| 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 | Array<int> to_Arr ( const ivec &indices ) { |
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| 27 | Array<int> a ( indices.size() ); |
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| 28 | for ( int i = 0; i < a.size(); i++ ) { |
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| 29 | a ( i ) = indices ( i ); |
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| 30 | } |
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| 31 | return a; |
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| 32 | } |
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| 33 | |
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| 34 | ivec linspace ( int from, int to ) { |
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| 35 | int n=to-from+1; |
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| 36 | int i; |
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| 37 | it_assert_debug ( n>0,"wrong linspace" ); |
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| 38 | ivec iv ( n ); for ( i=0;i<n;i++ ) iv ( i ) =from+i; |
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| 39 | return iv; |
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| 40 | }; |
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| 41 | |
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| 42 | void set_subvector ( vec &ov, const ivec &iv, const vec &v ) |
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| 43 | { |
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| 44 | it_assert_debug ( ( iv.length() <=v.length() ), |
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| 45 | "Vec<>::set_subvector(ivec, vec<Num_T>): Indexing out " |
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| 46 | "of range of v" ); |
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| 47 | for ( int i = 0; i < iv.length(); i++ ) { |
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| 48 | it_assert_debug ( iv ( i ) <ov.length(), |
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| 49 | "Vec<>::set_subvector(ivec, vec<Num_T>): Indexing out " |
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| 50 | "of range of v" ); |
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| 51 | ov ( iv ( i ) ) = v ( i ); |
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| 52 | } |
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| 53 | } |
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| 54 | |
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| 55 | vec get_vec(const vec &v, const ivec &indexlist){ |
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| 56 | int size = indexlist.size(); |
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| 57 | vec temp(size); |
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| 58 | for (int i = 0; i < size; ++i) { |
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| 59 | temp(i) = v._data()[indexlist(i)]; |
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| 60 | } |
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| 61 | return temp; |
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| 62 | } |
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| 63 | |
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| 64 | // Gamma |
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| 65 | #define log std::log |
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| 66 | #define exp std::exp |
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| 67 | #define sqrt std::sqrt |
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| 68 | #define R_FINITE std::isfinite |
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| 69 | |
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| 70 | bvec operator>(const vec &t1, const vec &t2) { |
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| 71 | it_assert_debug(t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors"); |
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| 72 | bvec temp(t1.length()); |
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| 73 | for (int i = 0; i < t1.length(); i++) |
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| 74 | temp(i) = (t1[i] > t2[i]); |
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| 75 | return temp; |
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| 76 | } |
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| 77 | |
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| 78 | bvec operator<(const vec &t1, const vec &t2) { |
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| 79 | it_assert_debug(t1.length() == t2.length(), "Vec<>::operator>(): different size of vectors"); |
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| 80 | bvec temp(t1.length()); |
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| 81 | for (int i = 0; i < t1.length(); i++) |
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| 82 | temp(i) = (t1[i] < t2[i]); |
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| 83 | return temp; |
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| 84 | } |
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| 85 | |
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| 86 | |
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| 87 | bvec operator& ( const bvec &a, const bvec &b ) { |
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| 88 | it_assert_debug ( b.size() ==a.size(), "operator&(): Vectors of different lengths" ); |
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| 89 | |
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| 90 | bvec temp ( a.size() ); |
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| 91 | for ( int i = 0;i < a.size();i++ ) { |
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| 92 | temp ( i ) = a ( i ) & b ( i ); |
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| 93 | } |
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| 94 | return temp; |
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| 95 | } |
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| 96 | |
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| 97 | bvec operator| ( const bvec &a, const bvec &b ) { |
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| 98 | it_assert_debug ( b.size() !=a.size(), "operator&(): Vectors of different lengths" ); |
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| 99 | |
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| 100 | bvec temp ( a.size() ); |
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| 101 | for ( int i = 0;i < a.size();i++ ) { |
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| 102 | temp ( i ) = a ( i ) | b ( i ); |
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| 103 | } |
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| 104 | return temp; |
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| 105 | } |
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| 106 | |
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| 107 | //#if 0 |
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| 108 | Gamma_RNG::Gamma_RNG ( double a, double b ) { |
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| 109 | setup ( a,b ); |
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| 110 | } |
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| 111 | double Gamma_RNG::sample() { |
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| 112 | //A copy of rgamma code from the R package!! |
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| 113 | // |
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| 114 | |
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| 115 | /* Constants : */ |
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| 116 | const static double sqrt32 = 5.656854; |
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| 117 | const static double exp_m1 = 0.36787944117144232159;/* exp(-1) = 1/e */ |
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| 118 | |
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| 119 | /* Coefficients q[k] - for q0 = sum(q[k]*a^(-k)) |
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| 120 | * Coefficients a[k] - for q = q0+(t*t/2)*sum(a[k]*v^k) |
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| 121 | * Coefficients e[k] - for exp(q)-1 = sum(e[k]*q^k) |
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| 122 | */ |
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| 123 | const static double q1 = 0.04166669; |
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| 124 | const static double q2 = 0.02083148; |
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| 125 | const static double q3 = 0.00801191; |
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| 126 | const static double q4 = 0.00144121; |
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| 127 | const static double q5 = -7.388e-5; |
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| 128 | const static double q6 = 2.4511e-4; |
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| 129 | const static double q7 = 2.424e-4; |
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| 130 | |
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| 131 | const static double a1 = 0.3333333; |
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| 132 | const static double a2 = -0.250003; |
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| 133 | const static double a3 = 0.2000062; |
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| 134 | const static double a4 = -0.1662921; |
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| 135 | const static double a5 = 0.1423657; |
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| 136 | const static double a6 = -0.1367177; |
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| 137 | const static double a7 = 0.1233795; |
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| 138 | |
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| 139 | /* State variables [FIXME for threading!] :*/ |
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| 140 | static double aa = 0.; |
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| 141 | static double aaa = 0.; |
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| 142 | static double s, s2, d; /* no. 1 (step 1) */ |
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| 143 | static double q0, b, si, c;/* no. 2 (step 4) */ |
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| 144 | |
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| 145 | double e, p, q, r, t, u, v, w, x, ret_val; |
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| 146 | double a=alpha; |
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| 147 | double scale=1.0/beta; |
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| 148 | |
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| 149 | if ( !R_FINITE ( a ) || !R_FINITE ( scale ) || a < 0.0 || scale <= 0.0 ) |
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| 150 | {it_error ( "Gamma_RNG wrong parameters" );} |
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| 151 | |
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| 152 | if ( a < 1. ) { /* GS algorithm for parameters a < 1 */ |
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| 153 | if ( a == 0 ) |
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| 154 | return 0.; |
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| 155 | e = 1.0 + exp_m1 * a; |
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| 156 | for ( ;; ) { //VS repeat |
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| 157 | p = e * unif_rand(); |
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| 158 | if ( p >= 1.0 ) { |
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| 159 | x = -log ( ( e - p ) / a ); |
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| 160 | if ( exp_rand() >= ( 1.0 - a ) * log ( x ) ) |
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| 161 | break; |
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| 162 | } |
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| 163 | else { |
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| 164 | x = exp ( log ( p ) / a ); |
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| 165 | if ( exp_rand() >= x ) |
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| 166 | break; |
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| 167 | } |
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| 168 | } |
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| 169 | return scale * x; |
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| 170 | } |
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| 171 | |
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| 172 | /* --- a >= 1 : GD algorithm --- */ |
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| 173 | |
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| 174 | /* Step 1: Recalculations of s2, s, d if a has changed */ |
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| 175 | if ( a != aa ) { |
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| 176 | aa = a; |
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| 177 | s2 = a - 0.5; |
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| 178 | s = sqrt ( s2 ); |
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| 179 | d = sqrt32 - s * 12.0; |
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| 180 | } |
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| 181 | /* Step 2: t = standard normal deviate, |
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| 182 | x = (s,1/2) -normal deviate. */ |
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| 183 | |
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| 184 | /* immediate acceptance (i) */ |
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| 185 | t = norm_rand(); |
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| 186 | x = s + 0.5 * t; |
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| 187 | ret_val = x * x; |
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| 188 | if ( t >= 0.0 ) |
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| 189 | return scale * ret_val; |
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| 190 | |
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| 191 | /* Step 3: u = 0,1 - uniform sample. squeeze acceptance (s) */ |
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| 192 | u = unif_rand(); |
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| 193 | if ( ( d * u ) <= ( t * t * t ) ) |
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| 194 | return scale * ret_val; |
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| 195 | |
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| 196 | /* Step 4: recalculations of q0, b, si, c if necessary */ |
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| 197 | |
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| 198 | if ( a != aaa ) { |
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| 199 | aaa = a; |
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| 200 | r = 1.0 / a; |
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| 201 | q0 = ( ( ( ( ( ( q7 * r + q6 ) * r + q5 ) * r + q4 ) * r + q3 ) * r |
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| 202 | + q2 ) * r + q1 ) * r; |
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| 203 | |
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| 204 | /* Approximation depending on size of parameter a */ |
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| 205 | /* The constants in the expressions for b, si and c */ |
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| 206 | /* were established by numerical experiments */ |
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| 207 | |
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| 208 | if ( a <= 3.686 ) { |
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| 209 | b = 0.463 + s + 0.178 * s2; |
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| 210 | si = 1.235; |
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| 211 | c = 0.195 / s - 0.079 + 0.16 * s; |
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| 212 | } |
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| 213 | else if ( a <= 13.022 ) { |
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| 214 | b = 1.654 + 0.0076 * s2; |
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| 215 | si = 1.68 / s + 0.275; |
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| 216 | c = 0.062 / s + 0.024; |
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| 217 | } |
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| 218 | else { |
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| 219 | b = 1.77; |
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| 220 | si = 0.75; |
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| 221 | c = 0.1515 / s; |
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| 222 | } |
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| 223 | } |
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| 224 | /* Step 5: no quotient test if x not positive */ |
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| 225 | |
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| 226 | if ( x > 0.0 ) { |
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| 227 | /* Step 6: calculation of v and quotient q */ |
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| 228 | v = t / ( s + s ); |
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| 229 | if ( fabs ( v ) <= 0.25 ) |
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| 230 | q = q0 + 0.5 * t * t * ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v |
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| 231 | + a3 ) * v + a2 ) * v + a1 ) * v; |
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| 232 | else |
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| 233 | q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
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| 234 | |
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| 235 | |
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| 236 | /* Step 7: quotient acceptance (q) */ |
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| 237 | if ( log ( 1.0 - u ) <= q ) |
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| 238 | return scale * ret_val; |
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| 239 | } |
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| 240 | |
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| 241 | for ( ;; ) { //VS repeat |
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| 242 | /* Step 8: e = standard exponential deviate |
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| 243 | * u = 0,1 -uniform deviate |
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| 244 | * t = (b,si)-double exponential (laplace) sample */ |
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| 245 | e = exp_rand(); |
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| 246 | u = unif_rand(); |
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| 247 | u = u + u - 1.0; |
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| 248 | if ( u < 0.0 ) |
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| 249 | t = b - si * e; |
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| 250 | else |
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| 251 | t = b + si * e; |
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| 252 | /* Step 9: rejection if t < tau(1) = -0.71874483771719 */ |
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| 253 | if ( t >= -0.71874483771719 ) { |
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| 254 | /* Step 10: calculation of v and quotient q */ |
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| 255 | v = t / ( s + s ); |
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| 256 | if ( fabs ( v ) <= 0.25 ) |
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| 257 | q = q0 + 0.5 * t * t * |
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| 258 | ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v + a3 ) * v |
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| 259 | + a2 ) * v + a1 ) * v; |
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| 260 | else |
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| 261 | q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
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| 262 | /* Step 11: hat acceptance (h) */ |
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| 263 | /* (if q not positive go to step 8) */ |
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| 264 | if ( q > 0.0 ) { |
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| 265 | // TODO: w = expm1(q); |
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| 266 | w = exp ( q )-1; |
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| 267 | /* ^^^^^ original code had approximation with rel.err < 2e-7 */ |
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| 268 | /* if t is rejected sample again at step 8 */ |
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| 269 | if ( ( c * fabs ( u ) ) <= ( w * exp ( e - 0.5 * t * t ) ) ) |
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| 270 | break; |
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| 271 | } |
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| 272 | } |
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| 273 | } /* repeat .. until `t' is accepted */ |
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| 274 | x = s + 0.5 * t; |
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| 275 | return scale * x * x; |
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| 276 | } |
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| 277 | |
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| 278 | |
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| 279 | bool qr ( const mat &A, mat &R ) { |
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| 280 | int info; |
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| 281 | int m = A.rows(); |
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| 282 | int n = A.cols(); |
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| 283 | int lwork = n; |
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| 284 | int k = std::min ( m, n ); |
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| 285 | vec tau ( k ); |
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| 286 | vec work ( lwork ); |
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| 287 | |
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| 288 | R = A; |
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| 289 | |
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| 290 | // perform workspace query for optimum lwork value |
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| 291 | int lwork_tmp = -1; |
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| 292 | dgeqrf_ ( &m, &n, R._data(), &m, tau._data(), work._data(), &lwork_tmp, |
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| 293 | &info ); |
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| 294 | if ( info == 0 ) { |
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| 295 | lwork = static_cast<int> ( work ( 0 ) ); |
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| 296 | work.set_size ( lwork, false ); |
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| 297 | } |
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| 298 | dgeqrf_ ( &m, &n, R._data(), &m, tau._data(), work._data(), &lwork, &info ); |
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| 299 | |
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| 300 | // construct R |
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| 301 | for ( int i=0; i<m; i++ ) |
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| 302 | for ( int j=0; j<std::min ( i,n ); j++ ) |
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| 303 | R ( i,j ) = 0; |
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| 304 | |
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| 305 | return ( info==0 ); |
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| 306 | } |
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| 307 | |
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| 308 | //#endif |
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| 309 | std::string num2str(double d){ |
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| 310 | char tmp[20];//that should do |
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| 311 | sprintf(tmp,"%f",d); |
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| 312 | return std::string(tmp); |
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| 313 | }; |
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| 314 | std::string num2str(int i){ |
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| 315 | char tmp[10];//that should do |
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| 316 | sprintf(tmp,"%d",i); |
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| 317 | return std::string(tmp); |
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| 318 | }; |
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| 319 | |
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| 320 | // digamma |
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| 321 | // copied from C. Bonds' source |
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| 322 | #include <math.h> |
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| 323 | #define el 0.5772156649015329 |
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| 324 | |
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| 325 | double psi(double x) { |
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| 326 | double s,ps,xa,x2; |
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| 327 | int n,k; |
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| 328 | static double a[] = { |
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| 329 | -0.8333333333333e-01, |
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| 330 | 0.83333333333333333e-02, |
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| 331 | -0.39682539682539683e-02, |
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| 332 | 0.41666666666666667e-02, |
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| 333 | -0.75757575757575758e-02, |
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| 334 | 0.21092796092796093e-01, |
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| 335 | -0.83333333333333333e-01, |
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| 336 | 0.4432598039215686}; |
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| 337 | |
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| 338 | xa = fabs(x); |
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| 339 | s = 0.0; |
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| 340 | if ((x == (int)x) && (x <= 0.0)) { |
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| 341 | ps = 1e308; |
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| 342 | return ps; |
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| 343 | } |
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| 344 | if (xa == (int)xa) { |
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| 345 | n = xa; |
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| 346 | for (k=1;k<n;k++) { |
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| 347 | s += 1.0/k; |
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| 348 | } |
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| 349 | ps = s-el; |
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| 350 | } |
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| 351 | else if ((xa+0.5) == ((int)(xa+0.5))) { |
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| 352 | n = xa-0.5; |
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| 353 | for (k=1;k<=n;k++) { |
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| 354 | s += 1.0/(2.0*k-1.0); |
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| 355 | } |
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| 356 | ps = 2.0*s-el-1.386294361119891; |
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| 357 | } |
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| 358 | else { |
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| 359 | if (xa < 10.0) { |
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| 360 | n = 10-(int)xa; |
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| 361 | for (k=0;k<n;k++) { |
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| 362 | s += 1.0/(xa+k); |
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| 363 | } |
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| 364 | xa += n; |
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| 365 | } |
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| 366 | x2 = 1.0/(xa*xa); |
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| 367 | ps = log(xa)-0.5/xa+x2*(((((((a[7]*x2+a[6])*x2+a[5])*x2+ |
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| 368 | a[4])*x2+a[3])*x2+a[2])*x2+a[1])*x2+a[0]); |
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| 369 | ps -= s; |
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| 370 | } |
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| 371 | if (x < 0.0) |
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| 372 | ps = ps - M_PI*std::cos(M_PI*x)/std::sin(M_PI*x)-1.0/x; |
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| 373 | return ps; |
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| 374 | } |
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| 375 | |
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| 376 | } |
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