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See the 18 * GNU Lesser General Public License version 3 for more details 19 * (a copy is included in the LICENSE file that accompanied this code). 20 * 21 * You should have received a copy of the GNU Lesser General Public License 22 * version 3 along with OpenOffice.org. If not, see 23 * <http://www.openoffice.org/license.html> 24 * for a copy of the LGPLv3 License. 25 * 26 ************************************************************************/ 27 28 /** This method eliminates elements below main diagonal in the given 29 matrix by gaussian elimination. 30 31 @param matrix 32 The matrix to operate on. Last column is the result vector (right 33 hand side of the linear equation). After successful termination, 34 the matrix is upper triangular. The matrix is expected to be in 35 row major order. 36 37 @param rows 38 Number of rows in matrix 39 40 @param cols 41 Number of columns in matrix 42 43 @param minPivot 44 If the pivot element gets lesser than minPivot, this method fails, 45 otherwise, elimination succeeds and true is returned. 46 47 @return true, if elimination succeeded. 48 */ 49 template <class Matrix, typename BaseType> 50 bool eliminate( Matrix& matrix, 51 int rows, 52 int cols, 53 const BaseType& minPivot ) 54 { 55 BaseType temp; 56 int max, i, j, k; /* *must* be signed, when looping like: j>=0 ! */ 57 58 /* eliminate below main diagonal */ 59 for(i=0; i<cols-1; ++i) 60 { 61 /* find best pivot */ 62 max = i; 63 for(j=i+1; j<rows; ++j) 64 if( fabs(matrix[ j*cols + i ]) > fabs(matrix[ max*cols + i ]) ) 65 max = j; 66 67 /* check pivot value */ 68 if( fabs(matrix[ max*cols + i ]) < minPivot ) 69 return false; /* pivot too small! */ 70 71 /* interchange rows 'max' and 'i' */ 72 for(k=0; k<cols; ++k) 73 { 74 temp = matrix[ i*cols + k ]; 75 matrix[ i*cols + k ] = matrix[ max*cols + k ]; 76 matrix[ max*cols + k ] = temp; 77 } 78 79 /* eliminate column */ 80 for(j=i+1; j<rows; ++j) 81 for(k=cols-1; k>=i; --k) 82 matrix[ j*cols + k ] -= matrix[ i*cols + k ] * 83 matrix[ j*cols + i ] / matrix[ i*cols + i ]; 84 } 85 86 /* everything went well */ 87 return true; 88 } 89 90 91 /** Retrieve solution vector of linear system by substituting backwards. 92 93 This operation _relies_ on the previous successful 94 application of eliminate()! 95 96 @param matrix 97 Matrix in upper diagonal form, as e.g. generated by eliminate() 98 99 @param rows 100 Number of rows in matrix 101 102 @param cols 103 Number of columns in matrix 104 105 @param result 106 Result vector. Given matrix must have space for one column (rows entries). 107 108 @return true, if back substitution was possible (i.e. no division 109 by zero occured). 110 */ 111 template <class Matrix, class Vector, typename BaseType> 112 bool substitute( const Matrix& matrix, 113 int rows, 114 int cols, 115 Vector& result ) 116 { 117 BaseType temp; 118 int j,k; /* *must* be signed, when looping like: j>=0 ! */ 119 120 /* substitute backwards */ 121 for(j=rows-1; j>=0; --j) 122 { 123 temp = 0.0; 124 for(k=j+1; k<cols-1; ++k) 125 temp += matrix[ j*cols + k ] * result[k]; 126 127 if( matrix[ j*cols + j ] == 0.0 ) 128 return false; /* imminent division by zero! */ 129 130 result[j] = (matrix[ j*cols + cols-1 ] - temp) / matrix[ j*cols + j ]; 131 } 132 133 /* everything went well */ 134 return true; 135 } 136 137 138 /** This method determines solution of given linear system, if any 139 140 This is a wrapper for eliminate and substitute, given matrix must 141 contain right side of equation as the last column. 142 143 @param matrix 144 The matrix to operate on. Last column is the result vector (right 145 hand side of the linear equation). After successful termination, 146 the matrix is upper triangular. The matrix is expected to be in 147 row major order. 148 149 @param rows 150 Number of rows in matrix 151 152 @param cols 153 Number of columns in matrix 154 155 @param minPivot 156 If the pivot element gets lesser than minPivot, this method fails, 157 otherwise, elimination succeeds and true is returned. 158 159 @return true, if elimination succeeded. 160 */ 161 template <class Matrix, class Vector, typename BaseType> 162 bool solve( Matrix& matrix, 163 int rows, 164 int cols, 165 Vector& result, 166 BaseType minPivot ) 167 { 168 if( eliminate<Matrix,BaseType>(matrix, rows, cols, minPivot) ) 169 return substitute<Matrix,Vector,BaseType>(matrix, rows, cols, result); 170 171 return false; 172 } 173