| 87 | | // #define log std::log |
| 88 | | // #define exp std::exp |
| 89 | | // #define sqrt std::sqrt |
| 90 | | // #define R_FINITE std::isfinite |
| 91 | | // |
| 92 | | // double Gamma_RNG::sample() { |
| 93 | | // //A copy of rgamma code from the R package!! |
| 94 | | // // |
| 95 | | // |
| 96 | | // /* Constants : */ |
| 97 | | // const static double sqrt32 = 5.656854; |
| 98 | | // const static double exp_m1 = 0.36787944117144232159;/* exp(-1) = 1/e */ |
| 99 | | // |
| 100 | | // /* Coefficients q[k] - for q0 = sum(q[k]*a^(-k)) |
| 101 | | // * Coefficients a[k] - for q = q0+(t*t/2)*sum(a[k]*v^k) |
| 102 | | // * Coefficients e[k] - for exp(q)-1 = sum(e[k]*q^k) |
| 103 | | // */ |
| 104 | | // const static double q1 = 0.04166669; |
| 105 | | // const static double q2 = 0.02083148; |
| 106 | | // const static double q3 = 0.00801191; |
| 107 | | // const static double q4 = 0.00144121; |
| 108 | | // const static double q5 = -7.388e-5; |
| 109 | | // const static double q6 = 2.4511e-4; |
| 110 | | // const static double q7 = 2.424e-4; |
| 111 | | // |
| 112 | | // const static double a1 = 0.3333333; |
| 113 | | // const static double a2 = -0.250003; |
| 114 | | // const static double a3 = 0.2000062; |
| 115 | | // const static double a4 = -0.1662921; |
| 116 | | // const static double a5 = 0.1423657; |
| 117 | | // const static double a6 = -0.1367177; |
| 118 | | // const static double a7 = 0.1233795; |
| 119 | | // |
| 120 | | // /* State variables [FIXME for threading!] :*/ |
| 121 | | // static double aa = 0.; |
| 122 | | // static double aaa = 0.; |
| 123 | | // static double s, s2, d; /* no. 1 (step 1) */ |
| 124 | | // static double q0, b, si, c;/* no. 2 (step 4) */ |
| 125 | | // |
| 126 | | // double e, p, q, r, t, u, v, w, x, ret_val; |
| 127 | | // double a=alpha; |
| 128 | | // double scale=1.0/beta; |
| 129 | | // |
| 130 | | // if ( !R_FINITE ( a ) || !R_FINITE ( scale ) || a < 0.0 || scale <= 0.0 ) |
| 131 | | // {it_error ( "Gamma_RNG wrong parameters" );} |
| 132 | | // |
| 133 | | // if ( a < 1. ) { /* GS algorithm for parameters a < 1 */ |
| 134 | | // if ( a == 0 ) |
| 135 | | // return 0.; |
| 136 | | // e = 1.0 + exp_m1 * a; |
| 137 | | // for ( ;; ) { //VS repeat |
| 138 | | // p = e * unif_rand(); |
| 139 | | // if ( p >= 1.0 ) { |
| 140 | | // x = -log ( ( e - p ) / a ); |
| 141 | | // if ( exp_rand() >= ( 1.0 - a ) * log ( x ) ) |
| 142 | | // break; |
| 143 | | // } |
| 144 | | // else { |
| 145 | | // x = exp ( log ( p ) / a ); |
| 146 | | // if ( exp_rand() >= x ) |
| 147 | | // break; |
| 148 | | // } |
| 149 | | // } |
| 150 | | // return scale * x; |
| 151 | | // } |
| 152 | | // |
| 153 | | // /* --- a >= 1 : GD algorithm --- */ |
| 154 | | // |
| 155 | | // /* Step 1: Recalculations of s2, s, d if a has changed */ |
| 156 | | // if ( a != aa ) { |
| 157 | | // aa = a; |
| 158 | | // s2 = a - 0.5; |
| 159 | | // s = sqrt ( s2 ); |
| 160 | | // d = sqrt32 - s * 12.0; |
| 161 | | // } |
| 162 | | // /* Step 2: t = standard normal deviate, |
| 163 | | // x = (s,1/2) -normal deviate. */ |
| 164 | | // |
| 165 | | // /* immediate acceptance (i) */ |
| 166 | | // t = norm_rand(); |
| 167 | | // x = s + 0.5 * t; |
| 168 | | // ret_val = x * x; |
| 169 | | // if ( t >= 0.0 ) |
| 170 | | // return scale * ret_val; |
| 171 | | // |
| 172 | | // /* Step 3: u = 0,1 - uniform sample. squeeze acceptance (s) */ |
| 173 | | // u = unif_rand(); |
| 174 | | // if ( ( d * u ) <= ( t * t * t ) ) |
| 175 | | // return scale * ret_val; |
| 176 | | // |
| 177 | | // /* Step 4: recalculations of q0, b, si, c if necessary */ |
| 178 | | // |
| 179 | | // if ( a != aaa ) { |
| 180 | | // aaa = a; |
| 181 | | // r = 1.0 / a; |
| 182 | | // q0 = ( ( ( ( ( ( q7 * r + q6 ) * r + q5 ) * r + q4 ) * r + q3 ) * r |
| 183 | | // + q2 ) * r + q1 ) * r; |
| 184 | | // |
| 185 | | // /* Approximation depending on size of parameter a */ |
| 186 | | // /* The constants in the expressions for b, si and c */ |
| 187 | | // /* were established by numerical experiments */ |
| 188 | | // |
| 189 | | // if ( a <= 3.686 ) { |
| 190 | | // b = 0.463 + s + 0.178 * s2; |
| 191 | | // si = 1.235; |
| 192 | | // c = 0.195 / s - 0.079 + 0.16 * s; |
| 193 | | // } |
| 194 | | // else if ( a <= 13.022 ) { |
| 195 | | // b = 1.654 + 0.0076 * s2; |
| 196 | | // si = 1.68 / s + 0.275; |
| 197 | | // c = 0.062 / s + 0.024; |
| 198 | | // } |
| 199 | | // else { |
| 200 | | // b = 1.77; |
| 201 | | // si = 0.75; |
| 202 | | // c = 0.1515 / s; |
| 203 | | // } |
| 204 | | // } |
| 205 | | // /* Step 5: no quotient test if x not positive */ |
| 206 | | // |
| 207 | | // if ( x > 0.0 ) { |
| 208 | | // /* Step 6: calculation of v and quotient q */ |
| 209 | | // v = t / ( s + s ); |
| 210 | | // if ( fabs ( v ) <= 0.25 ) |
| 211 | | // q = q0 + 0.5 * t * t * ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v |
| 212 | | // + a3 ) * v + a2 ) * v + a1 ) * v; |
| 213 | | // else |
| 214 | | // q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
| 215 | | // |
| 216 | | // |
| 217 | | // /* Step 7: quotient acceptance (q) */ |
| 218 | | // if ( log ( 1.0 - u ) <= q ) |
| 219 | | // return scale * ret_val; |
| 220 | | // } |
| 221 | | // |
| 222 | | // for ( ;; ) { //VS repeat |
| 223 | | // /* Step 8: e = standard exponential deviate |
| 224 | | // * u = 0,1 -uniform deviate |
| 225 | | // * t = (b,si)-double exponential (laplace) sample */ |
| 226 | | // e = exp_rand(); |
| 227 | | // u = unif_rand(); |
| 228 | | // u = u + u - 1.0; |
| 229 | | // if ( u < 0.0 ) |
| 230 | | // t = b - si * e; |
| 231 | | // else |
| 232 | | // t = b + si * e; |
| 233 | | // /* Step 9: rejection if t < tau(1) = -0.71874483771719 */ |
| 234 | | // if ( t >= -0.71874483771719 ) { |
| 235 | | // /* Step 10: calculation of v and quotient q */ |
| 236 | | // v = t / ( s + s ); |
| 237 | | // if ( fabs ( v ) <= 0.25 ) |
| 238 | | // q = q0 + 0.5 * t * t * |
| 239 | | // ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v + a3 ) * v |
| 240 | | // + a2 ) * v + a1 ) * v; |
| 241 | | // else |
| 242 | | // q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
| 243 | | // /* Step 11: hat acceptance (h) */ |
| 244 | | // /* (if q not positive go to step 8) */ |
| 245 | | // if ( q > 0.0 ) { |
| 246 | | // // TODO: w = expm1(q); |
| 247 | | // w = exp ( q )-1; |
| 248 | | // /* ^^^^^ original code had approximation with rel.err < 2e-7 */ |
| 249 | | // /* if t is rejected sample again at step 8 */ |
| 250 | | // if ( ( c * fabs ( u ) ) <= ( w * exp ( e - 0.5 * t * t ) ) ) |
| 251 | | // break; |
| 252 | | // } |
| 253 | | // } |
| 254 | | // } /* repeat .. until `t' is accepted */ |
| 255 | | // x = s + 0.5 * t; |
| 256 | | // return scale * x * x; |
| 257 | | // } |
| | 87 | #define log std::log |
| | 88 | #define exp std::exp |
| | 89 | #define sqrt std::sqrt |
| | 90 | #define R_FINITE std::isfinite |
| | 91 | |
| | 92 | double Gamma_RNG::sample() { |
| | 93 | //A copy of rgamma code from the R package!! |
| | 94 | // |
| | 95 | |
| | 96 | /* Constants : */ |
| | 97 | const static double sqrt32 = 5.656854; |
| | 98 | const static double exp_m1 = 0.36787944117144232159;/* exp(-1) = 1/e */ |
| | 99 | |
| | 100 | /* Coefficients q[k] - for q0 = sum(q[k]*a^(-k)) |
| | 101 | * Coefficients a[k] - for q = q0+(t*t/2)*sum(a[k]*v^k) |
| | 102 | * Coefficients e[k] - for exp(q)-1 = sum(e[k]*q^k) |
| | 103 | */ |
| | 104 | const static double q1 = 0.04166669; |
| | 105 | const static double q2 = 0.02083148; |
| | 106 | const static double q3 = 0.00801191; |
| | 107 | const static double q4 = 0.00144121; |
| | 108 | const static double q5 = -7.388e-5; |
| | 109 | const static double q6 = 2.4511e-4; |
| | 110 | const static double q7 = 2.424e-4; |
| | 111 | |
| | 112 | const static double a1 = 0.3333333; |
| | 113 | const static double a2 = -0.250003; |
| | 114 | const static double a3 = 0.2000062; |
| | 115 | const static double a4 = -0.1662921; |
| | 116 | const static double a5 = 0.1423657; |
| | 117 | const static double a6 = -0.1367177; |
| | 118 | const static double a7 = 0.1233795; |
| | 119 | |
| | 120 | /* State variables [FIXME for threading!] :*/ |
| | 121 | static double aa = 0.; |
| | 122 | static double aaa = 0.; |
| | 123 | static double s, s2, d; /* no. 1 (step 1) */ |
| | 124 | static double q0, b, si, c;/* no. 2 (step 4) */ |
| | 125 | |
| | 126 | double e, p, q, r, t, u, v, w, x, ret_val; |
| | 127 | double a=alpha; |
| | 128 | double scale=1.0/beta; |
| | 129 | |
| | 130 | if ( !R_FINITE ( a ) || !R_FINITE ( scale ) || a < 0.0 || scale <= 0.0 ) |
| | 131 | {it_error ( "Gamma_RNG wrong parameters" );} |
| | 132 | |
| | 133 | if ( a < 1. ) { /* GS algorithm for parameters a < 1 */ |
| | 134 | if ( a == 0 ) |
| | 135 | return 0.; |
| | 136 | e = 1.0 + exp_m1 * a; |
| | 137 | for ( ;; ) { //VS repeat |
| | 138 | p = e * unif_rand(); |
| | 139 | if ( p >= 1.0 ) { |
| | 140 | x = -log ( ( e - p ) / a ); |
| | 141 | if ( exp_rand() >= ( 1.0 - a ) * log ( x ) ) |
| | 142 | break; |
| | 143 | } |
| | 144 | else { |
| | 145 | x = exp ( log ( p ) / a ); |
| | 146 | if ( exp_rand() >= x ) |
| | 147 | break; |
| | 148 | } |
| | 149 | } |
| | 150 | return scale * x; |
| | 151 | } |
| | 152 | |
| | 153 | /* --- a >= 1 : GD algorithm --- */ |
| | 154 | |
| | 155 | /* Step 1: Recalculations of s2, s, d if a has changed */ |
| | 156 | if ( a != aa ) { |
| | 157 | aa = a; |
| | 158 | s2 = a - 0.5; |
| | 159 | s = sqrt ( s2 ); |
| | 160 | d = sqrt32 - s * 12.0; |
| | 161 | } |
| | 162 | /* Step 2: t = standard normal deviate, |
| | 163 | x = (s,1/2) -normal deviate. */ |
| | 164 | |
| | 165 | /* immediate acceptance (i) */ |
| | 166 | t = norm_rand(); |
| | 167 | x = s + 0.5 * t; |
| | 168 | ret_val = x * x; |
| | 169 | if ( t >= 0.0 ) |
| | 170 | return scale * ret_val; |
| | 171 | |
| | 172 | /* Step 3: u = 0,1 - uniform sample. squeeze acceptance (s) */ |
| | 173 | u = unif_rand(); |
| | 174 | if ( ( d * u ) <= ( t * t * t ) ) |
| | 175 | return scale * ret_val; |
| | 176 | |
| | 177 | /* Step 4: recalculations of q0, b, si, c if necessary */ |
| | 178 | |
| | 179 | if ( a != aaa ) { |
| | 180 | aaa = a; |
| | 181 | r = 1.0 / a; |
| | 182 | q0 = ( ( ( ( ( ( q7 * r + q6 ) * r + q5 ) * r + q4 ) * r + q3 ) * r |
| | 183 | + q2 ) * r + q1 ) * r; |
| | 184 | |
| | 185 | /* Approximation depending on size of parameter a */ |
| | 186 | /* The constants in the expressions for b, si and c */ |
| | 187 | /* were established by numerical experiments */ |
| | 188 | |
| | 189 | if ( a <= 3.686 ) { |
| | 190 | b = 0.463 + s + 0.178 * s2; |
| | 191 | si = 1.235; |
| | 192 | c = 0.195 / s - 0.079 + 0.16 * s; |
| | 193 | } |
| | 194 | else if ( a <= 13.022 ) { |
| | 195 | b = 1.654 + 0.0076 * s2; |
| | 196 | si = 1.68 / s + 0.275; |
| | 197 | c = 0.062 / s + 0.024; |
| | 198 | } |
| | 199 | else { |
| | 200 | b = 1.77; |
| | 201 | si = 0.75; |
| | 202 | c = 0.1515 / s; |
| | 203 | } |
| | 204 | } |
| | 205 | /* Step 5: no quotient test if x not positive */ |
| | 206 | |
| | 207 | if ( x > 0.0 ) { |
| | 208 | /* Step 6: calculation of v and quotient q */ |
| | 209 | v = t / ( s + s ); |
| | 210 | if ( fabs ( v ) <= 0.25 ) |
| | 211 | q = q0 + 0.5 * t * t * ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v |
| | 212 | + a3 ) * v + a2 ) * v + a1 ) * v; |
| | 213 | else |
| | 214 | q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
| | 215 | |
| | 216 | |
| | 217 | /* Step 7: quotient acceptance (q) */ |
| | 218 | if ( log ( 1.0 - u ) <= q ) |
| | 219 | return scale * ret_val; |
| | 220 | } |
| | 221 | |
| | 222 | for ( ;; ) { //VS repeat |
| | 223 | /* Step 8: e = standard exponential deviate |
| | 224 | * u = 0,1 -uniform deviate |
| | 225 | * t = (b,si)-double exponential (laplace) sample */ |
| | 226 | e = exp_rand(); |
| | 227 | u = unif_rand(); |
| | 228 | u = u + u - 1.0; |
| | 229 | if ( u < 0.0 ) |
| | 230 | t = b - si * e; |
| | 231 | else |
| | 232 | t = b + si * e; |
| | 233 | /* Step 9: rejection if t < tau(1) = -0.71874483771719 */ |
| | 234 | if ( t >= -0.71874483771719 ) { |
| | 235 | /* Step 10: calculation of v and quotient q */ |
| | 236 | v = t / ( s + s ); |
| | 237 | if ( fabs ( v ) <= 0.25 ) |
| | 238 | q = q0 + 0.5 * t * t * |
| | 239 | ( ( ( ( ( ( a7 * v + a6 ) * v + a5 ) * v + a4 ) * v + a3 ) * v |
| | 240 | + a2 ) * v + a1 ) * v; |
| | 241 | else |
| | 242 | q = q0 - s * t + 0.25 * t * t + ( s2 + s2 ) * log ( 1.0 + v ); |
| | 243 | /* Step 11: hat acceptance (h) */ |
| | 244 | /* (if q not positive go to step 8) */ |
| | 245 | if ( q > 0.0 ) { |
| | 246 | // TODO: w = expm1(q); |
| | 247 | w = exp ( q )-1; |
| | 248 | /* ^^^^^ original code had approximation with rel.err < 2e-7 */ |
| | 249 | /* if t is rejected sample again at step 8 */ |
| | 250 | if ( ( c * fabs ( u ) ) <= ( w * exp ( e - 0.5 * t * t ) ) ) |
| | 251 | break; |
| | 252 | } |
| | 253 | } |
| | 254 | } /* repeat .. until `t' is accepted */ |
| | 255 | x = s + 0.5 * t; |
| | 256 | return scale * x * x; |
| | 257 | } |
