found ) uniq = concat ( uniq, in ( i ) ); |
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475 | } |
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476 | return uniq; |
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477 | } |
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478 | |
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479 | } |
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