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/* |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% % |
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% % |
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% % |
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% M M AAA TTTTT RRRR IIIII X X % |
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% MM MM A A T R R I X X % |
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% M M M AAAAA T RRRR I X % |
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% M M A A T R R I X X % |
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% M M A A T R R IIIII X X % |
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% % |
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% % |
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% MagickCore Matrix Methods % |
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% % |
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% Software Design % |
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% Cristy % |
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% August 2007 % |
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% % |
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% % |
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% Copyright 1999-2016 ImageMagick Studio LLC, a non-profit organization % |
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% dedicated to making software imaging solutions freely available. % |
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% % |
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% You may not use this file except in compliance with the License. You may % |
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% obtain a copy of the License at % |
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% % |
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% http://www.imagemagick.org/script/license.php % |
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% % |
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% Unless required by applicable law or agreed to in writing, software % |
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% distributed under the License is distributed on an "AS IS" BASIS, % |
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% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. % |
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% See the License for the specific language governing permissions and % |
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% limitations under the License. % |
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% % |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% |
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% |
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*/ |
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/* |
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Include declarations. |
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*/ |
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#include "MagickCore/studio.h" |
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#include "MagickCore/blob.h" |
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#include "MagickCore/blob-private.h" |
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#include "MagickCore/cache.h" |
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#include "MagickCore/exception.h" |
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#include "MagickCore/exception-private.h" |
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#include "MagickCore/image-private.h" |
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#include "MagickCore/matrix.h" |
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#include "MagickCore/memory_.h" |
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#include "MagickCore/pixel-accessor.h" |
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#include "MagickCore/pixel-private.h" |
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#include "MagickCore/resource_.h" |
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#include "MagickCore/semaphore.h" |
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#include "MagickCore/thread-private.h" |
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#include "MagickCore/utility.h" |
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/* |
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Typedef declaration. |
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*/ |
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struct _MatrixInfo |
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{ |
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CacheType |
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type; |
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size_t |
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columns, |
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rows, |
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stride; |
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MagickSizeType |
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length; |
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MagickBooleanType |
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mapped, |
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synchronize; |
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char |
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path[MagickPathExtent]; |
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int |
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file; |
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void |
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*elements; |
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SemaphoreInfo |
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*semaphore; |
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size_t |
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signature; |
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}; |
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/* |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% % |
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% % |
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% % |
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% A c q u i r e M a t r i x I n f o % |
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% % |
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% % |
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% % |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% |
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% AcquireMatrixInfo() allocates the ImageInfo structure. |
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% |
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% The format of the AcquireMatrixInfo method is: |
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% |
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% MatrixInfo *AcquireMatrixInfo(const size_t columns,const size_t rows, |
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% const size_t stride,ExceptionInfo *exception) |
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% |
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% A description of each parameter follows: |
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% |
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% o columns: the matrix columns. |
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% |
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% o rows: the matrix rows. |
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% |
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% o stride: the matrix stride. |
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% |
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% o exception: return any errors or warnings in this structure. |
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% |
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*/ |
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#if defined(SIGBUS) |
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static void MatrixSignalHandler(int status) |
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{ |
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ThrowFatalException(CacheFatalError,"UnableToExtendMatrixCache"); |
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} |
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#endif |
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static inline MagickOffsetType WriteMatrixElements( |
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const MatrixInfo *magick_restrict matrix_info,const MagickOffsetType offset, |
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const MagickSizeType length,const unsigned char *magick_restrict buffer) |
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{ |
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register MagickOffsetType |
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i; |
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ssize_t |
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count; |
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#if !defined(MAGICKCORE_HAVE_PWRITE) |
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LockSemaphoreInfo(matrix_info->semaphore); |
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if (lseek(matrix_info->file,offset,SEEK_SET) < 0) |
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{ |
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UnlockSemaphoreInfo(matrix_info->semaphore); |
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return((MagickOffsetType) -1); |
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} |
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#endif |
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count=0; |
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for (i=0; i < (MagickOffsetType) length; i+=count) |
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{ |
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#if !defined(MAGICKCORE_HAVE_PWRITE) |
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count=write(matrix_info->file,buffer+i,(size_t) MagickMin(length-i, |
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(MagickSizeType) SSIZE_MAX)); |
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#else |
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count=pwrite(matrix_info->file,buffer+i,(size_t) MagickMin(length-i, |
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(MagickSizeType) SSIZE_MAX),(off_t) (offset+i)); |
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#endif |
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if (count <= 0) |
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{ |
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count=0; |
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if (errno != EINTR) |
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break; |
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} |
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} |
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#if !defined(MAGICKCORE_HAVE_PWRITE) |
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UnlockSemaphoreInfo(matrix_info->semaphore); |
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#endif |
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return(i); |
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} |
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static MagickBooleanType SetMatrixExtent( |
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MatrixInfo *magick_restrict matrix_info, |
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MagickSizeType length) |
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{ |
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MagickOffsetType |
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count, |
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extent, |
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offset; |
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if (length != (MagickSizeType) ((MagickOffsetType) length)) |
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return(MagickFalse); |
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offset=(MagickOffsetType) lseek(matrix_info->file,0,SEEK_END); |
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if (offset < 0) |
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return(MagickFalse); |
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if ((MagickSizeType) offset >= length) |
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return(MagickTrue); |
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extent=(MagickOffsetType) length-1; |
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count=WriteMatrixElements(matrix_info,extent,1,(const unsigned char *) ""); |
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#if defined(MAGICKCORE_HAVE_POSIX_FALLOCATE) |
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if (matrix_info->synchronize != MagickFalse) |
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(void) posix_fallocate(matrix_info->file,offset+1,extent-offset); |
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#endif |
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#if defined(SIGBUS) |
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(void) signal(SIGBUS,MatrixSignalHandler); |
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#endif |
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return(count != (MagickOffsetType) 1 ? MagickFalse : MagickTrue); |
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} |
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MagickExport MatrixInfo *AcquireMatrixInfo(const size_t columns, |
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const size_t rows,const size_t stride,ExceptionInfo *exception) |
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{ |
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char |
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*synchronize; |
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MagickBooleanType |
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status; |
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MatrixInfo |
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*matrix_info; |
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matrix_info=(MatrixInfo *) AcquireMagickMemory(sizeof(*matrix_info)); |
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if (matrix_info == (MatrixInfo *) NULL) |
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return((MatrixInfo *) NULL); |
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(void) ResetMagickMemory(matrix_info,0,sizeof(*matrix_info)); |
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matrix_info->signature=MagickCoreSignature; |
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matrix_info->columns=columns; |
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matrix_info->rows=rows; |
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matrix_info->stride=stride; |
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matrix_info->semaphore=AcquireSemaphoreInfo(); |
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synchronize=GetEnvironmentValue("MAGICK_SYNCHRONIZE"); |
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if (synchronize != (const char *) NULL) |
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{ |
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matrix_info->synchronize=IsStringTrue(synchronize); |
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synchronize=DestroyString(synchronize); |
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} |
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matrix_info->length=(MagickSizeType) columns*rows*stride; |
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if (matrix_info->columns != (size_t) (matrix_info->length/rows/stride)) |
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{ |
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(void) ThrowMagickException(exception,GetMagickModule(),CacheError, |
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"CacheResourcesExhausted","`%s'","matrix cache"); |
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return(DestroyMatrixInfo(matrix_info)); |
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} |
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matrix_info->type=MemoryCache; |
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status=AcquireMagickResource(AreaResource,matrix_info->length); |
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if ((status != MagickFalse) && |
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(matrix_info->length == (MagickSizeType) ((size_t) matrix_info->length))) |
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{ |
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status=AcquireMagickResource(MemoryResource,matrix_info->length); |
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if (status != MagickFalse) |
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{ |
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matrix_info->mapped=MagickFalse; |
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matrix_info->elements=AcquireMagickMemory((size_t) |
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matrix_info->length); |
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if (matrix_info->elements == NULL) |
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{ |
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matrix_info->mapped=MagickTrue; |
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matrix_info->elements=MapBlob(-1,IOMode,0,(size_t) |
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matrix_info->length); |
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} |
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if (matrix_info->elements == (unsigned short *) NULL) |
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RelinquishMagickResource(MemoryResource,matrix_info->length); |
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} |
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} |
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matrix_info->file=(-1); |
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if (matrix_info->elements == (unsigned short *) NULL) |
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{ |
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status=AcquireMagickResource(DiskResource,matrix_info->length); |
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if (status == MagickFalse) |
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{ |
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(void) ThrowMagickException(exception,GetMagickModule(),CacheError, |
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"CacheResourcesExhausted","`%s'","matrix cache"); |
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return(DestroyMatrixInfo(matrix_info)); |
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} |
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matrix_info->type=DiskCache; |
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(void) AcquireMagickResource(MemoryResource,matrix_info->length); |
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matrix_info->file=AcquireUniqueFileResource(matrix_info->path); |
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if (matrix_info->file == -1) |
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return(DestroyMatrixInfo(matrix_info)); |
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status=AcquireMagickResource(MapResource,matrix_info->length); |
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if (status != MagickFalse) |
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{ |
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status=SetMatrixExtent(matrix_info,matrix_info->length); |
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if (status != MagickFalse) |
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{ |
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matrix_info->elements=(void *) MapBlob(matrix_info->file,IOMode,0, |
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(size_t) matrix_info->length); |
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if (matrix_info->elements != NULL) |
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matrix_info->type=MapCache; |
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else |
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RelinquishMagickResource(MapResource,matrix_info->length); |
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} |
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} |
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} |
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return(matrix_info); |
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} |
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/* |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% % |
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% % |
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% % |
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% A c q u i r e M a g i c k M a t r i x % |
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% % |
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% % |
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% % |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% |
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% AcquireMagickMatrix() allocates and returns a matrix in the form of an |
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% array of pointers to an array of doubles, with all values pre-set to zero. |
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% |
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% This used to generate the two dimensional matrix, and vectors required |
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|
% for the GaussJordanElimination() method below, solving some system of |
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% simultanious equations. |
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% |
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% The format of the AcquireMagickMatrix method is: |
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% |
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% double **AcquireMagickMatrix(const size_t number_rows, |
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% const size_t size) |
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% |
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% A description of each parameter follows: |
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% |
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% o number_rows: the number pointers for the array of pointers |
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|
% (first dimension). |
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% |
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% o size: the size of the array of doubles each pointer points to |
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% (second dimension). |
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% |
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*/ |
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MagickExport double **AcquireMagickMatrix(const size_t number_rows, |
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const size_t size) |
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{ |
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double |
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**matrix; |
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register ssize_t |
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i, |
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j; |
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matrix=(double **) AcquireQuantumMemory(number_rows,sizeof(*matrix)); |
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if (matrix == (double **) NULL) |
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return((double **) NULL); |
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for (i=0; i < (ssize_t) number_rows; i++) |
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{ |
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matrix[i]=(double *) AcquireQuantumMemory(size,sizeof(*matrix[i])); |
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if (matrix[i] == (double *) NULL) |
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{ |
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for (j=0; j < i; j++) |
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matrix[j]=(double *) RelinquishMagickMemory(matrix[j]); |
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matrix=(double **) RelinquishMagickMemory(matrix); |
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return((double **) NULL); |
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} |
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for (j=0; j < (ssize_t) size; j++) |
|
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matrix[i][j]=0.0; |
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} |
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return(matrix); |
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} |
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/* |
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|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% % |
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% % |
|
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% % |
|
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% D e s t r o y M a t r i x I n f o % |
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% % |
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% % |
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% % |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% |
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% DestroyMatrixInfo() dereferences a matrix, deallocating memory associated |
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% with the matrix. |
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% |
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% The format of the DestroyImage method is: |
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% |
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|
% MatrixInfo *DestroyMatrixInfo(MatrixInfo *matrix_info) |
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% |
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|
% A description of each parameter follows: |
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% |
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% o matrix_info: the matrix. |
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% |
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*/ |
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MagickExport MatrixInfo *DestroyMatrixInfo(MatrixInfo *matrix_info) |
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{ |
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assert(matrix_info != (MatrixInfo *) NULL); |
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assert(matrix_info->signature == MagickCoreSignature); |
|
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LockSemaphoreInfo(matrix_info->semaphore); |
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switch (matrix_info->type) |
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{ |
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case MemoryCache: |
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{ |
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if (matrix_info->mapped == MagickFalse) |
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matrix_info->elements=RelinquishMagickMemory(matrix_info->elements); |
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else |
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{ |
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(void) UnmapBlob(matrix_info->elements,(size_t) matrix_info->length); |
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matrix_info->elements=(unsigned short *) NULL; |
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} |
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RelinquishMagickResource(MemoryResource,matrix_info->length); |
|
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break; |
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} |
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case MapCache: |
|
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{ |
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|
(void) UnmapBlob(matrix_info->elements,(size_t) matrix_info->length); |
|
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matrix_info->elements=NULL; |
|
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RelinquishMagickResource(MapResource,matrix_info->length); |
|
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} |
|
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case DiskCache: |
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{ |
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|
if (matrix_info->file != -1) |
|
|
(void) close(matrix_info->file); |
|
|
(void) RelinquishUniqueFileResource(matrix_info->path); |
|
|
RelinquishMagickResource(DiskResource,matrix_info->length); |
|
|
break; |
|
|
} |
|
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default: |
|
|
break; |
|
|
} |
|
|
UnlockSemaphoreInfo(matrix_info->semaphore); |
|
|
RelinquishSemaphoreInfo(&matrix_info->semaphore); |
|
|
return((MatrixInfo *) RelinquishMagickMemory(matrix_info)); |
|
|
} |
|
|
|
|
|
/* |
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|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
% % |
|
|
% % |
|
|
% % |
|
|
+ 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: |
|
|
% |
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|
% 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_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. |
|
|
% |
|
|
*/ |
|
|
MagickExport MagickBooleanType NullMatrix(MatrixInfo *matrix_info) |
|
|
{ |
|
|
register ssize_t |
|
|
x; |
|
|
|
|
|
ssize_t |
|
|
count, |
|
|
y; |
|
|
|
|
|
unsigned char |
|
|
value; |
|
|
|
|
|
assert(matrix_info != (const MatrixInfo *) NULL); |
|
|
assert(matrix_info->signature == MagickCoreSignature); |
|
|
if (matrix_info->type != DiskCache) |
|
|
{ |
|
|
(void) ResetMagickMemory(matrix_info->elements,0,(size_t) |
|
|
matrix_info->length); |
|
|
return(MagickTrue); |
|
|
} |
|
|
value=0; |
|
|
(void) lseek(matrix_info->file,0,SEEK_SET); |
|
|
for (y=0; y < (ssize_t) matrix_info->rows; y++) |
|
|
{ |
|
|
for (x=0; x < (ssize_t) matrix_info->length; x++) |
|
|
{ |
|
|
count=write(matrix_info->file,&value,sizeof(value)); |
|
|
if (count != (ssize_t) sizeof(value)) |
|
|
break; |
|
|
} |
|
|
if (x < (ssize_t) matrix_info->length) |
|
|
break; |
|
|
} |
|
|
return(y < (ssize_t) matrix_info->rows ? MagickFalse : MagickTrue); |
|
|
} |
|
|
|
|
|
/* |
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
% % |
|
|
% % |
|
|
% % |
|
|
% R e l i n q u i s h M a g i c k M a t r i x % |
|
|
% % |
|
|
% % |
|
|
% % |
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
% |
|
|
% RelinquishMagickMatrix() frees the previously acquired matrix (array of |
|
|
% pointers to arrays of doubles). |
|
|
% |
|
|
% The format of the RelinquishMagickMatrix method is: |
|
|
% |
|
|
% double **RelinquishMagickMatrix(double **matrix, |
|
|
% const size_t number_rows) |
|
|
% |
|
|
% A description of each parameter follows: |
|
|
% |
|
|
% o matrix: the matrix to relinquish |
|
|
% |
|
|
% o number_rows: the first dimension of the acquired matrix (number of |
|
|
% pointers) |
|
|
% |
|
|
*/ |
|
|
MagickExport double **RelinquishMagickMatrix(double **matrix, |
|
|
const size_t number_rows) |
|
|
{ |
|
|
register ssize_t |
|
|
i; |
|
|
|
|
|
if (matrix == (double **) NULL ) |
|
|
return(matrix); |
|
|
for (i=0; i < (ssize_t) number_rows; i++) |
|
|
matrix[i]=(double *) RelinquishMagickMemory(matrix[i]); |
|
|
matrix=(double **) RelinquishMagickMemory(matrix); |
|
|
return(matrix); |
|
|
} |
|
|
|
|
|
/* |
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
% % |
|
|
% % |
|
|
% % |
|
|
% S e t M a t r i x E l e m e n t % |
|
|
% % |
|
|
% % |
|
|
% % |
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
|
|
% |
|
|
% SetMatrixElement() sets the specifed element in the matrix. |
|
|
% |
|
|
% The format of the SetMatrixElement method is: |
|
|
% |
|
|
% MagickBooleanType SetMatrixElement(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: set the matrix element to this value. |
|
|
% |
|
|
*/ |
|
|
|
|
|
MagickExport MagickBooleanType SetMatrixElement(const MatrixInfo *matrix_info, |
|
|
const ssize_t x,const ssize_t y,const void *value) |
|
|
{ |
|
|
MagickOffsetType |
|
|
count, |
|
|
i; |
|
|
|
|
|
assert(matrix_info != (const MatrixInfo *) NULL); |
|
|
assert(matrix_info->signature == MagickCoreSignature); |
|
|
i=(MagickOffsetType) y*matrix_info->columns+x; |
|
|
if ((i < 0) || |
|
|
((MagickSizeType) (i*matrix_info->stride) >= matrix_info->length)) |
|
|
return(MagickFalse); |
|
|
if (matrix_info->type != DiskCache) |
|
|
{ |
|
|
(void) memcpy((unsigned char *) matrix_info->elements+i* |
|
|
matrix_info->stride,value,matrix_info->stride); |
|
|
return(MagickTrue); |
|
|
} |
|
|
count=WriteMatrixElements(matrix_info,i*matrix_info->stride, |
|
|
matrix_info->stride,(unsigned char *) value); |
|
|
if (count != (MagickOffsetType) matrix_info->stride) |
|
|
return(MagickFalse); |
|
|
return(MagickTrue); |
|
|
}
|
|
|
|
