[349] | 1 | // This file is a part of Framsticks SDK. http://www.framsticks.com/ |
---|
| 2 | // Copyright (C) 1999-2015 Maciej Komosinski and Szymon Ulatowski. |
---|
| 3 | // See LICENSE.txt for details. |
---|
| 4 | /*M/////////////////////////////////////////////////////////////////////////////////////// |
---|
| 5 | // |
---|
| 6 | // IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. |
---|
| 7 | // |
---|
| 8 | // By downloading, copying, installing or using the software you agree to this license. |
---|
| 9 | // If you do not agree to this license, do not download, install, |
---|
| 10 | // copy or use the software. |
---|
| 11 | // |
---|
| 12 | // |
---|
| 13 | // License Agreement |
---|
| 14 | // For Open Source Computer Vision Library |
---|
| 15 | // |
---|
| 16 | // Copyright (C) 2000-2008, Intel Corporation, all rights reserved. |
---|
| 17 | // Copyright (C) 2009, Willow Garage Inc., all rights reserved. |
---|
| 18 | // Third party copyrights are property of their respective owners. |
---|
| 19 | // |
---|
| 20 | // Redistribution and use in source and binary forms, with or without modification, |
---|
| 21 | // are permitted provided that the following conditions are met: |
---|
| 22 | // |
---|
| 23 | // * Redistribution's of source code must retain the above copyright notice, |
---|
| 24 | // this list of conditions and the following disclaimer. |
---|
| 25 | // |
---|
| 26 | // * Redistribution's in binary form must reproduce the above copyright notice, |
---|
| 27 | // this list of conditions and the following disclaimer in the documentation |
---|
| 28 | // and/or other materials provided with the distribution. |
---|
| 29 | // |
---|
| 30 | // * The name of the copyright holders may not be used to endorse or promote products |
---|
| 31 | // derived from this software without specific prior written permission. |
---|
| 32 | // |
---|
| 33 | // This software is provided by the copyright holders and contributors "as is" and |
---|
| 34 | // any express or implied warranties, including, but not limited to, the implied |
---|
| 35 | // warranties of merchantability and fitness for a particular purpose are disclaimed. |
---|
| 36 | // In no event shall the Intel Corporation or contributors be liable for any direct, |
---|
| 37 | // indirect, incidental, special, exemplary, or consequential damages |
---|
| 38 | // (including, but not limited to, procurement of substitute goods or services; |
---|
| 39 | // loss of use, data, or profits; or business interruption) however caused |
---|
| 40 | // and on any theory of liability, whether in contract, strict liability, |
---|
| 41 | // or tort (including negligence or otherwise) arising in any way out of |
---|
| 42 | // the use of this software, even if advised of the possibility of such damage. |
---|
| 43 | // |
---|
| 44 | //M*/ |
---|
| 45 | /* |
---|
| 46 | * AutoBuffer from https://github.com/Itseez/opencv/blob/master/modules/core/include/opencv2/core/utility.hpp |
---|
| 47 | * VBLAS, JacobiSVDImpl_ from https://github.com/Itseez/opencv/blob/master/modules/core/src/lapack.cpp |
---|
| 48 | * changes: |
---|
| 49 | * - "RNG rng(0x12345678)" replaced with "srand (time(NULL))" |
---|
| 50 | * - "rng.next()" replaced with "rand()" |
---|
| 51 | */ |
---|
| 52 | #include <cstdlib> |
---|
| 53 | #include <algorithm> |
---|
| 54 | #include <cmath> |
---|
| 55 | #include <limits> |
---|
| 56 | #include <cfloat> |
---|
| 57 | #include <assert.h> |
---|
| 58 | #include "lapack.h" |
---|
| 59 | |
---|
| 60 | typedef unsigned char uchar; |
---|
| 61 | |
---|
| 62 | #if defined _M_IX86 && defined _MSC_VER && _MSC_VER < 1700 |
---|
| 63 | #pragma float_control(precise, on) |
---|
| 64 | #endif |
---|
| 65 | |
---|
| 66 | template<typename _Tp, size_t fixed_size = 1024 / sizeof (_Tp) + 8 > class AutoBuffer |
---|
| 67 | { |
---|
| 68 | public: |
---|
| 69 | typedef _Tp value_type; |
---|
| 70 | |
---|
| 71 | //! the default constructor |
---|
| 72 | AutoBuffer(); |
---|
| 73 | //! constructor taking the real buffer size |
---|
| 74 | AutoBuffer(size_t _size); |
---|
| 75 | |
---|
| 76 | //! the copy constructor |
---|
| 77 | AutoBuffer(const AutoBuffer<_Tp, fixed_size>& buf); |
---|
| 78 | //! the assignment operator |
---|
| 79 | AutoBuffer<_Tp, fixed_size>& operator=(const AutoBuffer<_Tp, fixed_size>& buf); |
---|
| 80 | |
---|
| 81 | //! destructor. calls deallocate() |
---|
| 82 | ~AutoBuffer(); |
---|
| 83 | |
---|
| 84 | //! allocates the new buffer of size _size. if the _size is small enough, stack-allocated buffer is used |
---|
| 85 | void allocate(size_t _size); |
---|
| 86 | //! deallocates the buffer if it was dynamically allocated |
---|
| 87 | void deallocate(); |
---|
| 88 | //! resizes the buffer and preserves the content |
---|
| 89 | void resize(size_t _size); |
---|
| 90 | //! returns the current buffer size |
---|
| 91 | size_t size() const; |
---|
| 92 | //! returns pointer to the real buffer, stack-allocated or head-allocated |
---|
| 93 | operator _Tp* (); |
---|
| 94 | //! returns read-only pointer to the real buffer, stack-allocated or head-allocated |
---|
| 95 | operator const _Tp* () const; |
---|
| 96 | |
---|
| 97 | protected: |
---|
| 98 | //! pointer to the real buffer, can point to buf if the buffer is small enough |
---|
| 99 | _Tp* ptr; |
---|
| 100 | //! size of the real buffer |
---|
| 101 | size_t sz; |
---|
| 102 | //! pre-allocated buffer. At least 1 element to confirm C++ standard reqirements |
---|
| 103 | _Tp buf[(fixed_size > 0) ? fixed_size : 1]; |
---|
| 104 | }; |
---|
| 105 | |
---|
| 106 | /////////////////////////////// AutoBuffer implementation //////////////////////////////////////// |
---|
| 107 | |
---|
| 108 | template<typename _Tp, size_t fixed_size> inline |
---|
| 109 | AutoBuffer<_Tp, fixed_size>::AutoBuffer() |
---|
| 110 | { |
---|
| 111 | ptr = buf; |
---|
| 112 | sz = fixed_size; |
---|
| 113 | } |
---|
| 114 | |
---|
| 115 | template<typename _Tp, size_t fixed_size> inline |
---|
| 116 | AutoBuffer<_Tp, fixed_size>::AutoBuffer(size_t _size) |
---|
| 117 | { |
---|
| 118 | ptr = buf; |
---|
| 119 | sz = fixed_size; |
---|
| 120 | allocate(_size); |
---|
| 121 | } |
---|
| 122 | |
---|
| 123 | template<typename _Tp, size_t fixed_size> inline |
---|
| 124 | AutoBuffer<_Tp, fixed_size>::AutoBuffer(const AutoBuffer<_Tp, fixed_size>& abuf) |
---|
| 125 | { |
---|
| 126 | ptr = buf; |
---|
| 127 | sz = fixed_size; |
---|
| 128 | allocate(abuf.size()); |
---|
| 129 | for (size_t i = 0; i < sz; i++) |
---|
| 130 | ptr[i] = abuf.ptr[i]; |
---|
| 131 | } |
---|
| 132 | |
---|
| 133 | template<typename _Tp, size_t fixed_size> inline AutoBuffer<_Tp, fixed_size>& |
---|
| 134 | AutoBuffer<_Tp, fixed_size>::operator=(const AutoBuffer<_Tp, fixed_size>& abuf) |
---|
| 135 | { |
---|
| 136 | if (this != &abuf) |
---|
| 137 | { |
---|
| 138 | deallocate(); |
---|
| 139 | allocate(abuf.size()); |
---|
| 140 | for (size_t i = 0; i < sz; i++) |
---|
| 141 | ptr[i] = abuf.ptr[i]; |
---|
| 142 | } |
---|
| 143 | return *this; |
---|
| 144 | } |
---|
| 145 | |
---|
| 146 | template<typename _Tp, size_t fixed_size> inline |
---|
| 147 | AutoBuffer<_Tp, fixed_size>::~AutoBuffer() |
---|
| 148 | { |
---|
| 149 | deallocate(); |
---|
| 150 | } |
---|
| 151 | |
---|
| 152 | template<typename _Tp, size_t fixed_size> inline void |
---|
| 153 | AutoBuffer<_Tp, fixed_size>::allocate(size_t _size) |
---|
| 154 | { |
---|
| 155 | if (_size <= sz) |
---|
| 156 | { |
---|
| 157 | sz = _size; |
---|
| 158 | return; |
---|
| 159 | } |
---|
| 160 | deallocate(); |
---|
| 161 | if (_size > fixed_size) |
---|
| 162 | { |
---|
| 163 | ptr = new _Tp[_size]; |
---|
| 164 | sz = _size; |
---|
| 165 | } |
---|
| 166 | } |
---|
| 167 | |
---|
| 168 | template<typename _Tp, size_t fixed_size> inline void |
---|
| 169 | AutoBuffer<_Tp, fixed_size>::deallocate() |
---|
| 170 | { |
---|
| 171 | if (ptr != buf) |
---|
| 172 | { |
---|
| 173 | delete[] ptr; |
---|
| 174 | ptr = buf; |
---|
| 175 | sz = fixed_size; |
---|
| 176 | } |
---|
| 177 | } |
---|
| 178 | |
---|
| 179 | template<typename _Tp, size_t fixed_size> inline void |
---|
| 180 | AutoBuffer<_Tp, fixed_size>::resize(size_t _size) |
---|
| 181 | { |
---|
| 182 | if (_size <= sz) |
---|
| 183 | { |
---|
| 184 | sz = _size; |
---|
| 185 | return; |
---|
| 186 | } |
---|
| 187 | //size_t i, prevsize = sz, minsize = MIN(prevsize, _size); |
---|
| 188 | size_t i, prevsize = sz, minsize = prevsize < _size ? prevsize : _size; |
---|
| 189 | _Tp* prevptr = ptr; |
---|
| 190 | |
---|
| 191 | ptr = _size > fixed_size ? new _Tp[_size] : buf; |
---|
| 192 | sz = _size; |
---|
| 193 | |
---|
| 194 | if (ptr != prevptr) |
---|
| 195 | for (i = 0; i < minsize; i++) |
---|
| 196 | ptr[i] = prevptr[i]; |
---|
| 197 | for (i = prevsize; i < _size; i++) |
---|
| 198 | ptr[i] = _Tp(); |
---|
| 199 | |
---|
| 200 | if (prevptr != buf) |
---|
| 201 | delete[] prevptr; |
---|
| 202 | } |
---|
| 203 | |
---|
| 204 | template<typename _Tp, size_t fixed_size> inline size_t |
---|
| 205 | AutoBuffer<_Tp, fixed_size>::size() const |
---|
| 206 | { |
---|
| 207 | return sz; |
---|
| 208 | } |
---|
| 209 | |
---|
| 210 | template<typename _Tp, size_t fixed_size> inline |
---|
| 211 | AutoBuffer<_Tp, fixed_size>::operator _Tp* () |
---|
| 212 | { |
---|
| 213 | return ptr; |
---|
| 214 | } |
---|
| 215 | |
---|
| 216 | template<typename _Tp, size_t fixed_size> inline |
---|
| 217 | AutoBuffer<_Tp, fixed_size>::operator const _Tp* () const |
---|
| 218 | { |
---|
| 219 | return ptr; |
---|
| 220 | } |
---|
| 221 | |
---|
| 222 | template<typename T> struct VBLAS |
---|
| 223 | { |
---|
| 224 | |
---|
| 225 | int dot(const T*, const T*, int, T*) const |
---|
| 226 | { |
---|
| 227 | return 0; |
---|
| 228 | } |
---|
| 229 | |
---|
| 230 | int givens(T*, T*, int, T, T) const |
---|
| 231 | { |
---|
| 232 | return 0; |
---|
| 233 | } |
---|
| 234 | |
---|
| 235 | int givensx(T*, T*, int, T, T, T*, T*) const |
---|
| 236 | { |
---|
| 237 | return 0; |
---|
| 238 | } |
---|
| 239 | }; |
---|
| 240 | |
---|
| 241 | template<typename _Tp> void |
---|
| 242 | JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* _W, _Tp* Vt, size_t vstep, |
---|
| 243 | int m, int n, int n1, double minval, _Tp eps) |
---|
| 244 | { |
---|
| 245 | VBLAS<_Tp> vblas; |
---|
| 246 | AutoBuffer<double> Wbuf(n); |
---|
| 247 | double* W = Wbuf; |
---|
| 248 | int i, j, k, iter, max_iter = std::max(m, 30); |
---|
| 249 | _Tp c, s; |
---|
| 250 | double sd; |
---|
| 251 | astep /= sizeof (At[0]); |
---|
| 252 | vstep /= sizeof (Vt[0]); |
---|
| 253 | |
---|
| 254 | for (i = 0; i < n; i++) |
---|
| 255 | { |
---|
| 256 | for (k = 0, sd = 0; k < m; k++) |
---|
| 257 | { |
---|
| 258 | _Tp t = At[i * astep + k]; |
---|
| 259 | sd += (double) t*t; |
---|
| 260 | } |
---|
| 261 | W[i] = sd; |
---|
| 262 | |
---|
| 263 | if (Vt) |
---|
| 264 | { |
---|
| 265 | for (k = 0; k < n; k++) |
---|
| 266 | Vt[i * vstep + k] = 0; |
---|
| 267 | Vt[i * vstep + i] = 1; |
---|
| 268 | } |
---|
| 269 | } |
---|
| 270 | |
---|
| 271 | for (iter = 0; iter < max_iter; iter++) |
---|
| 272 | { |
---|
| 273 | bool changed = false; |
---|
| 274 | |
---|
| 275 | for (i = 0; i < n - 1; i++) |
---|
| 276 | for (j = i + 1; j < n; j++) |
---|
| 277 | { |
---|
| 278 | _Tp *Ai = At + i*astep, *Aj = At + j*astep; |
---|
| 279 | double a = W[i], p = 0, b = W[j]; |
---|
| 280 | |
---|
| 281 | for (k = 0; k < m; k++) |
---|
| 282 | p += (double) Ai[k] * Aj[k]; |
---|
| 283 | |
---|
| 284 | if (std::abs(p) <= eps * std::sqrt((double) a * b)) |
---|
| 285 | continue; |
---|
| 286 | |
---|
| 287 | p *= 2; |
---|
| 288 | double beta = a - b, gamma = hypot((double) p, beta); |
---|
| 289 | if (beta < 0) |
---|
| 290 | { |
---|
| 291 | double delta = (gamma - beta)*0.5; |
---|
| 292 | s = (_Tp) std::sqrt(delta / gamma); |
---|
| 293 | c = (_Tp) (p / (gamma * s * 2)); |
---|
| 294 | } |
---|
| 295 | else |
---|
| 296 | { |
---|
| 297 | c = (_Tp) std::sqrt((gamma + beta) / (gamma * 2)); |
---|
| 298 | s = (_Tp) (p / (gamma * c * 2)); |
---|
| 299 | } |
---|
| 300 | |
---|
| 301 | a = b = 0; |
---|
| 302 | for (k = 0; k < m; k++) |
---|
| 303 | { |
---|
| 304 | _Tp t0 = c * Ai[k] + s * Aj[k]; |
---|
| 305 | _Tp t1 = -s * Ai[k] + c * Aj[k]; |
---|
| 306 | Ai[k] = t0; |
---|
| 307 | Aj[k] = t1; |
---|
| 308 | |
---|
| 309 | a += (double) t0*t0; |
---|
| 310 | b += (double) t1*t1; |
---|
| 311 | } |
---|
| 312 | W[i] = a; |
---|
| 313 | W[j] = b; |
---|
| 314 | |
---|
| 315 | changed = true; |
---|
| 316 | |
---|
| 317 | if (Vt) |
---|
| 318 | { |
---|
| 319 | _Tp *Vi = Vt + i*vstep, *Vj = Vt + j*vstep; |
---|
| 320 | k = vblas.givens(Vi, Vj, n, c, s); |
---|
| 321 | |
---|
| 322 | for (; k < n; k++) |
---|
| 323 | { |
---|
| 324 | _Tp t0 = c * Vi[k] + s * Vj[k]; |
---|
| 325 | _Tp t1 = -s * Vi[k] + c * Vj[k]; |
---|
| 326 | Vi[k] = t0; |
---|
| 327 | Vj[k] = t1; |
---|
| 328 | } |
---|
| 329 | } |
---|
| 330 | } |
---|
| 331 | if (!changed) |
---|
| 332 | break; |
---|
| 333 | } |
---|
| 334 | |
---|
| 335 | for (i = 0; i < n; i++) |
---|
| 336 | { |
---|
| 337 | for (k = 0, sd = 0; k < m; k++) |
---|
| 338 | { |
---|
| 339 | _Tp t = At[i * astep + k]; |
---|
| 340 | sd += (double) t*t; |
---|
| 341 | } |
---|
| 342 | W[i] = std::sqrt(sd); |
---|
| 343 | } |
---|
| 344 | |
---|
| 345 | for (i = 0; i < n - 1; i++) |
---|
| 346 | { |
---|
| 347 | j = i; |
---|
| 348 | for (k = i + 1; k < n; k++) |
---|
| 349 | { |
---|
| 350 | if (W[j] < W[k]) |
---|
| 351 | j = k; |
---|
| 352 | } |
---|
| 353 | if (i != j) |
---|
| 354 | { |
---|
| 355 | std::swap(W[i], W[j]); |
---|
| 356 | if (Vt) |
---|
| 357 | { |
---|
| 358 | for (k = 0; k < m; k++) |
---|
| 359 | std::swap(At[i * astep + k], At[j * astep + k]); |
---|
| 360 | |
---|
| 361 | for (k = 0; k < n; k++) |
---|
| 362 | std::swap(Vt[i * vstep + k], Vt[j * vstep + k]); |
---|
| 363 | } |
---|
| 364 | } |
---|
| 365 | } |
---|
| 366 | |
---|
| 367 | for (i = 0; i < n; i++) |
---|
| 368 | _W[i] = (_Tp) W[i]; |
---|
| 369 | |
---|
| 370 | if (!Vt) |
---|
| 371 | return; |
---|
| 372 | |
---|
| 373 | srand(time(NULL)); |
---|
| 374 | for (i = 0; i < n1; i++) |
---|
| 375 | { |
---|
| 376 | sd = i < n ? W[i] : 0; |
---|
| 377 | |
---|
| 378 | while (sd <= minval) |
---|
| 379 | { |
---|
| 380 | // if we got a zero singular value, then in order to get the corresponding left singular vector |
---|
| 381 | // we generate a random vector, project it to the previously computed left singular vectors, |
---|
| 382 | // subtract the projection and normalize the difference. |
---|
| 383 | const _Tp val0 = (_Tp) (1. / m); |
---|
| 384 | for (k = 0; k < m; k++) |
---|
| 385 | { |
---|
| 386 | _Tp val = (rand() & 256) != 0 ? val0 : -val0; |
---|
| 387 | At[i * astep + k] = val; |
---|
| 388 | } |
---|
| 389 | for (iter = 0; iter < 2; iter++) |
---|
| 390 | { |
---|
| 391 | for (j = 0; j < i; j++) |
---|
| 392 | { |
---|
| 393 | sd = 0; |
---|
| 394 | for (k = 0; k < m; k++) |
---|
| 395 | sd += At[i * astep + k] * At[j * astep + k]; |
---|
| 396 | _Tp asum = 0; |
---|
| 397 | for (k = 0; k < m; k++) |
---|
| 398 | { |
---|
| 399 | _Tp t = (_Tp) (At[i * astep + k] - sd * At[j * astep + k]); |
---|
| 400 | At[i * astep + k] = t; |
---|
| 401 | asum += std::abs(t); |
---|
| 402 | } |
---|
| 403 | asum = asum ? 1 / asum : 0; |
---|
| 404 | for (k = 0; k < m; k++) |
---|
| 405 | At[i * astep + k] *= asum; |
---|
| 406 | } |
---|
| 407 | } |
---|
| 408 | sd = 0; |
---|
| 409 | for (k = 0; k < m; k++) |
---|
| 410 | { |
---|
| 411 | _Tp t = At[i * astep + k]; |
---|
| 412 | sd += (double) t*t; |
---|
| 413 | } |
---|
| 414 | sd = std::sqrt(sd); |
---|
| 415 | } |
---|
| 416 | |
---|
| 417 | s = (_Tp) (1 / sd); |
---|
| 418 | for (k = 0; k < m; k++) |
---|
| 419 | At[i * astep + k] *= s; |
---|
| 420 | } |
---|
| 421 | } |
---|
| 422 | |
---|
| 423 | void Lapack::JacobiSVD(double* At, size_t astep, double* W, double* Vt, size_t vstep, int m, int n, int n1 = -1) |
---|
| 424 | { |
---|
| 425 | JacobiSVDImpl_(At, astep, W, Vt, vstep, m, n, !Vt ? 0 : n1 < 0 ? n : n1, DBL_MIN, DBL_EPSILON * 10); |
---|
| 426 | } |
---|