forked from ImageMagick/ImageMagick
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathmatrix.c
1133 lines (1072 loc) · 38.2 KB
/
matrix.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% M M AAA TTTTT RRRR IIIII X X %
% MM MM A A T R R I X X %
% M M M AAAAA T RRRR I X %
% M M A A T R R I X X %
% M M A A T R R IIIII X X %
% %
% %
% MagickCore Matrix Methods %
% %
% Software Design %
% Cristy %
% August 2007 %
% %
% %
% Copyright 1999-2018 ImageMagick Studio LLC, a non-profit organization %
% dedicated to making software imaging solutions freely available. %
% %
% You may not use this file except in compliance with the License. You may %
% obtain a copy of the License at %
% %
% https://www.imagemagick.org/script/license.php %
% %
% Unless required by applicable law or agreed to in writing, software %
% distributed under the License is distributed on an "AS IS" BASIS, %
% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. %
% See the License for the specific language governing permissions and %
% limitations under the License. %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
*/
/*
Include declarations.
*/
#include "MagickCore/studio.h"
#include "MagickCore/blob.h"
#include "MagickCore/blob-private.h"
#include "MagickCore/cache.h"
#include "MagickCore/exception.h"
#include "MagickCore/exception-private.h"
#include "MagickCore/image-private.h"
#include "MagickCore/matrix.h"
#include "MagickCore/matrix-private.h"
#include "MagickCore/memory_.h"
#include "MagickCore/pixel-accessor.h"
#include "MagickCore/pixel-private.h"
#include "MagickCore/resource_.h"
#include "MagickCore/semaphore.h"
#include "MagickCore/thread-private.h"
#include "MagickCore/utility.h"
/*
Typedef declaration.
*/
struct _MatrixInfo
{
CacheType
type;
size_t
columns,
rows,
stride;
MagickSizeType
length;
MagickBooleanType
mapped,
synchronize;
char
path[MagickPathExtent];
int
file;
void
*elements;
SemaphoreInfo
*semaphore;
size_t
signature;
};
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% A c q u i r e M a t r i x I n f o %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% AcquireMatrixInfo() allocates the ImageInfo structure.
%
% The format of the AcquireMatrixInfo method is:
%
% MatrixInfo *AcquireMatrixInfo(const size_t columns,const size_t rows,
% const size_t stride,ExceptionInfo *exception)
%
% A description of each parameter follows:
%
% o columns: the matrix columns.
%
% o rows: the matrix rows.
%
% o stride: the matrix stride.
%
% o exception: return any errors or warnings in this structure.
%
*/
#if defined(SIGBUS)
static void MatrixSignalHandler(int status)
{
ThrowFatalException(CacheFatalError,"UnableToExtendMatrixCache");
}
#endif
static inline MagickOffsetType WriteMatrixElements(
const MatrixInfo *magick_restrict matrix_info,const MagickOffsetType offset,
const MagickSizeType length,const unsigned char *magick_restrict buffer)
{
register MagickOffsetType
i;
ssize_t
count;
#if !defined(MAGICKCORE_HAVE_PWRITE)
LockSemaphoreInfo(matrix_info->semaphore);
if (lseek(matrix_info->file,offset,SEEK_SET) < 0)
{
UnlockSemaphoreInfo(matrix_info->semaphore);
return((MagickOffsetType) -1);
}
#endif
count=0;
for (i=0; i < (MagickOffsetType) length; i+=count)
{
#if !defined(MAGICKCORE_HAVE_PWRITE)
count=write(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
(MagickSizeType) SSIZE_MAX));
#else
count=pwrite(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
(MagickSizeType) SSIZE_MAX),(off_t) (offset+i));
#endif
if (count <= 0)
{
count=0;
if (errno != EINTR)
break;
}
}
#if !defined(MAGICKCORE_HAVE_PWRITE)
UnlockSemaphoreInfo(matrix_info->semaphore);
#endif
return(i);
}
static MagickBooleanType SetMatrixExtent(
MatrixInfo *magick_restrict matrix_info,MagickSizeType length)
{
MagickOffsetType
count,
extent,
offset;
if (length != (MagickSizeType) ((MagickOffsetType) length))
return(MagickFalse);
offset=(MagickOffsetType) lseek(matrix_info->file,0,SEEK_END);
if (offset < 0)
return(MagickFalse);
if ((MagickSizeType) offset >= length)
return(MagickTrue);
extent=(MagickOffsetType) length-1;
count=WriteMatrixElements(matrix_info,extent,1,(const unsigned char *) "");
#if defined(MAGICKCORE_HAVE_POSIX_FALLOCATE)
if (matrix_info->synchronize != MagickFalse)
(void) posix_fallocate(matrix_info->file,offset+1,extent-offset);
#endif
#if defined(SIGBUS)
(void) signal(SIGBUS,MatrixSignalHandler);
#endif
return(count != (MagickOffsetType) 1 ? MagickFalse : MagickTrue);
}
MagickExport MatrixInfo *AcquireMatrixInfo(const size_t columns,
const size_t rows,const size_t stride,ExceptionInfo *exception)
{
char
*synchronize;
MagickBooleanType
status;
MatrixInfo
*matrix_info;
matrix_info=(MatrixInfo *) AcquireMagickMemory(sizeof(*matrix_info));
if (matrix_info == (MatrixInfo *) NULL)
return((MatrixInfo *) NULL);
(void) ResetMagickMemory(matrix_info,0,sizeof(*matrix_info));
matrix_info->signature=MagickCoreSignature;
matrix_info->columns=columns;
matrix_info->rows=rows;
matrix_info->stride=stride;
matrix_info->semaphore=AcquireSemaphoreInfo();
synchronize=GetEnvironmentValue("MAGICK_SYNCHRONIZE");
if (synchronize != (const char *) NULL)
{
matrix_info->synchronize=IsStringTrue(synchronize);
synchronize=DestroyString(synchronize);
}
matrix_info->length=(MagickSizeType) columns*rows*stride;
if (matrix_info->columns != (size_t) (matrix_info->length/rows/stride))
{
(void) ThrowMagickException(exception,GetMagickModule(),CacheError,
"CacheResourcesExhausted","`%s'","matrix cache");
return(DestroyMatrixInfo(matrix_info));
}
matrix_info->type=MemoryCache;
status=AcquireMagickResource(AreaResource,matrix_info->length);
if ((status != MagickFalse) &&
(matrix_info->length == (MagickSizeType) ((size_t) matrix_info->length)))
{
status=AcquireMagickResource(MemoryResource,matrix_info->length);
if (status != MagickFalse)
{
matrix_info->mapped=MagickFalse;
matrix_info->elements=AcquireMagickMemory((size_t)
matrix_info->length);
if (matrix_info->elements == NULL)
{
matrix_info->mapped=MagickTrue;
matrix_info->elements=MapBlob(-1,IOMode,0,(size_t)
matrix_info->length);
}
if (matrix_info->elements == (unsigned short *) NULL)
RelinquishMagickResource(MemoryResource,matrix_info->length);
}
}
matrix_info->file=(-1);
if (matrix_info->elements == (unsigned short *) NULL)
{
status=AcquireMagickResource(DiskResource,matrix_info->length);
if (status == MagickFalse)
{
(void) ThrowMagickException(exception,GetMagickModule(),CacheError,
"CacheResourcesExhausted","`%s'","matrix cache");
return(DestroyMatrixInfo(matrix_info));
}
matrix_info->type=DiskCache;
matrix_info->file=AcquireUniqueFileResource(matrix_info->path);
if (matrix_info->file == -1)
return(DestroyMatrixInfo(matrix_info));
status=AcquireMagickResource(MapResource,matrix_info->length);
if (status != MagickFalse)
{
status=SetMatrixExtent(matrix_info,matrix_info->length);
if (status != MagickFalse)
matrix_info->elements=(void *) MapBlob(matrix_info->file,IOMode,0,
(size_t) matrix_info->length);
if (matrix_info->elements != NULL)
matrix_info->type=MapCache;
else
RelinquishMagickResource(MapResource,matrix_info->length);
}
}
return(matrix_info);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% A c q u i r e M a g i c k M a t r i x %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% AcquireMagickMatrix() allocates and returns a matrix in the form of an
% array of pointers to an array of doubles, with all values pre-set to zero.
%
% This used to generate the two dimensional matrix, and vectors required
% for the GaussJordanElimination() method below, solving some system of
% simultanious equations.
%
% The format of the AcquireMagickMatrix method is:
%
% double **AcquireMagickMatrix(const size_t number_rows,
% const size_t size)
%
% A description of each parameter follows:
%
% o number_rows: the number pointers for the array of pointers
% (first dimension).
%
% o size: the size of the array of doubles each pointer points to
% (second dimension).
%
*/
MagickExport double **AcquireMagickMatrix(const size_t number_rows,
const size_t size)
{
double
**matrix;
register ssize_t
i,
j;
matrix=(double **) AcquireQuantumMemory(number_rows,sizeof(*matrix));
if (matrix == (double **) NULL)
return((double **) NULL);
for (i=0; i < (ssize_t) number_rows; i++)
{
matrix[i]=(double *) AcquireQuantumMemory(size,sizeof(*matrix[i]));
if (matrix[i] == (double *) NULL)
{
for (j=0; j < i; j++)
matrix[j]=(double *) RelinquishMagickMemory(matrix[j]);
matrix=(double **) RelinquishMagickMemory(matrix);
return((double **) NULL);
}
for (j=0; j < (ssize_t) size; j++)
matrix[i][j]=0.0;
}
return(matrix);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% D e s t r o y M a t r i x I n f o %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% DestroyMatrixInfo() dereferences a matrix, deallocating memory associated
% with the matrix.
%
% The format of the DestroyImage method is:
%
% MatrixInfo *DestroyMatrixInfo(MatrixInfo *matrix_info)
%
% A description of each parameter follows:
%
% o matrix_info: the matrix.
%
*/
MagickExport MatrixInfo *DestroyMatrixInfo(MatrixInfo *matrix_info)
{
assert(matrix_info != (MatrixInfo *) NULL);
assert(matrix_info->signature == MagickCoreSignature);
LockSemaphoreInfo(matrix_info->semaphore);
switch (matrix_info->type)
{
case MemoryCache:
{
if (matrix_info->mapped == MagickFalse)
matrix_info->elements=RelinquishMagickMemory(matrix_info->elements);
else
{
(void) UnmapBlob(matrix_info->elements,(size_t) matrix_info->length);
matrix_info->elements=(unsigned short *) NULL;
}
RelinquishMagickResource(MemoryResource,matrix_info->length);
break;
}
case MapCache:
{
(void) UnmapBlob(matrix_info->elements,(size_t) matrix_info->length);
matrix_info->elements=NULL;
RelinquishMagickResource(MapResource,matrix_info->length);
}
case DiskCache:
{
if (matrix_info->file != -1)
(void) close(matrix_info->file);
(void) RelinquishUniqueFileResource(matrix_info->path);
RelinquishMagickResource(DiskResource,matrix_info->length);
break;
}
default:
break;
}
UnlockSemaphoreInfo(matrix_info->semaphore);
RelinquishSemaphoreInfo(&matrix_info->semaphore);
return((MatrixInfo *) RelinquishMagickMemory(matrix_info));
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ G a u s s J o r d a n E l i m i n a t i o n %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GaussJordanElimination() returns a matrix in reduced row echelon form,
% while simultaneously reducing and thus solving the augumented results
% matrix.
%
% See also http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
%
% The format of the GaussJordanElimination method is:
%
% MagickBooleanType GaussJordanElimination(double **matrix,
% double **vectors,const size_t rank,const size_t number_vectors)
%
% A description of each parameter follows:
%
% o matrix: the matrix to be reduced, as an 'array of row pointers'.
%
% o vectors: the additional matrix argumenting the matrix for row reduction.
% Producing an 'array of column vectors'.
%
% o rank: The size of the matrix (both rows and columns).
% Also represents the number terms that need to be solved.
%
% o number_vectors: Number of vectors columns, argumenting the above matrix.
% Usally 1, but can be more for more complex equation solving.
%
% Note that the 'matrix' is given as a 'array of row pointers' of rank size.
% That is values can be assigned as matrix[row][column] where 'row' is
% typically the equation, and 'column' is the term of the equation.
% That is the matrix is in the form of a 'row first array'.
%
% However 'vectors' is a 'array of column pointers' which can have any number
% of columns, with each column array the same 'rank' size as 'matrix'.
%
% This allows for simpler handling of the results, especially is only one
% column 'vector' is all that is required to produce the desired solution.
%
% For example, the 'vectors' can consist of a pointer to a simple array of
% doubles. when only one set of simultanious equations is to be solved from
% the given set of coefficient weighted terms.
%
% double **matrix = AcquireMagickMatrix(8UL,8UL);
% double coefficents[8];
% ...
% GaussJordanElimination(matrix, &coefficents, 8UL, 1UL);
%
% However by specifing more 'columns' (as an 'array of vector columns',
% you can use this function to solve a set of 'separable' equations.
%
% For example a distortion function where u = U(x,y) v = V(x,y)
% And the functions U() and V() have separate coefficents, but are being
% generated from a common x,y->u,v data set.
%
% Another example is generation of a color gradient from a set of colors at
% specific coordients, such as a list x,y -> r,g,b,a.
%
% You can also use the 'vectors' to generate an inverse of the given 'matrix'
% though as a 'column first array' rather than a 'row first array'. For
% details see http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
%
*/
MagickPrivate MagickBooleanType GaussJordanElimination(double **matrix,
double **vectors,const size_t rank,const size_t number_vectors)
{
#define GaussJordanSwap(x,y) \
{ \
if ((x) != (y)) \
{ \
(x)+=(y); \
(y)=(x)-(y); \
(x)=(x)-(y); \
} \
}
double
max,
scale;
register ssize_t
i,
j,
k;
ssize_t
column,
*columns,
*pivots,
row,
*rows;
columns=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*columns));
rows=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*rows));
pivots=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*pivots));
if ((rows == (ssize_t *) NULL) || (columns == (ssize_t *) NULL) ||
(pivots == (ssize_t *) NULL))
{
if (pivots != (ssize_t *) NULL)
pivots=(ssize_t *) RelinquishMagickMemory(pivots);
if (columns != (ssize_t *) NULL)
columns=(ssize_t *) RelinquishMagickMemory(columns);
if (rows != (ssize_t *) NULL)
rows=(ssize_t *) RelinquishMagickMemory(rows);
return(MagickFalse);
}
(void) ResetMagickMemory(columns,0,rank*sizeof(*columns));
(void) ResetMagickMemory(rows,0,rank*sizeof(*rows));
(void) ResetMagickMemory(pivots,0,rank*sizeof(*pivots));
column=0;
row=0;
for (i=0; i < (ssize_t) rank; i++)
{
max=0.0;
for (j=0; j < (ssize_t) rank; j++)
if (pivots[j] != 1)
{
for (k=0; k < (ssize_t) rank; k++)
if (pivots[k] != 0)
{
if (pivots[k] > 1)
return(MagickFalse);
}
else
if (fabs(matrix[j][k]) >= max)
{
max=fabs(matrix[j][k]);
row=j;
column=k;
}
}
pivots[column]++;
if (row != column)
{
for (k=0; k < (ssize_t) rank; k++)
GaussJordanSwap(matrix[row][k],matrix[column][k]);
for (k=0; k < (ssize_t) number_vectors; k++)
GaussJordanSwap(vectors[k][row],vectors[k][column]);
}
rows[i]=row;
columns[i]=column;
if (matrix[column][column] == 0.0)
return(MagickFalse); /* sigularity */
scale=PerceptibleReciprocal(matrix[column][column]);
matrix[column][column]=1.0;
for (j=0; j < (ssize_t) rank; j++)
matrix[column][j]*=scale;
for (j=0; j < (ssize_t) number_vectors; j++)
vectors[j][column]*=scale;
for (j=0; j < (ssize_t) rank; j++)
if (j != column)
{
scale=matrix[j][column];
matrix[j][column]=0.0;
for (k=0; k < (ssize_t) rank; k++)
matrix[j][k]-=scale*matrix[column][k];
for (k=0; k < (ssize_t) number_vectors; k++)
vectors[k][j]-=scale*vectors[k][column];
}
}
for (j=(ssize_t) rank-1; j >= 0; j--)
if (columns[j] != rows[j])
for (i=0; i < (ssize_t) rank; i++)
GaussJordanSwap(matrix[i][rows[j]],matrix[i][columns[j]]);
pivots=(ssize_t *) RelinquishMagickMemory(pivots);
rows=(ssize_t *) RelinquishMagickMemory(rows);
columns=(ssize_t *) RelinquishMagickMemory(columns);
return(MagickTrue);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% G e t M a t r i x C o l u m n s %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GetMatrixColumns() returns the number of columns in the matrix.
%
% The format of the GetMatrixColumns method is:
%
% size_t GetMatrixColumns(const MatrixInfo *matrix_info)
%
% A description of each parameter follows:
%
% o matrix_info: the matrix.
%
*/
MagickExport size_t GetMatrixColumns(const MatrixInfo *matrix_info)
{
assert(matrix_info != (MatrixInfo *) NULL);
assert(matrix_info->signature == MagickCoreSignature);
return(matrix_info->columns);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% G e t M a t r i x E l e m e n t %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GetMatrixElement() returns the specifed element in the matrix.
%
% The format of the GetMatrixElement method is:
%
% MagickBooleanType GetMatrixElement(const MatrixInfo *matrix_info,
% const ssize_t x,const ssize_t y,void *value)
%
% A description of each parameter follows:
%
% o matrix_info: the matrix columns.
%
% o x: the matrix x-offset.
%
% o y: the matrix y-offset.
%
% o value: return the matrix element in this buffer.
%
*/
static inline ssize_t EdgeX(const ssize_t x,const size_t columns)
{
if (x < 0L)
return(0L);
if (x >= (ssize_t) columns)
return((ssize_t) (columns-1));
return(x);
}
static inline ssize_t EdgeY(const ssize_t y,const size_t rows)
{
if (y < 0L)
return(0L);
if (y >= (ssize_t) rows)
return((ssize_t) (rows-1));
return(y);
}
static inline MagickOffsetType ReadMatrixElements(
const MatrixInfo *magick_restrict matrix_info,const MagickOffsetType offset,
const MagickSizeType length,unsigned char *magick_restrict buffer)
{
register MagickOffsetType
i;
ssize_t
count;
#if !defined(MAGICKCORE_HAVE_PREAD)
LockSemaphoreInfo(matrix_info->semaphore);
if (lseek(matrix_info->file,offset,SEEK_SET) < 0)
{
UnlockSemaphoreInfo(matrix_info->semaphore);
return((MagickOffsetType) -1);
}
#endif
count=0;
for (i=0; i < (MagickOffsetType) length; i+=count)
{
#if !defined(MAGICKCORE_HAVE_PREAD)
count=read(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
(MagickSizeType) SSIZE_MAX));
#else
count=pread(matrix_info->file,buffer+i,(size_t) MagickMin(length-i,
(MagickSizeType) SSIZE_MAX),(off_t) (offset+i));
#endif
if (count <= 0)
{
count=0;
if (errno != EINTR)
break;
}
}
#if !defined(MAGICKCORE_HAVE_PREAD)
UnlockSemaphoreInfo(matrix_info->semaphore);
#endif
return(i);
}
MagickExport MagickBooleanType GetMatrixElement(const MatrixInfo *matrix_info,
const ssize_t x,const ssize_t y,void *value)
{
MagickOffsetType
count,
i;
assert(matrix_info != (const MatrixInfo *) NULL);
assert(matrix_info->signature == MagickCoreSignature);
i=(MagickOffsetType) EdgeY(y,matrix_info->rows)*matrix_info->columns+
EdgeX(x,matrix_info->columns);
if (matrix_info->type != DiskCache)
{
(void) memcpy(value,(unsigned char *) matrix_info->elements+i*
matrix_info->stride,matrix_info->stride);
return(MagickTrue);
}
count=ReadMatrixElements(matrix_info,i*matrix_info->stride,
matrix_info->stride,(unsigned char *) value);
if (count != (MagickOffsetType) matrix_info->stride)
return(MagickFalse);
return(MagickTrue);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% G e t M a t r i x R o w s %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GetMatrixRows() returns the number of rows in the matrix.
%
% The format of the GetMatrixRows method is:
%
% size_t GetMatrixRows(const MatrixInfo *matrix_info)
%
% A description of each parameter follows:
%
% o matrix_info: the matrix.
%
*/
MagickExport size_t GetMatrixRows(const MatrixInfo *matrix_info)
{
assert(matrix_info != (const MatrixInfo *) NULL);
assert(matrix_info->signature == MagickCoreSignature);
return(matrix_info->rows);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ L e a s t S q u a r e s A d d T e r m s %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% LeastSquaresAddTerms() adds one set of terms and associate results to the
% given matrix and vectors for solving using least-squares function fitting.
%
% The format of the AcquireMagickMatrix method is:
%
% void LeastSquaresAddTerms(double **matrix,double **vectors,
% const double *terms,const double *results,const size_t rank,
% const size_t number_vectors);
%
% A description of each parameter follows:
%
% o matrix: the square matrix to add given terms/results to.
%
% o vectors: the result vectors to add terms/results to.
%
% o terms: the pre-calculated terms (without the unknown coefficent
% weights) that forms the equation being added.
%
% o results: the result(s) that should be generated from the given terms
% weighted by the yet-to-be-solved coefficents.
%
% o rank: the rank or size of the dimensions of the square matrix.
% Also the length of vectors, and number of terms being added.
%
% o number_vectors: Number of result vectors, and number or results being
% added. Also represents the number of separable systems of equations
% that is being solved.
%
% Example of use...
%
% 2 dimensional Affine Equations (which are separable)
% c0*x + c2*y + c4*1 => u
% c1*x + c3*y + c5*1 => v
%
% double **matrix = AcquireMagickMatrix(3UL,3UL);
% double **vectors = AcquireMagickMatrix(2UL,3UL);
% double terms[3], results[2];
% ...
% for each given x,y -> u,v
% terms[0] = x;
% terms[1] = y;
% terms[2] = 1;
% results[0] = u;
% results[1] = v;
% LeastSquaresAddTerms(matrix,vectors,terms,results,3UL,2UL);
% ...
% if ( GaussJordanElimination(matrix,vectors,3UL,2UL) ) {
% c0 = vectors[0][0];
% c2 = vectors[0][1];
% c4 = vectors[0][2];
% c1 = vectors[1][0];
% c3 = vectors[1][1];
% c5 = vectors[1][2];
% }
% else
% printf("Matrix unsolvable\n);
% RelinquishMagickMatrix(matrix,3UL);
% RelinquishMagickMatrix(vectors,2UL);
%
*/
MagickPrivate void LeastSquaresAddTerms(double **matrix,double **vectors,
const double *terms,const double *results,const size_t rank,
const size_t number_vectors)
{
register ssize_t
i,
j;
for (j=0; j < (ssize_t) rank; j++)
{
for (i=0; i < (ssize_t) rank; i++)
matrix[i][j]+=terms[i]*terms[j];
for (i=0; i < (ssize_t) number_vectors; i++)
vectors[i][j]+=results[i]*terms[j];
}
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% M a t r i x T o I m a g e %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% MatrixToImage() returns a matrix as an image. The matrix elements must be
% of type double otherwise nonsense is returned.
%
% The format of the MatrixToImage method is:
%
% Image *MatrixToImage(const MatrixInfo *matrix_info,
% ExceptionInfo *exception)
%
% A description of each parameter follows:
%
% o matrix_info: the matrix.
%
% o exception: return any errors or warnings in this structure.
%
*/
MagickExport Image *MatrixToImage(const MatrixInfo *matrix_info,
ExceptionInfo *exception)
{
CacheView
*image_view;
double
max_value,
min_value,
scale_factor,
value;
Image
*image;
MagickBooleanType
status;
ssize_t
y;
assert(matrix_info != (const MatrixInfo *) NULL);
assert(matrix_info->signature == MagickCoreSignature);
assert(exception != (ExceptionInfo *) NULL);
assert(exception->signature == MagickCoreSignature);
if (matrix_info->stride < sizeof(double))
return((Image *) NULL);
/*
Determine range of matrix.
*/
(void) GetMatrixElement(matrix_info,0,0,&value);
min_value=value;
max_value=value;
for (y=0; y < (ssize_t) matrix_info->rows; y++)
{
register ssize_t
x;
for (x=0; x < (ssize_t) matrix_info->columns; x++)
{
if (GetMatrixElement(matrix_info,x,y,&value) == MagickFalse)
continue;
if (value < min_value)
min_value=value;
else
if (value > max_value)
max_value=value;
}
}
if ((min_value == 0.0) && (max_value == 0.0))
scale_factor=0;
else
if (min_value == max_value)
{
scale_factor=(double) QuantumRange/min_value;
min_value=0;
}
else
scale_factor=(double) QuantumRange/(max_value-min_value);
/*
Convert matrix to image.
*/
image=AcquireImage((ImageInfo *) NULL,exception);
image->columns=matrix_info->columns;
image->rows=matrix_info->rows;
image->colorspace=GRAYColorspace;
status=MagickTrue;
image_view=AcquireAuthenticCacheView(image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(status) \
magick_number_threads(image,image,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
double
value;
register Quantum
*q;
register ssize_t
x;
if (status == MagickFalse)
continue;
q=QueueCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
if (q == (Quantum *) NULL)
{
status=MagickFalse;
continue;
}
for (x=0; x < (ssize_t) image->columns; x++)
{
if (GetMatrixElement(matrix_info,x,y,&value) == MagickFalse)
continue;
value=scale_factor*(value-min_value);
*q=ClampToQuantum(value);
q+=GetPixelChannels(image);
}
if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
status=MagickFalse;
}
image_view=DestroyCacheView(image_view);
if (status == MagickFalse)
image=DestroyImage(image);
return(image);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% N u l l M a t r i x %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% NullMatrix() sets all elements of the matrix to zero.
%
% The format of the ResetMagickMemory method is:
%
% MagickBooleanType *NullMatrix(MatrixInfo *matrix_info)
%
% A description of each parameter follows:
%
% o matrix_info: the matrix.
%