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 | |
---|
5 | //////////////////////////////////////////////////////////////////////////////////////// |
---|
6 | // |
---|
7 | // IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. |
---|
8 | // |
---|
9 | // By downloading, copying, installing or using the software you agree to this license. |
---|
10 | // If you do not agree to this license, do not download, install, |
---|
11 | // copy or use the software. |
---|
12 | // |
---|
13 | // |
---|
14 | // License Agreement |
---|
15 | // For Open Source Computer Vision Library |
---|
16 | // |
---|
17 | // Copyright (C) 2000-2008, Intel Corporation, all rights reserved. |
---|
18 | // Copyright (C) 2009, Willow Garage Inc., all rights reserved. |
---|
19 | // Third party copyrights are property of their respective owners. |
---|
20 | // |
---|
21 | // Redistribution and use in source and binary forms, with or without modification, |
---|
22 | // are permitted provided that the following conditions are met: |
---|
23 | // |
---|
24 | // * Redistribution's of source code must retain the above copyright notice, |
---|
25 | // this list of conditions and the following disclaimer. |
---|
26 | // |
---|
27 | // * Redistribution's in binary form must reproduce the above copyright notice, |
---|
28 | // this list of conditions and the following disclaimer in the documentation |
---|
29 | // and/or other materials provided with the distribution. |
---|
30 | // |
---|
31 | // * The name of the copyright holders may not be used to endorse or promote products |
---|
32 | // derived from this software without specific prior written permission. |
---|
33 | // |
---|
34 | // This software is provided by the copyright holders and contributors "as is" and |
---|
35 | // any express or implied warranties, including, but not limited to, the implied |
---|
36 | // warranties of merchantability and fitness for a particular purpose are disclaimed. |
---|
37 | // In no event shall the Intel Corporation or contributors be liable for any direct, |
---|
38 | // indirect, incidental, special, exemplary, or consequential damages |
---|
39 | // (including, but not limited to, procurement of substitute goods or services; |
---|
40 | // loss of use, data, or profits; or business interruption) however caused |
---|
41 | // and on any theory of liability, whether in contract, strict liability, |
---|
42 | // or tort (including negligence or otherwise) arising in any way out of |
---|
43 | // the use of this software, even if advised of the possibility of such damage. |
---|
44 | // |
---|
45 | // |
---|
46 | /* |
---|
47 | * AutoBuffer from https://github.com/Itseez/opencv/blob/master/modules/core/include/opencv2/core/utility.hpp |
---|
48 | * VBLAS, JacobiSVDImpl_ from https://github.com/Itseez/opencv/blob/master/modules/core/src/lapack.cpp |
---|
49 | * changes: |
---|
50 | * - "RNG rng(0x12345678)" replaced with "srand(time(NULL))" |
---|
51 | * - "rng.next()" replaced with "rand()" |
---|
52 | * MK, 04.2015: |
---|
53 | * - commented out "srand(time(NULL))" - this line would affect everything else that uses the standard global r.n.g., and would introduce uncontrolled indeterminism |
---|
54 | */ |
---|
55 | #include <cstdlib> |
---|
56 | #include <algorithm> |
---|
57 | #include <cmath> |
---|
58 | #include <limits> |
---|
59 | #include <cfloat> |
---|
60 | #include <assert.h> |
---|
61 | #include "lapack.h" |
---|
62 | |
---|
63 | typedef unsigned char uchar; |
---|
64 | |
---|
65 | #if defined _M_IX86 && defined _MSC_VER && _MSC_VER < 1700 |
---|
66 | #pragma float_control(precise, on) |
---|
67 | #endif |
---|
68 | |
---|
69 | template<typename _Tp, size_t fixed_size = 1024 / sizeof (_Tp) + 8 > class AutoBuffer |
---|
70 | { |
---|
71 | public: |
---|
72 | typedef _Tp value_type; |
---|
73 | |
---|
74 | //! the default constructor |
---|
75 | AutoBuffer(); |
---|
76 | //! constructor taking the real buffer size |
---|
77 | AutoBuffer(size_t _size); |
---|
78 | |
---|
79 | //! the copy constructor |
---|
80 | AutoBuffer(const AutoBuffer<_Tp, fixed_size>& buf); |
---|
81 | //! the assignment operator |
---|
82 | AutoBuffer<_Tp, fixed_size>& operator=(const AutoBuffer<_Tp, fixed_size>& buf); |
---|
83 | |
---|
84 | //! destructor. calls deallocate() |
---|
85 | ~AutoBuffer(); |
---|
86 | |
---|
87 | //! allocates the new buffer of size _size. if the _size is small enough, stack-allocated buffer is used |
---|
88 | void allocate(size_t _size); |
---|
89 | //! deallocates the buffer if it was dynamically allocated |
---|
90 | void deallocate(); |
---|
91 | //! resizes the buffer and preserves the content |
---|
92 | void resize(size_t _size); |
---|
93 | //! returns the current buffer size |
---|
94 | size_t size() const; |
---|
95 | //! returns pointer to the real buffer, stack-allocated or head-allocated |
---|
96 | operator _Tp* (); |
---|
97 | //! returns read-only pointer to the real buffer, stack-allocated or head-allocated |
---|
98 | operator const _Tp* () const; |
---|
99 | |
---|
100 | protected: |
---|
101 | //! pointer to the real buffer, can point to buf if the buffer is small enough |
---|
102 | _Tp* ptr; |
---|
103 | //! size of the real buffer |
---|
104 | size_t sz; |
---|
105 | //! pre-allocated buffer. At least 1 element to confirm C++ standard reqirements |
---|
106 | _Tp buf[(fixed_size > 0) ? fixed_size : 1]; |
---|
107 | }; |
---|
108 | |
---|
109 | /////////////////////////////// AutoBuffer implementation //////////////////////////////////////// |
---|
110 | |
---|
111 | template<typename _Tp, size_t fixed_size> inline |
---|
112 | AutoBuffer<_Tp, fixed_size>::AutoBuffer() |
---|
113 | { |
---|
114 | ptr = buf; |
---|
115 | sz = fixed_size; |
---|
116 | } |
---|
117 | |
---|
118 | template<typename _Tp, size_t fixed_size> inline |
---|
119 | AutoBuffer<_Tp, fixed_size>::AutoBuffer(size_t _size) |
---|
120 | { |
---|
121 | ptr = buf; |
---|
122 | sz = fixed_size; |
---|
123 | allocate(_size); |
---|
124 | } |
---|
125 | |
---|
126 | template<typename _Tp, size_t fixed_size> inline |
---|
127 | AutoBuffer<_Tp, fixed_size>::AutoBuffer(const AutoBuffer<_Tp, fixed_size>& abuf) |
---|
128 | { |
---|
129 | ptr = buf; |
---|
130 | sz = fixed_size; |
---|
131 | allocate(abuf.size()); |
---|
132 | for (size_t i = 0; i < sz; i++) |
---|
133 | ptr[i] = abuf.ptr[i]; |
---|
134 | } |
---|
135 | |
---|
136 | template<typename _Tp, size_t fixed_size> inline AutoBuffer<_Tp, fixed_size>& |
---|
137 | AutoBuffer<_Tp, fixed_size>::operator=(const AutoBuffer<_Tp, fixed_size>& abuf) |
---|
138 | { |
---|
139 | if (this != &abuf) |
---|
140 | { |
---|
141 | deallocate(); |
---|
142 | allocate(abuf.size()); |
---|
143 | for (size_t i = 0; i < sz; i++) |
---|
144 | ptr[i] = abuf.ptr[i]; |
---|
145 | } |
---|
146 | return *this; |
---|
147 | } |
---|
148 | |
---|
149 | template<typename _Tp, size_t fixed_size> inline |
---|
150 | AutoBuffer<_Tp, fixed_size>::~AutoBuffer() |
---|
151 | { |
---|
152 | deallocate(); |
---|
153 | } |
---|
154 | |
---|
155 | template<typename _Tp, size_t fixed_size> inline void |
---|
156 | AutoBuffer<_Tp, fixed_size>::allocate(size_t _size) |
---|
157 | { |
---|
158 | if (_size <= sz) |
---|
159 | { |
---|
160 | sz = _size; |
---|
161 | return; |
---|
162 | } |
---|
163 | deallocate(); |
---|
164 | if (_size > fixed_size) |
---|
165 | { |
---|
166 | ptr = new _Tp[_size]; |
---|
167 | sz = _size; |
---|
168 | } |
---|
169 | } |
---|
170 | |
---|
171 | template<typename _Tp, size_t fixed_size> inline void |
---|
172 | AutoBuffer<_Tp, fixed_size>::deallocate() |
---|
173 | { |
---|
174 | if (ptr != buf) |
---|
175 | { |
---|
176 | delete[] ptr; |
---|
177 | ptr = buf; |
---|
178 | sz = fixed_size; |
---|
179 | } |
---|
180 | } |
---|
181 | |
---|
182 | template<typename _Tp, size_t fixed_size> inline void |
---|
183 | AutoBuffer<_Tp, fixed_size>::resize(size_t _size) |
---|
184 | { |
---|
185 | if (_size <= sz) |
---|
186 | { |
---|
187 | sz = _size; |
---|
188 | return; |
---|
189 | } |
---|
190 | //size_t i, prevsize = sz, minsize = MIN(prevsize, _size); |
---|
191 | size_t i, prevsize = sz, minsize = prevsize < _size ? prevsize : _size; |
---|
192 | _Tp* prevptr = ptr; |
---|
193 | |
---|
194 | ptr = _size > fixed_size ? new _Tp[_size] : buf; |
---|
195 | sz = _size; |
---|
196 | |
---|
197 | if (ptr != prevptr) |
---|
198 | for (i = 0; i < minsize; i++) |
---|
199 | ptr[i] = prevptr[i]; |
---|
200 | for (i = prevsize; i < _size; i++) |
---|
201 | ptr[i] = _Tp(); |
---|
202 | |
---|
203 | if (prevptr != buf) |
---|
204 | delete[] prevptr; |
---|
205 | } |
---|
206 | |
---|
207 | template<typename _Tp, size_t fixed_size> inline size_t |
---|
208 | AutoBuffer<_Tp, fixed_size>::size() const |
---|
209 | { |
---|
210 | return sz; |
---|
211 | } |
---|
212 | |
---|
213 | template<typename _Tp, size_t fixed_size> inline |
---|
214 | AutoBuffer<_Tp, fixed_size>::operator _Tp* () |
---|
215 | { |
---|
216 | return ptr; |
---|
217 | } |
---|
218 | |
---|
219 | template<typename _Tp, size_t fixed_size> inline |
---|
220 | AutoBuffer<_Tp, fixed_size>::operator const _Tp* () const |
---|
221 | { |
---|
222 | return ptr; |
---|
223 | } |
---|
224 | |
---|
225 | template<typename T> struct VBLAS |
---|
226 | { |
---|
227 | |
---|
228 | int dot(const T*, const T*, int, T*) const |
---|
229 | { |
---|
230 | return 0; |
---|
231 | } |
---|
232 | |
---|
233 | int givens(T*, T*, int, T, T) const |
---|
234 | { |
---|
235 | return 0; |
---|
236 | } |
---|
237 | |
---|
238 | int givensx(T*, T*, int, T, T, T*, T*) const |
---|
239 | { |
---|
240 | return 0; |
---|
241 | } |
---|
242 | }; |
---|
243 | |
---|
244 | template<typename _Tp> void |
---|
245 | JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* _W, _Tp* Vt, size_t vstep, |
---|
246 | int m, int n, int n1, double minval, _Tp eps) |
---|
247 | { |
---|
248 | VBLAS<_Tp> vblas; |
---|
249 | AutoBuffer<double> Wbuf(n); |
---|
250 | double* W = Wbuf; |
---|
251 | int i, j, k, iter, max_iter = std::max(m, 30); |
---|
252 | _Tp c, s; |
---|
253 | double sd; |
---|
254 | astep /= sizeof (At[0]); |
---|
255 | vstep /= sizeof (Vt[0]); |
---|
256 | |
---|
257 | for (i = 0; i < n; i++) |
---|
258 | { |
---|
259 | for (k = 0, sd = 0; k < m; k++) |
---|
260 | { |
---|
261 | _Tp t = At[i * astep + k]; |
---|
262 | sd += (double) t*t; |
---|
263 | } |
---|
264 | W[i] = sd; |
---|
265 | |
---|
266 | if (Vt) |
---|
267 | { |
---|
268 | for (k = 0; k < n; k++) |
---|
269 | Vt[i * vstep + k] = 0; |
---|
270 | Vt[i * vstep + i] = 1; |
---|
271 | } |
---|
272 | } |
---|
273 | |
---|
274 | for (iter = 0; iter < max_iter; iter++) |
---|
275 | { |
---|
276 | bool changed = false; |
---|
277 | |
---|
278 | for (i = 0; i < n - 1; i++) |
---|
279 | for (j = i + 1; j < n; j++) |
---|
280 | { |
---|
281 | _Tp *Ai = At + i*astep, *Aj = At + j*astep; |
---|
282 | double a = W[i], p = 0, b = W[j]; |
---|
283 | |
---|
284 | for (k = 0; k < m; k++) |
---|
285 | p += (double) Ai[k] * Aj[k]; |
---|
286 | |
---|
287 | if (std::abs(p) <= eps * std::sqrt((double) a * b)) |
---|
288 | continue; |
---|
289 | |
---|
290 | p *= 2; |
---|
291 | double beta = a - b, gamma = hypot((double) p, beta); |
---|
292 | if (beta < 0) |
---|
293 | { |
---|
294 | double delta = (gamma - beta)*0.5; |
---|
295 | s = (_Tp) std::sqrt(delta / gamma); |
---|
296 | c = (_Tp) (p / (gamma * s * 2)); |
---|
297 | } |
---|
298 | else |
---|
299 | { |
---|
300 | c = (_Tp) std::sqrt((gamma + beta) / (gamma * 2)); |
---|
301 | s = (_Tp) (p / (gamma * c * 2)); |
---|
302 | } |
---|
303 | |
---|
304 | a = b = 0; |
---|
305 | for (k = 0; k < m; k++) |
---|
306 | { |
---|
307 | _Tp t0 = c * Ai[k] + s * Aj[k]; |
---|
308 | _Tp t1 = -s * Ai[k] + c * Aj[k]; |
---|
309 | Ai[k] = t0; |
---|
310 | Aj[k] = t1; |
---|
311 | |
---|
312 | a += (double) t0*t0; |
---|
313 | b += (double) t1*t1; |
---|
314 | } |
---|
315 | W[i] = a; |
---|
316 | W[j] = b; |
---|
317 | |
---|
318 | changed = true; |
---|
319 | |
---|
320 | if (Vt) |
---|
321 | { |
---|
322 | _Tp *Vi = Vt + i*vstep, *Vj = Vt + j*vstep; |
---|
323 | k = vblas.givens(Vi, Vj, n, c, s); |
---|
324 | |
---|
325 | for (; k < n; k++) |
---|
326 | { |
---|
327 | _Tp t0 = c * Vi[k] + s * Vj[k]; |
---|
328 | _Tp t1 = -s * Vi[k] + c * Vj[k]; |
---|
329 | Vi[k] = t0; |
---|
330 | Vj[k] = t1; |
---|
331 | } |
---|
332 | } |
---|
333 | } |
---|
334 | if (!changed) |
---|
335 | break; |
---|
336 | } |
---|
337 | |
---|
338 | for (i = 0; i < n; i++) |
---|
339 | { |
---|
340 | for (k = 0, sd = 0; k < m; k++) |
---|
341 | { |
---|
342 | _Tp t = At[i * astep + k]; |
---|
343 | sd += (double) t*t; |
---|
344 | } |
---|
345 | W[i] = std::sqrt(sd); |
---|
346 | } |
---|
347 | |
---|
348 | for (i = 0; i < n - 1; i++) |
---|
349 | { |
---|
350 | j = i; |
---|
351 | for (k = i + 1; k < n; k++) |
---|
352 | { |
---|
353 | if (W[j] < W[k]) |
---|
354 | j = k; |
---|
355 | } |
---|
356 | if (i != j) |
---|
357 | { |
---|
358 | std::swap(W[i], W[j]); |
---|
359 | if (Vt) |
---|
360 | { |
---|
361 | for (k = 0; k < m; k++) |
---|
362 | std::swap(At[i * astep + k], At[j * astep + k]); |
---|
363 | |
---|
364 | for (k = 0; k < n; k++) |
---|
365 | std::swap(Vt[i * vstep + k], Vt[j * vstep + k]); |
---|
366 | } |
---|
367 | } |
---|
368 | } |
---|
369 | |
---|
370 | for (i = 0; i < n; i++) |
---|
371 | _W[i] = (_Tp) W[i]; |
---|
372 | |
---|
373 | if (!Vt) |
---|
374 | return; |
---|
375 | |
---|
376 | //srand(time(NULL)); |
---|
377 | for (i = 0; i < n1; i++) |
---|
378 | { |
---|
379 | sd = i < n ? W[i] : 0; |
---|
380 | |
---|
381 | while (sd <= minval) |
---|
382 | { |
---|
383 | // if we got a zero singular value, then in order to get the corresponding left singular vector |
---|
384 | // we generate a random vector, project it to the previously computed left singular vectors, |
---|
385 | // subtract the projection and normalize the difference. |
---|
386 | const _Tp val0 = (_Tp) (1. / m); |
---|
387 | for (k = 0; k < m; k++) |
---|
388 | { |
---|
389 | _Tp val = (rand() & 256) != 0 ? val0 : -val0; |
---|
390 | At[i * astep + k] = val; |
---|
391 | } |
---|
392 | for (iter = 0; iter < 2; iter++) |
---|
393 | { |
---|
394 | for (j = 0; j < i; j++) |
---|
395 | { |
---|
396 | sd = 0; |
---|
397 | for (k = 0; k < m; k++) |
---|
398 | sd += At[i * astep + k] * At[j * astep + k]; |
---|
399 | _Tp asum = 0; |
---|
400 | for (k = 0; k < m; k++) |
---|
401 | { |
---|
402 | _Tp t = (_Tp) (At[i * astep + k] - sd * At[j * astep + k]); |
---|
403 | At[i * astep + k] = t; |
---|
404 | asum += std::abs(t); |
---|
405 | } |
---|
406 | asum = asum ? 1 / asum : 0; |
---|
407 | for (k = 0; k < m; k++) |
---|
408 | At[i * astep + k] *= asum; |
---|
409 | } |
---|
410 | } |
---|
411 | sd = 0; |
---|
412 | for (k = 0; k < m; k++) |
---|
413 | { |
---|
414 | _Tp t = At[i * astep + k]; |
---|
415 | sd += (double) t*t; |
---|
416 | } |
---|
417 | sd = std::sqrt(sd); |
---|
418 | } |
---|
419 | |
---|
420 | s = (_Tp) (1 / sd); |
---|
421 | for (k = 0; k < m; k++) |
---|
422 | At[i * astep + k] *= s; |
---|
423 | } |
---|
424 | } |
---|
425 | |
---|
426 | void Lapack::JacobiSVD(double* At, size_t astep, double* W, double* Vt, size_t vstep, int m, int n, int n1 = -1) |
---|
427 | { |
---|
428 | JacobiSVDImpl_(At, astep, W, Vt, vstep, m, n, !Vt ? 0 : n1 < 0 ? n : n1, DBL_MIN, DBL_EPSILON * 10); |
---|
429 | } |
---|