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conv2.cc
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1 /*
2 
3 Copyright (C) 1999-2017 Andy Adler
4 Copyright (C) 2010 VZLU Prague
5 
6 This file is part of Octave.
7 
8 Octave is free software; you can redistribute it and/or modify it
9 under the terms of the GNU General Public License as published by the
10 Free Software Foundation; either version 3 of the License, or (at your
11 option) any later version.
12 
13 Octave is distributed in the hope that it will be useful, but WITHOUT
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
16 for more details.
17 
18 You should have received a copy of the GNU General Public License
19 along with Octave; see the file COPYING. If not, see
20 <http://www.gnu.org/licenses/>.
21 
22 */
23 
24 #if defined (HAVE_CONFIG_H)
25 # include "config.h"
26 #endif
27 
28 #include "oct-convn.h"
29 
30 #include "defun.h"
31 #include "error.h"
32 #include "ovl.h"
33 #include "utils.h"
34 
36 
37 DEFUN (conv2, args, ,
38  doc: /* -*- texinfo -*-
39 @deftypefn {} {} conv2 (@var{A}, @var{B})
40 @deftypefnx {} {} conv2 (@var{v1}, @var{v2}, @var{m})
41 @deftypefnx {} {} conv2 (@dots{}, @var{shape})
42 Return the 2-D convolution of @var{A} and @var{B}.
43 
44 The size of the result is determined by the optional @var{shape} argument
45 which takes the following values
46 
47 @table @asis
48 @item @var{shape} = @qcode{"full"}
49 Return the full convolution. (default)
50 
51 @item @var{shape} = @qcode{"same"}
52 Return the central part of the convolution with the same size as @var{A}.
53 The central part of the convolution begins at the indices
54 @code{floor ([size(@var{B})/2] + 1)}.
55 
56 @item @var{shape} = @qcode{"valid"}
57 Return only the parts which do not include zero-padded edges.
58 The size of the result is @code{max (size (A) - size (B) + 1, 0)}.
59 @end table
60 
61 When the third argument is a matrix, return the convolution of the matrix
62 @var{m} by the vector @var{v1} in the column direction and by the vector
63 @var{v2} in the row direction.
64 @seealso{conv, convn}
65 @end deftypefn */)
66 {
67  int nargin = args.length ();
68 
69  if (nargin < 2 || nargin > 4)
70  print_usage ();
71 
72  std::string shape = "full"; // default
73  bool separable = false;
75 
76  if (nargin == 3)
77  {
78  if (args(2).is_string ())
79  shape = args(2).string_value ();
80  else
81  separable = true;
82  }
83  else if (nargin == 4)
84  {
85  separable = true;
86  shape = args(3).string_value ();
87  }
88 
89  if (args(0).ndims () > 2 || args(1).ndims () > 2)
90  error ("conv2: A and B must be 1-D vectors or 2-D matrices");
91 
92  if (shape == "full")
93  ct = convn_full;
94  else if (shape == "same")
95  ct = convn_same;
96  else if (shape == "valid")
97  ct = convn_valid;
98  else
99  error ("conv2: SHAPE type not valid");
100 
102 
103  if (separable)
104  {
105  // If user requests separable, check first two params are vectors
106  if (! (1 == args(0).rows () || 1 == args(0).columns ())
107  || ! (1 == args(1).rows () || 1 == args(1).columns ()))
108  error ("conv2: arguments must be vectors for separable option");
109 
110  if (args(0).is_single_type () || args(1).is_single_type ()
111  || args(2).is_single_type ())
112  {
113  if (args(0).is_complex_type () || args(1).is_complex_type ()
114  || args(2).is_complex_type ())
115  {
116  FloatComplexMatrix a (args(2).float_complex_matrix_value ());
117  if (args(1).is_real_type () && args(2).is_real_type ())
118  {
119  FloatColumnVector v1 (args(0).float_vector_value ());
120  FloatRowVector v2 (args(1).float_vector_value ());
121  retval = convn (a, v1, v2, ct);
122  }
123  else
124  {
125  FloatComplexColumnVector v1 (args(0).float_complex_vector_value ());
126  FloatComplexRowVector v2 (args(1).float_complex_vector_value ());
127  retval = convn (a, v1, v2, ct);
128  }
129  }
130  else
131  {
132  FloatColumnVector v1 (args(0).float_vector_value ());
133  FloatRowVector v2 (args(1).float_vector_value ());
134  FloatMatrix a (args(2).float_matrix_value ());
135  retval = convn (a, v1, v2, ct);
136  }
137  }
138  else
139  {
140  if (args(0).is_complex_type () || args(1).is_complex_type ()
141  || args(2).is_complex_type ())
142  {
143  ComplexMatrix a (args(2).complex_matrix_value ());
144  if (args(1).is_real_type () && args(2).is_real_type ())
145  {
146  ColumnVector v1 (args(0).vector_value ());
147  RowVector v2 (args(1).vector_value ());
148  retval = convn (a, v1, v2, ct);
149  }
150  else
151  {
152  ComplexColumnVector v1 (args(0).complex_vector_value ());
153  ComplexRowVector v2 (args(1).complex_vector_value ());
154  retval = convn (a, v1, v2, ct);
155  }
156  }
157  else
158  {
159  ColumnVector v1 (args(0).vector_value ());
160  RowVector v2 (args(1).vector_value ());
161  Matrix a (args(2).matrix_value ());
162  retval = convn (a, v1, v2, ct);
163  }
164  }
165  } // if (separable)
166  else
167  {
168  if (args(0).is_single_type () || args(1).is_single_type ())
169  {
170  if (args(0).is_complex_type () || args(1).is_complex_type ())
171  {
172  FloatComplexMatrix a (args(0).float_complex_matrix_value ());
173  if (args(1).is_real_type ())
174  {
175  FloatMatrix b (args(1).float_matrix_value ());
176  retval = convn (a, b, ct);
177  }
178  else
179  {
180  FloatComplexMatrix b (args(1).float_complex_matrix_value ());
181  retval = convn (a, b, ct);
182  }
183  }
184  else
185  {
186  FloatMatrix a (args(0).float_matrix_value ());
187  FloatMatrix b (args(1).float_matrix_value ());
188  retval = convn (a, b, ct);
189  }
190  }
191  else
192  {
193  if (args(0).is_complex_type () || args(1).is_complex_type ())
194  {
195  ComplexMatrix a (args(0).complex_matrix_value ());
196  if (args(1).is_real_type ())
197  {
198  Matrix b (args(1).matrix_value ());
199  retval = convn (a, b, ct);
200  }
201  else
202  {
203  ComplexMatrix b (args(1).complex_matrix_value ());
204  retval = convn (a, b, ct);
205  }
206  }
207  else
208  {
209  Matrix a (args(0).matrix_value ());
210  Matrix b (args(1).matrix_value ());
211  retval = convn (a, b, ct);
212  }
213  }
214 
215  } // if (separable)
216 
217  return retval;
218 }
219 
220 /*
221 %!test
222 %! c = [0,1,2,3;1,8,12,12;4,20,24,21;7,22,25,18];
223 %! assert (conv2 ([0,1;1,2], [1,2,3;4,5,6;7,8,9]), c);
224 
225 %!test
226 %! c = single ([0,1,2,3;1,8,12,12;4,20,24,21;7,22,25,18]);
227 %! assert (conv2 (single ([0,1;1,2]), single ([1,2,3;4,5,6;7,8,9])), c);
228 
229 %!test
230 %! c = [1,4,4;5,18,16;14,48,40;19,62,48;15,48,36];
231 %! assert (conv2 (1:3, 1:2, [1,2;3,4;5,6]), c);
232 
233 %!assert (conv2 (1:3, 1:2, [1,2;3,4;5,6], "full"),
234 %! conv2 (1:3, 1:2, [1,2;3,4;5,6]));
235 
236 %% Test shapes
237 %!shared A, B, C
238 %! A = rand (3, 4);
239 %! B = rand (4);
240 %! C = conv2 (A, B);
241 %!assert (conv2 (A,B, "full"), C)
242 %!assert (conv2 (A,B, "same"), C(3:5,3:6))
243 %!assert (conv2 (A,B, "valid"), zeros (0, 1))
244 %!assert (size (conv2 (B,A, "valid")), [2 1])
245 
246 %!test
247 %! B = rand (5);
248 %! C = conv2 (A, B);
249 %!assert (conv2 (A,B, "full"), C)
250 %!assert (conv2 (A,B, "same"), C(3:5,3:6))
251 %!assert (conv2 (A,B, "valid"), zeros (0, 0))
252 %!assert (size (conv2 (B,A, "valid")), [3 2])
253 
254 %% Clear shared variables so they are not reported for tests below
255 %!shared
256 
257 %% Test cases from Bug #34893
258 %!assert <34893> (conv2 ([1:5;1:5], [1:2], "same"),
259 %! [4 7 10 13 10; 4 7 10 13 10])
260 %!assert <34893> (conv2 ([1:5;1:5]', [1:2]', "same"),
261 %! [4 7 10 13 10; 4 7 10 13 10]')
262 %!assert <34893> (conv2 ([1:5;1:5], [1:2], "valid"),
263 %! [4 7 10 13; 4 7 10 13])
264 %!assert <34893> (conv2 ([1:5;1:5]', [1:2]', "valid"),
265 %! [4 7 10 13; 4 7 10 13]')
266 
267 %!test
268 %! rand ("seed", 42);
269 %! x = rand (100);
270 %! y = ones (5);
271 %! A = conv2 (x, y)(5:end-4,5:end-4);
272 %! B = conv2 (x, y, "valid");
273 %! assert (B, A); # Yes, this test is for *exact* equivalence.
274 
275 %% Test input validation
276 %!error conv2 ()
277 %!error conv2 (1)
278 %!error <must be 1-D vectors or 2-D matrices> conv2 (ones (2), ones (2,2,2))
279 %!error <SHAPE type not valid> conv2 (1,2, "NOT_A_SHAPE")
280 %% Test alternate calling form which should be 2 vectors and a matrix
281 %!error conv2 (ones (2), 1, 1)
282 %!error conv2 (1, ones (2), 1)
283 */
284 
285 DEFUN (convn, args, ,
286  doc: /* -*- texinfo -*-
287 @deftypefn {} {@var{C} =} convn (@var{A}, @var{B})
288 @deftypefnx {} {@var{C} =} convn (@var{A}, @var{B}, @var{shape})
289 Return the n-D convolution of @var{A} and @var{B}.
290 
291 The size of the result is determined by the optional @var{shape} argument
292 which takes the following values
293 
294 @table @asis
295 @item @var{shape} = @qcode{"full"}
296 Return the full convolution. (default)
297 
298 @item @var{shape} = @qcode{"same"}
299 Return central part of the convolution with the same size as @var{A}.
300 The central part of the convolution begins at the indices
301 @code{floor ([size(@var{B})/2] + 1)}.
302 
303 @item @var{shape} = @qcode{"valid"}
304 Return only the parts which do not include zero-padded edges.
305 The size of the result is @code{max (size (A) - size (B) + 1, 0)}.
306 @end table
307 
308 @seealso{conv2, conv}
309 @end deftypefn */)
310 {
311  int nargin = args.length ();
312 
313  if (nargin < 2 || nargin > 3)
314  print_usage ();
315 
316  std::string shape = "full"; // default
317  convn_type ct = convn_full;
318 
319  if (nargin == 3)
320  shape = args(2).xstring_value ("convn: SHAPE must be a string");
321 
322  if (shape == "full")
323  ct = convn_full;
324  else if (shape == "same")
325  ct = convn_same;
326  else if (shape == "valid")
327  ct = convn_valid;
328  else
329  error ("convn: SHAPE type not valid");
330 
332 
333  if (args(0).is_single_type () || args(1).is_single_type ())
334  {
335  if (args(0).is_complex_type () || args(1).is_complex_type ())
336  {
337  FloatComplexNDArray a (args(0).float_complex_array_value ());
338  if (args(1).is_real_type ())
339  {
340  FloatNDArray b (args(1).float_array_value ());
341  retval = convn (a, b, ct);
342  }
343  else
344  {
345  FloatComplexNDArray b (args(1).float_complex_array_value ());
346  retval = convn (a, b, ct);
347  }
348  }
349  else
350  {
351  FloatNDArray a (args(0).float_array_value ());
352  FloatNDArray b (args(1).float_array_value ());
353  retval = convn (a, b, ct);
354  }
355  }
356  else
357  {
358  if (args(0).is_complex_type () || args(1).is_complex_type ())
359  {
360  ComplexNDArray a (args(0).complex_array_value ());
361  if (args(1).is_real_type ())
362  {
363  NDArray b (args(1).array_value ());
364  retval = convn (a, b, ct);
365  }
366  else
367  {
368  ComplexNDArray b (args(1).complex_array_value ());
369  retval = convn (a, b, ct);
370  }
371  }
372  else
373  {
374  NDArray a (args(0).array_value ());
375  NDArray b (args(1).array_value ());
376  retval = convn (a, b, ct);
377  }
378  }
379 
380  return retval;
381 }
382 
383 /*
384 %!test <39314>
385 %! v = reshape ([1 2], [1 1 2]);
386 %! assert (convn (v, v), reshape ([1 4 4], [1 1 3]));
387 %! assert (convn (v, v, "same"), reshape ([4 4], [1 1 2]));
388 %! assert (convn (v, v, "valid"), 4);
389 
390 ## The following test may look weird since we are using the output
391 ## of convn to test itself. However, because calculations are done
392 ## differently based on the shape option, it will help to catch some
393 ## bugs. See also bug #39314.
394 ## FIXME: The "valid" option uses an entirely different code path
395 ## through C++ and Fortran to calculate inner convolution.
396 ## The terms in the convolution added in reverse order compared
397 ## to the "full" option. This produces differences on the order
398 ## of tens of eps. This should be fixed, but in the meantime
399 ## the tests will be marked as known failures.
400 %!shared a, b, c
401 %! ## test 3D by 3D
402 %! a = rand (10, 10, 10);
403 %! b = rand (3, 3, 3);
404 %! c = convn (a, b, "full");
405 %!assert (convn (a, b, "same"), c(2:11,2:11,2:11))
406 %!test <39314>
407 %! assert (convn (a, b, "valid"), c(3:10,3:10,3:10));
408 %!
409 %!test
410 %! ## test 3D by 2D
411 %! a = rand (10, 10, 10);
412 %! b = rand (3, 3);
413 %! c = convn (a, b, "full");
414 %!assert (convn (a, b, "same"), c(2:11,2:11,:))
415 %!test <39314>
416 %! assert (convn (a, b, "valid"), c(3:10,3:10,:));
417 %!
418 %!test
419 %! ## test 2D by 3D
420 %! a = rand (10, 10);
421 %! b = rand (3, 3, 3);
422 %! c = convn (a, b, "full");
423 %!assert (convn (a, b, "same"), c(2:11,2:11,2))
424 %!assert (convn (a, b, "valid"), c(3:10,3:10,3:2)) # a 7x7x0 matrix
425 %!
426 %!test
427 %! ## test multiple different number of dimensions, with odd and even numbers
428 %! a = rand (10, 15, 7, 8, 10);
429 %! b = rand (4, 3, 2, 3);
430 %! c = convn (a, b, "full");
431 %!assert (convn (a, b, "same"), c(3:12,2:16,2:8,2:9,:))
432 %!test <39314>
433 %! assert (convn (a, b, "valid"), c(4:10,3:15,2:7,3:8,:));
434 
435 %!test
436 %! a = reshape (floor (magic (16) /10), [4 8 4 2]);
437 %! b = reshape (magic (6), [4 3 3]);
438 %! c = zeros (7, 10, 6, 2);
439 %! c(:,:,1,1) = [
440 %! 875 1415 1215 741 288 264 635 1109 687 171
441 %! 110 467 1551 1790 1891 1651 1165 900 659 568
442 %! 883 1047 1475 1964 2181 2302 2117 1674 579 234
443 %! 940 2330 3099 2573 2306 2207 2442 2918 2272 1004
444 %! 161 500 1564 2066 2355 2270 2099 1621 1144 831
445 %! 644 622 886 1121 1652 1967 1907 1668 529 228
446 %! 160 752 1232 768 360 284 668 1132 1380 864];
447 %! c(:,:,2,1) = [
448 %! 150 1174 1903 1971 2030 1719 1467 1420 1220 472
449 %! 986 2243 2603 2385 2308 2530 2971 3181 2266 768
450 %! 914 2443 3750 3782 3976 3821 3723 3709 2599 1178
451 %! 1922 3374 5198 5472 5563 5853 5794 5543 3578 1820
452 %! 1060 2471 3846 3724 3682 3803 3812 3927 2876 1390
453 %! 470 2078 3283 3225 2701 2265 2165 2261 2324 1124
454 %! 700 1130 1486 1515 1830 2097 2081 2028 1009 348];
455 %! c(:,:,3,1) = [
456 %! 1350 2127 2461 2082 1694 1909 2230 2621 1681 683
457 %! 877 2473 4362 4556 4543 4314 3879 3703 2863 1497
458 %! 1934 4219 5874 6117 5966 6051 5984 5714 3891 1562
459 %! 1927 5997 8573 8456 8517 8025 7957 8101 6121 2500
460 %! 1558 3533 5595 6064 6453 6491 6275 5743 3794 1832
461 %! 1950 2762 3455 3423 4019 4578 4807 4857 2304 907
462 %! 525 1860 2731 2392 1872 1724 1961 2312 2315 1141];
463 %! c(:,:,4,1) = [
464 %! 150 1317 2230 2621 2996 2767 2472 2049 1514 583
465 %! 1429 3056 3879 3703 3756 3964 4394 4570 3111 1250
466 %! 1833 4037 5984 5714 5846 5788 5883 6129 4157 2011
467 %! 3143 5469 7957 8101 8063 8475 8564 8439 5306 2538
468 %! 2001 4514 6275 5743 5391 5389 5578 6110 4473 1953
469 %! 817 3196 4807 4857 4229 3659 3477 3375 3208 1400
470 %! 750 1365 1961 2312 2840 2993 2722 2344 1092 323];
471 %! c(:,:,5,1) = [
472 %! 475 734 1296 1352 1400 1595 1557 1517 960 490
473 %! 751 1977 2831 2746 2607 2665 2733 2833 2186 912
474 %! 1065 3142 4344 4150 3768 3734 3876 4086 3366 1327
475 %! 976 3712 5530 5921 6158 5802 5481 5071 3821 1491
476 %! 1397 2996 3971 4003 4088 4180 4199 4146 2649 985
477 %! 1273 2121 2555 2247 2378 2624 2908 3229 1788 705
478 %! 365 1108 1530 1652 1550 1407 1274 1127 889 264];
479 %! c(:,:,6,1) = [
480 %! 0 133 345 683 982 1058 960 623 310 100
481 %! 437 806 1313 1332 1383 1391 1397 1370 864 495
482 %! 928 1573 2201 1928 1864 1932 2183 2445 1557 855
483 %! 1199 2083 2739 2573 2507 2656 2786 2928 1795 736
484 %! 912 1997 2404 2028 1692 1591 1803 2159 1603 599
485 %! 345 1092 1526 1666 1593 1437 1275 1116 863 253
486 %! 50 235 510 811 998 894 615 318 77 0];
487 %! c(:,:,1,2) = [
488 %! 840 1350 1176 697 293 320 674 1153 717 180
489 %! 142 490 1563 1824 1929 1604 1132 857 624 587
490 %! 890 1084 1539 1979 2238 2333 2072 1610 509 202
491 %! 966 2263 3034 2518 2250 2235 2512 2992 2305 1016
492 %! 200 561 1607 2107 2361 2277 2030 1548 1102 818
493 %! 652 631 922 1128 1670 1997 1895 1665 467 197
494 %! 160 744 1192 692 292 256 708 1208 1448 900];
495 %! c(:,:,2,2) = [
496 %! 179 1199 1886 1987 1997 1716 1479 1383 1215 485
497 %! 988 2213 2552 2358 2304 2615 3011 3210 2246 744
498 %! 921 2483 3747 3768 3960 3835 3712 3698 2588 1183
499 %! 1903 3416 5254 5490 5572 5826 5761 5505 3502 1814
500 %! 1064 2507 3825 3666 3680 3748 3821 3958 2892 1395
501 %! 495 2129 3277 3228 2566 2216 2154 2250 2390 1154
502 %! 700 1105 1472 1524 1856 2113 2059 2019 975 325];
503 %! c(:,:,3,2) = [
504 %! 1302 2104 2439 2006 1723 1931 2280 2685 1678 690
505 %! 877 2507 4408 4580 4523 4233 3852 3647 2850 1516
506 %! 1949 4238 5895 6143 6018 6063 5930 5656 3847 1538
507 %! 1953 5975 8547 8433 8407 8060 7955 8069 6170 2506
508 %! 1621 3536 5624 6117 6459 6456 6180 5666 3735 1815
509 %! 1904 2751 3429 3366 4122 4622 4840 4864 2242 882
510 %! 517 1843 2674 2337 1777 1686 2005 2367 2385 1175];
511 %! c(:,:,4,2) = [
512 %! 198 1346 2280 2685 2980 2759 2396 1982 1497 576
513 %! 1413 2994 3852 3647 3756 4035 4418 4595 3109 1231
514 %! 1873 4025 5930 5656 5792 5772 5909 6152 4185 2035
515 %! 3110 5510 7955 8069 8139 8456 8541 8439 5276 2541
516 %! 1964 4462 6180 5666 5315 5409 5631 6178 4536 1998
517 %! 869 3215 4840 4864 4121 3579 3420 3386 3271 1430
518 %! 725 1361 2005 2367 2925 3006 2667 2297 1054 325];
519 %! c(:,:,5,2) = [
520 %! 462 754 1285 1359 1441 1605 1556 1488 938 488
521 %! 729 1967 2788 2732 2608 2683 2744 2830 2195 912
522 %! 1052 3139 4302 4101 3742 3730 3895 4103 3403 1335
523 %! 1007 3725 5577 5964 6165 5754 5407 5006 3846 1507
524 %! 1375 2969 3951 3990 4144 4183 4200 4150 2661 998
525 %! 1258 2090 2495 2188 2403 2664 2954 3279 1814 723
526 %! 388 1127 1551 1673 1525 1390 1253 1139 912 275];
527 %! c(:,:,6,2) = [
528 %! 19 147 384 716 1016 1059 927 570 276 80
529 %! 441 791 1298 1320 1401 1396 1409 1367 865 500
530 %! 932 1537 2155 1870 1860 1946 2221 2487 1584 874
531 %! 1201 2067 2705 2538 2512 2687 2806 2971 1812 756
532 %! 925 1976 2363 1971 1636 1600 1844 2239 1664 626
533 %! 372 1133 1558 1687 1570 1401 1243 1122 883 264
534 %! 60 270 556 857 1024 870 569 282 66 0];
535 %!assert (convn(a, b, "full"), c)
536 %!assert (convn(a, b, "same"), c(3:6,2:9,2:5,:))
537 %!assert (convn(a, b, "valid"), c(4,3:8,3:4,:))
538 
539 ## test correct class
540 %!assert (class (convn (rand(5), rand(3))), "double")
541 %!assert (class (convn (rand(5, "single"), rand(3))), "single")
542 %!assert (class (convn (rand(5), rand(3, "single"))), "single")
543 %!assert (class (convn (true (5), rand(3))), "double")
544 %!assert (class (convn (true (5), rand(3, "single"))), "single")
545 %!assert (class (convn (ones(5, "uint8"), rand(3))), "double")
546 %!assert (class (convn (rand (3, "single"), ones(5, "uint8"))), "single")
547 
548 %!error convn ()
549 %!error convn (1)
550 %!error <SHAPE type not valid> convn (1,2, "NOT_A_SHAPE")
551 %!error convn (rand (3), 1, 1)
552 */
convn_type
Definition: oct-convn.h:49
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Definition: defun.cc:52
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NDArray convn(const NDArray &a, const NDArray &b, convn_type ct)
Definition: oct-convn.cc:187
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b
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Shape
Definition: conv2.cc:35
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