MagickCore 6.9.13
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matrix.c
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 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 "magick/studio.h"
43#include "magick/blob.h"
44#include "magick/blob-private.h"
45#include "magick/exception.h"
46#include "magick/exception-private.h"
47#include "magick/image-private.h"
48#include "magick/matrix.h"
49#include "magick/memory_.h"
50#include "magick/pixel-private.h"
51#include "magick/resource_.h"
52#include "magick/semaphore.h"
53#include "magick/thread-private.h"
54#include "magick/utility.h"
55␌
56/*
57 Typedef declaration.
58*/
59struct _MatrixInfo
60{
61 CacheType
62 type;
63
64 size_t
65 columns,
66 rows,
67 stride;
68
69 MagickSizeType
70 length;
71
72 MagickBooleanType
73 mapped,
74 synchronize;
75
76 char
77 path[MaxTextExtent];
78
79 int
80 file;
81
82 void
83 *elements;
84
85 SemaphoreInfo
86 *semaphore;
87
88 size_t
89 signature;
90};
91␌
92/*
93%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
94% %
95% %
96% %
97% A c q u i r e M a t r i x I n f o %
98% %
99% %
100% %
101%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
102%
103% AcquireMatrixInfo() allocates the ImageInfo structure.
104%
105% The format of the AcquireMatrixInfo method is:
106%
107% MatrixInfo *AcquireMatrixInfo(const size_t columns,const size_t rows,
108% const size_t stride,ExceptionInfo *exception)
109%
110% A description of each parameter follows:
111%
112% o columns: the matrix columns.
113%
114% o rows: the matrix rows.
115%
116% o stride: the matrix stride.
117%
118% o exception: return any errors or warnings in this structure.
119%
120*/
121
122#if defined(SIGBUS)
123static void MatrixSignalHandler(int magick_unused(status))
124{
125 magick_unreferenced(status);
126 ThrowFatalException(CacheFatalError,"UnableToExtendMatrixCache");
127}
128#endif
129
130static inline MagickOffsetType WriteMatrixElements(
131 const MatrixInfo *magick_restrict matrix_info,const MagickOffsetType offset,
132 const MagickSizeType length,const unsigned char *magick_restrict buffer)
133{
134 MagickOffsetType
135 i;
136
137 ssize_t
138 count;
139
140#if !defined(MAGICKCORE_HAVE_PWRITE)
141 LockSemaphoreInfo(matrix_info->semaphore);
142 if (lseek(matrix_info->file,offset,SEEK_SET) < 0)
143 {
144 UnlockSemaphoreInfo(matrix_info->semaphore);
145 return((MagickOffsetType) -1);
146 }
147#endif
148 count=0;
149 for (i=0; i < (MagickOffsetType) length; i+=count)
150 {
151#if !defined(MAGICKCORE_HAVE_PWRITE)
152 count=write(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
153 (MagickSizeType) MagickMaxBufferExtent));
154#else
155 count=pwrite(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
156 (MagickSizeType) MagickMaxBufferExtent),(off_t) (offset+i));
157#endif
158 if (count <= 0)
159 {
160 count=0;
161 if (errno != EINTR)
162 break;
163 }
164 }
165#if !defined(MAGICKCORE_HAVE_PWRITE)
166 UnlockSemaphoreInfo(matrix_info->semaphore);
167#endif
168 return(i);
169}
170
171static MagickBooleanType SetMatrixExtent(
172 MatrixInfo *magick_restrict matrix_info,MagickSizeType length)
173{
174 MagickOffsetType
175 count,
176 extent,
177 offset;
178
179 if (length != (MagickSizeType) ((MagickOffsetType) length))
180 return(MagickFalse);
181 offset=(MagickOffsetType) lseek(matrix_info->file,0,SEEK_END);
182 if (offset < 0)
183 return(MagickFalse);
184 if ((MagickSizeType) offset >= length)
185 return(MagickTrue);
186 extent=(MagickOffsetType) length-1;
187 count=WriteMatrixElements(matrix_info,extent,1,(const unsigned char *) "");
188#if defined(MAGICKCORE_HAVE_POSIX_FALLOCATE)
189 if (matrix_info->synchronize != MagickFalse)
190 (void) posix_fallocate(matrix_info->file,offset+1,extent-offset);
191#endif
192#if defined(SIGBUS)
193 (void) signal(SIGBUS,MatrixSignalHandler);
194#endif
195 return(count != (MagickOffsetType) 1 ? MagickFalse : MagickTrue);
196}
197
198MagickExport MatrixInfo *AcquireMatrixInfo(const size_t columns,
199 const size_t rows,const size_t stride,ExceptionInfo *exception)
200{
201 char
202 *synchronize;
203
204 MagickBooleanType
205 status;
206
207 MatrixInfo
208 *matrix_info;
209
210 matrix_info=(MatrixInfo *) AcquireMagickMemory(sizeof(*matrix_info));
211 if (matrix_info == (MatrixInfo *) NULL)
212 return((MatrixInfo *) NULL);
213 (void) memset(matrix_info,0,sizeof(*matrix_info));
214 matrix_info->signature=MagickCoreSignature;
215 matrix_info->columns=columns;
216 matrix_info->rows=rows;
217 matrix_info->stride=stride;
218 matrix_info->semaphore=AllocateSemaphoreInfo();
219 synchronize=GetEnvironmentValue("MAGICK_SYNCHRONIZE");
220 if (synchronize != (const char *) NULL)
221 {
222 matrix_info->synchronize=IsStringTrue(synchronize);
223 synchronize=DestroyString(synchronize);
224 }
225 matrix_info->length=(MagickSizeType) columns*rows*stride;
226 if (matrix_info->columns != (size_t) (matrix_info->length/rows/stride))
227 {
228 (void) ThrowMagickException(exception,GetMagickModule(),CacheError,
229 "CacheResourcesExhausted","`%s'","matrix cache");
230 return(DestroyMatrixInfo(matrix_info));
231 }
232 matrix_info->type=MemoryCache;
233 status=AcquireMagickResource(AreaResource,matrix_info->length);
234 if ((status != MagickFalse) &&
235 (matrix_info->length == (MagickSizeType) ((size_t) matrix_info->length)))
236 {
237 status=AcquireMagickResource(MemoryResource,matrix_info->length);
238 if (status != MagickFalse)
239 {
240 matrix_info->mapped=MagickFalse;
241 matrix_info->elements=AcquireMagickMemory((size_t)
242 matrix_info->length);
243 if (matrix_info->elements == NULL)
244 {
245 matrix_info->mapped=MagickTrue;
246 matrix_info->elements=MapBlob(-1,IOMode,0,(size_t)
247 matrix_info->length);
248 }
249 if (matrix_info->elements == (unsigned short *) NULL)
250 RelinquishMagickResource(MemoryResource,matrix_info->length);
251 }
252 }
253 matrix_info->file=(-1);
254 if (matrix_info->elements == (unsigned short *) NULL)
255 {
256 status=AcquireMagickResource(DiskResource,matrix_info->length);
257 if (status == MagickFalse)
258 {
259 (void) ThrowMagickException(exception,GetMagickModule(),CacheError,
260 "CacheResourcesExhausted","`%s'","matrix cache");
261 return(DestroyMatrixInfo(matrix_info));
262 }
263 matrix_info->type=DiskCache;
264 matrix_info->file=AcquireUniqueFileResource(matrix_info->path);
265 if (matrix_info->file == -1)
266 return(DestroyMatrixInfo(matrix_info));
267 status=AcquireMagickResource(MapResource,matrix_info->length);
268 if (status != MagickFalse)
269 {
270 status=SetMatrixExtent(matrix_info,matrix_info->length);
271 if (status != MagickFalse)
272 matrix_info->elements=(void *) MapBlob(matrix_info->file,IOMode,0,
273 (size_t) matrix_info->length);
274 if (matrix_info->elements != NULL)
275 matrix_info->type=MapCache;
276 else
277 RelinquishMagickResource(MapResource,matrix_info->length);
278 }
279 }
280 return(matrix_info);
281}
282␌
283/*
284%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
285% %
286% %
287% %
288% A c q u i r e M a g i c k M a t r i x %
289% %
290% %
291% %
292%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
293%
294% AcquireMagickMatrix() allocates and returns a matrix in the form of an
295% array of pointers to an array of doubles, with all values pre-set to zero.
296%
297% This used to generate the two dimensional matrix, and vectors required
298% for the GaussJordanElimination() method below, solving some system of
299% simultaneous equations.
300%
301% The format of the AcquireMagickMatrix method is:
302%
303% double **AcquireMagickMatrix(const size_t number_rows,
304% const size_t size)
305%
306% A description of each parameter follows:
307%
308% o number_rows: the number pointers for the array of pointers
309% (first dimension).
310%
311% o size: the size of the array of doubles each pointer points to
312% (second dimension).
313%
314*/
315MagickExport double **AcquireMagickMatrix(const size_t number_rows,
316 const size_t size)
317{
318 double
319 **matrix;
320
321 ssize_t
322 i,
323 j;
324
325 matrix=(double **) AcquireQuantumMemory(number_rows,sizeof(*matrix));
326 if (matrix == (double **) NULL)
327 return((double **) NULL);
328 for (i=0; i < (ssize_t) number_rows; i++)
329 {
330 matrix[i]=(double *) AcquireQuantumMemory(size,sizeof(*matrix[i]));
331 if (matrix[i] == (double *) NULL)
332 {
333 for (j=0; j < i; j++)
334 matrix[j]=(double *) RelinquishMagickMemory(matrix[j]);
335 matrix=(double **) RelinquishMagickMemory(matrix);
336 return((double **) NULL);
337 }
338 for (j=0; j < (ssize_t) size; j++)
339 matrix[i][j]=0.0;
340 }
341 return(matrix);
342}
343␌
344/*
345%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
346% %
347% %
348% %
349% D e s t r o y M a t r i x I n f o %
350% %
351% %
352% %
353%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
354%
355% DestroyMatrixInfo() dereferences a matrix, deallocating memory associated
356% with the matrix.
357%
358% The format of the DestroyImage method is:
359%
360% MatrixInfo *DestroyMatrixInfo(MatrixInfo *matrix_info)
361%
362% A description of each parameter follows:
363%
364% o matrix_info: the matrix.
365%
366*/
367MagickExport MatrixInfo *DestroyMatrixInfo(MatrixInfo *matrix_info)
368{
369 assert(matrix_info != (MatrixInfo *) NULL);
370 assert(matrix_info->signature == MagickCoreSignature);
371 LockSemaphoreInfo(matrix_info->semaphore);
372 switch (matrix_info->type)
373 {
374 case MemoryCache:
375 {
376 if (matrix_info->mapped == MagickFalse)
377 matrix_info->elements=RelinquishMagickMemory(matrix_info->elements);
378 else
379 {
380 (void) UnmapBlob(matrix_info->elements,(size_t) matrix_info->length);
381 matrix_info->elements=(unsigned short *) NULL;
382 }
383 RelinquishMagickResource(MemoryResource,matrix_info->length);
384 break;
385 }
386 case MapCache:
387 {
388 (void) UnmapBlob(matrix_info->elements,(size_t) matrix_info->length);
389 matrix_info->elements=NULL;
390 RelinquishMagickResource(MapResource,matrix_info->length);
391 magick_fallthrough;
392 }
393 case DiskCache:
394 {
395 if (matrix_info->file != -1)
396 (void) close(matrix_info->file);
397 (void) RelinquishUniqueFileResource(matrix_info->path);
398 RelinquishMagickResource(DiskResource,matrix_info->length);
399 break;
400 }
401 default:
402 break;
403 }
404 UnlockSemaphoreInfo(matrix_info->semaphore);
405 DestroySemaphoreInfo(&matrix_info->semaphore);
406 return((MatrixInfo *) RelinquishMagickMemory(matrix_info));
407}
408␌
409/*
410%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
411% %
412% %
413% %
414% G a u s s J o r d a n E l i m i n a t i o n %
415% %
416% %
417% %
418%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
419%
420% GaussJordanElimination() returns a matrix in reduced row echelon form,
421% while simultaneously reducing and thus solving the augmented results
422% matrix.
423%
424% See also http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
425%
426% The format of the GaussJordanElimination method is:
427%
428% MagickBooleanType GaussJordanElimination(double **matrix,
429% double **vectors,const size_t rank,const size_t number_vectors)
430%
431% A description of each parameter follows:
432%
433% o matrix: the matrix to be reduced, as an 'array of row pointers'.
434%
435% o vectors: the additional matrix argumenting the matrix for row reduction.
436% Producing an 'array of column vectors'.
437%
438% o rank: The size of the matrix (both rows and columns). Also represents
439% the number terms that need to be solved.
440%
441% o number_vectors: Number of vectors columns, argumenting the above matrix.
442% Usually 1, but can be more for more complex equation solving.
443%
444% Note that the 'matrix' is given as a 'array of row pointers' of rank size.
445% That is values can be assigned as matrix[row][column] where 'row' is
446% typically the equation, and 'column' is the term of the equation.
447% That is the matrix is in the form of a 'row first array'.
448%
449% However 'vectors' is a 'array of column pointers' which can have any number
450% of columns, with each column array the same 'rank' size as 'matrix'.
451%
452% This allows for simpler handling of the results, especially is only one
453% column 'vector' is all that is required to produce the desired solution.
454%
455% For example, the 'vectors' can consist of a pointer to a simple array of
456% doubles. when only one set of simultaneous equations is to be solved from
457% the given set of coefficient weighted terms.
458%
459% double **matrix = AcquireMagickMatrix(8UL,8UL);
460% double coefficents[8];
461% ...
462% GaussJordanElimination(matrix, &coefficents, 8UL, 1UL);
463%
464% However by specifing more 'columns' (as an 'array of vector columns', you
465% can use this function to solve a set of 'separable' equations.
466%
467% For example a distortion function where u = U(x,y) v = V(x,y)
468% And the functions U() and V() have separate coefficents, but are being
469% generated from a common x,y->u,v data set.
470%
471% Another example is generation of a color gradient from a set of colors at
472% specific coordinates, such as a list x,y -> r,g,b,a.
473%
474% You can also use the 'vectors' to generate an inverse of the given 'matrix'
475% though as a 'column first array' rather than a 'row first array'. For
476% details see http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
477%
478*/
479MagickExport MagickBooleanType GaussJordanElimination(double **matrix,
480 double **vectors,const size_t rank,const size_t number_vectors)
481{
482#define GaussJordanSwap(x,y) \
483{ \
484 if ((x) != (y)) \
485 { \
486 (x)+=(y); \
487 (y)=(x)-(y); \
488 (x)=(x)-(y); \
489 } \
490}
491
492 double
493 max,
494 scale;
495
496 ssize_t
497 i,
498 j,
499 k;
500
501 ssize_t
502 column,
503 *columns,
504 *pivots,
505 row,
506 *rows;
507
508 columns=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*columns));
509 rows=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*rows));
510 pivots=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*pivots));
511 if ((rows == (ssize_t *) NULL) || (columns == (ssize_t *) NULL) ||
512 (pivots == (ssize_t *) NULL))
513 {
514 if (pivots != (ssize_t *) NULL)
515 pivots=(ssize_t *) RelinquishMagickMemory(pivots);
516 if (columns != (ssize_t *) NULL)
517 columns=(ssize_t *) RelinquishMagickMemory(columns);
518 if (rows != (ssize_t *) NULL)
519 rows=(ssize_t *) RelinquishMagickMemory(rows);
520 return(MagickFalse);
521 }
522 (void) memset(columns,0,rank*sizeof(*columns));
523 (void) memset(rows,0,rank*sizeof(*rows));
524 (void) memset(pivots,0,rank*sizeof(*pivots));
525 column=0;
526 row=0;
527 for (i=0; i < (ssize_t) rank; i++)
528 {
529 max=0.0;
530 for (j=0; j < (ssize_t) rank; j++)
531 if (pivots[j] != 1)
532 {
533 for (k=0; k < (ssize_t) rank; k++)
534 if (pivots[k] != 0)
535 {
536 if (pivots[k] > 1)
537 return(MagickFalse);
538 }
539 else
540 if (fabs(matrix[j][k]) >= max)
541 {
542 max=fabs(matrix[j][k]);
543 row=j;
544 column=k;
545 }
546 }
547 pivots[column]++;
548 if (row != column)
549 {
550 for (k=0; k < (ssize_t) rank; k++)
551 GaussJordanSwap(matrix[row][k],matrix[column][k]);
552 for (k=0; k < (ssize_t) number_vectors; k++)
553 GaussJordanSwap(vectors[k][row],vectors[k][column]);
554 }
555 rows[i]=row;
556 columns[i]=column;
557 if (matrix[column][column] == 0.0)
558 return(MagickFalse); /* singularity */
559 scale=PerceptibleReciprocal(matrix[column][column]);
560 matrix[column][column]=1.0;
561 for (j=0; j < (ssize_t) rank; j++)
562 matrix[column][j]*=scale;
563 for (j=0; j < (ssize_t) number_vectors; j++)
564 vectors[j][column]*=scale;
565 for (j=0; j < (ssize_t) rank; j++)
566 if (j != column)
567 {
568 scale=matrix[j][column];
569 matrix[j][column]=0.0;
570 for (k=0; k < (ssize_t) rank; k++)
571 matrix[j][k]-=scale*matrix[column][k];
572 for (k=0; k < (ssize_t) number_vectors; k++)
573 vectors[k][j]-=scale*vectors[k][column];
574 }
575 }
576 for (j=(ssize_t) rank-1; j >= 0; j--)
577 if (columns[j] != rows[j])
578 for (i=0; i < (ssize_t) rank; i++)
579 GaussJordanSwap(matrix[i][rows[j]],matrix[i][columns[j]]);
580 pivots=(ssize_t *) RelinquishMagickMemory(pivots);
581 rows=(ssize_t *) RelinquishMagickMemory(rows);
582 columns=(ssize_t *) RelinquishMagickMemory(columns);
583 return(MagickTrue);
584}
585␌
586/*
587%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
588% %
589% %
590% %
591% G e t M a t r i x C o l u m n s %
592% %
593% %
594% %
595%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
596%
597% GetMatrixColumns() returns the number of columns in the matrix.
598%
599% The format of the GetMatrixColumns method is:
600%
601% size_t GetMatrixColumns(const MatrixInfo *matrix_info)
602%
603% A description of each parameter follows:
604%
605% o matrix_info: the matrix.
606%
607*/
608MagickExport size_t GetMatrixColumns(const MatrixInfo *matrix_info)
609{
610 assert(matrix_info != (MatrixInfo *) NULL);
611 assert(matrix_info->signature == MagickCoreSignature);
612 return(matrix_info->columns);
613}
614␌
615/*
616%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
617% %
618% %
619% %
620% G e t M a t r i x E l e m e n t %
621% %
622% %
623% %
624%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
625%
626% GetMatrixElement() returns the specified element in the matrix.
627%
628% The format of the GetMatrixElement method is:
629%
630% MagickBooleanType GetMatrixElement(const MatrixInfo *matrix_info,
631% const ssize_t x,const ssize_t y,void *value)
632%
633% A description of each parameter follows:
634%
635% o matrix_info: the matrix columns.
636%
637% o x: the matrix x-offset.
638%
639% o y: the matrix y-offset.
640%
641% o value: return the matrix element in this buffer.
642%
643*/
644
645static inline ssize_t EdgeX(const ssize_t x,const size_t columns)
646{
647 if (x < 0L)
648 return(0L);
649 if (x >= (ssize_t) columns)
650 return((ssize_t) (columns-1));
651 return(x);
652}
653
654static inline ssize_t EdgeY(const ssize_t y,const size_t rows)
655{
656 if (y < 0L)
657 return(0L);
658 if (y >= (ssize_t) rows)
659 return((ssize_t) (rows-1));
660 return(y);
661}
662
663static inline MagickOffsetType ReadMatrixElements(
664 const MatrixInfo *magick_restrict matrix_info,const MagickOffsetType offset,
665 const MagickSizeType length,unsigned char *magick_restrict buffer)
666{
667 MagickOffsetType
668 i;
669
670 ssize_t
671 count;
672
673#if !defined(MAGICKCORE_HAVE_PREAD)
674 LockSemaphoreInfo(matrix_info->semaphore);
675 if (lseek(matrix_info->file,offset,SEEK_SET) < 0)
676 {
677 UnlockSemaphoreInfo(matrix_info->semaphore);
678 return((MagickOffsetType) -1);
679 }
680#endif
681 count=0;
682 for (i=0; i < (MagickOffsetType) length; i+=count)
683 {
684#if !defined(MAGICKCORE_HAVE_PREAD)
685 count=read(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
686 (MagickSizeType) MagickMaxBufferExtent));
687#else
688 count=pread(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
689 (MagickSizeType) MagickMaxBufferExtent),(off_t) (offset+i));
690#endif
691 if (count <= 0)
692 {
693 count=0;
694 if (errno != EINTR)
695 break;
696 }
697 }
698#if !defined(MAGICKCORE_HAVE_PREAD)
699 UnlockSemaphoreInfo(matrix_info->semaphore);
700#endif
701 return(i);
702}
703
704MagickExport MagickBooleanType GetMatrixElement(const MatrixInfo *matrix_info,
705 const ssize_t x,const ssize_t y,void *value)
706{
707 MagickOffsetType
708 count,
709 i;
710
711 assert(matrix_info != (const MatrixInfo *) NULL);
712 assert(matrix_info->signature == MagickCoreSignature);
713 i=(MagickOffsetType) EdgeY(y,matrix_info->rows)*matrix_info->columns+
714 EdgeX(x,matrix_info->columns);
715 if (matrix_info->type != DiskCache)
716 {
717 (void) memcpy(value,(unsigned char *) matrix_info->elements+i*
718 matrix_info->stride,matrix_info->stride);
719 return(MagickTrue);
720 }
721 count=ReadMatrixElements(matrix_info,i*matrix_info->stride,
722 matrix_info->stride,(unsigned char *) value);
723 if (count != (MagickOffsetType) matrix_info->stride)
724 return(MagickFalse);
725 return(MagickTrue);
726}
727␌
728/*
729%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
730% %
731% %
732% %
733% G e t M a t r i x R o w s %
734% %
735% %
736% %
737%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
738%
739% GetMatrixRows() returns the number of rows in the matrix.
740%
741% The format of the GetMatrixRows method is:
742%
743% size_t GetMatrixRows(const MatrixInfo *matrix_info)
744%
745% A description of each parameter follows:
746%
747% o matrix_info: the matrix.
748%
749*/
750MagickExport size_t GetMatrixRows(const MatrixInfo *matrix_info)
751{
752 assert(matrix_info != (const MatrixInfo *) NULL);
753 assert(matrix_info->signature == MagickCoreSignature);
754 return(matrix_info->rows);
755}
756␌
757/*
758%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
759% %
760% %
761% %
762% L e a s t S q u a r e s A d d T e r m s %
763% %
764% %
765% %
766%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
767%
768% LeastSquaresAddTerms() adds one set of terms and associate results to the
769% given matrix and vectors for solving using least-squares function fitting.
770%
771% The format of the AcquireMagickMatrix method is:
772%
773% void LeastSquaresAddTerms(double **matrix,double **vectors,
774% const double *terms,const double *results,const size_t rank,
775% const size_t number_vectors);
776%
777% A description of each parameter follows:
778%
779% o matrix: the square matrix to add given terms/results to.
780%
781% o vectors: the result vectors to add terms/results to.
782%
783% o terms: the pre-calculated terms (without the unknown coefficient
784% weights) that forms the equation being added.
785%
786% o results: the result(s) that should be generated from the given terms
787% weighted by the yet-to-be-solved coefficients.
788%
789% o rank: the rank or size of the dimensions of the square matrix.
790% Also the length of vectors, and number of terms being added.
791%
792% o number_vectors: Number of result vectors, and number or results being
793% added. Also represents the number of separable systems of equations
794% that is being solved.
795%
796% Example of use...
797%
798% 2 dimensional Affine Equations (which are separable)
799% c0*x + c2*y + c4*1 => u
800% c1*x + c3*y + c5*1 => v
801%
802% double **matrix = AcquireMagickMatrix(3UL,3UL);
803% double **vectors = AcquireMagickMatrix(2UL,3UL);
804% double terms[3], results[2];
805% ...
806% for each given x,y -> u,v
807% terms[0] = x;
808% terms[1] = y;
809% terms[2] = 1;
810% results[0] = u;
811% results[1] = v;
812% LeastSquaresAddTerms(matrix,vectors,terms,results,3UL,2UL);
813% ...
814% if ( GaussJordanElimination(matrix,vectors,3UL,2UL) ) {
815% c0 = vectors[0][0];
816% c2 = vectors[0][1];
817% c4 = vectors[0][2];
818% c1 = vectors[1][0];
819% c3 = vectors[1][1];
820% c5 = vectors[1][2];
821% }
822% else
823% printf("Matrix unsolvable\n);
824% RelinquishMagickMatrix(matrix,3UL);
825% RelinquishMagickMatrix(vectors,2UL);
826%
827*/
828MagickExport void LeastSquaresAddTerms(double **matrix,double **vectors,
829 const double *terms,const double *results,const size_t rank,
830 const size_t number_vectors)
831{
832 ssize_t
833 i,
834 j;
835
836 for (j=0; j < (ssize_t) rank; j++)
837 {
838 for (i=0; i < (ssize_t) rank; i++)
839 matrix[i][j]+=terms[i]*terms[j];
840 for (i=0; i < (ssize_t) number_vectors; i++)
841 vectors[i][j]+=results[i]*terms[j];
842 }
843}
844␌
845/*
846%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
847% %
848% %
849% %
850% M a t r i x T o I m a g e %
851% %
852% %
853% %
854%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
855%
856% MatrixToImage() returns a matrix as an image. The matrix elements must be
857% of type double otherwise nonsense is returned.
858%
859% The format of the MatrixToImage method is:
860%
861% Image *MatrixToImage(const MatrixInfo *matrix_info,
862% ExceptionInfo *exception)
863%
864% A description of each parameter follows:
865%
866% o matrix_info: the matrix.
867%
868% o exception: return any errors or warnings in this structure.
869%
870*/
871MagickExport Image *MatrixToImage(const MatrixInfo *matrix_info,
872 ExceptionInfo *exception)
873{
874 CacheView
875 *image_view;
876
877 double
878 max_value,
879 min_value,
880 scale_factor,
881 value;
882
883 Image
884 *image;
885
886 MagickBooleanType
887 status;
888
889 ssize_t
890 y;
891
892 assert(matrix_info != (const MatrixInfo *) NULL);
893 assert(matrix_info->signature == MagickCoreSignature);
894 assert(exception != (ExceptionInfo *) NULL);
895 assert(exception->signature == MagickCoreSignature);
896 if (matrix_info->stride < sizeof(double))
897 return((Image *) NULL);
898 /*
899 Determine range of matrix.
900 */
901 (void) GetMatrixElement(matrix_info,0,0,&value);
902 min_value=value;
903 max_value=value;
904 for (y=0; y < (ssize_t) matrix_info->rows; y++)
905 {
906 ssize_t
907 x;
908
909 for (x=0; x < (ssize_t) matrix_info->columns; x++)
910 {
911 if (GetMatrixElement(matrix_info,x,y,&value) == MagickFalse)
912 continue;
913 if (value < min_value)
914 min_value=value;
915 else
916 if (value > max_value)
917 max_value=value;
918 }
919 }
920 if ((min_value == 0.0) && (max_value == 0.0))
921 scale_factor=0;
922 else
923 if (min_value == max_value)
924 {
925 scale_factor=(double) QuantumRange/min_value;
926 min_value=0;
927 }
928 else
929 scale_factor=(double) QuantumRange/(max_value-min_value);
930 /*
931 Convert matrix to image.
932 */
933 image=AcquireImage((ImageInfo *) NULL);
934 image->columns=matrix_info->columns;
935 image->rows=matrix_info->rows;
936 image->colorspace=GRAYColorspace;
937 status=MagickTrue;
938 image_view=AcquireAuthenticCacheView(image,exception);
939#if defined(MAGICKCORE_OPENMP_SUPPORT)
940 #pragma omp parallel for schedule(static) shared(status) \
941 magick_number_threads(image,image,image->rows,2)
942#endif
943 for (y=0; y < (ssize_t) image->rows; y++)
944 {
945 double
946 value;
947
948 PixelPacket
949 *q;
950
951 ssize_t
952 x;
953
954 if (status == MagickFalse)
955 continue;
956 q=QueueCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
957 if (q == (PixelPacket *) NULL)
958 {
959 status=MagickFalse;
960 continue;
961 }
962 for (x=0; x < (ssize_t) image->columns; x++)
963 {
964 if (GetMatrixElement(matrix_info,x,y,&value) == MagickFalse)
965 continue;
966 value=scale_factor*(value-min_value);
967 q->red=ClampToQuantum(value);
968 q->green=q->red;
969 q->blue=q->red;
970 q++;
971 }
972 if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
973 status=MagickFalse;
974 }
975 image_view=DestroyCacheView(image_view);
976 if (status == MagickFalse)
977 image=DestroyImage(image);
978 return(image);
979}
980␌
981/*
982%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
983% %
984% %
985% %
986% N u l l M a t r i x %
987% %
988% %
989% %
990%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
991%
992% NullMatrix() sets all elements of the matrix to zero.
993%
994% The format of the memset method is:
995%
996% MagickBooleanType *NullMatrix(MatrixInfo *matrix_info)
997%
998% A description of each parameter follows:
999%
1000% o matrix_info: the matrix.
1001%
1002*/
1003MagickExport MagickBooleanType NullMatrix(MatrixInfo *matrix_info)
1004{
1005 ssize_t
1006 x;
1007
1008 ssize_t
1009 count,
1010 y;
1011
1012 unsigned char
1013 value;
1014
1015 assert(matrix_info != (const MatrixInfo *) NULL);
1016 assert(matrix_info->signature == MagickCoreSignature);
1017 if (matrix_info->type != DiskCache)
1018 {
1019 (void) memset(matrix_info->elements,0,(size_t)
1020 matrix_info->length);
1021 return(MagickTrue);
1022 }
1023 value=0;
1024 (void) lseek(matrix_info->file,0,SEEK_SET);
1025 for (y=0; y < (ssize_t) matrix_info->rows; y++)
1026 {
1027 for (x=0; x < (ssize_t) matrix_info->length; x++)
1028 {
1029 count=write(matrix_info->file,&value,sizeof(value));
1030 if (count != (ssize_t) sizeof(value))
1031 break;
1032 }
1033 if (x < (ssize_t) matrix_info->length)
1034 break;
1035 }
1036 return(y < (ssize_t) matrix_info->rows ? MagickFalse : MagickTrue);
1037}
1038␌
1039/*
1040%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1041% %
1042% %
1043% %
1044% R e l i n q u i s h M a g i c k M a t r i x %
1045% %
1046% %
1047% %
1048%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1049%
1050% RelinquishMagickMatrix() frees the previously acquired matrix (array of
1051% pointers to arrays of doubles).
1052%
1053% The format of the RelinquishMagickMatrix method is:
1054%
1055% double **RelinquishMagickMatrix(double **matrix,
1056% const size_t number_rows)
1057%
1058% A description of each parameter follows:
1059%
1060% o matrix: the matrix to relinquish
1061%
1062% o number_rows: the first dimension of the acquired matrix (number of
1063% pointers)
1064%
1065*/
1066MagickExport double **RelinquishMagickMatrix(double **matrix,
1067 const size_t number_rows)
1068{
1069 ssize_t
1070 i;
1071
1072 if (matrix == (double **) NULL )
1073 return(matrix);
1074 for (i=0; i < (ssize_t) number_rows; i++)
1075 matrix[i]=(double *) RelinquishMagickMemory(matrix[i]);
1076 matrix=(double **) RelinquishMagickMemory(matrix);
1077 return(matrix);
1078}
1079␌
1080/*
1081%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1082% %
1083% %
1084% %
1085% S e t M a t r i x E l e m e n t %
1086% %
1087% %
1088% %
1089%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1090%
1091% SetMatrixElement() sets the specified element in the matrix.
1092%
1093% The format of the SetMatrixElement method is:
1094%
1095% MagickBooleanType SetMatrixElement(const MatrixInfo *matrix_info,
1096% const ssize_t x,const ssize_t y,void *value)
1097%
1098% A description of each parameter follows:
1099%
1100% o matrix_info: the matrix columns.
1101%
1102% o x: the matrix x-offset.
1103%
1104% o y: the matrix y-offset.
1105%
1106% o value: set the matrix element to this value.
1107%
1108*/
1109
1110MagickExport MagickBooleanType SetMatrixElement(const MatrixInfo *matrix_info,
1111 const ssize_t x,const ssize_t y,const void *value)
1112{
1113 MagickOffsetType
1114 count,
1115 i;
1116
1117 assert(matrix_info != (const MatrixInfo *) NULL);
1118 assert(matrix_info->signature == MagickCoreSignature);
1119 i=(MagickOffsetType) y*matrix_info->columns+x;
1120 if ((i < 0) ||
1121 ((MagickSizeType) (i*matrix_info->stride) >= matrix_info->length))
1122 return(MagickFalse);
1123 if (matrix_info->type != DiskCache)
1124 {
1125 (void) memcpy((unsigned char *) matrix_info->elements+i*
1126 matrix_info->stride,value,matrix_info->stride);
1127 return(MagickTrue);
1128 }
1129 count=WriteMatrixElements(matrix_info,i*matrix_info->stride,
1130 matrix_info->stride,(unsigned char *) value);
1131 if (count != (MagickOffsetType) matrix_info->stride)
1132 return(MagickFalse);
1133 return(MagickTrue);
1134}
_CacheView
Definition cache-view.c:66
_ExceptionInfo
Definition exception.h:103
_ImageInfo
Definition image.h:346
_Image
Definition image.h:134
_MatrixInfo
Definition matrix.c:60
_PixelPacket
Definition pixel.h:132