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multi_fft.hxx |

1 /************************************************************************/
2 /* */
3 /* Copyright 2009-2010 by Ullrich Koethe */
4 /* */
5 /* This file is part of the VIGRA computer vision library. */
6 /* The VIGRA Website is */
7 /* http://hci.iwr.uni-heidelberg.de/vigra/ */
8 /* Please direct questions, bug reports, and contributions to */
9 /* ullrich.koethe@iwr.uni-heidelberg.de or */
10 /* vigra@informatik.uni-hamburg.de */
11 /* */
12 /* Permission is hereby granted, free of charge, to any person */
13 /* obtaining a copy of this software and associated documentation */
14 /* files (the "Software"), to deal in the Software without */
15 /* restriction, including without limitation the rights to use, */
16 /* copy, modify, merge, publish, distribute, sublicense, and/or */
17 /* sell copies of the Software, and to permit persons to whom the */
18 /* Software is furnished to do so, subject to the following */
19 /* conditions: */
20 /* */
21 /* The above copyright notice and this permission notice shall be */
22 /* included in all copies or substantial portions of the */
23 /* Software. */
24 /* */
25 /* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND */
26 /* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES */
27 /* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND */
28 /* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT */
29 /* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, */
30 /* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING */
31 /* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR */
32 /* OTHER DEALINGS IN THE SOFTWARE. */
33 /* */
34 /************************************************************************/
35
36 #ifndef VIGRA_MULTI_FFT_HXX
37 #define VIGRA_MULTI_FFT_HXX
38
39 #include "fftw3.hxx"
40 #include "multi_array.hxx"
41 #include "navigator.hxx"
42 #include "copyimage.hxx"
43
44 namespace vigra {
45
46 /********************************************************/
47 /* */
48 /* Fourier Transform */
49 /* */
50 /********************************************************/
51
52 /** \addtogroup FourierTransform
53 */
54 //@{
55
56 namespace detail {
57
58 template <unsigned int N, class T, class C>
59 void moveDCToCenterImpl(MultiArrayView<N, T, C> a, unsigned int startDimension)
60 {
61 typedef typename MultiArrayView<N, T, C>::traverser Traverser;
62 typedef MultiArrayNavigator<Traverser, N> Navigator;
63 typedef typename Navigator::iterator Iterator;
64
65 for(unsigned int d = startDimension; d < N; ++d)
66 {
67 Navigator nav(a.traverser_begin(), a.shape(), d);
68
69 for( ; nav.hasMore(); nav++ )
70 {
71 Iterator i = nav.begin();
72 int s = nav.end() - i;
73 int s2 = s/2;
74
75 if(even(s))
76 {
77 for(int k=0; k<s2; ++k)
78 {
79 std::swap(i[k], i[k+s2]);
80 }
81 }
82 else
83 {
84 T v = i[0];
85 for(int k=0; k<s2; ++k)
86 {
87 i[k] = i[k+s2+1];
88 i[k+s2+1] = i[k+1];
89 }
90 i[s2] = v;
91 }
92 }
93 }
94 }
95
96 template <unsigned int N, class T, class C>
97 void moveDCToUpperLeftImpl(MultiArrayView<N, T, C> a, unsigned int startDimension)
98 {
99 typedef typename MultiArrayView<N, T, C>::traverser Traverser;
100 typedef MultiArrayNavigator<Traverser, N> Navigator;
101 typedef typename Navigator::iterator Iterator;
102
103 for(unsigned int d = startDimension; d < N; ++d)
104 {
105 Navigator nav(a.traverser_begin(), a.shape(), d);
106
107 for( ; nav.hasMore(); nav++ )
108 {
109 Iterator i = nav.begin();
110 int s = nav.end() - i;
111 int s2 = s/2;
112
113 if(even(s))
114 {
115 for(int k=0; k<s2; ++k)
116 {
117 std::swap(i[k], i[k+s2]);
118 }
119 }
120 else
121 {
122 T v = i[s2];
123 for(int k=s2; k>0; --k)
124 {
125 i[k] = i[k+s2];
126 i[k+s2] = i[k-1];
127 }
128 i[0] = v;
129 }
130 }
131 }
132 }
133
134 } // namespace detail
135
136 /********************************************************/
137 /* */
138 /* moveDCToCenter */
139 /* */
140 /********************************************************/
141
142 template <unsigned int N, class T, class C>
143 inline void moveDCToCenter(MultiArrayView<N, T, C> a)
144 {
145 detail::moveDCToCenterImpl(a, 0);
146 }
147
148 template <unsigned int N, class T, class C>
149 inline void moveDCToUpperLeft(MultiArrayView<N, T, C> a)
150 {
151 detail::moveDCToUpperLeftImpl(a, 0);
152 }
153
154 template <unsigned int N, class T, class C>
155 inline void moveDCToHalfspaceCenter(MultiArrayView<N, T, C> a)
156 {
157 detail::moveDCToCenterImpl(a, 1);
158 }
159
160 template <unsigned int N, class T, class C>
161 inline void moveDCToHalfspaceUpperLeft(MultiArrayView<N, T, C> a)
162 {
163 detail::moveDCToUpperLeftImpl(a, 1);
164 }
165
166 namespace detail
167 {
168
169 inline fftw_plan
170 fftwPlanCreate(unsigned int N, int* shape,
171 FFTWComplex<double> * in, int* instrides, int instep,
172 FFTWComplex<double> * out, int* outstrides, int outstep,
173 int sign, unsigned int planner_flags)
174 {
175 return fftw_plan_many_dft(N, shape, 1,
176 (fftw_complex *)in, instrides, instep, 0,
177 (fftw_complex *)out, outstrides, outstep, 0,
178 sign, planner_flags);
179 }
180
181 inline fftw_plan
182 fftwPlanCreate(unsigned int N, int* shape,
183 double * in, int* instrides, int instep,
184 FFTWComplex<double> * out, int* outstrides, int outstep,
185 int /*sign is ignored*/, unsigned int planner_flags)
186 {
187 return fftw_plan_many_dft_r2c(N, shape, 1,
188 in, instrides, instep, 0,
189 (fftw_complex *)out, outstrides, outstep, 0,
190 planner_flags);
191 }
192
193 inline fftw_plan
194 fftwPlanCreate(unsigned int N, int* shape,
195 FFTWComplex<double> * in, int* instrides, int instep,
196 double * out, int* outstrides, int outstep,
197 int /*sign is ignored*/, unsigned int planner_flags)
198 {
199 return fftw_plan_many_dft_c2r(N, shape, 1,
200 (fftw_complex *)in, instrides, instep, 0,
201 out, outstrides, outstep, 0,
202 planner_flags);
203 }
204
205 inline fftwf_plan
206 fftwPlanCreate(unsigned int N, int* shape,
207 FFTWComplex<float> * in, int* instrides, int instep,
208 FFTWComplex<float> * out, int* outstrides, int outstep,
209 int sign, unsigned int planner_flags)
210 {
211 return fftwf_plan_many_dft(N, shape, 1,
212 (fftwf_complex *)in, instrides, instep, 0,
213 (fftwf_complex *)out, outstrides, outstep, 0,
214 sign, planner_flags);
215 }
216
217 inline fftwf_plan
218 fftwPlanCreate(unsigned int N, int* shape,
219 float * in, int* instrides, int instep,
220 FFTWComplex<float> * out, int* outstrides, int outstep,
221 int /*sign is ignored*/, unsigned int planner_flags)
222 {
223 return fftwf_plan_many_dft_r2c(N, shape, 1,
224 in, instrides, instep, 0,
225 (fftwf_complex *)out, outstrides, outstep, 0,
226 planner_flags);
227 }
228
229 inline fftwf_plan
230 fftwPlanCreate(unsigned int N, int* shape,
231 FFTWComplex<float> * in, int* instrides, int instep,
232 float * out, int* outstrides, int outstep,
233 int /*sign is ignored*/, unsigned int planner_flags)
234 {
235 return fftwf_plan_many_dft_c2r(N, shape, 1,
236 (fftwf_complex *)in, instrides, instep, 0,
237 out, outstrides, outstep, 0,
238 planner_flags);
239 }
240
241 inline fftwl_plan
242 fftwPlanCreate(unsigned int N, int* shape,
243 FFTWComplex<long double> * in, int* instrides, int instep,
244 FFTWComplex<long double> * out, int* outstrides, int outstep,
245 int sign, unsigned int planner_flags)
246 {
247 return fftwl_plan_many_dft(N, shape, 1,
248 (fftwl_complex *)in, instrides, instep, 0,
249 (fftwl_complex *)out, outstrides, outstep, 0,
250 sign, planner_flags);
251 }
252
253 inline fftwl_plan
254 fftwPlanCreate(unsigned int N, int* shape,
255 long double * in, int* instrides, int instep,
256 FFTWComplex<long double> * out, int* outstrides, int outstep,
257 int /*sign is ignored*/, unsigned int planner_flags)
258 {
259 return fftwl_plan_many_dft_r2c(N, shape, 1,
260 in, instrides, instep, 0,
261 (fftwl_complex *)out, outstrides, outstep, 0,
262 planner_flags);
263 }
264
265 inline fftwl_plan
266 fftwPlanCreate(unsigned int N, int* shape,
267 FFTWComplex<long double> * in, int* instrides, int instep,
268 long double * out, int* outstrides, int outstep,
269 int /*sign is ignored*/, unsigned int planner_flags)
270 {
271 return fftwl_plan_many_dft_c2r(N, shape, 1,
272 (fftwl_complex *)in, instrides, instep, 0,
273 out, outstrides, outstep, 0,
274 planner_flags);
275 }
276
277 inline void fftwPlanDestroy(fftw_plan plan)
278 {
279 if(plan != 0)
280 fftw_destroy_plan(plan);
281 }
282
283 inline void fftwPlanDestroy(fftwf_plan plan)
284 {
285 if(plan != 0)
286 fftwf_destroy_plan(plan);
287 }
288
289 inline void fftwPlanDestroy(fftwl_plan plan)
290 {
291 if(plan != 0)
292 fftwl_destroy_plan(plan);
293 }
294
295 inline void
296 fftwPlanExecute(fftw_plan plan)
297 {
298 fftw_execute(plan);
299 }
300
301 inline void
302 fftwPlanExecute(fftwf_plan plan)
303 {
304 fftwf_execute(plan);
305 }
306
307 inline void
308 fftwPlanExecute(fftwl_plan plan)
309 {
310 fftwl_execute(plan);
311 }
312
313 inline void
314 fftwPlanExecute(fftw_plan plan, FFTWComplex<double> * in, FFTWComplex<double> * out)
315 {
316 fftw_execute_dft(plan, (fftw_complex *)in, (fftw_complex *)out);
317 }
318
319 inline void
320 fftwPlanExecute(fftw_plan plan, double * in, FFTWComplex<double> * out)
321 {
322 fftw_execute_dft_r2c(plan, in, (fftw_complex *)out);
323 }
324
325 inline void
326 fftwPlanExecute(fftw_plan plan, FFTWComplex<double> * in, double * out)
327 {
328 fftw_execute_dft_c2r(plan, (fftw_complex *)in, out);
329 }
330
331 inline void
332 fftwPlanExecute(fftwf_plan plan, FFTWComplex<float> * in, FFTWComplex<float> * out)
333 {
334 fftwf_execute_dft(plan, (fftwf_complex *)in, (fftwf_complex *)out);
335 }
336
337 inline void
338 fftwPlanExecute(fftwf_plan plan, float * in, FFTWComplex<float> * out)
339 {
340 fftwf_execute_dft_r2c(plan, in, (fftwf_complex *)out);
341 }
342
343 inline void
344 fftwPlanExecute(fftwf_plan plan, FFTWComplex<float> * in, float * out)
345 {
346 fftwf_execute_dft_c2r(plan, (fftwf_complex *)in, out);
347 }
348
349 inline void
350 fftwPlanExecute(fftwl_plan plan, FFTWComplex<long double> * in, FFTWComplex<long double> * out)
351 {
352 fftwl_execute_dft(plan, (fftwl_complex *)in, (fftwl_complex *)out);
353 }
354
355 inline void
356 fftwPlanExecute(fftwl_plan plan, long double * in, FFTWComplex<long double> * out)
357 {
358 fftwl_execute_dft_r2c(plan, in, (fftwl_complex *)out);
359 }
360
361 inline void
362 fftwPlanExecute(fftwl_plan plan, FFTWComplex<long double> * in, long double * out)
363 {
364 fftwl_execute_dft_c2r(plan, (fftwl_complex *)in, out);
365 }
366
367 template <int DUMMY>
368 struct FFTWPaddingSize
369 {
370 static const int size = 1330;
371 static const int evenSize = 1063;
372 static int goodSizes[size];
373 static int goodEvenSizes[evenSize];
374
375 static inline int find(int s)
376 {
377 if(s <= 0 || s >= goodSizes[size-1])
378 return s;
379 // find the smallest padding size that is at least as large as 's'
380 int * upperBound = std::upper_bound(goodSizes, goodSizes+size, s);
381 if(upperBound > goodSizes && upperBound[-1] == s)
382 return s;
383 else
384 return *upperBound;
385 }
386
387 static inline int findEven(int s)
388 {
389 if(s <= 0 || s >= goodEvenSizes[evenSize-1])
390 return s;
391 // find the smallest padding size that is at least as large as 's'
392 int * upperBound = std::upper_bound(goodEvenSizes, goodEvenSizes+evenSize, s);
393 if(upperBound > goodEvenSizes && upperBound[-1] == s)
394 return s;
395 else
396 return *upperBound;
397 }
398 };
399
400 // Image sizes where FFTW is fast. The list contains all
401 // numbers less than 100000 whose prime decomposition is of the form
402 // 2^a*3^b*5^c*7^d*11^e*13^f, where e+f is either 0 or 1, and the
403 // other exponents are arbitrary
404 template <int DUMMY>
405 int FFTWPaddingSize<DUMMY>::goodSizes[size] = {
406 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
407 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48,
408 49, 50, 52, 54, 55, 56, 60, 63, 64, 65, 66, 70, 72, 75, 77, 78, 80, 81,
409 84, 88, 90, 91, 96, 98, 99, 100, 104, 105, 108, 110, 112, 117, 120, 125,
410 126, 128, 130, 132, 135, 140, 144, 147, 150, 154, 156, 160, 162, 165,
411 168, 175, 176, 180, 182, 189, 192, 195, 196, 198, 200, 208, 210, 216,
412 220, 224, 225, 231, 234, 240, 243, 245, 250, 252, 256, 260, 264, 270,
413 273, 275, 280, 288, 294, 297, 300, 308, 312, 315, 320, 324, 325, 330,
414 336, 343, 350, 351, 352, 360, 364, 375, 378, 384, 385, 390, 392, 396,
415 400, 405, 416, 420, 432, 440, 441, 448, 450, 455, 462, 468, 480, 486,
416 490, 495, 500, 504, 512, 520, 525, 528, 539, 540, 546, 550, 560, 567,
417 576, 585, 588, 594, 600, 616, 624, 625, 630, 637, 640, 648, 650, 660,
418 672, 675, 686, 693, 700, 702, 704, 720, 728, 729, 735, 750, 756, 768,
419 770, 780, 784, 792, 800, 810, 819, 825, 832, 840, 864, 875, 880, 882,
420 891, 896, 900, 910, 924, 936, 945, 960, 972, 975, 980, 990, 1000, 1008,
421 1024, 1029, 1040, 1050, 1053, 1056, 1078, 1080, 1092, 1100, 1120, 1125,
422 1134, 1152, 1155, 1170, 1176, 1188, 1200, 1215, 1225, 1232, 1248, 1250,
423 1260, 1274, 1280, 1296, 1300, 1320, 1323, 1344, 1350, 1365, 1372, 1375,
424 1386, 1400, 1404, 1408, 1440, 1456, 1458, 1470, 1485, 1500, 1512, 1536,
425 1540, 1560, 1568, 1575, 1584, 1600, 1617, 1620, 1625, 1638, 1650, 1664,
426 1680, 1701, 1715, 1728, 1750, 1755, 1760, 1764, 1782, 1792, 1800, 1820,
427 1848, 1872, 1875, 1890, 1911, 1920, 1925, 1944, 1950, 1960, 1980, 2000,
428 2016, 2025, 2048, 2058, 2079, 2080, 2100, 2106, 2112, 2156, 2160, 2184,
429 2187, 2200, 2205, 2240, 2250, 2268, 2275, 2304, 2310, 2340, 2352, 2376,
430 2400, 2401, 2430, 2450, 2457, 2464, 2475, 2496, 2500, 2520, 2548, 2560,
431 2592, 2600, 2625, 2640, 2646, 2673, 2688, 2695, 2700, 2730, 2744, 2750,
432 2772, 2800, 2808, 2816, 2835, 2880, 2912, 2916, 2925, 2940, 2970, 3000,
433 3024, 3072, 3080, 3087, 3120, 3125, 3136, 3150, 3159, 3168, 3185, 3200,
434 3234, 3240, 3250, 3276, 3300, 3328, 3360, 3375, 3402, 3430, 3456, 3465,
435 3500, 3510, 3520, 3528, 3564, 3584, 3600, 3640, 3645, 3675, 3696, 3744,
436 3750, 3773, 3780, 3822, 3840, 3850, 3888, 3900, 3920, 3960, 3969, 4000,
437 4032, 4050, 4095, 4096, 4116, 4125, 4158, 4160, 4200, 4212, 4224, 4312,
438 4320, 4368, 4374, 4375, 4400, 4410, 4455, 4459, 4480, 4500, 4536, 4550,
439 4608, 4620, 4680, 4704, 4725, 4752, 4800, 4802, 4851, 4860, 4875, 4900,
440 4914, 4928, 4950, 4992, 5000, 5040, 5096, 5103, 5120, 5145, 5184, 5200,
441 5250, 5265, 5280, 5292, 5346, 5376, 5390, 5400, 5460, 5488, 5500, 5544,
442 5600, 5616, 5625, 5632, 5670, 5733, 5760, 5775, 5824, 5832, 5850, 5880,
443 5940, 6000, 6048, 6075, 6125, 6144, 6160, 6174, 6237, 6240, 6250, 6272,
444 6300, 6318, 6336, 6370, 6400, 6468, 6480, 6500, 6552, 6561, 6600, 6615,
445 6656, 6720, 6750, 6804, 6825, 6860, 6875, 6912, 6930, 7000, 7020, 7040,
446 7056, 7128, 7168, 7200, 7203, 7280, 7290, 7350, 7371, 7392, 7425, 7488,
447 7500, 7546, 7560, 7644, 7680, 7700, 7776, 7800, 7840, 7875, 7920, 7938,
448 8000, 8019, 8064, 8085, 8100, 8125, 8190, 8192, 8232, 8250, 8316, 8320,
449 8400, 8424, 8448, 8505, 8575, 8624, 8640, 8736, 8748, 8750, 8775, 8800,
450 8820, 8910, 8918, 8960, 9000, 9072, 9100, 9216, 9240, 9261, 9360, 9375,
451 9408, 9450, 9477, 9504, 9555, 9600, 9604, 9625, 9702, 9720, 9750, 9800,
452 9828, 9856, 9900, 9984, 10000, 10080, 10125, 10192, 10206, 10240, 10290,
453 10368, 10395, 10400, 10500, 10530, 10560, 10584, 10692, 10752, 10780,
454 10800, 10920, 10935, 10976, 11000, 11025, 11088, 11200, 11232, 11250,
455 11264, 11319, 11340, 11375, 11466, 11520, 11550, 11648, 11664, 11700,
456 11760, 11880, 11907, 12000, 12005, 12096, 12150, 12250, 12285, 12288,
457 12320, 12348, 12375, 12474, 12480, 12500, 12544, 12600, 12636, 12672,
458 12740, 12800, 12936, 12960, 13000, 13104, 13122, 13125, 13200, 13230,
459 13312, 13365, 13377, 13440, 13475, 13500, 13608, 13650, 13720, 13750,
460 13824, 13860, 14000, 14040, 14080, 14112, 14175, 14256, 14336, 14400,
461 14406, 14553, 14560, 14580, 14625, 14700, 14742, 14784, 14850, 14976,
462 15000, 15092, 15120, 15288, 15309, 15360, 15400, 15435, 15552, 15600,
463 15625, 15680, 15750, 15795, 15840, 15876, 15925, 16000, 16038, 16128,
464 16170, 16200, 16250, 16380, 16384, 16464, 16500, 16632, 16640, 16800,
465 16807, 16848, 16875, 16896, 17010, 17150, 17199, 17248, 17280, 17325,
466 17472, 17496, 17500, 17550, 17600, 17640, 17820, 17836, 17920, 18000,
467 18144, 18200, 18225, 18375, 18432, 18480, 18522, 18711, 18720, 18750,
468 18816, 18865, 18900, 18954, 19008, 19110, 19200, 19208, 19250, 19404,
469 19440, 19500, 19600, 19656, 19683, 19712, 19800, 19845, 19968, 20000,
470 20160, 20250, 20384, 20412, 20475, 20480, 20580, 20625, 20736, 20790,
471 20800, 21000, 21060, 21120, 21168, 21384, 21504, 21560, 21600, 21609,
472 21840, 21870, 21875, 21952, 22000, 22050, 22113, 22176, 22275, 22295,
473 22400, 22464, 22500, 22528, 22638, 22680, 22750, 22932, 23040, 23100,
474 23296, 23328, 23400, 23520, 23625, 23760, 23814, 24000, 24010, 24057,
475 24192, 24255, 24300, 24375, 24500, 24570, 24576, 24640, 24696, 24750,
476 24948, 24960, 25000, 25088, 25200, 25272, 25344, 25480, 25515, 25600,
477 25725, 25872, 25920, 26000, 26208, 26244, 26250, 26325, 26400, 26411,
478 26460, 26624, 26730, 26754, 26880, 26950, 27000, 27216, 27300, 27440,
479 27500, 27648, 27720, 27783, 28000, 28080, 28125, 28160, 28224, 28350,
480 28431, 28512, 28665, 28672, 28800, 28812, 28875, 29106, 29120, 29160,
481 29250, 29400, 29484, 29568, 29700, 29952, 30000, 30184, 30240, 30375,
482 30576, 30618, 30625, 30720, 30800, 30870, 31104, 31185, 31200, 31213,
483 31250, 31360, 31500, 31590, 31680, 31752, 31850, 32000, 32076, 32256,
484 32340, 32400, 32500, 32760, 32768, 32805, 32928, 33000, 33075, 33264,
485 33280, 33600, 33614, 33696, 33750, 33792, 33957, 34020, 34125, 34300,
486 34375, 34398, 34496, 34560, 34650, 34944, 34992, 35000, 35100, 35200,
487 35280, 35640, 35672, 35721, 35840, 36000, 36015, 36288, 36400, 36450,
488 36750, 36855, 36864, 36960, 37044, 37125, 37422, 37440, 37500, 37632,
489 37730, 37800, 37908, 38016, 38220, 38400, 38416, 38500, 38808, 38880,
490 39000, 39200, 39312, 39366, 39375, 39424, 39600, 39690, 39936, 40000,
491 40095, 40131, 40320, 40425, 40500, 40625, 40768, 40824, 40950, 40960,
492 41160, 41250, 41472, 41580, 41600, 42000, 42120, 42240, 42336, 42525,
493 42768, 42875, 43008, 43120, 43200, 43218, 43659, 43680, 43740, 43750,
494 43875, 43904, 44000, 44100, 44226, 44352, 44550, 44590, 44800, 44928,
495 45000, 45056, 45276, 45360, 45500, 45864, 45927, 46080, 46200, 46305,
496 46592, 46656, 46800, 46875, 47040, 47250, 47385, 47520, 47628, 47775,
497 48000, 48020, 48114, 48125, 48384, 48510, 48600, 48750, 49000, 49140,
498 49152, 49280, 49392, 49500, 49896, 49920, 50000, 50176, 50400, 50421,
499 50544, 50625, 50688, 50960, 51030, 51200, 51450, 51597, 51744, 51840,
500 51975, 52000, 52416, 52488, 52500, 52650, 52800, 52822, 52920, 53248,
501 53460, 53508, 53760, 53900, 54000, 54432, 54600, 54675, 54880, 55000,
502 55125, 55296, 55440, 55566, 56000, 56133, 56160, 56250, 56320, 56448,
503 56595, 56700, 56862, 56875, 57024, 57330, 57344, 57600, 57624, 57750,
504 58212, 58240, 58320, 58500, 58800, 58968, 59049, 59136, 59400, 59535,
505 59904, 60000, 60025, 60368, 60480, 60750, 61152, 61236, 61250, 61425,
506 61440, 61600, 61740, 61875, 62208, 62370, 62400, 62426, 62500, 62720,
507 63000, 63180, 63360, 63504, 63700, 64000, 64152, 64512, 64680, 64800,
508 64827, 65000, 65520, 65536, 65610, 65625, 65856, 66000, 66150, 66339,
509 66528, 66560, 66825, 66885, 67200, 67228, 67375, 67392, 67500, 67584,
510 67914, 68040, 68250, 68600, 68750, 68796, 68992, 69120, 69300, 69888,
511 69984, 70000, 70200, 70400, 70560, 70875, 71280, 71344, 71442, 71680,
512 72000, 72030, 72171, 72576, 72765, 72800, 72900, 73125, 73500, 73710,
513 73728, 73920, 74088, 74250, 74844, 74880, 75000, 75264, 75460, 75600,
514 75816, 76032, 76440, 76545, 76800, 76832, 77000, 77175, 77616, 77760,
515 78000, 78125, 78400, 78624, 78732, 78750, 78848, 78975, 79200, 79233,
516 79380, 79625, 79872, 80000, 80190, 80262, 80640, 80850, 81000, 81250,
517 81536, 81648, 81900, 81920, 82320, 82500, 82944, 83160, 83200, 83349,
518 84000, 84035, 84240, 84375, 84480, 84672, 85050, 85293, 85536, 85750,
519 85995, 86016, 86240, 86400, 86436, 86625, 87318, 87360, 87480, 87500,
520 87750, 87808, 88000, 88200, 88452, 88704, 89100, 89180, 89600, 89856,
521 90000, 90112, 90552, 90720, 91000, 91125, 91728, 91854, 91875, 92160,
522 92400, 92610, 93184, 93312, 93555, 93600, 93639, 93750, 94080, 94325,
523 94500, 94770, 95040, 95256, 95550, 96000, 96040, 96228, 96250, 96768,
524 97020, 97200, 97500, 98000, 98280, 98304, 98415, 98560, 98784, 99000,
525 99225, 99792, 99840
526 };
527
528 template <int DUMMY>
529 int FFTWPaddingSize<DUMMY>::goodEvenSizes[evenSize] = {
530 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22,
531 24, 26, 28, 30, 32, 36, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 66, 70,
532 72, 78, 80, 84, 88, 90, 96, 98, 100, 104, 108, 110, 112, 120, 126, 128,
533 130, 132, 140, 144, 150, 154, 156, 160, 162, 168, 176, 180, 182, 192,
534 196, 198, 200, 208, 210, 216, 220, 224, 234, 240, 250, 252, 256, 260,
535 264, 270, 280, 288, 294, 300, 308, 312, 320, 324, 330, 336, 350, 352,
536 360, 364, 378, 384, 390, 392, 396, 400, 416, 420, 432, 440, 448, 450,
537 462, 468, 480, 486, 490, 500, 504, 512, 520, 528, 540, 546, 550, 560,
538 576, 588, 594, 600, 616, 624, 630, 640, 648, 650, 660, 672, 686, 700,
539 702, 704, 720, 728, 750, 756, 768, 770, 780, 784, 792, 800, 810, 832,
540 840, 864, 880, 882, 896, 900, 910, 924, 936, 960, 972, 980, 990, 1000,
541 1008, 1024, 1040, 1050, 1056, 1078, 1080, 1092, 1100, 1120, 1134, 1152,
542 1170, 1176, 1188, 1200, 1232, 1248, 1250, 1260, 1274, 1280, 1296, 1300,
543 1320, 1344, 1350, 1372, 1386, 1400, 1404, 1408, 1440, 1456, 1458, 1470,
544 1500, 1512, 1536, 1540, 1560, 1568, 1584, 1600, 1620, 1638, 1650, 1664,
545 1680, 1728, 1750, 1760, 1764, 1782, 1792, 1800, 1820, 1848, 1872, 1890,
546 1920, 1944, 1950, 1960, 1980, 2000, 2016, 2048, 2058, 2080, 2100, 2106,
547 2112, 2156, 2160, 2184, 2200, 2240, 2250, 2268, 2304, 2310, 2340, 2352,
548 2376, 2400, 2430, 2450, 2464, 2496, 2500, 2520, 2548, 2560, 2592, 2600,
549 2640, 2646, 2688, 2700, 2730, 2744, 2750, 2772, 2800, 2808, 2816, 2880,
550 2912, 2916, 2940, 2970, 3000, 3024, 3072, 3080, 3120, 3136, 3150, 3168,
551 3200, 3234, 3240, 3250, 3276, 3300, 3328, 3360, 3402, 3430, 3456, 3500,
552 3510, 3520, 3528, 3564, 3584, 3600, 3640, 3696, 3744, 3750, 3780, 3822,
553 3840, 3850, 3888, 3900, 3920, 3960, 4000, 4032, 4050, 4096, 4116, 4158,
554 4160, 4200, 4212, 4224, 4312, 4320, 4368, 4374, 4400, 4410, 4480, 4500,
555 4536, 4550, 4608, 4620, 4680, 4704, 4752, 4800, 4802, 4860, 4900, 4914,
556 4928, 4950, 4992, 5000, 5040, 5096, 5120, 5184, 5200, 5250, 5280, 5292,
557 5346, 5376, 5390, 5400, 5460, 5488, 5500, 5544, 5600, 5616, 5632, 5670,
558 5760, 5824, 5832, 5850, 5880, 5940, 6000, 6048, 6144, 6160, 6174, 6240,
559 6250, 6272, 6300, 6318, 6336, 6370, 6400, 6468, 6480, 6500, 6552, 6600,
560 6656, 6720, 6750, 6804, 6860, 6912, 6930, 7000, 7020, 7040, 7056, 7128,
561 7168, 7200, 7280, 7290, 7350, 7392, 7488, 7500, 7546, 7560, 7644, 7680,
562 7700, 7776, 7800, 7840, 7920, 7938, 8000, 8064, 8100, 8190, 8192, 8232,
563 8250, 8316, 8320, 8400, 8424, 8448, 8624, 8640, 8736, 8748, 8750, 8800,
564 8820, 8910, 8918, 8960, 9000, 9072, 9100, 9216, 9240, 9360, 9408, 9450,
565 9504, 9600, 9604, 9702, 9720, 9750, 9800, 9828, 9856, 9900, 9984, 10000,
566 10080, 10192, 10206, 10240, 10290, 10368, 10400, 10500, 10530, 10560,
567 10584, 10692, 10752, 10780, 10800, 10920, 10976, 11000, 11088, 11200,
568 11232, 11250, 11264, 11340, 11466, 11520, 11550, 11648, 11664, 11700,
569 11760, 11880, 12000, 12096, 12150, 12250, 12288, 12320, 12348, 12474,
570 12480, 12500, 12544, 12600, 12636, 12672, 12740, 12800, 12936, 12960,
571 13000, 13104, 13122, 13200, 13230, 13312, 13440, 13500, 13608, 13650,
572 13720, 13750, 13824, 13860, 14000, 14040, 14080, 14112, 14256, 14336,
573 14400, 14406, 14560, 14580, 14700, 14742, 14784, 14850, 14976, 15000,
574 15092, 15120, 15288, 15360, 15400, 15552, 15600, 15680, 15750, 15840,
575 15876, 16000, 16038, 16128, 16170, 16200, 16250, 16380, 16384, 16464,
576 16500, 16632, 16640, 16800, 16848, 16896, 17010, 17150, 17248, 17280,
577 17472, 17496, 17500, 17550, 17600, 17640, 17820, 17836, 17920, 18000,
578 18144, 18200, 18432, 18480, 18522, 18720, 18750, 18816, 18900, 18954,
579 19008, 19110, 19200, 19208, 19250, 19404, 19440, 19500, 19600, 19656,
580 19712, 19800, 19968, 20000, 20160, 20250, 20384, 20412, 20480, 20580,
581 20736, 20790, 20800, 21000, 21060, 21120, 21168, 21384, 21504, 21560,
582 21600, 21840, 21870, 21952, 22000, 22050, 22176, 22400, 22464, 22500,
583 22528, 22638, 22680, 22750, 22932, 23040, 23100, 23296, 23328, 23400,
584 23520, 23760, 23814, 24000, 24010, 24192, 24300, 24500, 24570, 24576,
585 24640, 24696, 24750, 24948, 24960, 25000, 25088, 25200, 25272, 25344,
586 25480, 25600, 25872, 25920, 26000, 26208, 26244, 26250, 26400, 26460,
587 26624, 26730, 26754, 26880, 26950, 27000, 27216, 27300, 27440, 27500,
588 27648, 27720, 28000, 28080, 28160, 28224, 28350, 28512, 28672, 28800,
589 28812, 29106, 29120, 29160, 29250, 29400, 29484, 29568, 29700, 29952,
590 30000, 30184, 30240, 30576, 30618, 30720, 30800, 30870, 31104, 31200,
591 31250, 31360, 31500, 31590, 31680, 31752, 31850, 32000, 32076, 32256,
592 32340, 32400, 32500, 32760, 32768, 32928, 33000, 33264, 33280, 33600,
593 33614, 33696, 33750, 33792, 34020, 34300, 34398, 34496, 34560, 34650,
594 34944, 34992, 35000, 35100, 35200, 35280, 35640, 35672, 35840, 36000,
595 36288, 36400, 36450, 36750, 36864, 36960, 37044, 37422, 37440, 37500,
596 37632, 37730, 37800, 37908, 38016, 38220, 38400, 38416, 38500, 38808,
597 38880, 39000, 39200, 39312, 39366, 39424, 39600, 39690, 39936, 40000,
598 40320, 40500, 40768, 40824, 40950, 40960, 41160, 41250, 41472, 41580,
599 41600, 42000, 42120, 42240, 42336, 42768, 43008, 43120, 43200, 43218,
600 43680, 43740, 43750, 43904, 44000, 44100, 44226, 44352, 44550, 44590,
601 44800, 44928, 45000, 45056, 45276, 45360, 45500, 45864, 46080, 46200,
602 46592, 46656, 46800, 47040, 47250, 47520, 47628, 48000, 48020, 48114,
603 48384, 48510, 48600, 48750, 49000, 49140, 49152, 49280, 49392, 49500,
604 49896, 49920, 50000, 50176, 50400, 50544, 50688, 50960, 51030, 51200,
605 51450, 51744, 51840, 52000, 52416, 52488, 52500, 52650, 52800, 52822,
606 52920, 53248, 53460, 53508, 53760, 53900, 54000, 54432, 54600, 54880,
607 55000, 55296, 55440, 55566, 56000, 56160, 56250, 56320, 56448, 56700,
608 56862, 57024, 57330, 57344, 57600, 57624, 57750, 58212, 58240, 58320,
609 58500, 58800, 58968, 59136, 59400, 59904, 60000, 60368, 60480, 60750,
610 61152, 61236, 61250, 61440, 61600, 61740, 62208, 62370, 62400, 62426,
611 62500, 62720, 63000, 63180, 63360, 63504, 63700, 64000, 64152, 64512,
612 64680, 64800, 65000, 65520, 65536, 65610, 65856, 66000, 66150, 66528,
613 66560, 67200, 67228, 67392, 67500, 67584, 67914, 68040, 68250, 68600,
614 68750, 68796, 68992, 69120, 69300, 69888, 69984, 70000, 70200, 70400,
615 70560, 71280, 71344, 71442, 71680, 72000, 72030, 72576, 72800, 72900,
616 73500, 73710, 73728, 73920, 74088, 74250, 74844, 74880, 75000, 75264,
617 75460, 75600, 75816, 76032, 76440, 76800, 76832, 77000, 77616, 77760,
618 78000, 78400, 78624, 78732, 78750, 78848, 79200, 79380, 79872, 80000,
619 80190, 80262, 80640, 80850, 81000, 81250, 81536, 81648, 81900, 81920,
620 82320, 82500, 82944, 83160, 83200, 84000, 84240, 84480, 84672, 85050,
621 85536, 85750, 86016, 86240, 86400, 86436, 87318, 87360, 87480, 87500,
622 87750, 87808, 88000, 88200, 88452, 88704, 89100, 89180, 89600, 89856,
623 90000, 90112, 90552, 90720, 91000, 91728, 91854, 92160, 92400, 92610,
624 93184, 93312, 93600, 93750, 94080, 94500, 94770, 95040, 95256, 95550,
625 96000, 96040, 96228, 96250, 96768, 97020, 97200, 97500, 98000, 98280,
626 98304, 98560, 98784, 99000, 99792, 99840
627 };
628
629 template <int M>
630 struct FFTEmbedKernel
631 {
632 template <unsigned int N, class Real, class C, class Shape>
633 static void
634 exec(MultiArrayView<N, Real, C> & out, Shape const & kernelShape,
635 Shape & srcPoint, Shape & destPoint, bool copyIt)
636 {
637 for(srcPoint[M]=0; srcPoint[M]<kernelShape[M]; ++srcPoint[M])
638 {
639 if(srcPoint[M] < (kernelShape[M] + 1) / 2)
640 {
641 destPoint[M] = srcPoint[M];
642 }
643 else
644 {
645 destPoint[M] = srcPoint[M] + out.shape(M) - kernelShape[M];
646 copyIt = true;
647 }
648 FFTEmbedKernel<M-1>::exec(out, kernelShape, srcPoint, destPoint, copyIt);
649 }
650 }
651 };
652
653 template <>
654 struct FFTEmbedKernel<0>
655 {
656 template <unsigned int N, class Real, class C, class Shape>
657 static void
658 exec(MultiArrayView<N, Real, C> & out, Shape const & kernelShape,
659 Shape & srcPoint, Shape & destPoint, bool copyIt)
660 {
661 for(srcPoint[0]=0; srcPoint[0]<kernelShape[0]; ++srcPoint[0])
662 {
663 if(srcPoint[0] < (kernelShape[0] + 1) / 2)
664 {
665 destPoint[0] = srcPoint[0];
666 }
667 else
668 {
669 destPoint[0] = srcPoint[0] + out.shape(0) - kernelShape[0];
670 copyIt = true;
671 }
672 if(copyIt)
673 {
674 out[destPoint] = out[srcPoint];
675 out[srcPoint] = 0.0;
676 }
677 }
678 }
679 };
680
681 template <unsigned int N, class Real, class C1, class C2>
682 void
683 fftEmbedKernel(MultiArrayView<N, Real, C1> kernel,
684 MultiArrayView<N, Real, C2> out,
685 Real norm = 1.0)
686 {
687 typedef typename MultiArrayShape<N>::type Shape;
688
689 MultiArrayView<N, Real, C2> kout = out.subarray(Shape(), kernel.shape());
690
691 out.init(0.0);
692 kout = kernel;
693 if (norm != 1.0)
694 kout *= norm;
695 moveDCToUpperLeft(kout);
696
697 Shape srcPoint, destPoint;
698 FFTEmbedKernel<(int)N-1>::exec(out, kernel.shape(), srcPoint, destPoint, false);
699 }
700
701 template <unsigned int N, class Real, class C1, class C2>
702 void
703 fftEmbedArray(MultiArrayView<N, Real, C1> in,
704 MultiArrayView<N, Real, C2> out)
705 {
706 typedef typename MultiArrayShape<N>::type Shape;
707
708 Shape diff = out.shape() - in.shape(),
709 leftDiff = div(diff, MultiArrayIndex(2)),
710 rightDiff = diff - leftDiff,
711 right = in.shape() + leftDiff;
712
713 out.subarray(leftDiff, right) = in;
714
715 typedef typename MultiArrayView<N, Real, C2>::traverser Traverser;
716 typedef MultiArrayNavigator<Traverser, N> Navigator;
717 typedef typename Navigator::iterator Iterator;
718
719 for(unsigned int d = 0; d < N; ++d)
720 {
721 Navigator nav(out.traverser_begin(), out.shape(), d);
722
723 for( ; nav.hasMore(); nav++ )
724 {
725 Iterator i = nav.begin();
726 for(int k=1; k<=leftDiff[d]; ++k)
727 i[leftDiff[d] - k] = i[leftDiff[d] + k];
728 for(int k=0; k<rightDiff[d]; ++k)
729 i[right[d] + k] = i[right[d] - k - 2];
730 }
731 }
732 }
733
734 } // namespace detail
735
736 template <class T, int N>
737 TinyVector<T, N>
738 fftwBestPaddedShape(TinyVector<T, N> shape)
739 {
740 for(unsigned int k=0; k<N; ++k)
741 shape[k] = detail::FFTWPaddingSize<0>::find(shape[k]);
742 return shape;
743 }
744
745 template <class T, int N>
746 TinyVector<T, N>
747 fftwBestPaddedShapeR2C(TinyVector<T, N> shape)
748 {
749 shape[0] = detail::FFTWPaddingSize<0>::findEven(shape[0]);
750 for(unsigned int k=1; k<N; ++k)
751 shape[k] = detail::FFTWPaddingSize<0>::find(shape[k]);
752 return shape;
753 }
754
755 /** \brief Find frequency domain shape for a R2C Fourier transform.
756
757 When a real valued array is transformed to the frequency domain, about half of the
758 Fourier coefficients are redundant. The transform can be optimized as a <a href="http://www.fftw.org/doc/Multi_002dDimensional-DFTs-of-Real-Data.html">R2C
759 transform</a> that doesn't compute and store the redundant coefficients. This function
760 computes the appropriate frequency domain shape for a given shape in the spatial domain.
761 It simply replaces <tt>shape[0]</tt> with <tt>shape[0] / 2 + 1</tt>.
762
763 <b>\#include</b> <vigra/multi_fft.hxx><br/>
764 Namespace: vigra
765 */
766 template <class T, int N>
767 TinyVector<T, N>
768 fftwCorrespondingShapeR2C(TinyVector<T, N> shape)
769 {
770 shape[0] = shape[0] / 2 + 1;
771 return shape;
772 }
773
774 template <class T, int N>
775 TinyVector<T, N>
776 fftwCorrespondingShapeC2R(TinyVector<T, N> shape, bool oddDimension0 = false)
777 {
778 shape[0] = oddDimension0
779 ? (shape[0] - 1) * 2 + 1
780 : (shape[0] - 1) * 2;
781 return shape;
782 }
783
784 /********************************************************/
785 /* */
786 /* FFTWPlan */
787 /* */
788 /********************************************************/
789
790 /** C++ wrapper for FFTW plans.
791
792 The class encapsulates the calls to <tt>fftw_plan_dft_2d</tt>, <tt>fftw_execute</tt>, and
793 <tt>fftw_destroy_plan</tt> (and their <tt>float</tt> and <tt>long double</tt> counterparts)
794 in an easy-to-use interface.
795
796 Usually, you use this class only indirectly via \ref fourierTransform()
797 and \ref fourierTransformInverse(). You only need this class if you want to have more control
798 about FFTW's planning process (by providing non-default planning flags) and/or want to re-use
799 plans for several transformations.
800
801 <b> Usage:</b>
802
803 <b>\#include</b> <vigra/multi_fft.hxx><br>
804 Namespace: vigra
805
806 \code
807 // compute complex Fourier transform of a real image
808 MultiArray<2, double> src(Shape2(w, h));
809 MultiArray<2, FFTWComplex<double> > fourier(Shape2(w, h));
810
811 // create an optimized plan by measuring the speed of several algorithm variants
812 FFTWPlan<2, double> plan(src, fourier, FFTW_MEASURE);
813
814 plan.execute(src, fourier);
815 \endcode
816 */
817 template <unsigned int N, class Real = double>
818 class FFTWPlan
819 {
820 typedef ArrayVector<int> Shape;
821 typedef typename FFTWReal2Complex<Real>::plan_type PlanType;
822 typedef typename FFTWComplex<Real>::complex_type Complex;
823
824 PlanType plan;
825 Shape shape, instrides, outstrides;
826 int sign;
827
828 public:
829 /** \brief Create an empty plan.
830
831 The plan can be initialized later by one of the init() functions.
832 */
833 FFTWPlan()
834 : plan(0)
835 {}
836
837 /** \brief Create a plan for a complex-to-complex transform.
838
839 \arg SIGN must be <tt>FFTW_FORWARD</tt> or <tt>FFTW_BACKWARD</tt> according to the
840 desired transformation direction.
841 \arg planner_flags must be a combination of the <a href="http://www.fftw.org/doc/Planner-Flags.html">planner
842 flags</a> defined by the FFTW library. The default <tt>FFTW_ESTIMATE</tt> will guess
843 optimal algorithm settings or read them from pre-loaded <a href="http://www.fftw.org/doc/Wisdom.html">"wisdom"</a>.
844 */
845 template <class C1, class C2>
846 FFTWPlan(MultiArrayView<N, FFTWComplex<Real>, C1> in,
847 MultiArrayView<N, FFTWComplex<Real>, C2> out,
848 int SIGN, unsigned int planner_flags = FFTW_ESTIMATE)
849 : plan(0)
850 {
851 init(in, out, SIGN, planner_flags);
852 }
853
854 /** \brief Create a plan for a real-to-complex transform.
855
856 This always refers to a forward transform. The shape of the output determines
857 if a standard transform (when <tt>out.shape() == in.shape()</tt>) or an
858 <a href="http://www.fftw.org/doc/Multi_002dDimensional-DFTs-of-Real-Data.html">R2C
859 transform</a> (when <tt>out.shape() == fftwCorrespondingShapeR2C(in.shape())</tt>) will be executed.
860
861 \arg planner_flags must be a combination of the <a href="http://www.fftw.org/doc/Planner-Flags.html">planner
862 flags</a> defined by the FFTW library. The default <tt>FFTW_ESTIMATE</tt> will guess
863 optimal algorithm settings or read them from pre-loaded <a href="http://www.fftw.org/doc/Wisdom.html">"wisdom"</a>.
864 */
865 template <class C1, class C2>
866 FFTWPlan(MultiArrayView<N, Real, C1> in,
867 MultiArrayView<N, FFTWComplex<Real>, C2> out,
868 unsigned int planner_flags = FFTW_ESTIMATE)
869 : plan(0)
870 {
871 init(in, out, planner_flags);
872 }
873
874 /** \brief Create a plan for a complex-to-real transform.
875
876 This always refers to a inverse transform. The shape of the input determines
877 if a standard transform (when <tt>in.shape() == out.shape()</tt>) or a
878 <a href="http://www.fftw.org/doc/Multi_002dDimensional-DFTs-of-Real-Data.html">C2R
879 transform</a> (when <tt>in.shape() == fftwCorrespondingShapeR2C(out.shape())</tt>) will be executed.
880
881 \arg planner_flags must be a combination of the <a href="http://www.fftw.org/doc/Planner-Flags.html">planner
882 flags</a> defined by the FFTW library. The default <tt>FFTW_ESTIMATE</tt> will guess
883 optimal algorithm settings or read them from pre-loaded <a href="http://www.fftw.org/doc/Wisdom.html">"wisdom"</a>.
884 */
885 template <class C1, class C2>
886 FFTWPlan(MultiArrayView<N, FFTWComplex<Real>, C1> in,
887 MultiArrayView<N, Real, C2> out,
888 unsigned int planner_flags = FFTW_ESTIMATE)
889 : plan(0)
890 {
891 init(in, out, planner_flags);
892 }
893
894 /** \brief Copy constructor.
895 */
896 FFTWPlan(FFTWPlan const & other)
897 : plan(other.plan),
898 sign(other.sign)
899 {
900 FFTWPlan & o = const_cast<FFTWPlan &>(other);
901 shape.swap(o.shape);
902 instrides.swap(o.instrides);
903 outstrides.swap(o.outstrides);
904 o.plan = 0; // act like std::auto_ptr
905 }
906
907 /** \brief Copy assigment.
908 */
909 FFTWPlan & operator=(FFTWPlan const & other)
910 {
911 if(this != &other)
912 {
913 FFTWPlan & o = const_cast<FFTWPlan &>(other);
914 plan = o.plan;
915 shape.swap(o.shape);
916 instrides.swap(o.instrides);
917 outstrides.swap(o.outstrides);
918 sign = o.sign;
919 o.plan = 0; // act like std::auto_ptr
920 }
921 return *this;
922 }
923
924 /** \brief Destructor.
925 */
926 ~FFTWPlan()
927 {
928 detail::fftwPlanDestroy(plan);
929 }
930
931 /** \brief Init a complex-to-complex transform.
932
933 See the constructor with the same signature for details.
934 */
935 template <class C1, class C2>
936 void init(MultiArrayView<N, FFTWComplex<Real>, C1> in,
937 MultiArrayView<N, FFTWComplex<Real>, C2> out,
938 int SIGN, unsigned int planner_flags = FFTW_ESTIMATE)
939 {
940 vigra_precondition(in.strideOrdering() == out.strideOrdering(),
941 "FFTWPlan.init(): input and output must have the same stride ordering.");
942
943 initImpl(in.permuteStridesDescending(), out.permuteStridesDescending(),
944 SIGN, planner_flags);
945 }
946
947 /** \brief Init a real-to-complex transform.
948
949 See the constructor with the same signature for details.
950 */
951 template <class C1, class C2>
952 void init(MultiArrayView<N, Real, C1> in,
953 MultiArrayView<N, FFTWComplex<Real>, C2> out,
954 unsigned int planner_flags = FFTW_ESTIMATE)
955 {
956 vigra_precondition(in.strideOrdering() == out.strideOrdering(),
957 "FFTWPlan.init(): input and output must have the same stride ordering.");
958
959 initImpl(in.permuteStridesDescending(), out.permuteStridesDescending(),
960 FFTW_FORWARD, planner_flags);
961 }
962
963 /** \brief Init a complex-to-real transform.
964
965 See the constructor with the same signature for details.
966 */
967 template <class C1, class C2>
968 void init(MultiArrayView<N, FFTWComplex<Real>, C1> in,
969 MultiArrayView<N, Real, C2> out,
970 unsigned int planner_flags = FFTW_ESTIMATE)
971 {
972 vigra_precondition(in.strideOrdering() == out.strideOrdering(),
973 "FFTWPlan.init(): input and output must have the same stride ordering.");
974
975 initImpl(in.permuteStridesDescending(), out.permuteStridesDescending(),
976 FFTW_BACKWARD, planner_flags);
977 }
978
979 /** \brief Execute a complex-to-complex transform.
980
981 The array shapes must be the same as in the corresponding init function
982 or constructor. However, execute() can be called several times on
983 the same plan, even with different arrays, as long as they have the appropriate
984 shapes.
985 */
986 template <class C1, class C2>
987 void execute(MultiArrayView<N, FFTWComplex<Real>, C1> in,
988 MultiArrayView<N, FFTWComplex<Real>, C2> out) const
989 {
990 executeImpl(in.permuteStridesDescending(), out.permuteStridesDescending());
991 }
992
993 /** \brief Execute a real-to-complex transform.
994
995 The array shapes must be the same as in the corresponding init function
996 or constructor. However, execute() can be called several times on
997 the same plan, even with different arrays, as long as they have the appropriate
998 shapes.
999 */
1000 template <class C1, class C2>
1001 void execute(MultiArrayView<N, Real, C1> in,
1002 MultiArrayView<N, FFTWComplex<Real>, C2> out) const
1003 {
1004 executeImpl(in.permuteStridesDescending(), out.permuteStridesDescending());
1005 }
1006
1007 /** \brief Execute a complex-to-real transform.
1008
1009 The array shapes must be the same as in the corresponding init function
1010 or constructor. However, execute() can be called several times on
1011 the same plan, even with different arrays, as long as they have the appropriate
1012 shapes.
1013 */
1014 template <class C1, class C2>
1015 void execute(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1016 MultiArrayView<N, Real, C2> out) const
1017 {
1018 executeImpl(in.permuteStridesDescending(), out.permuteStridesDescending());
1019 }
1020
1021 private:
1022
1023 template <class MI, class MO>
1024 void initImpl(MI ins, MO outs, int SIGN, unsigned int planner_flags);
1025
1026 template <class MI, class MO>
1027 void executeImpl(MI ins, MO outs) const;
1028
1029 void checkShapes(MultiArrayView<N, FFTWComplex<Real>, StridedArrayTag> in,
1030 MultiArrayView<N, FFTWComplex<Real>, StridedArrayTag> out) const
1031 {
1032 vigra_precondition(in.shape() == out.shape(),
1033 "FFTWPlan.init(): input and output must have the same shape.");
1034 }
1035
1036 void checkShapes(MultiArrayView<N, Real, StridedArrayTag> ins,
1037 MultiArrayView<N, FFTWComplex<Real>, StridedArrayTag> outs) const
1038 {
1039 for(int k=0; k<(int)N-1; ++k)
1040 vigra_precondition(ins.shape(k) == outs.shape(k),
1041 "FFTWPlan.init(): input and output must have matching shapes.");
1042 vigra_precondition(ins.shape(N-1) / 2 + 1 == outs.shape(N-1),
1043 "FFTWPlan.init(): input and output must have matching shapes.");
1044 }
1045
1046 void checkShapes(MultiArrayView<N, FFTWComplex<Real>, StridedArrayTag> ins,
1047 MultiArrayView<N, Real, StridedArrayTag> outs) const
1048 {
1049 for(int k=0; k<(int)N-1; ++k)
1050 vigra_precondition(ins.shape(k) == outs.shape(k),
1051 "FFTWPlan.init(): input and output must have matching shapes.");
1052 vigra_precondition(outs.shape(N-1) / 2 + 1 == ins.shape(N-1),
1053 "FFTWPlan.init(): input and output must have matching shapes.");
1054 }
1055 };
1056
1057 template <unsigned int N, class Real>
1058 template <class MI, class MO>
1059 void
1060 FFTWPlan<N, Real>::initImpl(MI ins, MO outs, int SIGN, unsigned int planner_flags)
1061 {
1062 checkShapes(ins, outs);
1063
1064 typename MultiArrayShape<N>::type logicalShape(SIGN == FFTW_FORWARD
1065 ? ins.shape()
1066 : outs.shape());
1067
1068 Shape newShape(logicalShape.begin(), logicalShape.end()),
1069 newIStrides(ins.stride().begin(), ins.stride().end()),
1070 newOStrides(outs.stride().begin(), outs.stride().end()),
1071 itotal(ins.shape().begin(), ins.shape().end()),
1072 ototal(outs.shape().begin(), outs.shape().end());
1073
1074 for(unsigned int j=1; j<N; ++j)
1075 {
1076 itotal[j] = ins.stride(j-1) / ins.stride(j);
1077 ototal[j] = outs.stride(j-1) / outs.stride(j);
1078 }
1079
1080 PlanType newPlan = detail::fftwPlanCreate(N, newShape.begin(),
1081 ins.data(), itotal.begin(), ins.stride(N-1),
1082 outs.data(), ototal.begin(), outs.stride(N-1),
1083 SIGN, planner_flags);
1084 detail::fftwPlanDestroy(plan);
1085 plan = newPlan;
1086 shape.swap(newShape);
1087 instrides.swap(newIStrides);
1088 outstrides.swap(newOStrides);
1089 sign = SIGN;
1090 }
1091
1092 template <unsigned int N, class Real>
1093 template <class MI, class MO>
1094 void FFTWPlan<N, Real>::executeImpl(MI ins, MO outs) const
1095 {
1096 vigra_precondition(plan != 0, "FFTWPlan::execute(): plan is NULL.");
1097
1098 typename MultiArrayShape<N>::type lshape(sign == FFTW_FORWARD
1099 ? ins.shape()
1100 : outs.shape());
1101
1102 vigra_precondition((lshape == TinyVectorView<int, N>(shape.data())),
1103 "FFTWPlan::execute(): shape mismatch between plan and data.");
1104 vigra_precondition((ins.stride() == TinyVectorView<int, N>(instrides.data())),
1105 "FFTWPlan::execute(): strides mismatch between plan and input data.");
1106 vigra_precondition((outs.stride() == TinyVectorView<int, N>(outstrides.data())),
1107 "FFTWPlan::execute(): strides mismatch between plan and output data.");
1108
1109 detail::fftwPlanExecute(plan, ins.data(), outs.data());
1110
1111 typedef typename MO::value_type V;
1112 if(sign == FFTW_BACKWARD)
1113 outs *= V(1.0) / Real(outs.size());
1114 }
1115
1116 /********************************************************/
1117 /* */
1118 /* FFTWConvolvePlan */
1119 /* */
1120 /********************************************************/
1121
1122 /** C++ wrapper for a pair of FFTW plans used to perform FFT-based convolution.
1123
1124 The class encapsulates the calls to <tt>fftw_plan_dft_2d</tt>, <tt>fftw_execute</tt>, and
1125 <tt>fftw_destroy_plan</tt> (and their <tt>float</tt> and <tt>long double</tt> counterparts)
1126 in an easy-to-use interface. It always creates a pair of plans, one for the forward and one
1127 for the inverse transform required for convolution.
1128
1129 Usually, you use this class only indirectly via \ref convolveFFT() and its variants.
1130 You only need this class if you want to have more control about FFTW's planning process
1131 (by providing non-default planning flags) and/or want to re-use plans for several convolutions.
1132
1133 <b> Usage:</b>
1134
1135 <b>\#include</b> <vigra/multi_fft.hxx><br>
1136 Namespace: vigra
1137
1138 \code
1139 // convolve a real array with a real kernel
1140 MultiArray<2, double> src(Shape2(w, h)), dest(Shape2(w, h));
1141
1142 MultiArray<2, double> spatial_kernel(Shape2(9, 9));
1143 Gaussian<double> gauss(1.0);
1144
1145 for(int y=0; y<9; ++y)
1146 for(int x=0; x<9; ++x)
1147 spatial_kernel(x, y) = gauss(x-4.0)*gauss(y-4.0);
1148
1149 // create an optimized plan by measuring the speed of several algorithm variants
1150 FFTWConvolvePlan<2, double> plan(src, spatial_kernel, dest, FFTW_MEASURE);
1151
1152 plan.execute(src, spatial_kernel, dest);
1153 \endcode
1154 */
1155 template <unsigned int N, class Real>
1156 class FFTWConvolvePlan
1157 {
1158 typedef FFTWComplex<Real> Complex;
1159 typedef MultiArrayView<N, Real, UnstridedArrayTag > RArray;
1160 typedef MultiArray<N, Complex, FFTWAllocator<Complex> > CArray;
1161
1162 FFTWPlan<N, Real> forward_plan, backward_plan;
1163 RArray realArray, realKernel;
1164 CArray fourierArray, fourierKernel;
1165 bool useFourierKernel;
1166
1167 public:
1168
1169 typedef typename MultiArrayShape<N>::type Shape;
1170
1171 /** \brief Create an empty plan.
1172
1173 The plan can be initialized later by one of the init() functions.
1174 */
1175 FFTWConvolvePlan()
1176 : useFourierKernel(false)
1177 {}
1178
1179 /** \brief Create a plan to convolve a real array with a real kernel.
1180
1181 The kernel must be defined in the spatial domain.
1182 See \ref convolveFFT() for detailed information on required shapes and internal padding.
1183
1184 \arg planner_flags must be a combination of the
1185 <a href="http://www.fftw.org/doc/Planner-Flags.html">planner
1186 flags</a> defined by the FFTW library. The default <tt>FFTW_ESTIMATE</tt> will guess
1187 optimal algorithm settings or read them from pre-loaded
1188 <a href="http://www.fftw.org/doc/Wisdom.html">"wisdom"</a>.
1189 */
1190 template <class C1, class C2, class C3>
1191 FFTWConvolvePlan(MultiArrayView<N, Real, C1> in,
1192 MultiArrayView<N, Real, C2> kernel,
1193 MultiArrayView<N, Real, C3> out,
1194 unsigned int planner_flags = FFTW_ESTIMATE)
1195 : useFourierKernel(false)
1196 {
1197 init(in, kernel, out, planner_flags);
1198 }
1199
1200 /** \brief Create a plan to convolve a real array with a complex kernel.
1201
1202 The kernel must be defined in the Fourier domain, using the half-space format.
1203 See \ref convolveFFT() for detailed information on required shapes and internal padding.
1204
1205 \arg planner_flags must be a combination of the
1206 <a href="http://www.fftw.org/doc/Planner-Flags.html">planner
1207 flags</a> defined by the FFTW library. The default <tt>FFTW_ESTIMATE</tt> will guess
1208 optimal algorithm settings or read them from pre-loaded
1209 <a href="http://www.fftw.org/doc/Wisdom.html">"wisdom"</a>.
1210 */
1211 template <class C1, class C2, class C3>
1212 FFTWConvolvePlan(MultiArrayView<N, Real, C1> in,
1213 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
1214 MultiArrayView<N, Real, C3> out,
1215 unsigned int planner_flags = FFTW_ESTIMATE)
1216 : useFourierKernel(true)
1217 {
1218 init(in, kernel, out, planner_flags);
1219 }
1220
1221 /** \brief Create a plan to convolve a complex array with a complex kernel.
1222
1223 See \ref convolveFFT() for detailed information on required shapes and internal padding.
1224
1225 \arg fourierDomainKernel determines if the kernel is defined in the spatial or
1226 Fourier domain.
1227 \arg planner_flags must be a combination of the
1228 <a href="http://www.fftw.org/doc/Planner-Flags.html">planner
1229 flags</a> defined by the FFTW library. The default <tt>FFTW_ESTIMATE</tt> will guess
1230 optimal algorithm settings or read them from pre-loaded
1231 <a href="http://www.fftw.org/doc/Wisdom.html">"wisdom"</a>.
1232 */
1233 template <class C1, class C2, class C3>
1234 FFTWConvolvePlan(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1235 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
1236 MultiArrayView<N, FFTWComplex<Real>, C3> out,
1237 bool fourierDomainKernel,
1238 unsigned int planner_flags = FFTW_ESTIMATE)
1239 {
1240 init(in, kernel, out, fourierDomainKernel, planner_flags);
1241 }
1242
1243
1244 /** \brief Create a plan from just the shape information.
1245
1246 See \ref convolveFFT() for detailed information on required shapes and internal padding.
1247
1248 \arg fourierDomainKernel determines if the kernel is defined in the spatial or
1249 Fourier domain.
1250 \arg planner_flags must be a combination of the
1251 <a href="http://www.fftw.org/doc/Planner-Flags.html">planner
1252 flags</a> defined by the FFTW library. The default <tt>FFTW_ESTIMATE</tt> will guess
1253 optimal algorithm settings or read them from pre-loaded
1254 <a href="http://www.fftw.org/doc/Wisdom.html">"wisdom"</a>.
1255 */
1256 template <class C1, class C2, class C3>
1257 FFTWConvolvePlan(Shape inOut, Shape kernel,
1258 bool useFourierKernel = false,
1259 unsigned int planner_flags = FFTW_ESTIMATE)
1260 {
1261 if(useFourierKernel)
1262 init(inOut, kernel, planner_flags);
1263 else
1264 initFourierKernel(inOut, kernel, planner_flags);
1265 }
1266
1267 /** \brief Init a plan to convolve a real array with a real kernel.
1268
1269 See the constructor with the same signature for details.
1270 */
1271 template <class C1, class C2, class C3>
1272 void init(MultiArrayView<N, Real, C1> in,
1273 MultiArrayView<N, Real, C2> kernel,
1274 MultiArrayView<N, Real, C3> out,
1275 unsigned int planner_flags = FFTW_ESTIMATE)
1276 {
1277 vigra_precondition(in.shape() == out.shape(),
1278 "FFTWConvolvePlan::init(): input and output must have the same shape.");
1279 init(in.shape(), kernel.shape(), planner_flags);
1280 }
1281
1282 /** \brief Init a plan to convolve a real array with a complex kernel.
1283
1284 See the constructor with the same signature for details.
1285 */
1286 template <class C1, class C2, class C3>
1287 void init(MultiArrayView<N, Real, C1> in,
1288 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
1289 MultiArrayView<N, Real, C3> out,
1290 unsigned int planner_flags = FFTW_ESTIMATE)
1291 {
1292 vigra_precondition(in.shape() == out.shape(),
1293 "FFTWConvolvePlan::init(): input and output must have the same shape.");
1294 initFourierKernel(in.shape(), kernel.shape(), planner_flags);
1295 }
1296
1297 /** \brief Init a plan to convolve a complex array with a complex kernel.
1298
1299 See the constructor with the same signature for details.
1300 */
1301 template <class C1, class C2, class C3>
1302 void init(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1303 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
1304 MultiArrayView<N, FFTWComplex<Real>, C3> out,
1305 bool fourierDomainKernel,
1306 unsigned int planner_flags = FFTW_ESTIMATE)
1307 {
1308 vigra_precondition(in.shape() == out.shape(),
1309 "FFTWConvolvePlan::init(): input and output must have the same shape.");
1310 useFourierKernel = fourierDomainKernel;
1311 initComplex(in.shape(), kernel.shape(), planner_flags);
1312 }
1313
1314 /** \brief Init a plan to convolve a real array with a sequence of kernels.
1315
1316 The kernels can be either real or complex. The sequences \a kernels and \a outs
1317 must have the same length. See the corresponding constructors
1318 for single kernels for details.
1319 */
1320 template <class C1, class KernelIterator, class OutIterator>
1321 void initMany(MultiArrayView<N, Real, C1> in,
1322 KernelIterator kernels, KernelIterator kernelsEnd,
1323 OutIterator outs, unsigned int planner_flags = FFTW_ESTIMATE)
1324 {
1325 typedef typename std::iterator_traits<KernelIterator>::value_type KernelArray;
1326 typedef typename KernelArray::value_type KernelValue;
1327 typedef typename std::iterator_traits<OutIterator>::value_type OutArray;
1328 typedef typename OutArray::value_type OutValue;
1329
1330 bool realKernel = IsSameType<KernelValue, Real>::value;
1331 bool fourierKernel = IsSameType<KernelValue, Complex>::value;
1332
1333 vigra_precondition(realKernel || fourierKernel,
1334 "FFTWConvolvePlan::initMany(): kernels have unsuitable value_type.");
1335 vigra_precondition((IsSameType<OutValue, Real>::value),
1336 "FFTWConvolvePlan::initMany(): outputs have unsuitable value_type.");
1337
1338 if(realKernel)
1339 {
1340 initMany(in.shape(), checkShapes(in.shape(), kernels, kernelsEnd, outs),
1341 planner_flags);
1342 }
1343 else
1344 {
1345 initFourierKernelMany(in.shape(),
1346 checkShapesFourier(in.shape(), kernels, kernelsEnd, outs),
1347 planner_flags);
1348 }
1349 }
1350
1351 /** \brief Init a plan to convolve a complex array with a sequence of kernels.
1352
1353 The kernels must be complex as well. The sequences \a kernels and \a outs
1354 must have the same length. See the corresponding constructors
1355 for single kernels for details.
1356 */
1357 template <class C1, class KernelIterator, class OutIterator>
1358 void initMany(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1359 KernelIterator kernels, KernelIterator kernelsEnd,
1360 OutIterator outs,
1361 bool fourierDomainKernels,
1362 unsigned int planner_flags = FFTW_ESTIMATE)
1363 {
1364 typedef typename std::iterator_traits<KernelIterator>::value_type KernelArray;
1365 typedef typename KernelArray::value_type KernelValue;
1366 typedef typename std::iterator_traits<OutIterator>::value_type OutArray;
1367 typedef typename OutArray::value_type OutValue;
1368
1369 vigra_precondition((IsSameType<KernelValue, Complex>::value),
1370 "FFTWConvolvePlan::initMany(): kernels have unsuitable value_type.");
1371 vigra_precondition((IsSameType<OutValue, Complex>::value),
1372 "FFTWConvolvePlan::initMany(): outputs have unsuitable value_type.");
1373
1374 useFourierKernel = fourierDomainKernels;
1375
1376 Shape paddedShape = checkShapesComplex(in.shape(), kernels, kernelsEnd, outs);
1377
1378 CArray newFourierArray(paddedShape), newFourierKernel(paddedShape);
1379
1380 FFTWPlan<N, Real> fplan(newFourierArray, newFourierArray, FFTW_FORWARD, planner_flags);
1381 FFTWPlan<N, Real> bplan(newFourierArray, newFourierArray, FFTW_BACKWARD, planner_flags);
1382
1383 forward_plan = fplan;
1384 backward_plan = bplan;
1385 fourierArray.swap(newFourierArray);
1386 fourierKernel.swap(newFourierKernel);
1387 }
1388
1389 void init(Shape inOut, Shape kernel,
1390 unsigned int planner_flags = FFTW_ESTIMATE);
1391
1392 void initFourierKernel(Shape inOut, Shape kernel,
1393 unsigned int planner_flags = FFTW_ESTIMATE);
1394
1395 void initComplex(Shape inOut, Shape kernel,
1396 unsigned int planner_flags = FFTW_ESTIMATE);
1397
1398 void initMany(Shape inOut, Shape maxKernel,
1399 unsigned int planner_flags = FFTW_ESTIMATE)
1400 {
1401 init(inOut, maxKernel, planner_flags);
1402 }
1403
1404 void initFourierKernelMany(Shape inOut, Shape kernels,
1405 unsigned int planner_flags = FFTW_ESTIMATE)
1406 {
1407 initFourierKernel(inOut, kernels, planner_flags);
1408 }
1409
1410 /** \brief Execute a plan to convolve a real array with a real kernel.
1411
1412 The array shapes must be the same as in the corresponding init function
1413 or constructor. However, execute() can be called several times on
1414 the same plan, even with different arrays, as long as they have the appropriate
1415 shapes.
1416 */
1417 template <class C1, class C2, class C3>
1418 void execute(MultiArrayView<N, Real, C1> in,
1419 MultiArrayView<N, Real, C2> kernel,
1420 MultiArrayView<N, Real, C3> out);
1421
1422 /** \brief Execute a plan to convolve a real array with a complex kernel.
1423
1424 The array shapes must be the same as in the corresponding init function
1425 or constructor. However, execute() can be called several times on
1426 the same plan, even with different arrays, as long as they have the appropriate
1427 shapes.
1428 */
1429 template <class C1, class C2, class C3>
1430 void execute(MultiArrayView<N, Real, C1> in,
1431 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
1432 MultiArrayView<N, Real, C3> out);
1433
1434 /** \brief Execute a plan to convolve a complex array with a complex kernel.
1435
1436 The array shapes must be the same as in the corresponding init function
1437 or constructor. However, execute() can be called several times on
1438 the same plan, even with different arrays, as long as they have the appropriate
1439 shapes.
1440 */
1441 template <class C1, class C2, class C3>
1442 void execute(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1443 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
1444 MultiArrayView<N, FFTWComplex<Real>, C3> out);
1445
1446
1447 /** \brief Execute a plan to convolve a complex array with a sequence of kernels.
1448
1449 The array shapes must be the same as in the corresponding init function
1450 or constructor. However, executeMany() can be called several times on
1451 the same plan, even with different arrays, as long as they have the appropriate
1452 shapes.
1453 */
1454 template <class C1, class KernelIterator, class OutIterator>
1455 void executeMany(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1456 KernelIterator kernels, KernelIterator kernelsEnd,
1457 OutIterator outs);
1458
1459 /** \brief Execute a plan to convolve a real array with a sequence of kernels.
1460
1461 The array shapes must be the same as in the corresponding init function
1462 or constructor. However, executeMany() can be called several times on
1463 the same plan, even with different arrays, as long as they have the appropriate
1464 shapes.
1465 */
1466 template <class C1, class KernelIterator, class OutIterator>
1467 void executeMany(MultiArrayView<N, Real, C1> in,
1468 KernelIterator kernels, KernelIterator kernelsEnd,
1469 OutIterator outs)
1470 {
1471 typedef typename std::iterator_traits<KernelIterator>::value_type KernelArray;
1472 typedef typename KernelArray::value_type KernelValue;
1473 typedef typename IsSameType<KernelValue, Complex>::type UseFourierKernel;
1474 typedef typename std::iterator_traits<OutIterator>::value_type OutArray;
1475 typedef typename OutArray::value_type OutValue;
1476
1477 bool realKernel = IsSameType<KernelValue, Real>::value;
1478 bool fourierKernel = IsSameType<KernelValue, Complex>::value;
1479
1480 vigra_precondition(realKernel || fourierKernel,
1481 "FFTWConvolvePlan::executeMany(): kernels have unsuitable value_type.");
1482 vigra_precondition((IsSameType<OutValue, Real>::value),
1483 "FFTWConvolvePlan::executeMany(): outputs have unsuitable value_type.");
1484
1485 executeManyImpl(in, kernels, kernelsEnd, outs, UseFourierKernel());
1486 }
1487
1488 private:
1489
1490 template <class KernelIterator, class OutIterator>
1491 Shape checkShapes(Shape in,
1492 KernelIterator kernels, KernelIterator kernelsEnd,
1493 OutIterator outs);
1494
1495 template <class KernelIterator, class OutIterator>
1496 Shape checkShapesFourier(Shape in,
1497 KernelIterator kernels, KernelIterator kernelsEnd,
1498 OutIterator outs);
1499
1500 template <class KernelIterator, class OutIterator>
1501 Shape checkShapesComplex(Shape in,
1502 KernelIterator kernels, KernelIterator kernelsEnd,
1503 OutIterator outs);
1504
1505 template <class C1, class KernelIterator, class OutIterator>
1506 void
1507 executeManyImpl(MultiArrayView<N, Real, C1> in,
1508 KernelIterator kernels, KernelIterator kernelsEnd,
1509 OutIterator outs, VigraFalseType /* useFourierKernel*/);
1510
1511 template <class C1, class KernelIterator, class OutIterator>
1512 void
1513 executeManyImpl(MultiArrayView<N, Real, C1> in,
1514 KernelIterator kernels, KernelIterator kernelsEnd,
1515 OutIterator outs, VigraTrueType /* useFourierKernel*/);
1516
1517 };
1518
1519 template <unsigned int N, class Real>
1520 void
1521 FFTWConvolvePlan<N, Real>::init(Shape in, Shape kernel,
1522 unsigned int planner_flags)
1523 {
1524 Shape paddedShape = fftwBestPaddedShapeR2C(in + kernel - Shape(1)),
1525 complexShape = fftwCorrespondingShapeR2C(paddedShape);
1526
1527 CArray newFourierArray(complexShape), newFourierKernel(complexShape);
1528
1529 Shape realStrides = 2*newFourierArray.stride();
1530 realStrides[0] = 1;
1531 RArray newRealArray(paddedShape, realStrides, (Real*)newFourierArray.data());
1532 RArray newRealKernel(paddedShape, realStrides, (Real*)newFourierKernel.data());
1533
1534 FFTWPlan<N, Real> fplan(newRealArray, newFourierArray, planner_flags);
1535 FFTWPlan<N, Real> bplan(newFourierArray, newRealArray, planner_flags);
1536
1537 forward_plan = fplan;
1538 backward_plan = bplan;
1539 realArray = newRealArray;
1540 realKernel = newRealKernel;
1541 fourierArray.swap(newFourierArray);
1542 fourierKernel.swap(newFourierKernel);
1543 useFourierKernel = false;
1544 }
1545
1546 template <unsigned int N, class Real>
1547 void
1548 FFTWConvolvePlan<N, Real>::initFourierKernel(Shape in, Shape kernel,
1549 unsigned int planner_flags)
1550 {
1551 Shape complexShape = kernel,
1552 paddedShape = fftwCorrespondingShapeC2R(complexShape);
1553
1554 for(unsigned int k=0; k<N; ++k)
1555 vigra_precondition(in[k] <= paddedShape[k],
1556 "FFTWConvolvePlan::init(): kernel too small for given input.");
1557
1558 CArray newFourierArray(complexShape), newFourierKernel(complexShape);
1559
1560 Shape realStrides = 2*newFourierArray.stride();
1561 realStrides[0] = 1;
1562 RArray newRealArray(paddedShape, realStrides, (Real*)newFourierArray.data());
1563 RArray newRealKernel(paddedShape, realStrides, (Real*)newFourierKernel.data());
1564
1565 FFTWPlan<N, Real> fplan(newRealArray, newFourierArray, planner_flags);
1566 FFTWPlan<N, Real> bplan(newFourierArray, newRealArray, planner_flags);
1567
1568 forward_plan = fplan;
1569 backward_plan = bplan;
1570 realArray = newRealArray;
1571 realKernel = newRealKernel;
1572 fourierArray.swap(newFourierArray);
1573 fourierKernel.swap(newFourierKernel);
1574 useFourierKernel = true;
1575 }
1576
1577 template <unsigned int N, class Real>
1578 void
1579 FFTWConvolvePlan<N, Real>::initComplex(Shape in, Shape kernel,
1580 unsigned int planner_flags)
1581 {
1582 Shape paddedShape;
1583
1584 if(useFourierKernel)
1585 {
1586 for(unsigned int k=0; k<N; ++k)
1587 vigra_precondition(in[k] <= kernel[k],
1588 "FFTWConvolvePlan::init(): kernel too small for given input.");
1589
1590 paddedShape = kernel;
1591 }
1592 else
1593 {
1594 paddedShape = fftwBestPaddedShape(in + kernel - Shape(1));
1595 }
1596
1597 CArray newFourierArray(paddedShape), newFourierKernel(paddedShape);
1598
1599 FFTWPlan<N, Real> fplan(newFourierArray, newFourierArray, FFTW_FORWARD, planner_flags);
1600 FFTWPlan<N, Real> bplan(newFourierArray, newFourierArray, FFTW_BACKWARD, planner_flags);
1601
1602 forward_plan = fplan;
1603 backward_plan = bplan;
1604 fourierArray.swap(newFourierArray);
1605 fourierKernel.swap(newFourierKernel);
1606 }
1607
1608 #ifndef DOXYGEN // doxygen documents these functions as free functions
1609
1610 template <unsigned int N, class Real>
1611 template <class C1, class C2, class C3>
1612 void
1613 FFTWConvolvePlan<N, Real>::execute(MultiArrayView<N, Real, C1> in,
1614 MultiArrayView<N, Real, C2> kernel,
1615 MultiArrayView<N, Real, C3> out)
1616 {
1617 vigra_precondition(!useFourierKernel,
1618 "FFTWConvolvePlan::execute(): plan was generated for Fourier kernel, got spatial kernel.");
1619
1620 vigra_precondition(in.shape() == out.shape(),
1621 "FFTWConvolvePlan::execute(): input and output must have the same shape.");
1622
1623 Shape paddedShape = fftwBestPaddedShapeR2C(in.shape() + kernel.shape() - Shape(1)),
1624 diff = paddedShape - in.shape(),
1625 left = div(diff, MultiArrayIndex(2)),
1626 right = in.shape() + left;
1627
1628 vigra_precondition(paddedShape == realArray.shape(),
1629 "FFTWConvolvePlan::execute(): shape mismatch between input and plan.");
1630
1631 detail::fftEmbedArray(in, realArray);
1632 forward_plan.execute(realArray, fourierArray);
1633
1634 detail::fftEmbedKernel(kernel, realKernel);
1635 forward_plan.execute(realKernel, fourierKernel);
1636
1637 fourierArray *= fourierKernel;
1638
1639 backward_plan.execute(fourierArray, realArray);
1640
1641 out = realArray.subarray(left, right);
1642 }
1643
1644 template <unsigned int N, class Real>
1645 template <class C1, class C2, class C3>
1646 void
1647 FFTWConvolvePlan<N, Real>::execute(MultiArrayView<N, Real, C1> in,
1648 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
1649 MultiArrayView<N, Real, C3> out)
1650 {
1651 vigra_precondition(useFourierKernel,
1652 "FFTWConvolvePlan::execute(): plan was generated for spatial kernel, got Fourier kernel.");
1653
1654 vigra_precondition(in.shape() == out.shape(),
1655 "FFTWConvolvePlan::execute(): input and output must have the same shape.");
1656
1657 vigra_precondition(kernel.shape() == fourierArray.shape(),
1658 "FFTWConvolvePlan::execute(): shape mismatch between kernel and plan.");
1659
1660 Shape paddedShape = fftwCorrespondingShapeC2R(kernel.shape(), odd(in.shape(0))),
1661 diff = paddedShape - in.shape(),
1662 left = div(diff, MultiArrayIndex(2)),
1663 right = in.shape() + left;
1664
1665 vigra_precondition(paddedShape == realArray.shape(),
1666 "FFTWConvolvePlan::execute(): shape mismatch between input and plan.");
1667
1668 detail::fftEmbedArray(in, realArray);
1669 forward_plan.execute(realArray, fourierArray);
1670
1671 fourierKernel = kernel;
1672 moveDCToHalfspaceUpperLeft(fourierKernel);
1673
1674 fourierArray *= fourierKernel;
1675
1676 backward_plan.execute(fourierArray, realArray);
1677
1678 out = realArray.subarray(left, right);
1679 }
1680
1681 template <unsigned int N, class Real>
1682 template <class C1, class C2, class C3>
1683 void
1684 FFTWConvolvePlan<N, Real>::execute(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1685 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
1686 MultiArrayView<N, FFTWComplex<Real>, C3> out)
1687 {
1688 vigra_precondition(in.shape() == out.shape(),
1689 "FFTWConvolvePlan::execute(): input and output must have the same shape.");
1690
1691 Shape paddedShape = fourierArray.shape(),
1692 diff = paddedShape - in.shape(),
1693 left = div(diff, MultiArrayIndex(2)),
1694 right = in.shape() + left;
1695
1696 if(useFourierKernel)
1697 {
1698 vigra_precondition(kernel.shape() == fourierArray.shape(),
1699 "FFTWConvolvePlan::execute(): shape mismatch between kernel and plan.");
1700
1701 fourierKernel = kernel;
1702 moveDCToUpperLeft(fourierKernel);
1703 }
1704 else
1705 {
1706 detail::fftEmbedKernel(kernel, fourierKernel);
1707 forward_plan.execute(fourierKernel, fourierKernel);
1708 }
1709
1710 detail::fftEmbedArray(in, fourierArray);
1711 forward_plan.execute(fourierArray, fourierArray);
1712
1713 fourierArray *= fourierKernel;
1714
1715 backward_plan.execute(fourierArray, fourierArray);
1716
1717 out = fourierArray.subarray(left, right);
1718 }
1719
1720 template <unsigned int N, class Real>
1721 template <class C1, class KernelIterator, class OutIterator>
1722 void
1723 FFTWConvolvePlan<N, Real>::executeManyImpl(MultiArrayView<N, Real, C1> in,
1724 KernelIterator kernels, KernelIterator kernelsEnd,
1725 OutIterator outs, VigraFalseType /*useFourierKernel*/)
1726 {
1727 vigra_precondition(!useFourierKernel,
1728 "FFTWConvolvePlan::execute(): plan was generated for Fourier kernel, got spatial kernel.");
1729
1730 Shape kernelMax = checkShapes(in.shape(), kernels, kernelsEnd, outs),
1731 paddedShape = fftwBestPaddedShapeR2C(in.shape() + kernelMax - Shape(1)),
1732 diff = paddedShape - in.shape(),
1733 left = div(diff, MultiArrayIndex(2)),
1734 right = in.shape() + left;
1735
1736 vigra_precondition(paddedShape == realArray.shape(),
1737 "FFTWConvolvePlan::executeMany(): shape mismatch between input and plan.");
1738
1739 detail::fftEmbedArray(in, realArray);
1740 forward_plan.execute(realArray, fourierArray);
1741
1742 for(; kernels != kernelsEnd; ++kernels, ++outs)
1743 {
1744 detail::fftEmbedKernel(*kernels, realKernel);
1745 forward_plan.execute(realKernel, fourierKernel);
1746
1747 fourierKernel *= fourierArray;
1748
1749 backward_plan.execute(fourierKernel, realKernel);
1750
1751 *outs = realKernel.subarray(left, right);
1752 }
1753 }
1754
1755 template <unsigned int N, class Real>
1756 template <class C1, class KernelIterator, class OutIterator>
1757 void
1758 FFTWConvolvePlan<N, Real>::executeManyImpl(MultiArrayView<N, Real, C1> in,
1759 KernelIterator kernels, KernelIterator kernelsEnd,
1760 OutIterator outs, VigraTrueType /*useFourierKernel*/)
1761 {
1762 vigra_precondition(useFourierKernel,
1763 "FFTWConvolvePlan::execute(): plan was generated for spatial kernel, got Fourier kernel.");
1764
1765 Shape complexShape = checkShapesFourier(in.shape(), kernels, kernelsEnd, outs),
1766 paddedShape = fftwCorrespondingShapeC2R(complexShape, odd(in.shape(0))),
1767 diff = paddedShape - in.shape(),
1768 left = div(diff, MultiArrayIndex(2)),
1769 right = in.shape() + left;
1770
1771 vigra_precondition(complexShape == fourierArray.shape(),
1772 "FFTWConvolvePlan::executeFourierKernelMany(): shape mismatch between kernels and plan.");
1773
1774 vigra_precondition(paddedShape == realArray.shape(),
1775 "FFTWConvolvePlan::executeFourierKernelMany(): shape mismatch between input and plan.");
1776
1777 detail::fftEmbedArray(in, realArray);
1778 forward_plan.execute(realArray, fourierArray);
1779
1780 for(; kernels != kernelsEnd; ++kernels, ++outs)
1781 {
1782 fourierKernel = *kernels;
1783 moveDCToHalfspaceUpperLeft(fourierKernel);
1784 fourierKernel *= fourierArray;
1785
1786 backward_plan.execute(fourierKernel, realKernel);
1787
1788 *outs = realKernel.subarray(left, right);
1789 }
1790 }
1791
1792 template <unsigned int N, class Real>
1793 template <class C1, class KernelIterator, class OutIterator>
1794 void
1795 FFTWConvolvePlan<N, Real>::executeMany(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1796 KernelIterator kernels, KernelIterator kernelsEnd,
1797 OutIterator outs)
1798 {
1799 typedef typename std::iterator_traits<KernelIterator>::value_type KernelArray;
1800 typedef typename KernelArray::value_type KernelValue;
1801 typedef typename std::iterator_traits<OutIterator>::value_type OutArray;
1802 typedef typename OutArray::value_type OutValue;
1803
1804 vigra_precondition((IsSameType<KernelValue, Complex>::value),
1805 "FFTWConvolvePlan::executeMany(): kernels have unsuitable value_type.");
1806 vigra_precondition((IsSameType<OutValue, Complex>::value),
1807 "FFTWConvolvePlan::executeMany(): outputs have unsuitable value_type.");
1808
1809 Shape paddedShape = checkShapesComplex(in.shape(), kernels, kernelsEnd, outs),
1810 diff = paddedShape - in.shape(),
1811 left = div(diff, MultiArrayIndex(2)),
1812 right = in.shape() + left;
1813
1814 detail::fftEmbedArray(in, fourierArray);
1815 forward_plan.execute(fourierArray, fourierArray);
1816
1817 for(; kernels != kernelsEnd; ++kernels, ++outs)
1818 {
1819 if(useFourierKernel)
1820 {
1821 fourierKernel = *kernels;
1822 moveDCToUpperLeft(fourierKernel);
1823 }
1824 else
1825 {
1826 detail::fftEmbedKernel(*kernels, fourierKernel);
1827 forward_plan.execute(fourierKernel, fourierKernel);
1828 }
1829
1830 fourierKernel *= fourierArray;
1831
1832 backward_plan.execute(fourierKernel, fourierKernel);
1833
1834 *outs = fourierKernel.subarray(left, right);
1835 }
1836 }
1837
1838 #endif // DOXYGEN
1839
1840 template <unsigned int N, class Real>
1841 template <class KernelIterator, class OutIterator>
1842 typename FFTWConvolvePlan<N, Real>::Shape
1843 FFTWConvolvePlan<N, Real>::checkShapes(Shape in,
1844 KernelIterator kernels, KernelIterator kernelsEnd,
1845 OutIterator outs)
1846 {
1847 vigra_precondition(kernels != kernelsEnd,
1848 "FFTWConvolvePlan::checkShapes(): empty kernel sequence.");
1849
1850 Shape kernelMax;
1851 for(; kernels != kernelsEnd; ++kernels, ++outs)
1852 {
1853 vigra_precondition(in == outs->shape(),
1854 "FFTWConvolvePlan::checkShapes(): shape mismatch between input and (one) output.");
1855 kernelMax = max(kernelMax, kernels->shape());
1856 }
1857 vigra_precondition(prod(kernelMax) > 0,
1858 "FFTWConvolvePlan::checkShapes(): all kernels have size 0.");
1859 return kernelMax;
1860 }
1861
1862 template <unsigned int N, class Real>
1863 template <class KernelIterator, class OutIterator>
1864 typename FFTWConvolvePlan<N, Real>::Shape
1865 FFTWConvolvePlan<N, Real>::checkShapesFourier(Shape in,
1866 KernelIterator kernels, KernelIterator kernelsEnd,
1867 OutIterator outs)
1868 {
1869 vigra_precondition(kernels != kernelsEnd,
1870 "FFTWConvolvePlan::checkShapesFourier(): empty kernel sequence.");
1871
1872 Shape complexShape = kernels->shape(),
1873 paddedShape = fftwCorrespondingShapeC2R(complexShape);
1874
1875 for(unsigned int k=0; k<N; ++k)
1876 vigra_precondition(in[k] <= paddedShape[k],
1877 "FFTWConvolvePlan::checkShapesFourier(): kernels too small for given input.");
1878
1879 for(; kernels != kernelsEnd; ++kernels, ++outs)
1880 {
1881 vigra_precondition(in == outs->shape(),
1882 "FFTWConvolvePlan::checkShapesFourier(): shape mismatch between input and (one) output.");
1883 vigra_precondition(complexShape == kernels->shape(),
1884 "FFTWConvolvePlan::checkShapesFourier(): all kernels must have the same size.");
1885 }
1886 return complexShape;
1887 }
1888
1889 template <unsigned int N, class Real>
1890 template <class KernelIterator, class OutIterator>
1891 typename FFTWConvolvePlan<N, Real>::Shape
1892 FFTWConvolvePlan<N, Real>::checkShapesComplex(Shape in,
1893 KernelIterator kernels, KernelIterator kernelsEnd,
1894 OutIterator outs)
1895 {
1896 vigra_precondition(kernels != kernelsEnd,
1897 "FFTWConvolvePlan::checkShapesComplex(): empty kernel sequence.");
1898
1899 Shape kernelShape = kernels->shape();
1900 for(; kernels != kernelsEnd; ++kernels, ++outs)
1901 {
1902 vigra_precondition(in == outs->shape(),
1903 "FFTWConvolvePlan::checkShapesComplex(): shape mismatch between input and (one) output.");
1904 if(useFourierKernel)
1905 {
1906 vigra_precondition(kernelShape == kernels->shape(),
1907 "FFTWConvolvePlan::checkShapesComplex(): Fourier domain kernels must have identical size.");
1908 }
1909 else
1910 {
1911 kernelShape = max(kernelShape, kernels->shape());
1912 }
1913 }
1914 vigra_precondition(prod(kernelShape) > 0,
1915 "FFTWConvolvePlan::checkShapesComplex(): all kernels have size 0.");
1916
1917 if(useFourierKernel)
1918 {
1919 for(unsigned int k=0; k<N; ++k)
1920 vigra_precondition(in[k] <= kernelShape[k],
1921 "FFTWConvolvePlan::checkShapesComplex(): kernels too small for given input.");
1922 return kernelShape;
1923 }
1924 else
1925 {
1926 return fftwBestPaddedShape(in + kernelShape - Shape(1));
1927 }
1928 }
1929
1930
1931 /********************************************************/
1932 /* */
1933 /* fourierTransform */
1934 /* */
1935 /********************************************************/
1936
1937 template <unsigned int N, class Real, class C1, class C2>
1938 inline void
1939 fourierTransform(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1940 MultiArrayView<N, FFTWComplex<Real>, C2> out)
1941 {
1942 FFTWPlan<N, Real>(in, out, FFTW_FORWARD).execute(in, out);
1943 }
1944
1945 template <unsigned int N, class Real, class C1, class C2>
1946 inline void
1947 fourierTransformInverse(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1948 MultiArrayView<N, FFTWComplex<Real>, C2> out)
1949 {
1950 FFTWPlan<N, Real>(in, out, FFTW_BACKWARD).execute(in, out);
1951 }
1952
1953 template <unsigned int N, class Real, class C1, class C2>
1954 void
1955 fourierTransform(MultiArrayView<N, Real, C1> in,
1956 MultiArrayView<N, FFTWComplex<Real>, C2> out)
1957 {
1958 if(in.shape() == out.shape())
1959 {
1960 // copy the input array into the output and then perform an in-place FFT
1961 out = in;
1962 FFTWPlan<N, Real>(out, out, FFTW_FORWARD).execute(out, out);
1963 }
1964 else if(out.shape() == fftwCorrespondingShapeR2C(in.shape()))
1965 {
1966 FFTWPlan<N, Real>(in, out).execute(in, out);
1967 }
1968 else
1969 vigra_precondition(false,
1970 "fourierTransform(): shape mismatch between input and output.");
1971 }
1972
1973 template <unsigned int N, class Real, class C1, class C2>
1974 void
1975 fourierTransformInverse(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1976 MultiArrayView<N, Real, C2> out)
1977 {
1978 vigra_precondition(in.shape() == fftwCorrespondingShapeR2C(out.shape()),
1979 "fourierTransformInverse(): shape mismatch between input and output.");
1980 FFTWPlan<N, Real>(in, out).execute(in, out);
1981 }
1982
1983 //@}
1984
1985 /** \addtogroup MultiArrayConvolutionFilters
1986 */
1987 //@{
1988
1989 /********************************************************/
1990 /* */
1991 /* convolveFFT */
1992 /* */
1993 /********************************************************/
1994
1995 /** \brief Convolve an array with a kernel by means of the Fourier transform.
1996
1997 Thanks to the convolution theorem of Fourier theory, a convolution in the spatial domain
1998 is equivalent to a multiplication in the frequency domain. Thus, for certain kernels
1999 (especially large, non-separable ones), it is advantageous to perform the convolution by first
2000 transforming both array and kernel to the frequency domain, multiplying the frequency
2001 representations, and transforming the result back into the spatial domain.
2002 Some kernels have a much simpler definition in the frequency domain, so that they are readily
2003 computed there directly, avoiding Fourier transformation of those kernels.
2004
2005 The following functions implement various variants of FFT-based convolution:
2006
2007 <DL>
2008 <DT><b>convolveFFT</b><DD> Convolve a real-valued input array with a kernel such that the
2009 result is also real-valued. That is, the kernel is either provided
2010 as a real-valued array in the spatial domain, or as a
2011 complex-valued array in the Fourier domain, using the half-space format
2012 of the R2C Fourier transform (see below).
2013 <DT><b>convolveFFTMany</b><DD> Like <tt>convolveFFT</tt>, but you may provide many kernels at once
2014 (using an iterator pair specifying the kernel sequence).
2015 This has the advantage that the forward transform of the input array needs
2016 to be executed only once.
2017 <DT><b>convolveFFTComplex</b><DD> Convolve a complex-valued input array with a complex-valued kernel,
2018 resulting in a complex-valued output array. An additional flag is used to
2019 specify whether the kernel is defined in the spatial or frequency domain.
2020 <DT><b>convolveFFTComplexMany</b><DD> Like <tt>convolveFFTComplex</tt>, but you may provide many kernels at once
2021 (using an iterator pair specifying the kernel sequence).
2022 This has the advantage that the forward transform of the input array needs
2023 to be executed only once.
2024 </DL>
2025
2026 The output arrays must have the same shape as the input arrays. In the "Many" variants of the
2027 convolution functions, the kernels must all have the same shape.
2028
2029 The origin of the kernel is always assumed to be in the center of the kernel array (precisely,
2030 at the point <tt>floor(kernel.shape() / 2.0)</tt>, except when the half-space format is used, see below).
2031 The function \ref moveDCToUpperLeft() will be called internally to align the kernel with the transformed
2032 input as appropriate.
2033
2034 If a real input is combined with a real kernel, the kernel is automatically assumed to be defined
2035 in the spatial domain. If a real input is combined with a complex kernel, the kernel is assumed
2036 to be defined in the Fourier domain in half-space format. If the input array is complex, a flag
2037 <tt>fourierDomainKernel</tt> determines where the kernel is defined.
2038
2039 When the kernel is defined in the spatial domain, the convolution functions will automatically pad
2040 (enlarge) the input array by at least the kernel radius in each direction. The newly added space is
2041 filled according to reflective boundary conditions in order to minimize border artifacts during
2042 convolution. It is thus ensured that convolution in the Fourier domain yields the same results as
2043 convolution in the spatial domain (e.g. when \ref separableConvolveMultiArray() is called with the
2044 same kernel). A little further padding may be added to make sure that the padded array shape
2045 uses integers which have only small prime factors, because FFTW is then able to use the fastest
2046 possible algorithms. Any padding is automatically removed from the result arrays before the function
2047 returns.
2048
2049 When the kernel is defined in the frequency domain, it must be complex-valued, and its shape determines
2050 the shape of the Fourier representation (i.e. the input is padded according to the shape of the kernel).
2051 If we are going to perform a complex-valued convolution, the kernel must be defined for the entire
2052 frequency domain, and its shape directly determines the size of the FFT.
2053
2054 In contrast, a frequency domain kernel for a real-valued convolution must have symmetry properties
2055 that allow to drop half of the kernel coefficients, as in the
2056 <a href="http://www.fftw.org/doc/Multi_002dDimensional-DFTs-of-Real-Data.html">R2C transform</a>.
2057 That is, the kernel must have the <i>half-space format</i>, that is the shape returned by <tt>fftwCorrespondingShapeR2C(fourier_shape)</tt>, where <tt>fourier_shape</tt> is the desired
2058 logical shape of the frequency representation (and thus the size of the padded input). The origin
2059 of the kernel must be at the point
2060 <tt>(0, floor(fourier_shape[0] / 2.0), ..., floor(fourier_shape[N-1] / 2.0))</tt>
2061 (i.e. as in a regular kernel except for the first dimension).
2062
2063 The <tt>Real</tt> type in the declarations can be <tt>double</tt>, <tt>float</tt>, and
2064 <tt>long double</tt>. Your program must always link against <tt>libfftw3</tt>. If you use
2065 <tt>float</tt> or <tt>long double</tt> arrays, you must <i>additionally</i> link against
2066 <tt>libfftw3f</tt> and <tt>libfftw3l</tt> respectively.
2067
2068 The Fourier transform functions internally create <a href="http://www.fftw.org/doc/Using-Plans.html">FFTW plans</a>
2069 which control the algorithm details. The plans are creates with the flag <tt>FFTW_ESTIMATE</tt>, i.e.
2070 optimal settings are guessed or read from saved "wisdom" files. If you need more control over planning,
2071 you can use the class \ref FFTWConvolvePlan.
2072
2073 See also \ref applyFourierFilter() for corresponding functionality on the basis of the
2074 old image iterator interface.
2075
2076 <b> Declarations:</b>
2077
2078 Real-valued convolution with kernel in the spatial domain:
2079 \code
2080 namespace vigra {
2081 template <unsigned int N, class Real, class C1, class C2, class C3>
2082 void
2083 convolveFFT(MultiArrayView<N, Real, C1> in,
2084 MultiArrayView<N, Real, C2> kernel,
2085 MultiArrayView<N, Real, C3> out);
2086 }
2087 \endcode
2088
2089 Real-valued convolution with kernel in the Fourier domain (half-space format):
2090 \code
2091 namespace vigra {
2092 template <unsigned int N, class Real, class C1, class C2, class C3>
2093 void
2094 convolveFFT(MultiArrayView<N, Real, C1> in,
2095 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
2096 MultiArrayView<N, Real, C3> out);
2097 }
2098 \endcode
2099
2100 Series of real-valued convolutions with kernels in the spatial or Fourier domain
2101 (the kernel and out sequences must have the same length):
2102 \code
2103 namespace vigra {
2104 template <unsigned int N, class Real, class C1,
2105 class KernelIterator, class OutIterator>
2106 void
2107 convolveFFTMany(MultiArrayView<N, Real, C1> in,
2108 KernelIterator kernels, KernelIterator kernelsEnd,
2109 OutIterator outs);
2110 }
2111 \endcode
2112
2113 Complex-valued convolution (parameter <tt>fourierDomainKernel</tt> determines if
2114 the kernel is defined in the spatial or Fourier domain):
2115 \code
2116 namespace vigra {
2117 template <unsigned int N, class Real, class C1, class C2, class C3>
2118 void
2119 convolveFFTComplex(MultiArrayView<N, FFTWComplex<Real>, C1> in,
2120 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
2121 MultiArrayView<N, FFTWComplex<Real>, C3> out,
2122 bool fourierDomainKernel);
2123 }
2124 \endcode
2125
2126 Series of complex-valued convolutions (parameter <tt>fourierDomainKernel</tt>
2127 determines if the kernels are defined in the spatial or Fourier domain,
2128 the kernel and out sequences must have the same length):
2129 \code
2130 namespace vigra {
2131 template <unsigned int N, class Real, class C1,
2132 class KernelIterator, class OutIterator>
2133 void
2134 convolveFFTComplexMany(MultiArrayView<N, FFTWComplex<Real>, C1> in,
2135 KernelIterator kernels, KernelIterator kernelsEnd,
2136 OutIterator outs,
2137 bool fourierDomainKernel);
2138 }
2139 \endcode
2140
2141 <b> Usage:</b>
2142
2143 <b>\#include</b> <vigra/multi_fft.hxx><br>
2144 Namespace: vigra
2145
2146 \code
2147 // convolve real array with a Gaussian (sigma=1) defined in the spatial domain
2148 // (implicitly uses padding by at least 4 pixels)
2149 MultiArray<2, double> src(Shape2(w, h)), dest(Shape2(w,h));
2150
2151 MultiArray<2, double> spatial_kernel(Shape2(9, 9));
2152 Gaussian<double> gauss(1.0);
2153
2154 for(int y=0; y<9; ++y)
2155 for(int x=0; x<9; ++x)
2156 spatial_kernel(x, y) = gauss(x-4.0)*gauss(y-4.0);
2157
2158 convolveFFT(src, spatial_kernel, dest);
2159
2160 // convolve real array with a Gaussian (sigma=1) defined in the Fourier domain
2161 // (uses no padding, because the kernel size corresponds to the input size)
2162 MultiArray<2, FFTWComplex<double> > fourier_kernel(fftwCorrespondingShapeR2C(src.shape()));
2163 int y0 = h / 2;
2164
2165 for(int y=0; y<fourier_kernel.shape(1); ++y)
2166 for(int x=0; x<fourier_kernel.shape(0); ++x)
2167 fourier_kernel(x, y) = exp(-0.5*sq(x / double(w))) * exp(-0.5*sq((y-y0)/double(h)));
2168
2169 convolveFFT(src, fourier_kernel, dest);
2170 \endcode
2171 */
2172 doxygen_overloaded_function(template <...> void convolveFFT)
2173
2174 template <unsigned int N, class Real, class C1, class C2, class C3>
2175 void
2176 convolveFFT(MultiArrayView<N, Real, C1> in,
2177 MultiArrayView<N, Real, C2> kernel,
2178 MultiArrayView<N, Real, C3> out)
2179 {
2180 FFTWConvolvePlan<N, Real>(in, kernel, out).execute(in, kernel, out);
2181 }
2182
2183 template <unsigned int N, class Real, class C1, class C2, class C3>
2184 void
2185 convolveFFT(MultiArrayView<N, Real, C1> in,
2186 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
2187 MultiArrayView<N, Real, C3> out)
2188 {
2189 FFTWConvolvePlan<N, Real>(in, kernel, out).execute(in, kernel, out);
2190 }
2191
2192 /** \brief Convolve a complex-valued array by means of the Fourier transform.
2193
2194 See \ref convolveFFT() for details.
2195 */
2196 doxygen_overloaded_function(template <...> void convolveFFTComplex)
2197
2198 template <unsigned int N, class Real, class C1, class C2, class C3>
2199 void
2200 convolveFFTComplex(MultiArrayView<N, FFTWComplex<Real>, C1> in,
2201 MultiArrayView<N, FFTWComplex<Real>, C2> kernel,
2202 MultiArrayView<N, FFTWComplex<Real>, C3> out,
2203 bool fourierDomainKernel)
2204 {
2205 FFTWConvolvePlan<N, Real>(in, kernel, out, fourierDomainKernel).execute(in, kernel, out);
2206 }
2207
2208 /** \brief Convolve a real-valued array with a sequence of kernels by means of the Fourier transform.
2209
2210 See \ref convolveFFT() for details.
2211 */
2212 doxygen_overloaded_function(template <...> void convolveFFTMany)
2213
2214 template <unsigned int N, class Real, class C1,
2215 class KernelIterator, class OutIterator>
2216 void
2217 convolveFFTMany(MultiArrayView<N, Real, C1> in,
2218 KernelIterator kernels, KernelIterator kernelsEnd,
2219 OutIterator outs)
2220 {
2221 FFTWConvolvePlan<N, Real> plan;
2222 plan.initMany(in, kernels, kernelsEnd, outs);
2223 plan.executeMany(in, kernels, kernelsEnd, outs);
2224 }
2225
2226 /** \brief Convolve a complex-valued array with a sequence of kernels by means of the Fourier transform.
2227
2228 See \ref convolveFFT() for details.
2229 */
2230 doxygen_overloaded_function(template <...> void convolveFFTComplexMany)
2231
2232 template <unsigned int N, class Real, class C1,
2233 class KernelIterator, class OutIterator>
2234 void
2235 convolveFFTComplexMany(MultiArrayView<N, FFTWComplex<Real>, C1> in,
2236 KernelIterator kernels, KernelIterator kernelsEnd,
2237 OutIterator outs,
2238 bool fourierDomainKernel)
2239 {
2240 FFTWConvolvePlan<N, Real> plan;
2241 plan.initMany(in, kernels, kernelsEnd, outs, fourierDomainKernel);
2242 plan.executeMany(in, kernels, kernelsEnd, outs);
2243 }
2244
2245 //@}
2246
2247 } // namespace vigra
2248
2249 #endif // VIGRA_MULTI_FFT_HXX

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.10.0 (Mon Nov 18 2013)