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