root/magick/matrix.c

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DEFINITIONS

This source file includes following definitions.
  1. MatrixSignalHandler
  2. WriteMatrixElements
  3. SetMatrixExtent
  4. AcquireMatrixInfo
  5. AcquireMagickMatrix
  6. DestroyMatrixInfo
  7. GaussJordanElimination
  8. GetMatrixColumns
  9. EdgeX
  10. EdgeY
  11. ReadMatrixElements
  12. GetMatrixElement
  13. GetMatrixRows
  14. LeastSquaresAddTerms
  15. MatrixToImage
  16. NullMatrix
  17. RelinquishMagickMatrix
  18. SetMatrixElement

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%                  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 1999-2016 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                                            %
%                                                                             %
%    http://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 "magick/studio.h"
#include "magick/blob.h"
#include "magick/blob-private.h"
#include "magick/exception.h"
#include "magick/exception-private.h"
#include "magick/image-private.h"
#include "magick/matrix.h"
#include "magick/memory_.h"
#include "magick/pixel-private.h"
#include "magick/resource_.h"
#include "magick/semaphore.h"
#include "magick/thread-private.h"
#include "magick/utility.h"

/*
  Typedef declaration.
*/
struct _MatrixInfo
{
  CacheType
    type;

  size_t
    columns,
    rows,
    stride;

  MagickSizeType
    length;

  MagickBooleanType
    mapped,
    synchronize;

  char
    path[MaxTextExtent];

  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=MagickSignature;
  matrix_info->columns=columns;
  matrix_info->rows=rows;
  matrix_info->stride=stride;
  matrix_info->semaphore=AllocateSemaphoreInfo();
  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;
      (void) AcquireMagickResource(MemoryResource,matrix_info->length);
      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 == MagickSignature);
  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);
  DestroySemaphoreInfo(&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.
%      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 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
%
*/
MagickExport 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 == MagickSignature);
  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 == MagickSignature);
  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 == MagickSignature);
  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);
%
*/
MagickExport 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 == MagickSignature);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickSignature);
  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);
  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 PixelPacket
      *q;

    register ssize_t
      x;

    if (status == MagickFalse)
      continue;
    q=QueueCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
    if (q == (PixelPacket *) 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->red=ClampToQuantum(value);
      q->green=q->red;
      q->blue=q->red;
      q++;
    }
    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 == MagickSignature);
  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 == MagickSignature);
  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);
}

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