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* @date 10/11/2004 |
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* @version 1.0 |
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*/ |
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#ifndef MATH_SQUAREMATRIX_HPP |
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#ifndef MATH_SQUAREMATRIX_HPP |
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#define MATH_SQUAREMATRIX_HPP |
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|
35 |
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#include "math/RectMatrix.hpp" |
45 |
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template<typename Real, int Dim> |
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class SquareMatrix : public RectMatrix<Real, Dim, Dim> { |
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public: |
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typedef Real ElemType; |
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typedef Real* ElemPoinerType; |
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|
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/** default constructor */ |
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SquareMatrix() { |
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for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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data_[i][j] = 0.0; |
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} |
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/** default constructor */ |
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SquareMatrix() { |
53 |
> |
for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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data_[i][j] = 0.0; |
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} |
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|
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/** copy constructor */ |
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SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
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} |
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|
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/** copy assignment operator */ |
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SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { |
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RectMatrix<Real, Dim, Dim>::operator=(m); |
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return *this; |
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} |
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|
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/** Retunrs an identity matrix*/ |
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/** Constructs and initializes every element of this matrix to a scalar */ |
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SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){ |
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} |
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|
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static SquareMatrix<Real, Dim> identity() { |
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SquareMatrix<Real, Dim> m; |
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/** Constructs and initializes from an array */ |
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SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){ |
64 |
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} |
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|
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|
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/** copy constructor */ |
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SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
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} |
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|
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for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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if (i == j) |
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m(i, j) = 1.0; |
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else |
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m(i, j) = 0.0; |
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/** copy assignment operator */ |
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SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { |
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RectMatrix<Real, Dim, Dim>::operator=(m); |
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return *this; |
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} |
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|
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/** Retunrs an identity matrix*/ |
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|
|
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return m; |
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} |
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static SquareMatrix<Real, Dim> identity() { |
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SquareMatrix<Real, Dim> m; |
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|
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for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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if (i == j) |
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m(i, j) = 1.0; |
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else |
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m(i, j) = 0.0; |
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|
|
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/** Retunrs the inversion of this matrix. */ |
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SquareMatrix<Real, Dim> inverse() { |
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SquareMatrix<Real, Dim> result; |
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return m; |
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} |
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|
|
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return result; |
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} |
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/** |
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* Retunrs the inversion of this matrix. |
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* @todo need implementation |
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*/ |
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SquareMatrix<Real, Dim> inverse() { |
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SquareMatrix<Real, Dim> result; |
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|
|
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|
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return result; |
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} |
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|
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/** Returns the determinant of this matrix. */ |
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double determinant() const { |
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double det; |
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return det; |
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} |
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/** |
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* Returns the determinant of this matrix. |
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* @todo need implementation |
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*/ |
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Real determinant() const { |
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Real det; |
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return det; |
109 |
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} |
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|
|
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/** Returns the trace of this matrix. */ |
112 |
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double trace() const { |
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double tmp = 0; |
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|
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for (unsigned int i = 0; i < Dim ; i++) |
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tmp += data_[i][i]; |
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/** Returns the trace of this matrix. */ |
112 |
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Real trace() const { |
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Real tmp = 0; |
114 |
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|
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for (unsigned int i = 0; i < Dim ; i++) |
116 |
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tmp += data_[i][i]; |
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|
|
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return tmp; |
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} |
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return tmp; |
119 |
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} |
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|
|
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/** Tests if this matrix is symmetrix. */ |
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bool isSymmetric() const { |
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< |
for (unsigned int i = 0; i < Dim - 1; i++) |
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for (unsigned int j = i; j < Dim; j++) |
125 |
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if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon) |
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return false; |
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|
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return true; |
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} |
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/** Tests if this matrix is symmetrix. */ |
122 |
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bool isSymmetric() const { |
123 |
> |
for (unsigned int i = 0; i < Dim - 1; i++) |
124 |
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for (unsigned int j = i; j < Dim; j++) |
125 |
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if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon) |
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return false; |
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|
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return true; |
129 |
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} |
130 |
|
|
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/** Tests if this matrix is orthogona. */ |
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bool isOrthogonal() { |
133 |
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SquareMatrix<Real, Dim> tmp; |
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/** Tests if this matrix is orthogonal. */ |
132 |
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bool isOrthogonal() { |
133 |
> |
SquareMatrix<Real, Dim> tmp; |
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|
|
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tmp = *this * transpose(); |
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tmp = *this * transpose(); |
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|
|
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return tmp.isUnitMatrix(); |
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} |
137 |
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return tmp.isDiagonal(); |
138 |
> |
} |
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|
|
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/** Tests if this matrix is diagonal. */ |
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bool isDiagonal() const { |
142 |
< |
for (unsigned int i = 0; i < Dim ; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
144 |
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if (i !=j && fabs(data_[i][j]) > oopse::epsilon) |
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return false; |
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|
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return true; |
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} |
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/** Tests if this matrix is diagonal. */ |
141 |
> |
bool isDiagonal() const { |
142 |
> |
for (unsigned int i = 0; i < Dim ; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
144 |
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if (i !=j && fabs(data_[i][j]) > oopse::epsilon) |
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return false; |
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|
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return true; |
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} |
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|
|
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/** Tests if this matrix is the unit matrix. */ |
151 |
< |
bool isUnitMatrix() const { |
152 |
< |
if (!isDiagonal()) |
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return false; |
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|
140 |
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for (unsigned int i = 0; i < Dim ; i++) |
141 |
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if (fabs(data_[i][i] - 1) > oopse::epsilon) |
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> |
/** Tests if this matrix is the unit matrix. */ |
151 |
> |
bool isUnitMatrix() const { |
152 |
> |
if (!isDiagonal()) |
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|
return false; |
154 |
|
|
155 |
< |
return true; |
156 |
< |
} |
155 |
> |
for (unsigned int i = 0; i < Dim ; i++) |
156 |
> |
if (fabs(data_[i][i] - 1) > oopse::epsilon) |
157 |
> |
return false; |
158 |
> |
|
159 |
> |
return true; |
160 |
> |
} |
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|
|
162 |
+ |
/** @todo need implementation */ |
163 |
+ |
void diagonalize() { |
164 |
+ |
//jacobi(m, eigenValues, ortMat); |
165 |
+ |
} |
166 |
+ |
|
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/** |
168 |
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* Jacobi iteration routines for computing eigenvalues/eigenvectors of |
169 |
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* real symmetric matrix |
170 |
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* |
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* @return true if success, otherwise return false |
172 |
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* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
173 |
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* overwritten |
174 |
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* @param w will contain the eigenvalues of the matrix On return of this function |
175 |
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* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
176 |
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* normalized and mutually orthogonal. |
177 |
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*/ |
178 |
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|
179 |
+ |
static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d, |
180 |
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SquareMatrix<Real, Dim>& v); |
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|
};//end SquareMatrix |
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|
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|
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/*========================================================================= |
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|
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Program: Visualization Toolkit |
187 |
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Module: $RCSfile: SquareMatrix.hpp,v $ |
188 |
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|
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Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen |
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All rights reserved. |
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See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
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|
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This software is distributed WITHOUT ANY WARRANTY; without even |
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
195 |
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PURPOSE. See the above copyright notice for more information. |
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|
197 |
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=========================================================================*/ |
198 |
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|
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+ |
#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\ |
200 |
+ |
a(k, l)=h+s*(g-h*tau) |
201 |
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|
202 |
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#define VTK_MAX_ROTATIONS 20 |
203 |
+ |
|
204 |
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// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn |
205 |
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// real symmetric matrix. Square nxn matrix a; size of matrix in n; |
206 |
+ |
// output eigenvalues in w; and output eigenvectors in v. Resulting |
207 |
+ |
// eigenvalues/vectors are sorted in decreasing order; eigenvectors are |
208 |
+ |
// normalized. |
209 |
+ |
template<typename Real, int Dim> |
210 |
+ |
int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, |
211 |
+ |
SquareMatrix<Real, Dim>& v) { |
212 |
+ |
const int n = Dim; |
213 |
+ |
int i, j, k, iq, ip, numPos; |
214 |
+ |
Real tresh, theta, tau, t, sm, s, h, g, c, tmp; |
215 |
+ |
Real bspace[4], zspace[4]; |
216 |
+ |
Real *b = bspace; |
217 |
+ |
Real *z = zspace; |
218 |
+ |
|
219 |
+ |
// only allocate memory if the matrix is large |
220 |
+ |
if (n > 4) { |
221 |
+ |
b = new Real[n]; |
222 |
+ |
z = new Real[n]; |
223 |
+ |
} |
224 |
+ |
|
225 |
+ |
// initialize |
226 |
+ |
for (ip=0; ip<n; ip++) { |
227 |
+ |
for (iq=0; iq<n; iq++) { |
228 |
+ |
v(ip, iq) = 0.0; |
229 |
+ |
} |
230 |
+ |
v(ip, ip) = 1.0; |
231 |
+ |
} |
232 |
+ |
for (ip=0; ip<n; ip++) { |
233 |
+ |
b[ip] = w[ip] = a(ip, ip); |
234 |
+ |
z[ip] = 0.0; |
235 |
+ |
} |
236 |
+ |
|
237 |
+ |
// begin rotation sequence |
238 |
+ |
for (i=0; i<VTK_MAX_ROTATIONS; i++) { |
239 |
+ |
sm = 0.0; |
240 |
+ |
for (ip=0; ip<n-1; ip++) { |
241 |
+ |
for (iq=ip+1; iq<n; iq++) { |
242 |
+ |
sm += fabs(a(ip, iq)); |
243 |
+ |
} |
244 |
+ |
} |
245 |
+ |
if (sm == 0.0) { |
246 |
+ |
break; |
247 |
+ |
} |
248 |
+ |
|
249 |
+ |
if (i < 3) { // first 3 sweeps |
250 |
+ |
tresh = 0.2*sm/(n*n); |
251 |
+ |
} else { |
252 |
+ |
tresh = 0.0; |
253 |
+ |
} |
254 |
+ |
|
255 |
+ |
for (ip=0; ip<n-1; ip++) { |
256 |
+ |
for (iq=ip+1; iq<n; iq++) { |
257 |
+ |
g = 100.0*fabs(a(ip, iq)); |
258 |
+ |
|
259 |
+ |
// after 4 sweeps |
260 |
+ |
if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
261 |
+ |
&& (fabs(w[iq])+g) == fabs(w[iq])) { |
262 |
+ |
a(ip, iq) = 0.0; |
263 |
+ |
} else if (fabs(a(ip, iq)) > tresh) { |
264 |
+ |
h = w[iq] - w[ip]; |
265 |
+ |
if ( (fabs(h)+g) == fabs(h)) { |
266 |
+ |
t = (a(ip, iq)) / h; |
267 |
+ |
} else { |
268 |
+ |
theta = 0.5*h / (a(ip, iq)); |
269 |
+ |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
270 |
+ |
if (theta < 0.0) { |
271 |
+ |
t = -t; |
272 |
+ |
} |
273 |
+ |
} |
274 |
+ |
c = 1.0 / sqrt(1+t*t); |
275 |
+ |
s = t*c; |
276 |
+ |
tau = s/(1.0+c); |
277 |
+ |
h = t*a(ip, iq); |
278 |
+ |
z[ip] -= h; |
279 |
+ |
z[iq] += h; |
280 |
+ |
w[ip] -= h; |
281 |
+ |
w[iq] += h; |
282 |
+ |
a(ip, iq)=0.0; |
283 |
+ |
|
284 |
+ |
// ip already shifted left by 1 unit |
285 |
+ |
for (j = 0;j <= ip-1;j++) { |
286 |
+ |
VTK_ROTATE(a,j,ip,j,iq); |
287 |
+ |
} |
288 |
+ |
// ip and iq already shifted left by 1 unit |
289 |
+ |
for (j = ip+1;j <= iq-1;j++) { |
290 |
+ |
VTK_ROTATE(a,ip,j,j,iq); |
291 |
+ |
} |
292 |
+ |
// iq already shifted left by 1 unit |
293 |
+ |
for (j=iq+1; j<n; j++) { |
294 |
+ |
VTK_ROTATE(a,ip,j,iq,j); |
295 |
+ |
} |
296 |
+ |
for (j=0; j<n; j++) { |
297 |
+ |
VTK_ROTATE(v,j,ip,j,iq); |
298 |
+ |
} |
299 |
+ |
} |
300 |
+ |
} |
301 |
+ |
} |
302 |
+ |
|
303 |
+ |
for (ip=0; ip<n; ip++) { |
304 |
+ |
b[ip] += z[ip]; |
305 |
+ |
w[ip] = b[ip]; |
306 |
+ |
z[ip] = 0.0; |
307 |
+ |
} |
308 |
+ |
} |
309 |
+ |
|
310 |
+ |
//// this is NEVER called |
311 |
+ |
if ( i >= VTK_MAX_ROTATIONS ) { |
312 |
+ |
std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; |
313 |
+ |
return 0; |
314 |
+ |
} |
315 |
+ |
|
316 |
+ |
// sort eigenfunctions these changes do not affect accuracy |
317 |
+ |
for (j=0; j<n-1; j++) { // boundary incorrect |
318 |
+ |
k = j; |
319 |
+ |
tmp = w[k]; |
320 |
+ |
for (i=j+1; i<n; i++) { // boundary incorrect, shifted already |
321 |
+ |
if (w[i] >= tmp) { // why exchage if same? |
322 |
+ |
k = i; |
323 |
+ |
tmp = w[k]; |
324 |
+ |
} |
325 |
+ |
} |
326 |
+ |
if (k != j) { |
327 |
+ |
w[k] = w[j]; |
328 |
+ |
w[j] = tmp; |
329 |
+ |
for (i=0; i<n; i++) { |
330 |
+ |
tmp = v(i, j); |
331 |
+ |
v(i, j) = v(i, k); |
332 |
+ |
v(i, k) = tmp; |
333 |
+ |
} |
334 |
+ |
} |
335 |
+ |
} |
336 |
+ |
// insure eigenvector consistency (i.e., Jacobi can compute vectors that |
337 |
+ |
// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can |
338 |
+ |
// reek havoc in hyperstreamline/other stuff. We will select the most |
339 |
+ |
// positive eigenvector. |
340 |
+ |
int ceil_half_n = (n >> 1) + (n & 1); |
341 |
+ |
for (j=0; j<n; j++) { |
342 |
+ |
for (numPos=0, i=0; i<n; i++) { |
343 |
+ |
if ( v(i, j) >= 0.0 ) { |
344 |
+ |
numPos++; |
345 |
+ |
} |
346 |
+ |
} |
347 |
+ |
// if ( numPos < ceil(double(n)/double(2.0)) ) |
348 |
+ |
if ( numPos < ceil_half_n) { |
349 |
+ |
for (i=0; i<n; i++) { |
350 |
+ |
v(i, j) *= -1.0; |
351 |
+ |
} |
352 |
+ |
} |
353 |
+ |
} |
354 |
+ |
|
355 |
+ |
if (n > 4) { |
356 |
+ |
delete [] b; |
357 |
+ |
delete [] z; |
358 |
+ |
} |
359 |
+ |
return 1; |
360 |
+ |
} |
361 |
+ |
|
362 |
+ |
|
363 |
|
} |
364 |
|
#endif //MATH_SQUAREMATRIX_HPP |
365 |
+ |
|