basegfx/source/workbench/gauss.hxx

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  19
  20 /** This method eliminates elements below main diagonal in the given
  21     matrix by gaussian elimination.
  22
  23     @param matrix
  24     The matrix to operate on. Last column is the result vector (right
  25     hand side of the linear equation). After successful termination,
  26     the matrix is upper triangular. The matrix is expected to be in
  27     row major order.
  28
  29     @param rows
  30     Number of rows in matrix
  31
  32     @param cols
  33     Number of columns in matrix
  34
  35     @param minPivot
  36     If the pivot element gets lesser than minPivot, this method fails,
  37     otherwise, elimination succeeds and true is returned.
  38
  39     @return true, if elimination succeeded.
  40  */
  41
  42 #pragma once
  43
  44 template <class Matrix, typename BaseType>
  45 bool eliminate(     Matrix&         matrix,
  46                     int             rows,
  47                     int             cols,
  48                     const BaseType& minPivot    )
  49 {
  50     /* i, j, k *must* be signed, when looping like: j>=0 ! */
  51     /* eliminate below main diagonal */
  52     for(int i=0; i<cols-1; ++i)
  53     {
  54         /* find best pivot */
  55         int max = i;
  56         for(int j=i+1; j<rows; ++j)
  57             if( fabs(matrix[ j*cols + i ]) > fabs(matrix[ max*cols + i ]) )
  58                 max = j;
  59
  60         /* check pivot value */
  61         if( fabs(matrix[ max*cols + i ]) < minPivot )
  62             return false;   /* pivot too small! */
  63
  64         /* interchange rows 'max' and 'i' */
  65         for(int k=0; k<cols; ++k)
  66         {
  67             std::swap(matrix[ i*cols + k ], matrix[ max*cols + k ]);
  68         }
  69
  70         /* eliminate column */
  71         for(int j=i+1; j<rows; ++j)
  72             for(int k=cols-1; k>=i; --k)
  73                 matrix[ j*cols + k ] -= matrix[ i*cols + k ] *
  74                     matrix[ j*cols + i ] / matrix[ i*cols + i ];
  75     }
  76
  77     /* everything went well */
  78     return true;
  79 }
  80
  81 /** Retrieve solution vector of linear system by substituting backwards.
  82
  83     This operation _relies_ on the previous successful
  84     application of eliminate()!
  85
  86     @param matrix
  87     Matrix in upper diagonal form, as e.g. generated by eliminate()
  88
  89     @param rows
  90     Number of rows in matrix
  91
  92     @param cols
  93     Number of columns in matrix
  94
  95     @param result
  96     Result vector. Given matrix must have space for one column (rows entries).
  97
  98     @return true, if back substitution was possible (i.e. no division
  99     by zero occurred).
 100  */
 101 template <class Matrix, class Vector, typename BaseType>
 102 bool substitute(    const Matrix&   matrix,
 103                     int             rows,
 104                     int             cols,
 105                     Vector&         result  )
 106 {
 107     BaseType    temp;
 108
 109     /* j, k *must* be signed, when looping like: j>=0 ! */
 110     /* substitute backwards */
 111     for(int j=rows-1; j>=0; --j)
 112     {
 113         temp = 0.0;
 114         for(int k=j+1; k<cols-1; ++k)
 115             temp += matrix[ j*cols + k ] * result[k];
 116
 117         if( matrix[ j*cols + j ] == 0.0 )
 118             return false;   /* imminent division by zero! */
 119
 120         result[j] = (matrix[ j*cols + cols-1 ] - temp) / matrix[ j*cols + j ];
 121     }
 122
 123     /* everything went well */
 124     return true;
 125 }
 126
 127 /** This method determines solution of given linear system, if any
 128
 129     This is a wrapper for eliminate and substitute, given matrix must
 130     contain right side of equation as the last column.
 131
 132     @param matrix
 133     The matrix to operate on. Last column is the result vector (right
 134     hand side of the linear equation). After successful termination,
 135     the matrix is upper triangular. The matrix is expected to be in
 136     row major order.
 137
 138     @param rows
 139     Number of rows in matrix
 140
 141     @param cols
 142     Number of columns in matrix
 143
 144     @param minPivot
 145     If the pivot element gets lesser than minPivot, this method fails,
 146     otherwise, elimination succeeds and true is returned.
 147
 148     @return true, if elimination succeeded.
 149  */
 150 template <class Matrix, class Vector, typename BaseType>
 151 bool solve( Matrix&     matrix,
 152             int         rows,
 153             int         cols,
 154             Vector&     result,
 155             BaseType    minPivot    )
 156 {
 157     if( eliminate<Matrix,BaseType>(matrix, rows, cols, minPivot) )
 158         return substitute<Matrix,Vector,BaseType>(matrix, rows, cols, result);
 159
 160     return false;
 161 }
 162
 163 /* vim:set shiftwidth=4 softtabstop=4 expandtab: */