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/* |
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* Copyright (C) 2000-2004 Object Oriented Parallel Simulation Engine (OOPSE) project |
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* |
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* Contact: oopse@oopse.org |
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* |
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* This program is free software; you can redistribute it and/or |
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* modify it under the terms of the GNU Lesser General Public License |
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* as published by the Free Software Foundation; either version 2.1 |
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* of the License, or (at your option) any later version. |
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* All we ask is that proper credit is given for our work, which includes |
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* - but is not limited to - adding the above copyright notice to the beginning |
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* of your source code files, and to any copyright notice that you may distribute |
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* with programs based on this work. |
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* |
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* This program is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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* GNU Lesser General Public License for more details. |
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* |
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* You should have received a copy of the GNU Lesser General Public License |
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* along with this program; if not, write to the Free Software |
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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* |
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*/ |
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|
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/** |
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* @file SquareMatrix.hpp |
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* @author Teng Lin |
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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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#define MATH_SQUAREMATRIX_HPP |
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|
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#include "math/RectMatrix.hpp" |
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|
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namespace oopse { |
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|
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/** |
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* @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp" |
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* @brief A square matrix class |
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* @template Real the element type |
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* @template Dim the dimension of the square matrix |
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*/ |
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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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|
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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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|
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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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|
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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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return m; |
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} |
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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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|
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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 trace of this matrix. */ |
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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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|
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return tmp; |
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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++) |
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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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|
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/** Tests if this matrix is orthogonal. */ |
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bool isOrthogonal() { |
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SquareMatrix<Real, Dim> tmp; |
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|
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tmp = *this * transpose(); |
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|
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return tmp.isDiagonal(); |
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} |
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|
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/** Tests if this matrix is diagonal. */ |
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bool isDiagonal() const { |
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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 && 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. */ |
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bool isUnitMatrix() const { |
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if (!isDiagonal()) |
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return false; |
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|
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for (unsigned int i = 0; i < Dim ; i++) |
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if (fabs(data_[i][i] - 1) > 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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void diagonalize() { |
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jacobi(m, eigenValues, ortMat); |
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} |
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|
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/** |
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* Finds the eigenvalues and eigenvectors of a symmetric matrix |
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* @param eigenvals a reference to a vector3 where the |
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* eigenvalues will be stored. The eigenvalues are ordered so |
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* that eigenvals[0] <= eigenvals[1] <= eigenvals[2]. |
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* @return an orthogonal matrix whose ith column is an |
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* eigenvector for the eigenvalue eigenvals[i] |
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*/ |
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SquareMatrix<Real, Dim> findEigenvectors(Vector<Real, Dim>& eigenValues) { |
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SquareMatrix<Real, Dim> ortMat; |
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|
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if ( !isSymmetric()){ |
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throw(); |
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} |
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|
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SquareMatrix<Real, Dim> m(*this); |
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jacobi(m, eigenValues, ortMat); |
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|
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return ortMat; |
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} |
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/** |
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* Jacobi iteration routines for computing eigenvalues/eigenvectors of |
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* real symmetric matrix |
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* |
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* @return true if success, otherwise return false |
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* @param a source matrix |
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* @param w output eigenvalues |
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* @param v output eigenvectors |
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*/ |
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void jacobi(const SquareMatrix<Real, Dim>& a, |
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Vector<Real, Dim>& w, |
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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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#define ROT(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);a(k, l)=h+s*(g-h*tau) |
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#define MAX_ROTATIONS 60 |
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|
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template<Real, int Dim> |
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void SquareMatrix<Real, int Dim>::jacobi(SquareMatrix<Real, Dim>& a, |
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Vector<Real, Dim>& w, |
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SquareMatrix<Real, Dim>& v) { |
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const int N = Dim; |
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int i, j, k, iq, ip; |
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double tresh, theta, tau, t, sm, s, h, g, c; |
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double tmp; |
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Vector<Real, Dim> b, z; |
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|
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// initialize |
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for (ip=0; ip<N; ip++) |
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{ |
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for (iq=0; iq<N; iq++) v(ip, iq) = 0.0; |
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v(ip, ip) = 1.0; |
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} |
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for (ip=0; ip<N; ip++) |
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{ |
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b(ip) = w(ip) = a(ip, ip); |
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z(ip) = 0.0; |
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} |
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|
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// begin rotation sequence |
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for (i=0; i<MAX_ROTATIONS; i++) |
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{ |
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sm = 0.0; |
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for (ip=0; ip<2; ip++) |
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{ |
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for (iq=ip+1; iq<N; iq++) sm += fabs(a(ip, iq)); |
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} |
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if (sm == 0.0) break; |
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|
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if (i < 4) tresh = 0.2*sm/(9); |
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else tresh = 0.0; |
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|
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for (ip=0; ip<2; ip++) |
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{ |
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for (iq=ip+1; iq<N; iq++) |
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{ |
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g = 100.0*fabs(a(ip, iq)); |
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if (i > 4 && (fabs(w(ip))+g) == fabs(w(ip)) |
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&& (fabs(w(iq))+g) == fabs(w(iq))) |
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{ |
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a(ip, iq) = 0.0; |
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} |
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else if (fabs(a(ip, iq)) > tresh) |
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{ |
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h = w(iq) - w(ip); |
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if ( (fabs(h)+g) == fabs(h)) t = (a(ip, iq)) / h; |
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else |
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{ |
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theta = 0.5*h / (a(ip, iq)); |
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t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
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if (theta < 0.0) t = -t; |
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} |
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c = 1.0 / sqrt(1+t*t); |
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s = t*c; |
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tau = s/(1.0+c); |
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h = t*a(ip, iq); |
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z(ip) -= h; |
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z(iq) += h; |
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w(ip) -= h; |
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w(iq) += h; |
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a(ip, iq)=0.0; |
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for (j=0;j<ip-1;j++) |
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{ |
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ROT(a,j,ip,j,iq); |
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} |
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for (j=ip+1;j<iq-1;j++) |
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{ |
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ROT(a,ip,j,j,iq); |
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} |
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for (j=iq+1; j<N; j++) |
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{ |
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ROT(a,ip,j,iq,j); |
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} |
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for (j=0; j<N; j++) |
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{ |
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ROT(v,j,ip,j,iq); |
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} |
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} |
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} |
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} |
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|
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for (ip=0; ip<N; ip++) |
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{ |
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b(ip) += z(ip); |
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w(ip) = b(ip); |
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z(ip) = 0.0; |
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} |
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} |
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|
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if ( i >= MAX_ROTATIONS ) |
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return false; |
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|
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// sort eigenfunctions |
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for (j=0; j<N; j++) |
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{ |
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k = j; |
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tmp = w(k); |
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for (i=j; i<N; i++) |
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{ |
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if (w(i) >= tmp) |
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{ |
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k = i; |
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tmp = w(k); |
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} |
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} |
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if (k != j) |
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{ |
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w(k) = w(j); |
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w(j) = tmp; |
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for (i=0; i<N; i++) |
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{ |
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tmp = v(i, j); |
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v(i, j) = v(i, k); |
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v(i, k) = tmp; |
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} |
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} |
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} |
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|
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// insure eigenvector consistency (i.e., Jacobi can compute |
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// vectors that are negative of one another (.707,.707,0) and |
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// (-.707,-.707,0). This can reek havoc in |
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// hyperstreamline/other stuff. We will select the most |
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// positive eigenvector. |
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int numPos; |
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for (j=0; j<N; j++) |
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{ |
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for (numPos=0, i=0; i<N; i++) if ( v(i, j) >= 0.0 ) numPos++; |
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if ( numPos < 2 ) for(i=0; i<N; i++) v(i, j) *= -1.0; |
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} |
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|
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return true; |
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} |
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|
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#undef ROT |
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#undef MAX_ROTATIONS |
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|
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} |
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|
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|
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} |
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#endif //MATH_SQUAREMATRIX_HPP |
