1 /*
2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 % %
4 % %
5 % %
6 % M M AAA TTTTT RRRR IIIII X X %
7 % MM MM A A T R R I X X %
8 % M M M AAAAA T RRRR I X %
9 % M M A A T R R I X X %
10 % M M A A T R R IIIII X X %
11 % %
12 % %
13 % MagickCore Matrix Methods %
14 % %
15 % Software Design %
16 % Cristy %
17 % August 2007 %
18 % %
19 % %
20 % Copyright 1999-2019 ImageMagick Studio LLC, a non-profit organization %
21 % dedicated to making software imaging solutions freely available. %
22 % %
23 % You may not use this file except in compliance with the License. You may %
24 % obtain a copy of the License at %
25 % %
26 % https://imagemagick.org/script/license.php %
27 % %
28 % Unless required by applicable law or agreed to in writing, software %
29 % distributed under the License is distributed on an "AS IS" BASIS, %
30 % WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. %
31 % See the License for the specific language governing permissions and %
32 % limitations under the License. %
33 % %
34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
35 %
36 %
37 */
38
39 /*
40 Include declarations.
41 */
42 #include "MagickCore/studio.h"
43 #include "MagickCore/blob.h"
44 #include "MagickCore/blob-private.h"
45 #include "MagickCore/cache.h"
46 #include "MagickCore/exception.h"
47 #include "MagickCore/exception-private.h"
48 #include "MagickCore/image-private.h"
49 #include "MagickCore/matrix.h"
50 #include "MagickCore/matrix-private.h"
51 #include "MagickCore/memory_.h"
52 #include "MagickCore/pixel-accessor.h"
53 #include "MagickCore/pixel-private.h"
54 #include "MagickCore/resource_.h"
55 #include "MagickCore/semaphore.h"
56 #include "MagickCore/thread-private.h"
57 #include "MagickCore/utility.h"
58
59 /*
60 Typedef declaration.
61 */
62 struct _MatrixInfo
63 {
64 CacheType
65 type;
66
67 size_t
68 columns,
69 rows,
70 stride;
71
72 MagickSizeType
73 length;
74
75 MagickBooleanType
76 mapped,
77 synchronize;
78
79 char
80 path[MagickPathExtent];
81
82 int
83 file;
84
85 void
86 *elements;
87
88 SemaphoreInfo
89 *semaphore;
90
91 size_t
92 signature;
93 };
94
95 /*
96 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
97 % %
98 % %
99 % %
100 % A c q u i r e M a t r i x I n f o %
101 % %
102 % %
103 % %
104 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
105 %
106 % AcquireMatrixInfo() allocates the ImageInfo structure.
107 %
108 % The format of the AcquireMatrixInfo method is:
109 %
110 % MatrixInfo *AcquireMatrixInfo(const size_t columns,const size_t rows,
111 % const size_t stride,ExceptionInfo *exception)
112 %
113 % A description of each parameter follows:
114 %
115 % o columns: the matrix columns.
116 %
117 % o rows: the matrix rows.
118 %
119 % o stride: the matrix stride.
120 %
121 % o exception: return any errors or warnings in this structure.
122 %
123 */
124
125 #if defined(SIGBUS)
MatrixSignalHandler(int status)126 static void MatrixSignalHandler(int status)
127 {
128 ThrowFatalException(CacheFatalError,"UnableToExtendMatrixCache");
129 }
130 #endif
131
WriteMatrixElements(const MatrixInfo * magick_restrict matrix_info,const MagickOffsetType offset,const MagickSizeType length,const unsigned char * magick_restrict buffer)132 static inline MagickOffsetType WriteMatrixElements(
133 const MatrixInfo *magick_restrict matrix_info,const MagickOffsetType offset,
134 const MagickSizeType length,const unsigned char *magick_restrict buffer)
135 {
136 register MagickOffsetType
137 i;
138
139 ssize_t
140 count;
141
142 #if !defined(MAGICKCORE_HAVE_PWRITE)
143 LockSemaphoreInfo(matrix_info->semaphore);
144 if (lseek(matrix_info->file,offset,SEEK_SET) < 0)
145 {
146 UnlockSemaphoreInfo(matrix_info->semaphore);
147 return((MagickOffsetType) -1);
148 }
149 #endif
150 count=0;
151 for (i=0; i < (MagickOffsetType) length; i+=count)
152 {
153 #if !defined(MAGICKCORE_HAVE_PWRITE)
154 count=write(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
155 (MagickSizeType) SSIZE_MAX));
156 #else
157 count=pwrite(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
158 (MagickSizeType) SSIZE_MAX),(off_t) (offset+i));
159 #endif
160 if (count <= 0)
161 {
162 count=0;
163 if (errno != EINTR)
164 break;
165 }
166 }
167 #if !defined(MAGICKCORE_HAVE_PWRITE)
168 UnlockSemaphoreInfo(matrix_info->semaphore);
169 #endif
170 return(i);
171 }
172
SetMatrixExtent(MatrixInfo * magick_restrict matrix_info,MagickSizeType length)173 static MagickBooleanType SetMatrixExtent(
174 MatrixInfo *magick_restrict matrix_info,MagickSizeType length)
175 {
176 MagickOffsetType
177 count,
178 extent,
179 offset;
180
181 if (length != (MagickSizeType) ((MagickOffsetType) length))
182 return(MagickFalse);
183 offset=(MagickOffsetType) lseek(matrix_info->file,0,SEEK_END);
184 if (offset < 0)
185 return(MagickFalse);
186 if ((MagickSizeType) offset >= length)
187 return(MagickTrue);
188 extent=(MagickOffsetType) length-1;
189 count=WriteMatrixElements(matrix_info,extent,1,(const unsigned char *) "");
190 #if defined(MAGICKCORE_HAVE_POSIX_FALLOCATE)
191 if (matrix_info->synchronize != MagickFalse)
192 (void) posix_fallocate(matrix_info->file,offset+1,extent-offset);
193 #endif
194 #if defined(SIGBUS)
195 (void) signal(SIGBUS,MatrixSignalHandler);
196 #endif
197 return(count != (MagickOffsetType) 1 ? MagickFalse : MagickTrue);
198 }
199
AcquireMatrixInfo(const size_t columns,const size_t rows,const size_t stride,ExceptionInfo * exception)200 MagickExport MatrixInfo *AcquireMatrixInfo(const size_t columns,
201 const size_t rows,const size_t stride,ExceptionInfo *exception)
202 {
203 char
204 *synchronize;
205
206 MagickBooleanType
207 status;
208
209 MatrixInfo
210 *matrix_info;
211
212 matrix_info=(MatrixInfo *) AcquireMagickMemory(sizeof(*matrix_info));
213 if (matrix_info == (MatrixInfo *) NULL)
214 return((MatrixInfo *) NULL);
215 (void) memset(matrix_info,0,sizeof(*matrix_info));
216 matrix_info->signature=MagickCoreSignature;
217 matrix_info->columns=columns;
218 matrix_info->rows=rows;
219 matrix_info->stride=stride;
220 matrix_info->semaphore=AcquireSemaphoreInfo();
221 synchronize=GetEnvironmentValue("MAGICK_SYNCHRONIZE");
222 if (synchronize != (const char *) NULL)
223 {
224 matrix_info->synchronize=IsStringTrue(synchronize);
225 synchronize=DestroyString(synchronize);
226 }
227 matrix_info->length=(MagickSizeType) columns*rows*stride;
228 if (matrix_info->columns != (size_t) (matrix_info->length/rows/stride))
229 {
230 (void) ThrowMagickException(exception,GetMagickModule(),CacheError,
231 "CacheResourcesExhausted","`%s'","matrix cache");
232 return(DestroyMatrixInfo(matrix_info));
233 }
234 matrix_info->type=MemoryCache;
235 status=AcquireMagickResource(AreaResource,matrix_info->length);
236 if ((status != MagickFalse) &&
237 (matrix_info->length == (MagickSizeType) ((size_t) matrix_info->length)))
238 {
239 status=AcquireMagickResource(MemoryResource,matrix_info->length);
240 if (status != MagickFalse)
241 {
242 matrix_info->mapped=MagickFalse;
243 matrix_info->elements=AcquireMagickMemory((size_t)
244 matrix_info->length);
245 if (matrix_info->elements == NULL)
246 {
247 matrix_info->mapped=MagickTrue;
248 matrix_info->elements=MapBlob(-1,IOMode,0,(size_t)
249 matrix_info->length);
250 }
251 if (matrix_info->elements == (unsigned short *) NULL)
252 RelinquishMagickResource(MemoryResource,matrix_info->length);
253 }
254 }
255 matrix_info->file=(-1);
256 if (matrix_info->elements == (unsigned short *) NULL)
257 {
258 status=AcquireMagickResource(DiskResource,matrix_info->length);
259 if (status == MagickFalse)
260 {
261 (void) ThrowMagickException(exception,GetMagickModule(),CacheError,
262 "CacheResourcesExhausted","`%s'","matrix cache");
263 return(DestroyMatrixInfo(matrix_info));
264 }
265 matrix_info->type=DiskCache;
266 matrix_info->file=AcquireUniqueFileResource(matrix_info->path);
267 if (matrix_info->file == -1)
268 return(DestroyMatrixInfo(matrix_info));
269 status=AcquireMagickResource(MapResource,matrix_info->length);
270 if (status != MagickFalse)
271 {
272 status=SetMatrixExtent(matrix_info,matrix_info->length);
273 if (status != MagickFalse)
274 matrix_info->elements=(void *) MapBlob(matrix_info->file,IOMode,0,
275 (size_t) matrix_info->length);
276 if (matrix_info->elements != NULL)
277 matrix_info->type=MapCache;
278 else
279 RelinquishMagickResource(MapResource,matrix_info->length);
280 }
281 }
282 return(matrix_info);
283 }
284
285 /*
286 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
287 % %
288 % %
289 % %
290 % A c q u i r e M a g i c k M a t r i x %
291 % %
292 % %
293 % %
294 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
295 %
296 % AcquireMagickMatrix() allocates and returns a matrix in the form of an
297 % array of pointers to an array of doubles, with all values pre-set to zero.
298 %
299 % This used to generate the two dimensional matrix, and vectors required
300 % for the GaussJordanElimination() method below, solving some system of
301 % simultanious equations.
302 %
303 % The format of the AcquireMagickMatrix method is:
304 %
305 % double **AcquireMagickMatrix(const size_t number_rows,
306 % const size_t size)
307 %
308 % A description of each parameter follows:
309 %
310 % o number_rows: the number pointers for the array of pointers
311 % (first dimension).
312 %
313 % o size: the size of the array of doubles each pointer points to
314 % (second dimension).
315 %
316 */
AcquireMagickMatrix(const size_t number_rows,const size_t size)317 MagickExport double **AcquireMagickMatrix(const size_t number_rows,
318 const size_t size)
319 {
320 double
321 **matrix;
322
323 register ssize_t
324 i,
325 j;
326
327 matrix=(double **) AcquireQuantumMemory(number_rows,sizeof(*matrix));
328 if (matrix == (double **) NULL)
329 return((double **) NULL);
330 for (i=0; i < (ssize_t) number_rows; i++)
331 {
332 matrix[i]=(double *) AcquireQuantumMemory(size,sizeof(*matrix[i]));
333 if (matrix[i] == (double *) NULL)
334 {
335 for (j=0; j < i; j++)
336 matrix[j]=(double *) RelinquishMagickMemory(matrix[j]);
337 matrix=(double **) RelinquishMagickMemory(matrix);
338 return((double **) NULL);
339 }
340 for (j=0; j < (ssize_t) size; j++)
341 matrix[i][j]=0.0;
342 }
343 return(matrix);
344 }
345
346 /*
347 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
348 % %
349 % %
350 % %
351 % D e s t r o y M a t r i x I n f o %
352 % %
353 % %
354 % %
355 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
356 %
357 % DestroyMatrixInfo() dereferences a matrix, deallocating memory associated
358 % with the matrix.
359 %
360 % The format of the DestroyImage method is:
361 %
362 % MatrixInfo *DestroyMatrixInfo(MatrixInfo *matrix_info)
363 %
364 % A description of each parameter follows:
365 %
366 % o matrix_info: the matrix.
367 %
368 */
DestroyMatrixInfo(MatrixInfo * matrix_info)369 MagickExport MatrixInfo *DestroyMatrixInfo(MatrixInfo *matrix_info)
370 {
371 assert(matrix_info != (MatrixInfo *) NULL);
372 assert(matrix_info->signature == MagickCoreSignature);
373 LockSemaphoreInfo(matrix_info->semaphore);
374 switch (matrix_info->type)
375 {
376 case MemoryCache:
377 {
378 if (matrix_info->mapped == MagickFalse)
379 matrix_info->elements=RelinquishMagickMemory(matrix_info->elements);
380 else
381 {
382 (void) UnmapBlob(matrix_info->elements,(size_t) matrix_info->length);
383 matrix_info->elements=(unsigned short *) NULL;
384 }
385 RelinquishMagickResource(MemoryResource,matrix_info->length);
386 break;
387 }
388 case MapCache:
389 {
390 (void) UnmapBlob(matrix_info->elements,(size_t) matrix_info->length);
391 matrix_info->elements=NULL;
392 RelinquishMagickResource(MapResource,matrix_info->length);
393 }
394 case DiskCache:
395 {
396 if (matrix_info->file != -1)
397 (void) close(matrix_info->file);
398 (void) RelinquishUniqueFileResource(matrix_info->path);
399 RelinquishMagickResource(DiskResource,matrix_info->length);
400 break;
401 }
402 default:
403 break;
404 }
405 UnlockSemaphoreInfo(matrix_info->semaphore);
406 RelinquishSemaphoreInfo(&matrix_info->semaphore);
407 return((MatrixInfo *) RelinquishMagickMemory(matrix_info));
408 }
409
410 /*
411 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
412 % %
413 % %
414 % %
415 + G a u s s J o r d a n E l i m i n a t i o n %
416 % %
417 % %
418 % %
419 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
420 %
421 % GaussJordanElimination() returns a matrix in reduced row echelon form,
422 % while simultaneously reducing and thus solving the augumented results
423 % matrix.
424 %
425 % See also http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
426 %
427 % The format of the GaussJordanElimination method is:
428 %
429 % MagickBooleanType GaussJordanElimination(double **matrix,
430 % double **vectors,const size_t rank,const size_t number_vectors)
431 %
432 % A description of each parameter follows:
433 %
434 % o matrix: the matrix to be reduced, as an 'array of row pointers'.
435 %
436 % o vectors: the additional matrix argumenting the matrix for row reduction.
437 % Producing an 'array of column vectors'.
438 %
439 % o rank: The size of the matrix (both rows and columns).
440 % Also represents the number terms that need to be solved.
441 %
442 % o number_vectors: Number of vectors columns, argumenting the above matrix.
443 % Usally 1, but can be more for more complex equation solving.
444 %
445 % Note that the 'matrix' is given as a 'array of row pointers' of rank size.
446 % That is values can be assigned as matrix[row][column] where 'row' is
447 % typically the equation, and 'column' is the term of the equation.
448 % That is the matrix is in the form of a 'row first array'.
449 %
450 % However 'vectors' is a 'array of column pointers' which can have any number
451 % of columns, with each column array the same 'rank' size as 'matrix'.
452 %
453 % This allows for simpler handling of the results, especially is only one
454 % column 'vector' is all that is required to produce the desired solution.
455 %
456 % For example, the 'vectors' can consist of a pointer to a simple array of
457 % doubles. when only one set of simultanious equations is to be solved from
458 % the given set of coefficient weighted terms.
459 %
460 % double **matrix = AcquireMagickMatrix(8UL,8UL);
461 % double coefficents[8];
462 % ...
463 % GaussJordanElimination(matrix, &coefficents, 8UL, 1UL);
464 %
465 % However by specifing more 'columns' (as an 'array of vector columns',
466 % you can use this function to solve a set of 'separable' equations.
467 %
468 % For example a distortion function where u = U(x,y) v = V(x,y)
469 % And the functions U() and V() have separate coefficents, but are being
470 % generated from a common x,y->u,v data set.
471 %
472 % Another example is generation of a color gradient from a set of colors at
473 % specific coordients, such as a list x,y -> r,g,b,a.
474 %
475 % You can also use the 'vectors' to generate an inverse of the given 'matrix'
476 % though as a 'column first array' rather than a 'row first array'. For
477 % details see http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
478 %
479 */
GaussJordanElimination(double ** matrix,double ** vectors,const size_t rank,const size_t number_vectors)480 MagickPrivate MagickBooleanType GaussJordanElimination(double **matrix,
481 double **vectors,const size_t rank,const size_t number_vectors)
482 {
483 #define GaussJordanSwap(x,y) \
484 { \
485 if ((x) != (y)) \
486 { \
487 (x)+=(y); \
488 (y)=(x)-(y); \
489 (x)=(x)-(y); \
490 } \
491 }
492
493 double
494 max,
495 scale;
496
497 register ssize_t
498 i,
499 j,
500 k;
501
502 ssize_t
503 column,
504 *columns,
505 *pivots,
506 row,
507 *rows;
508
509 columns=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*columns));
510 rows=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*rows));
511 pivots=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*pivots));
512 if ((rows == (ssize_t *) NULL) || (columns == (ssize_t *) NULL) ||
513 (pivots == (ssize_t *) NULL))
514 {
515 if (pivots != (ssize_t *) NULL)
516 pivots=(ssize_t *) RelinquishMagickMemory(pivots);
517 if (columns != (ssize_t *) NULL)
518 columns=(ssize_t *) RelinquishMagickMemory(columns);
519 if (rows != (ssize_t *) NULL)
520 rows=(ssize_t *) RelinquishMagickMemory(rows);
521 return(MagickFalse);
522 }
523 (void) memset(columns,0,rank*sizeof(*columns));
524 (void) memset(rows,0,rank*sizeof(*rows));
525 (void) memset(pivots,0,rank*sizeof(*pivots));
526 column=0;
527 row=0;
528 for (i=0; i < (ssize_t) rank; i++)
529 {
530 max=0.0;
531 for (j=0; j < (ssize_t) rank; j++)
532 if (pivots[j] != 1)
533 {
534 for (k=0; k < (ssize_t) rank; k++)
535 if (pivots[k] != 0)
536 {
537 if (pivots[k] > 1)
538 return(MagickFalse);
539 }
540 else
541 if (fabs(matrix[j][k]) >= max)
542 {
543 max=fabs(matrix[j][k]);
544 row=j;
545 column=k;
546 }
547 }
548 pivots[column]++;
549 if (row != column)
550 {
551 for (k=0; k < (ssize_t) rank; k++)
552 GaussJordanSwap(matrix[row][k],matrix[column][k]);
553 for (k=0; k < (ssize_t) number_vectors; k++)
554 GaussJordanSwap(vectors[k][row],vectors[k][column]);
555 }
556 rows[i]=row;
557 columns[i]=column;
558 if (matrix[column][column] == 0.0)
559 return(MagickFalse); /* sigularity */
560 scale=PerceptibleReciprocal(matrix[column][column]);
561 matrix[column][column]=1.0;
562 for (j=0; j < (ssize_t) rank; j++)
563 matrix[column][j]*=scale;
564 for (j=0; j < (ssize_t) number_vectors; j++)
565 vectors[j][column]*=scale;
566 for (j=0; j < (ssize_t) rank; j++)
567 if (j != column)
568 {
569 scale=matrix[j][column];
570 matrix[j][column]=0.0;
571 for (k=0; k < (ssize_t) rank; k++)
572 matrix[j][k]-=scale*matrix[column][k];
573 for (k=0; k < (ssize_t) number_vectors; k++)
574 vectors[k][j]-=scale*vectors[k][column];
575 }
576 }
577 for (j=(ssize_t) rank-1; j >= 0; j--)
578 if (columns[j] != rows[j])
579 for (i=0; i < (ssize_t) rank; i++)
580 GaussJordanSwap(matrix[i][rows[j]],matrix[i][columns[j]]);
581 pivots=(ssize_t *) RelinquishMagickMemory(pivots);
582 rows=(ssize_t *) RelinquishMagickMemory(rows);
583 columns=(ssize_t *) RelinquishMagickMemory(columns);
584 return(MagickTrue);
585 }
586
587 /*
588 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
589 % %
590 % %
591 % %
592 % G e t M a t r i x C o l u m n s %
593 % %
594 % %
595 % %
596 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
597 %
598 % GetMatrixColumns() returns the number of columns in the matrix.
599 %
600 % The format of the GetMatrixColumns method is:
601 %
602 % size_t GetMatrixColumns(const MatrixInfo *matrix_info)
603 %
604 % A description of each parameter follows:
605 %
606 % o matrix_info: the matrix.
607 %
608 */
GetMatrixColumns(const MatrixInfo * matrix_info)609 MagickExport size_t GetMatrixColumns(const MatrixInfo *matrix_info)
610 {
611 assert(matrix_info != (MatrixInfo *) NULL);
612 assert(matrix_info->signature == MagickCoreSignature);
613 return(matrix_info->columns);
614 }
615
616 /*
617 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
618 % %
619 % %
620 % %
621 % G e t M a t r i x E l e m e n t %
622 % %
623 % %
624 % %
625 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
626 %
627 % GetMatrixElement() returns the specifed element in the matrix.
628 %
629 % The format of the GetMatrixElement method is:
630 %
631 % MagickBooleanType GetMatrixElement(const MatrixInfo *matrix_info,
632 % const ssize_t x,const ssize_t y,void *value)
633 %
634 % A description of each parameter follows:
635 %
636 % o matrix_info: the matrix columns.
637 %
638 % o x: the matrix x-offset.
639 %
640 % o y: the matrix y-offset.
641 %
642 % o value: return the matrix element in this buffer.
643 %
644 */
645
EdgeX(const ssize_t x,const size_t columns)646 static inline ssize_t EdgeX(const ssize_t x,const size_t columns)
647 {
648 if (x < 0L)
649 return(0L);
650 if (x >= (ssize_t) columns)
651 return((ssize_t) (columns-1));
652 return(x);
653 }
654
EdgeY(const ssize_t y,const size_t rows)655 static inline ssize_t EdgeY(const ssize_t y,const size_t rows)
656 {
657 if (y < 0L)
658 return(0L);
659 if (y >= (ssize_t) rows)
660 return((ssize_t) (rows-1));
661 return(y);
662 }
663
ReadMatrixElements(const MatrixInfo * magick_restrict matrix_info,const MagickOffsetType offset,const MagickSizeType length,unsigned char * magick_restrict buffer)664 static inline MagickOffsetType ReadMatrixElements(
665 const MatrixInfo *magick_restrict matrix_info,const MagickOffsetType offset,
666 const MagickSizeType length,unsigned char *magick_restrict buffer)
667 {
668 register MagickOffsetType
669 i;
670
671 ssize_t
672 count;
673
674 #if !defined(MAGICKCORE_HAVE_PREAD)
675 LockSemaphoreInfo(matrix_info->semaphore);
676 if (lseek(matrix_info->file,offset,SEEK_SET) < 0)
677 {
678 UnlockSemaphoreInfo(matrix_info->semaphore);
679 return((MagickOffsetType) -1);
680 }
681 #endif
682 count=0;
683 for (i=0; i < (MagickOffsetType) length; i+=count)
684 {
685 #if !defined(MAGICKCORE_HAVE_PREAD)
686 count=read(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
687 (MagickSizeType) SSIZE_MAX));
688 #else
689 count=pread(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
690 (MagickSizeType) SSIZE_MAX),(off_t) (offset+i));
691 #endif
692 if (count <= 0)
693 {
694 count=0;
695 if (errno != EINTR)
696 break;
697 }
698 }
699 #if !defined(MAGICKCORE_HAVE_PREAD)
700 UnlockSemaphoreInfo(matrix_info->semaphore);
701 #endif
702 return(i);
703 }
704
GetMatrixElement(const MatrixInfo * matrix_info,const ssize_t x,const ssize_t y,void * value)705 MagickExport MagickBooleanType GetMatrixElement(const MatrixInfo *matrix_info,
706 const ssize_t x,const ssize_t y,void *value)
707 {
708 MagickOffsetType
709 count,
710 i;
711
712 assert(matrix_info != (const MatrixInfo *) NULL);
713 assert(matrix_info->signature == MagickCoreSignature);
714 i=(MagickOffsetType) EdgeY(y,matrix_info->rows)*matrix_info->columns+
715 EdgeX(x,matrix_info->columns);
716 if (matrix_info->type != DiskCache)
717 {
718 (void) memcpy(value,(unsigned char *) matrix_info->elements+i*
719 matrix_info->stride,matrix_info->stride);
720 return(MagickTrue);
721 }
722 count=ReadMatrixElements(matrix_info,i*matrix_info->stride,
723 matrix_info->stride,(unsigned char *) value);
724 if (count != (MagickOffsetType) matrix_info->stride)
725 return(MagickFalse);
726 return(MagickTrue);
727 }
728
729 /*
730 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
731 % %
732 % %
733 % %
734 % G e t M a t r i x R o w s %
735 % %
736 % %
737 % %
738 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
739 %
740 % GetMatrixRows() returns the number of rows in the matrix.
741 %
742 % The format of the GetMatrixRows method is:
743 %
744 % size_t GetMatrixRows(const MatrixInfo *matrix_info)
745 %
746 % A description of each parameter follows:
747 %
748 % o matrix_info: the matrix.
749 %
750 */
GetMatrixRows(const MatrixInfo * matrix_info)751 MagickExport size_t GetMatrixRows(const MatrixInfo *matrix_info)
752 {
753 assert(matrix_info != (const MatrixInfo *) NULL);
754 assert(matrix_info->signature == MagickCoreSignature);
755 return(matrix_info->rows);
756 }
757
758 /*
759 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
760 % %
761 % %
762 % %
763 + L e a s t S q u a r e s A d d T e r m s %
764 % %
765 % %
766 % %
767 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
768 %
769 % LeastSquaresAddTerms() adds one set of terms and associate results to the
770 % given matrix and vectors for solving using least-squares function fitting.
771 %
772 % The format of the AcquireMagickMatrix method is:
773 %
774 % void LeastSquaresAddTerms(double **matrix,double **vectors,
775 % const double *terms,const double *results,const size_t rank,
776 % const size_t number_vectors);
777 %
778 % A description of each parameter follows:
779 %
780 % o matrix: the square matrix to add given terms/results to.
781 %
782 % o vectors: the result vectors to add terms/results to.
783 %
784 % o terms: the pre-calculated terms (without the unknown coefficent
785 % weights) that forms the equation being added.
786 %
787 % o results: the result(s) that should be generated from the given terms
788 % weighted by the yet-to-be-solved coefficents.
789 %
790 % o rank: the rank or size of the dimensions of the square matrix.
791 % Also the length of vectors, and number of terms being added.
792 %
793 % o number_vectors: Number of result vectors, and number or results being
794 % added. Also represents the number of separable systems of equations
795 % that is being solved.
796 %
797 % Example of use...
798 %
799 % 2 dimensional Affine Equations (which are separable)
800 % c0*x + c2*y + c4*1 => u
801 % c1*x + c3*y + c5*1 => v
802 %
803 % double **matrix = AcquireMagickMatrix(3UL,3UL);
804 % double **vectors = AcquireMagickMatrix(2UL,3UL);
805 % double terms[3], results[2];
806 % ...
807 % for each given x,y -> u,v
808 % terms[0] = x;
809 % terms[1] = y;
810 % terms[2] = 1;
811 % results[0] = u;
812 % results[1] = v;
813 % LeastSquaresAddTerms(matrix,vectors,terms,results,3UL,2UL);
814 % ...
815 % if ( GaussJordanElimination(matrix,vectors,3UL,2UL) ) {
816 % c0 = vectors[0][0];
817 % c2 = vectors[0][1];
818 % c4 = vectors[0][2];
819 % c1 = vectors[1][0];
820 % c3 = vectors[1][1];
821 % c5 = vectors[1][2];
822 % }
823 % else
824 % printf("Matrix unsolvable\n);
825 % RelinquishMagickMatrix(matrix,3UL);
826 % RelinquishMagickMatrix(vectors,2UL);
827 %
828 */
LeastSquaresAddTerms(double ** matrix,double ** vectors,const double * terms,const double * results,const size_t rank,const size_t number_vectors)829 MagickPrivate void LeastSquaresAddTerms(double **matrix,double **vectors,
830 const double *terms,const double *results,const size_t rank,
831 const size_t number_vectors)
832 {
833 register ssize_t
834 i,
835 j;
836
837 for (j=0; j < (ssize_t) rank; j++)
838 {
839 for (i=0; i < (ssize_t) rank; i++)
840 matrix[i][j]+=terms[i]*terms[j];
841 for (i=0; i < (ssize_t) number_vectors; i++)
842 vectors[i][j]+=results[i]*terms[j];
843 }
844 }
845
846 /*
847 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
848 % %
849 % %
850 % %
851 % M a t r i x T o I m a g e %
852 % %
853 % %
854 % %
855 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
856 %
857 % MatrixToImage() returns a matrix as an image. The matrix elements must be
858 % of type double otherwise nonsense is returned.
859 %
860 % The format of the MatrixToImage method is:
861 %
862 % Image *MatrixToImage(const MatrixInfo *matrix_info,
863 % ExceptionInfo *exception)
864 %
865 % A description of each parameter follows:
866 %
867 % o matrix_info: the matrix.
868 %
869 % o exception: return any errors or warnings in this structure.
870 %
871 */
MatrixToImage(const MatrixInfo * matrix_info,ExceptionInfo * exception)872 MagickExport Image *MatrixToImage(const MatrixInfo *matrix_info,
873 ExceptionInfo *exception)
874 {
875 CacheView
876 *image_view;
877
878 double
879 max_value,
880 min_value,
881 scale_factor,
882 value;
883
884 Image
885 *image;
886
887 MagickBooleanType
888 status;
889
890 ssize_t
891 y;
892
893 assert(matrix_info != (const MatrixInfo *) NULL);
894 assert(matrix_info->signature == MagickCoreSignature);
895 assert(exception != (ExceptionInfo *) NULL);
896 assert(exception->signature == MagickCoreSignature);
897 if (matrix_info->stride < sizeof(double))
898 return((Image *) NULL);
899 /*
900 Determine range of matrix.
901 */
902 (void) GetMatrixElement(matrix_info,0,0,&value);
903 min_value=value;
904 max_value=value;
905 for (y=0; y < (ssize_t) matrix_info->rows; y++)
906 {
907 register ssize_t
908 x;
909
910 for (x=0; x < (ssize_t) matrix_info->columns; x++)
911 {
912 if (GetMatrixElement(matrix_info,x,y,&value) == MagickFalse)
913 continue;
914 if (value < min_value)
915 min_value=value;
916 else
917 if (value > max_value)
918 max_value=value;
919 }
920 }
921 if ((min_value == 0.0) && (max_value == 0.0))
922 scale_factor=0;
923 else
924 if (min_value == max_value)
925 {
926 scale_factor=(double) QuantumRange/min_value;
927 min_value=0;
928 }
929 else
930 scale_factor=(double) QuantumRange/(max_value-min_value);
931 /*
932 Convert matrix to image.
933 */
934 image=AcquireImage((ImageInfo *) NULL,exception);
935 image->columns=matrix_info->columns;
936 image->rows=matrix_info->rows;
937 image->colorspace=GRAYColorspace;
938 status=MagickTrue;
939 image_view=AcquireAuthenticCacheView(image,exception);
940 #if defined(MAGICKCORE_OPENMP_SUPPORT)
941 #pragma omp parallel for schedule(static) shared(status) \
942 magick_number_threads(image,image,image->rows,1)
943 #endif
944 for (y=0; y < (ssize_t) image->rows; y++)
945 {
946 double
947 value;
948
949 register Quantum
950 *q;
951
952 register ssize_t
953 x;
954
955 if (status == MagickFalse)
956 continue;
957 q=QueueCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
958 if (q == (Quantum *) NULL)
959 {
960 status=MagickFalse;
961 continue;
962 }
963 for (x=0; x < (ssize_t) image->columns; x++)
964 {
965 if (GetMatrixElement(matrix_info,x,y,&value) == MagickFalse)
966 continue;
967 value=scale_factor*(value-min_value);
968 *q=ClampToQuantum(value);
969 q+=GetPixelChannels(image);
970 }
971 if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
972 status=MagickFalse;
973 }
974 image_view=DestroyCacheView(image_view);
975 if (status == MagickFalse)
976 image=DestroyImage(image);
977 return(image);
978 }
979
980 /*
981 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
982 % %
983 % %
984 % %
985 % N u l l M a t r i x %
986 % %
987 % %
988 % %
989 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
990 %
991 % NullMatrix() sets all elements of the matrix to zero.
992 %
993 % The format of the memset method is:
994 %
995 % MagickBooleanType *NullMatrix(MatrixInfo *matrix_info)
996 %
997 % A description of each parameter follows:
998 %
999 % o matrix_info: the matrix.
1000 %
1001 */
NullMatrix(MatrixInfo * matrix_info)1002 MagickExport MagickBooleanType NullMatrix(MatrixInfo *matrix_info)
1003 {
1004 register ssize_t
1005 x;
1006
1007 ssize_t
1008 count,
1009 y;
1010
1011 unsigned char
1012 value;
1013
1014 assert(matrix_info != (const MatrixInfo *) NULL);
1015 assert(matrix_info->signature == MagickCoreSignature);
1016 if (matrix_info->type != DiskCache)
1017 {
1018 (void) memset(matrix_info->elements,0,(size_t)
1019 matrix_info->length);
1020 return(MagickTrue);
1021 }
1022 value=0;
1023 (void) lseek(matrix_info->file,0,SEEK_SET);
1024 for (y=0; y < (ssize_t) matrix_info->rows; y++)
1025 {
1026 for (x=0; x < (ssize_t) matrix_info->length; x++)
1027 {
1028 count=write(matrix_info->file,&value,sizeof(value));
1029 if (count != (ssize_t) sizeof(value))
1030 break;
1031 }
1032 if (x < (ssize_t) matrix_info->length)
1033 break;
1034 }
1035 return(y < (ssize_t) matrix_info->rows ? MagickFalse : MagickTrue);
1036 }
1037
1038 /*
1039 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1040 % %
1041 % %
1042 % %
1043 % R e l i n q u i s h M a g i c k M a t r i x %
1044 % %
1045 % %
1046 % %
1047 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1048 %
1049 % RelinquishMagickMatrix() frees the previously acquired matrix (array of
1050 % pointers to arrays of doubles).
1051 %
1052 % The format of the RelinquishMagickMatrix method is:
1053 %
1054 % double **RelinquishMagickMatrix(double **matrix,
1055 % const size_t number_rows)
1056 %
1057 % A description of each parameter follows:
1058 %
1059 % o matrix: the matrix to relinquish
1060 %
1061 % o number_rows: the first dimension of the acquired matrix (number of
1062 % pointers)
1063 %
1064 */
RelinquishMagickMatrix(double ** matrix,const size_t number_rows)1065 MagickExport double **RelinquishMagickMatrix(double **matrix,
1066 const size_t number_rows)
1067 {
1068 register ssize_t
1069 i;
1070
1071 if (matrix == (double **) NULL )
1072 return(matrix);
1073 for (i=0; i < (ssize_t) number_rows; i++)
1074 matrix[i]=(double *) RelinquishMagickMemory(matrix[i]);
1075 matrix=(double **) RelinquishMagickMemory(matrix);
1076 return(matrix);
1077 }
1078
1079 /*
1080 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1081 % %
1082 % %
1083 % %
1084 % S e t M a t r i x E l e m e n t %
1085 % %
1086 % %
1087 % %
1088 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1089 %
1090 % SetMatrixElement() sets the specifed element in the matrix.
1091 %
1092 % The format of the SetMatrixElement method is:
1093 %
1094 % MagickBooleanType SetMatrixElement(const MatrixInfo *matrix_info,
1095 % const ssize_t x,const ssize_t y,void *value)
1096 %
1097 % A description of each parameter follows:
1098 %
1099 % o matrix_info: the matrix columns.
1100 %
1101 % o x: the matrix x-offset.
1102 %
1103 % o y: the matrix y-offset.
1104 %
1105 % o value: set the matrix element to this value.
1106 %
1107 */
1108
SetMatrixElement(const MatrixInfo * matrix_info,const ssize_t x,const ssize_t y,const void * value)1109 MagickExport MagickBooleanType SetMatrixElement(const MatrixInfo *matrix_info,
1110 const ssize_t x,const ssize_t y,const void *value)
1111 {
1112 MagickOffsetType
1113 count,
1114 i;
1115
1116 assert(matrix_info != (const MatrixInfo *) NULL);
1117 assert(matrix_info->signature == MagickCoreSignature);
1118 i=(MagickOffsetType) y*matrix_info->columns+x;
1119 if ((i < 0) ||
1120 ((MagickSizeType) (i*matrix_info->stride) >= matrix_info->length))
1121 return(MagickFalse);
1122 if (matrix_info->type != DiskCache)
1123 {
1124 (void) memcpy((unsigned char *) matrix_info->elements+i*
1125 matrix_info->stride,value,matrix_info->stride);
1126 return(MagickTrue);
1127 }
1128 count=WriteMatrixElements(matrix_info,i*matrix_info->stride,
1129 matrix_info->stride,(unsigned char *) value);
1130 if (count != (MagickOffsetType) matrix_info->stride)
1131 return(MagickFalse);
1132 return(MagickTrue);
1133 }
1134