% August 2007 %
% %
% %
-% Copyright 1999-2011 ImageMagick Studio LLC, a non-profit organization %
+% Copyright 1999-2012 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 %
*/
#include "MagickCore/studio.h"
#include "MagickCore/matrix.h"
+#include "MagickCore/matrix-private.h"
#include "MagickCore/memory_.h"
-#include "MagickCore/utility.h"
\f
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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.
+% This used to generate the two dimensional matrix, that can be referenced
+% using the simple C-code of the form "matrix[y][x]".
+%
+% This matrix is typically used for perform for the GaussJordanElimination()
+% method below, solving some system of simultanious equations.
%
% The format of the AcquireMagickMatrix method is:
%
matrix=(double **) AcquireQuantumMemory(number_rows,sizeof(*matrix));
if (matrix == (double **) NULL)
- return((double **)NULL);
+ return((double **) NULL);
for (i=0; i < (ssize_t) number_rows; i++)
{
matrix[i]=(double *) AcquireQuantumMemory(size,sizeof(*matrix[i]));
%
% The format of the GaussJordanElimination method is:
%
-% MagickBooleanType GaussJordanElimination(double **matrix,double **vectors,
-% const size_t rank,const size_t number_vectors)
+% MagickBooleanType GaussJordanElimination(double **matrix,
+% double **vectors,const size_t rank,const size_t number_vectors)
%
% A description of each parameter follows:
%
% 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).
+% o rank: The size of the square 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.
%
% 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'.
+% It is assigned vector[column][row] where 'column' is the specific
+% 'result' and 'row' is the 'values' for that answer. After processing
+% the same vector array contains the 'weights' (answers) for each of the
+% 'separatable' results.
%
% This allows for simpler handling of the results, especially is only one
-% column 'vector' is all that is required to produce the desired solution.
+% column 'vector' is all that is required to produce the desired solution
+% for that specific set of equations.
%
% 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
% ...
% 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.
+% However by specifing more 'columns' (as an 'array of vector columns'),
+% you can use this function to solve multiple sets 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
%
% 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
-% (Reference to be added - Anthony)
+%
+% See LeastSquaresAddTerms() below for such an example.
%
% 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
+% though as a 'column first array' rather than a 'row first array' (matrix
+% is transposed).
+%
+% For details of this process see...
+% http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
%
*/
-MagickExport MagickBooleanType GaussJordanElimination(double **matrix,
+MagickPrivate MagickBooleanType GaussJordanElimination(double **matrix,
double **vectors,const size_t rank,const size_t number_vectors)
{
#define GaussJordanSwap(x,y) \
rows[i]=row;
columns[i]=column;
if (matrix[column][column] == 0.0)
- return(MagickFalse); /* sigularity */
+ return(MagickFalse); /* singularity */
scale=1.0/matrix[column][column];
matrix[column][column]=1.0;
for (j=0; j < (ssize_t) rank; j++)
% 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.
+% 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.
+% weighted by the yet-to-be-solved coefficents.
%
% o rank: the rank or size of the dimentions of the square matrix.
-% Also the length of vectors, and number of terms being added.
+% 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
% ...
% if ( GaussJordanElimination(matrix,vectors,3UL,2UL) ) {
% c0 = vectors[0][0];
-% c2 = vectors[0][1];
+% c2 = vectors[0][1]; %* weights to calculate u from any given x,y *%
% c4 = vectors[0][2];
% c1 = vectors[1][0];
-% c3 = vectors[1][1];
+% c3 = vectors[1][1]; %* weights for calculate v from any given x,y *%
% c5 = vectors[1][2];
% }
% else
% RelinquishMagickMatrix(matrix,3UL);
% RelinquishMagickMatrix(vectors,2UL);
%
+% More examples can be found in "distort.c"
+%
*/
-MagickExport void LeastSquaresAddTerms(double **matrix,double **vectors,
+MagickPrivate void LeastSquaresAddTerms(double **matrix,double **vectors,
const double *terms,const double *results,const size_t rank,
const size_t number_vectors)
{
for (i=0; i < (ssize_t) number_vectors; i++)
vectors[i][j]+=results[i]*terms[j];
}
- return;
}
\f
/*
matrix=(double **) RelinquishMagickMemory(matrix);
return(matrix);
}
-
projects / imagemagick / blobdiff