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matrix.c
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% 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 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://imagemagick.org/license/ %
% %
% 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/memory-private.h"
#include "MagickCore/nt-base-private.h"
#include "MagickCore/pixel-accessor.h"
#include "MagickCore/resource_.h"
#include "MagickCore/semaphore.h"
#include "MagickCore/thread-private.h"
#include "MagickCore/utility.h"
#include "MagickCore/utility-private.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 magick_unused(status))
{
magick_unreferenced(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)
{
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-
(MagickSizeType) i,(MagickSizeType) MagickMaxBufferExtent));
#else
count=pwrite(matrix_info->file,buffer+i,(size_t) MagickMin(length-
(MagickSizeType) i,(MagickSizeType) MagickMaxBufferExtent),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) memset(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)) &&
((size_t) matrix_info->length <= GetMaxMemoryRequest()))
{
status=AcquireMagickResource(MemoryResource,matrix_info->length);
if (status != MagickFalse)
{
matrix_info->mapped=MagickFalse;
matrix_info->elements=MagickAssumeAligned(AcquireAlignedMemory(1,
(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
% simultaneous 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;
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=RelinquishAlignedMemory(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);
magick_fallthrough;
}
case DiskCache:
{
if (matrix_info->file != -1)
(void) close_utf8(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 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 specified 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)
{
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) MagickMaxBufferExtent));
#else
count=pread(matrix_info->file,buffer+i,(size_t) MagickMin(length-
(MagickSizeType) i,(MagickSizeType) MagickMaxBufferExtent),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=EdgeY(y,matrix_info->rows)*(MagickOffsetType) matrix_info->columns+
EdgeX(x,matrix_info->columns);
if (matrix_info->type != DiskCache)
{
(void) memcpy(value,(unsigned char *) matrix_info->elements+i*
(MagickOffsetType) matrix_info->stride,matrix_info->stride);
return(MagickTrue);
}
count=ReadMatrixElements(matrix_info,i*(MagickOffsetType) 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 coefficient
% 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 coefficients.
%
% 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)
{
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];
}
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ G a u s s J o r d a n E l i m n a t i o n %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GaussJordanElimination() returns a matrix in reduced row echelon form,
% while simultaneously reducing and thus solving the augmented results
% matrix.
%
% 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.
% Usually 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 simultaneous equations is to be solved from
% the given set of coefficient weighted terms.
%
% double **matrix = AcquireMagickMatrix(8UL,8UL);
% double coefficients[8];
% ...
% GaussJordanElimination(matrix,&coefficients,8UL,1UL);
%
% However by specifying 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 coefficients, 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 coordinates, 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) \
{ \
double temp = (x); \
(x)=(y); \
(y)=temp; \
}
#define GaussJordanSwapLD(x,y) \
{ \
long double temp = (x); \
(x)=(y); \
(y)=temp; \
}
#define ThrowGaussJordanException() \
{ \
for (i=0; i < (ssize_t) rank; i++) \
hp_matrix[i]=(long double *) RelinquishMagickMemory(hp_matrix[i]); \
hp_matrix=(long double **) RelinquishMagickMemory(hp_matrix); \
if (pivots != (ssize_t *) NULL) \
pivots=(ssize_t *) RelinquishMagickMemory(pivots); \
if (rows != (ssize_t *) NULL) \
rows=(ssize_t *) RelinquishMagickMemory(rows); \
if (columns != (ssize_t *) NULL) \
columns=(ssize_t *) RelinquishMagickMemory(columns); \
return(MagickFalse); \
}
long double
**hp_matrix = (long double **) NULL,
scale;
ssize_t
column,
*columns = (ssize_t *) NULL,
i,
j,
*pivots = (ssize_t *) NULL,
row,
*rows = (ssize_t *) NULL;
/*
Allocate high precision matrix.
*/
hp_matrix=(long double **) AcquireQuantumMemory(rank,sizeof(*hp_matrix));
if (hp_matrix == (long double **) NULL)
return(MagickFalse);
for (i=0; i < (ssize_t) rank; i++)
{
hp_matrix[i]=(long double *) AcquireQuantumMemory(rank,
sizeof(*hp_matrix[i]));
if (hp_matrix[i] == (long double *) NULL)
ThrowGaussJordanException();
for (j=0; j < (ssize_t) rank; j++)
hp_matrix[i][j]=(long double)matrix[i][j];
}
columns=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*columns));
rows=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*rows));
pivots=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*pivots));
if ((columns == (ssize_t *) NULL) || (rows == (ssize_t *) NULL) ||
(pivots == (ssize_t *) NULL))
ThrowGaussJordanException();
(void) memset(columns,0,rank*sizeof(*columns));
(void) memset(rows,0,rank*sizeof(*rows));
(void) memset(pivots,0,rank*sizeof(*pivots));
for (i=0; i < (ssize_t) rank; i++)
{
long double
max = 0.0;
ssize_t
k;
/*
Partial pivoting: find the largest absolute value in the unreduced
submatrix.
*/
column=(-1);
row=(-1);
for (j=0; j < (ssize_t) rank; j++)
if (pivots[j] != 1)
for (k=0; k < (ssize_t) rank; k++)
if ((pivots[k] == 0) && (fabsl(hp_matrix[j][k]) > max))
{
max=fabsl(hp_matrix[j][k]);
row=j;
column=k;
}
if ((column == -1) || (row == -1) || (fabsl(max) < LDBL_MIN))
ThrowGaussJordanException(); /* Singular or nearly singular matrix */
pivots[column]++;
if (row != column)
{
for (k=0; k < (ssize_t) rank; k++)
GaussJordanSwapLD(hp_matrix[row][k],hp_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 (fabsl(hp_matrix[column][column]) < LDBL_MIN)
ThrowGaussJordanException(); /* Singular matrix */
scale=1.0L/hp_matrix[column][column];
hp_matrix[column][column]=1.0;
for (j=0; j < (ssize_t) rank; j++)
hp_matrix[column][j]*=scale;
for (j=0; j < (ssize_t) number_vectors; j++)
vectors[j][column]*=(double) scale;
for (j=0; j < (ssize_t) rank; j++)
if (j != column)
{
scale=hp_matrix[j][column];
hp_matrix[j][column]=0.0;
for (k=0; k < (ssize_t) rank; k++)
hp_matrix[j][k]-=scale*hp_matrix[column][k];
for (k=0; k < (ssize_t) number_vectors; k++)
vectors[k][j]-=(double)(scale*(long double) 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++)
GaussJordanSwapLD(hp_matrix[i][columns[j]],hp_matrix[i][rows[j]]);
/*
Copy back the result to the original matrix.
*/
for (i=0; i < (ssize_t) rank; i++)
for (j=0; j < (ssize_t) rank; j++)
matrix[i][j]=(double)hp_matrix[i][j];
/*
Free resources.
*/
for (i=0; i < (ssize_t) rank; i++)
hp_matrix[i]=(long double *) RelinquishMagickMemory(hp_matrix[i]);
hp_matrix=(long double **) RelinquishMagickMemory(hp_matrix);
pivots=(ssize_t *) RelinquishMagickMemory(pivots);
rows=(ssize_t *) RelinquishMagickMemory(rows);
columns=(ssize_t *) RelinquishMagickMemory(columns);
return(MagickTrue);
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% 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;
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,&min_value);
max_value=min_value;
for (y=0; y < (ssize_t) matrix_info->rows; y++)
{
ssize_t
x;
for (x=0; x < (ssize_t) matrix_info->columns; x++)
{
double
value;
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) shared(status) \
magick_number_threads(image,image,image->rows,2)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
double
value;
Quantum
*q;
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+=(ptrdiff_t) 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 memset method is:
%
% MagickBooleanType *NullMatrix(MatrixInfo *matrix_info)
%
% A description of each parameter follows:
%
% o matrix_info: the matrix.
%
*/
MagickExport MagickBooleanType NullMatrix(MatrixInfo *matrix_info)
{
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) memset(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)
{
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 specified 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=y*(MagickOffsetType) 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*
(MagickOffsetType) matrix_info->stride,value,matrix_info->stride);
return(MagickTrue);
}
count=WriteMatrixElements(matrix_info,i*(MagickOffsetType)
matrix_info->stride,matrix_info->stride,(unsigned char *) value);
if (count != (MagickOffsetType) matrix_info->stride)
return(MagickFalse);
return(MagickTrue);
}
SemaphoreInfo
Definition semaphore.c:61
_MatrixInfo
Definition matrix.c:65