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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 "Vector3d.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{ |
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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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/** Constructs and initializes every element of this matrix to a scalar */ |
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SquareMatrix(double s) { |
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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] = s; |
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} |
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|
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/** copy constructor */ |
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SquareMatrix(const SquareMatrix<Real, Dim>& m) { |
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*this = m; |
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} |
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|
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/** destructor*/ |
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~SquareMatrix() {} |
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|
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/** copy assignment operator */ |
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SquareMatrix<Real, Dim>& operator =(const SquareMatrix<Real, Dim>& m) { |
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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] = m.data_[i][j]; |
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} |
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|
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/** |
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* Return the reference of a single element of this matrix. |
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* @return the reference of a single element of this matrix |
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* @param i row index |
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* @param j colum index |
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*/ |
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double& operator()(unsigned int i, unsigned int j) { |
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return data_[i][j]; |
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} |
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|
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/** |
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* Return the value of a single element of this matrix. |
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* @return the value of a single element of this matrix |
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* @param i row index |
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* @param j colum index |
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*/ |
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double operator()(unsigned int i, unsigned int j) const { |
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return data_[i][j]; |
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} |
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|
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/** |
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* Returns a row of this matrix as a vector. |
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* @return a row of this matrix as a vector |
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* @param row the row index |
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*/ |
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Vector<Real, Dim> getRow(unsigned int row) { |
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Vector<Real, Dim> v; |
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|
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for (unsigned int i = 0; i < Dim; i++) |
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v[i] = data_[row][i]; |
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|
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return v; |
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} |
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|
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/** |
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* Sets a row of this matrix |
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* @param row the row index |
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* @param v the vector to be set |
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*/ |
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void setRow(unsigned int row, const Vector<Real, Dim>& v) { |
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Vector<Real, Dim> v; |
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|
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for (unsigned int i = 0; i < Dim; i++) |
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data_[row][i] = v[i]; |
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} |
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|
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/** |
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* Returns a column of this matrix as a vector. |
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* @return a column of this matrix as a vector |
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* @param col the column index |
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*/ |
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Vector<Real, Dim> getColum(unsigned int col) { |
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Vector<Real, Dim> v; |
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|
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for (unsigned int i = 0; i < Dim; i++) |
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v[i] = data_[i][col]; |
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|
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return v; |
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} |
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|
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/** |
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* Sets a column of this matrix |
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* @param col the column index |
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* @param v the vector to be set |
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*/ |
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void setColum(unsigned int col, const Vector<Real, Dim>& v){ |
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Vector<Real, Dim> v; |
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|
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for (unsigned int i = 0; i < Dim; i++) |
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data_[i][col] = v[i]; |
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} |
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|
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/** Negates the value of this matrix in place. */ |
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inline void negate() { |
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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] = -data_[i][j]; |
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} |
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|
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/** |
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* Sets the value of this matrix to the negation of matrix m. |
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* @param m the source matrix |
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*/ |
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inline void negate(const SquareMatrix<Real, Dim>& m) { |
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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] = -m.data_[i][j]; |
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} |
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|
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/** |
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* Sets the value of this matrix to the sum of itself and m (*this += m). |
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* @param m the other matrix |
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*/ |
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inline void add( const SquareMatrix<Real, Dim>& m ) { |
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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] += m.data_[i][j]; |
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} |
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|
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/** |
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* Sets the value of this matrix to the sum of m1 and m2 (*this = m1 + m2). |
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* @param m1 the first matrix |
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* @param m2 the second matrix |
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*/ |
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inline void add( const SquareMatrix<Real, Dim>& m1, const SquareMatrix<Real, Dim>& m2 ) { |
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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] = m1.data_[i][j] + m2.data_[i][j]; |
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} |
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|
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/** |
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* Sets the value of this matrix to the difference of itself and m (*this -= m). |
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* @param m the other matrix |
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*/ |
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inline void sub( const SquareMatrix<Real, Dim>& m ) { |
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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] -= m.data_[i][j]; |
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} |
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|
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/** |
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* Sets the value of this matrix to the difference of matrix m1 and m2 (*this = m1 - m2). |
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* @param m1 the first matrix |
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* @param m2 the second matrix |
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*/ |
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inline void sub( const SquareMatrix<Real, Dim>& m1, const Vector &m2){ |
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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] = m1.data_[i][j] - m2.data_[i][j]; |
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} |
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|
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/** |
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* Sets the value of this matrix to the scalar multiplication of itself (*this *= s). |
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* @param s the scalar value |
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*/ |
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inline void mul( double s ) { |
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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] *= s; |
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} |
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|
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/** |
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* Sets the value of this matrix to the scalar multiplication of matrix m (*this = s * m). |
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* @param s the scalar value |
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* @param m the matrix |
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*/ |
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inline void mul( double s, const SquareMatrix<Real, Dim>& m ) { |
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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] = s * m.data_[i][j]; |
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} |
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|
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/** |
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* Sets the value of this matrix to the multiplication of this matrix and matrix m |
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* (*this = *this * m). |
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* @param m the matrix |
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*/ |
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inline void mul(const SquareMatrix<Real, Dim>& m ) { |
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SquareMatrix<Real, Dim> tmp(*this); |
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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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|
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data_[i][j] = 0.0; |
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for (unsigned int k = 0; k < Dim; k++) |
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data_[i][j] = tmp.data_[i][k] * m.data_[k][j] |
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} |
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} |
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|
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/** |
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* Sets the value of this matrix to the left multiplication of matrix m into itself |
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* (*this = m * *this). |
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* @param m the matrix |
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*/ |
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inline void leftmul(const SquareMatrix<Real, Dim>& m ) { |
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SquareMatrix<Real, Dim> tmp(*this); |
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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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|
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data_[i][j] = 0.0; |
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for (unsigned int k = 0; k < Dim; k++) |
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data_[i][j] = m.data_[i][k] * tmp.data_[k][j] |
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} |
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} |
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|
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/** |
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* Sets the value of this matrix to the multiplication of matrix m1 and matrix m2 |
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* (*this = m1 * m2). |
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* @param m1 the first matrix |
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* @param m2 the second matrix |
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*/ |
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inline void mul(const SquareMatrix<Real, Dim>& m1, |
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const SquareMatrix<Real, Dim>& m2 ) { |
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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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|
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data_[i][j] = 0.0; |
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for (unsigned int k = 0; k < Dim; k++) |
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data_[i][j] = m1.data_[i][k] * m2.data_[k][j] |
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} |
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|
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} |
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|
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/** |
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* Sets the value of this matrix to the scalar division of itself (*this /= s ). |
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* @param s the scalar value |
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*/ |
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inline void div( double s) { |
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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] /= s; |
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} |
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|
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inline SquareMatrix<Real, Dim>& operator=(const SquareMatrix<Real, Dim>& v) { |
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if (this == &v) |
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return *this; |
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|
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for (unsigned int i = 0; i < Dim; i++) |
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data_[i] = v[i]; |
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|
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return *this; |
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} |
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|
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/** |
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* Sets the value of this matrix to the scalar division of matrix v1 (*this = v1 / s ). |
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* @paran v1 the source matrix |
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* @param s the scalar value |
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*/ |
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inline void div( const SquareMatrix<Real, Dim>& v1, double s ) { |
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for (unsigned int i = 0; i < Dim; i++) |
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data_[i] = v1.data_[i] / s; |
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} |
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|
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/** |
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* Multiples a scalar into every element of this matrix. |
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* @param s the scalar value |
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*/ |
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SquareMatrix<Real, Dim>& operator *=(const double s) { |
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this->mul(s); |
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return *this; |
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} |
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|
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/** |
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* Divides every element of this matrix by a scalar. |
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* @param s the scalar value |
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*/ |
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SquareMatrix<Real, Dim>& operator /=(const double s) { |
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this->div(s); |
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return *this; |
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} |
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|
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/** |
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* Sets the value of this matrix to the sum of the other matrix and itself (*this += m). |
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* @param m the other matrix |
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*/ |
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SquareMatrix<Real, Dim>& operator += (const SquareMatrix<Real, Dim>& m) { |
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add(m); |
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return *this; |
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} |
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|
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/** |
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* Sets the value of this matrix to the differerence of itself and the other matrix (*this -= m) |
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* @param m the other matrix |
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*/ |
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SquareMatrix<Real, Dim>& operator -= (const SquareMatrix<Real, Dim>& m){ |
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sub(m); |
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return *this; |
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} |
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|
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/** set this matrix to an identity matrix*/ |
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|
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void identity() { |
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for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int i = 0; i < Dim; i++) |
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if (i == j) |
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data_[i][j] = 1.0; |
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else |
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data_[i][j] = 0.0; |
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} |
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|
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/** Sets the value of this matrix to the inversion of itself. */ |
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void inverse() { |
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inverse(*this); |
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} |
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|
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/** |
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* Sets the value of this matrix to the inversion of other matrix. |
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* @ param m the source matrix |
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*/ |
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void inverse(const SquareMatrix<Real, Dim>& m); |
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|
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/** Sets the value of this matrix to the transpose of itself. */ |
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void transpose() { |
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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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std::swap(data_[i][j], data_[j][i]); |
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} |
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|
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/** |
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* Sets the value of this matrix to the transpose of other matrix. |
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* @ param m the source matrix |
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*/ |
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void transpose(const SquareMatrix<Real, Dim>& m) { |
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|
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if (this == &m) { |
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transpose(); |
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} else { |
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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] = m.data_[i][j]; |
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} |
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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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|
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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]) > 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 orthogona. */ |
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bool isOrthogonal() const { |
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SquareMatrix<Real, Dim> t(*this); |
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|
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t.transpose(); |
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|
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return isUnitMatrix(*this * t); |
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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]) > 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) > 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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protected: |
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double data_[Dim][Dim]; /**< matrix element */ |
| 450 |
|
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};//end SquareMatrix |
| 452 |
|
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|
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/** Negate the value of every element of this matrix. */ |
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template<typename Real, int Dim> |
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inline SquareMatrix<Real, Dim> operator -(const SquareMatrix& m) { |
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SquareMatrix<Real, Dim> result(m); |
| 458 |
|
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result.negate(); |
| 460 |
|
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return result; |
| 462 |
} |
| 463 |
|
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/** |
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* Return the sum of two matrixes (m1 + m2). |
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* @return the sum of two matrixes |
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* @param m1 the first matrix |
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* @param m2 the second matrix |
| 469 |
*/ |
| 470 |
template<typename Real, int Dim> |
| 471 |
inline SquareMatrix<Real, Dim> operator + (const SquareMatrix<Real, Dim>& m1, |
| 472 |
const SquareMatrix<Real, Dim>& m2) { |
| 473 |
SquareMatrix<Real, Dim>result; |
| 474 |
|
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result.add(m1, m2); |
| 476 |
|
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return result; |
| 478 |
} |
| 479 |
|
| 480 |
/** |
| 481 |
* Return the difference of two matrixes (m1 - m2). |
| 482 |
* @return the sum of two matrixes |
| 483 |
* @param m1 the first matrix |
| 484 |
* @param m2 the second matrix |
| 485 |
*/ |
| 486 |
template<typename Real, int Dim> |
| 487 |
inline SquareMatrix<Real, Dim> operator - (const SquareMatrix<Real, Dim>& m1, |
| 488 |
const SquareMatrix<Real, Dim>& m2) { |
| 489 |
SquareMatrix<Real, Dim>result; |
| 490 |
|
| 491 |
result.sub(m1, m2); |
| 492 |
|
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return result; |
| 494 |
} |
| 495 |
|
| 496 |
/** |
| 497 |
* Return the multiplication of two matrixes (m1 * m2). |
| 498 |
* @return the multiplication of two matrixes |
| 499 |
* @param m1 the first matrix |
| 500 |
* @param m2 the second matrix |
| 501 |
*/ |
| 502 |
template<typename Real, int Dim> |
| 503 |
inline SquareMatrix<Real, Dim> operator *(const SquareMatrix<Real, Dim>& m1, |
| 504 |
const SquareMatrix<Real, Dim>& m2) { |
| 505 |
SquareMatrix<Real, Dim> result; |
| 506 |
|
| 507 |
result.mul(m1, m2); |
| 508 |
|
| 509 |
return result; |
| 510 |
} |
| 511 |
|
| 512 |
/** |
| 513 |
* Return the multiplication of matrixes m and vector v (m * v). |
| 514 |
* @return the multiplication of matrixes and vector |
| 515 |
* @param m the matrix |
| 516 |
* @param v the vector |
| 517 |
*/ |
| 518 |
template<typename Real, int Dim> |
| 519 |
inline Vector<Real, Dim> operator *(const SquareMatrix<Real, Dim>& m, |
| 520 |
const SquareMatrix<Real, Dim>& v) { |
| 521 |
Vector<Real, Dim> result; |
| 522 |
|
| 523 |
for (unsigned int i = 0; i < Dim ; i++) |
| 524 |
for (unsigned int j = 0; j < Dim ; j++) |
| 525 |
result[i] += m(i, j) * v[j]; |
| 526 |
|
| 527 |
return result; |
| 528 |
} |
| 529 |
} |
| 530 |
#endif //MATH_SQUAREMATRIX_HPP |
