| /* |
| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| % % |
| % % |
| % % |
| % 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 1999-2014 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 "MagickCore/studio.h" |
| #include "MagickCore/matrix.h" |
| #include "MagickCore/matrix-private.h" |
| #include "MagickCore/pixel-private.h" |
| #include "MagickCore/memory_.h" |
| |
| /* |
| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| % % |
| % % |
| % % |
| % 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, 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: |
| % |
| % 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); |
| } |
| |
| /* |
| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| % % |
| % % |
| % % |
| % 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 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. |
| % 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'. |
| % 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 |
| % 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 |
| % 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 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 |
| % 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 |
| % |
| % 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' (matrix |
| % is transposed). |
| % |
| % For details of this process 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); /* singularity */ |
| 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); |
| } |
| |
| /* |
| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| % % |
| % % |
| % % |
| % 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 dimentions 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]; %* weights to calculate u from any given x,y *% |
| % c4 = vectors[0][2]; |
| % c1 = vectors[1][0]; |
| % c3 = vectors[1][1]; %* weights for calculate v from any given x,y *% |
| % c5 = vectors[1][2]; |
| % } |
| % else |
| % printf("Matrix unsolvable\n); |
| % RelinquishMagickMatrix(matrix,3UL); |
| % RelinquishMagickMatrix(vectors,2UL); |
| % |
| % More examples can be found in "distort.c" |
| % |
| */ |
| 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]; |
| } |
| } |
| |
| /* |
| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| % % |
| % % |
| % % |
| % 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); |
| } |