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21
22
23
24 /** This method eliminates elements below main diagonal in the given
25 matrix by gaussian elimination.
26
27 @param matrix
28 The matrix to operate on. Last column is the result vector (right
29 hand side of the linear equation). After successful termination,
30 the matrix is upper triangular. The matrix is expected to be in
31 row major order.
32
33 @param rows
34 Number of rows in matrix
35
36 @param cols
37 Number of columns in matrix
38
39 @param minPivot
40 If the pivot element gets lesser than minPivot, this method fails,
41 otherwise, elimination succeeds and true is returned.
42
43 @return true, if elimination succeeded.
44 */
45 template <class Matrix, typename BaseType>
eliminate(Matrix & matrix,int rows,int cols,const BaseType & minPivot)46 bool eliminate( Matrix& matrix,
47 int rows,
48 int cols,
49 const BaseType& minPivot )
50 {
51 BaseType temp;
52 int max, i, j, k; /* *must* be signed, when looping like: j>=0 ! */
53
54 /* eliminate below main diagonal */
55 for(i=0; i<cols-1; ++i)
56 {
57 /* find best pivot */
58 max = i;
59 for(j=i+1; j<rows; ++j)
60 if( fabs(matrix[ j*cols + i ]) > fabs(matrix[ max*cols + i ]) )
61 max = j;
62
63 /* check pivot value */
64 if( fabs(matrix[ max*cols + i ]) < minPivot )
65 return false; /* pivot too small! */
66
67 /* interchange rows 'max' and 'i' */
68 for(k=0; k<cols; ++k)
69 {
70 temp = matrix[ i*cols + k ];
71 matrix[ i*cols + k ] = matrix[ max*cols + k ];
72 matrix[ max*cols + k ] = temp;
73 }
74
75 /* eliminate column */
76 for(j=i+1; j<rows; ++j)
77 for(k=cols-1; k>=i; --k)
78 matrix[ j*cols + k ] -= matrix[ i*cols + k ] *
79 matrix[ j*cols + i ] / matrix[ i*cols + i ];
80 }
81
82 /* everything went well */
83 return true;
84 }
85
86
87 /** Retrieve solution vector of linear system by substituting backwards.
88
89 This operation _relies_ on the previous successful
90 application of eliminate()!
91
92 @param matrix
93 Matrix in upper diagonal form, as e.g. generated by eliminate()
94
95 @param rows
96 Number of rows in matrix
97
98 @param cols
99 Number of columns in matrix
100
101 @param result
102 Result vector. Given matrix must have space for one column (rows entries).
103
104 @return true, if back substitution was possible (i.e. no division
105 by zero occured).
106 */
107 template <class Matrix, class Vector, typename BaseType>
substitute(const Matrix & matrix,int rows,int cols,Vector & result)108 bool substitute( const Matrix& matrix,
109 int rows,
110 int cols,
111 Vector& result )
112 {
113 BaseType temp;
114 int j,k; /* *must* be signed, when looping like: j>=0 ! */
115
116 /* substitute backwards */
117 for(j=rows-1; j>=0; --j)
118 {
119 temp = 0.0;
120 for(k=j+1; k<cols-1; ++k)
121 temp += matrix[ j*cols + k ] * result[k];
122
123 if( matrix[ j*cols + j ] == 0.0 )
124 return false; /* imminent division by zero! */
125
126 result[j] = (matrix[ j*cols + cols-1 ] - temp) / matrix[ j*cols + j ];
127 }
128
129 /* everything went well */
130 return true;
131 }
132
133
134 /** This method determines solution of given linear system, if any
135
136 This is a wrapper for eliminate and substitute, given matrix must
137 contain right side of equation as the last column.
138
139 @param matrix
140 The matrix to operate on. Last column is the result vector (right
141 hand side of the linear equation). After successful termination,
142 the matrix is upper triangular. The matrix is expected to be in
143 row major order.
144
145 @param rows
146 Number of rows in matrix
147
148 @param cols
149 Number of columns in matrix
150
151 @param minPivot
152 If the pivot element gets lesser than minPivot, this method fails,
153 otherwise, elimination succeeds and true is returned.
154
155 @return true, if elimination succeeded.
156 */
157 template <class Matrix, class Vector, typename BaseType>
solve(Matrix & matrix,int rows,int cols,Vector & result,BaseType minPivot)158 bool solve( Matrix& matrix,
159 int rows,
160 int cols,
161 Vector& result,
162 BaseType minPivot )
163 {
164 if( eliminate<Matrix,BaseType>(matrix, rows, cols, minPivot) )
165 return substitute<Matrix,Vector,BaseType>(matrix, rows, cols, result);
166
167 return false;
168 }
169