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/* |
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* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
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* |
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* The University of Notre Dame grants you ("Licensee") a |
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* non-exclusive, royalty free, license to use, modify and |
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* redistribute this software in source and binary code form, provided |
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* that the following conditions are met: |
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* |
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* 1. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* |
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* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in the |
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* documentation and/or other materials provided with the |
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* distribution. |
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* |
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* This software is provided "AS IS," without a warranty of any |
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* kind. All express or implied conditions, representations and |
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* warranties, including any implied warranty of merchantability, |
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* fitness for a particular purpose or non-infringement, are hereby |
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* excluded. The University of Notre Dame and its licensors shall not |
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* be liable for any damages suffered by licensee as a result of |
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* using, modifying or distributing the software or its |
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* derivatives. In no event will the University of Notre Dame or its |
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* licensors be liable for any lost revenue, profit or data, or for |
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* direct, indirect, special, consequential, incidental or punitive |
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* damages, however caused and regardless of the theory of liability, |
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* arising out of the use of or inability to use software, even if the |
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* University of Notre Dame has been advised of the possibility of |
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* such damages. |
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* |
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* SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your |
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* research, please cite the appropriate papers when you publish your |
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* work. Good starting points are: |
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* |
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* [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005). |
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* [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006). |
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* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008). |
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* [4] Kuang & Gezelter, J. Chem. Phys. 133, 164101 (2010). |
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* [5] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011). |
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*/ |
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|
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/** |
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* @file RectMatrix.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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|
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#ifndef MATH_RECTMATRIX_HPP |
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#define MATH_RECTMATRIX_HPP |
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#include <math.h> |
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#include <cmath> |
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#include "Vector.hpp" |
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|
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namespace OpenMD { |
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|
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/** |
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* @class RectMatrix RectMatrix.hpp "math/RectMatrix.hpp" |
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* @brief rectangular matrix class |
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*/ |
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template<typename Real, unsigned int Row, unsigned int Col> |
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class RectMatrix { |
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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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RectMatrix() { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->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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RectMatrix(Real s) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->data_[i][j] = s; |
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} |
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|
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RectMatrix(Real* array) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->data_[i][j] = array[i * Row + j]; |
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} |
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|
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/** copy constructor */ |
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RectMatrix(const RectMatrix<Real, Row, Col>& m) { |
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*this = m; |
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} |
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|
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/** destructor*/ |
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~RectMatrix() {} |
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|
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/** copy assignment operator */ |
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RectMatrix<Real, Row, Col>& operator =(const RectMatrix<Real, Row, Col>& m) { |
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if (this == &m) |
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return *this; |
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|
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->data_[i][j] = m.data_[i][j]; |
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return *this; |
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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 Column index |
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*/ |
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Real& operator()(unsigned int i, unsigned int j) { |
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//assert( i < Row && j < Col); |
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return this->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 Column index |
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*/ |
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Real operator()(unsigned int i, unsigned int j) const { |
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|
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return this->data_[i][j]; |
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} |
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|
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/** |
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* Copy the internal data to an array |
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* @param array the pointer of destination array |
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*/ |
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void getArray(Real* array) { |
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for (unsigned int i = 0; i < Row; i++) { |
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for (unsigned int j = 0; j < Col; j++) { |
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array[i * Row + j] = this->data_[i][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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/** Returns the pointer of internal array */ |
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Real* getArrayPointer() { |
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return &this->data_[0][0]; |
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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, Row> getRow(unsigned int row) { |
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Vector<Real, Row> v; |
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|
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for (unsigned int i = 0; i < Col; i++) |
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v[i] = this->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, Row>& v) { |
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|
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for (unsigned int i = 0; i < Col; i++) |
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this->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, Col> getColumn(unsigned int col) { |
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Vector<Real, Col> v; |
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|
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for (unsigned int j = 0; j < Row; j++) |
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v[j] = this->data_[j][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 setColumn(unsigned int col, const Vector<Real, Col>& v){ |
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|
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for (unsigned int j = 0; j < Row; j++) |
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this->data_[j][col] = v[j]; |
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} |
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|
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/** |
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* swap two rows of this matrix |
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* @param i the first row |
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* @param j the second row |
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*/ |
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void swapRow(unsigned int i, unsigned int j){ |
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assert(i < Row && j < Row); |
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|
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for (unsigned int k = 0; k < Col; k++) |
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std::swap(this->data_[i][k], this->data_[j][k]); |
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} |
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|
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/** |
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* swap two Columns of this matrix |
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* @param i the first Column |
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* @param j the second Column |
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*/ |
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void swapColumn(unsigned int i, unsigned int j){ |
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assert(i < Col && j < Col); |
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|
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for (unsigned int k = 0; k < Row; k++) |
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std::swap(this->data_[k][i], this->data_[k][j]); |
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} |
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|
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/** |
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* Tests if this matrix is identical to matrix m |
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* @return true if this matrix is equal to the matrix m, return false otherwise |
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* @param m matrix to be compared |
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* |
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* @todo replace operator == by template function equal |
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*/ |
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bool operator ==(const RectMatrix<Real, Row, Col>& m) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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if (!equal(this->data_[i][j], m.data_[i][j])) |
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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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/** |
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* Tests if this matrix is not equal to matrix m |
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* @return true if this matrix is not equal to the matrix m, return false otherwise |
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* @param m matrix to be compared |
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*/ |
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bool operator !=(const RectMatrix<Real, Row, Col>& m) { |
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return !(*this == m); |
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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 < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->data_[i][j] = -this->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 RectMatrix<Real, Row, Col>& m) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->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 RectMatrix<Real, Row, Col>& m ) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->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 RectMatrix<Real, Row, Col>& m1, const RectMatrix<Real, Row, Col>& m2 ) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->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 RectMatrix<Real, Row, Col>& m ) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->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 RectMatrix<Real, Row, Col>& m1, const RectMatrix<Real, Row, Col>& m2){ |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->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( Real s ) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->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( Real s, const RectMatrix<Real, Row, Col>& m ) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->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 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( Real s) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->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 division of matrix m (*this = m /s). |
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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 div( Real s, const RectMatrix<Real, Row, Col>& m ) { |
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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this->data_[i][j] = m.data_[i][j] / 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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RectMatrix<Real, Row, Col>& operator *=(const Real 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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RectMatrix<Real, Row, Col>& operator /=(const Real 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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RectMatrix<Real, Row, Col>& operator += (const RectMatrix<Real, Row, Col>& 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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RectMatrix<Real, Row, Col>& operator -= (const RectMatrix<Real, Row, Col>& 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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/** Return the transpose of this matrix */ |
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RectMatrix<Real, Col, Row> transpose() const{ |
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RectMatrix<Real, Col, Row> result; |
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|
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for (unsigned int i = 0; i < Row; i++) |
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for (unsigned int j = 0; j < Col; j++) |
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result(j, i) = this->data_[i][j]; |
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|
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return result; |
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} |
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|
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template<class MatrixType> |
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void setSubMatrix(unsigned int beginRow, unsigned int beginCol, const MatrixType& m) { |
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assert(beginRow + m.getNRow() -1 <= getNRow()); |
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assert(beginCol + m.getNCol() -1 <= getNCol()); |
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|
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for (unsigned int i = 0; i < m.getNRow(); ++i) |
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for (unsigned int j = 0; j < m.getNCol(); ++j) |
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this->data_[beginRow+i][beginCol+j] = m(i, j); |
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} |
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|
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template<class MatrixType> |
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void getSubMatrix(unsigned int beginRow, unsigned int beginCol, MatrixType& m) { |
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assert(beginRow + m.getNRow() -1 <= getNRow()); |
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assert(beginCol + m.getNCol() - 1 <= getNCol()); |
| 408 |
|
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for (unsigned int i = 0; i < m.getNRow(); ++i) |
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for (unsigned int j = 0; j < m.getNCol(); ++j) |
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m(i, j) = this->data_[beginRow+i][beginCol+j]; |
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} |
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|
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unsigned int getNRow() const {return Row;} |
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unsigned int getNCol() const {return Col;} |
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|
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protected: |
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Real data_[Row][Col]; |
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}; |
| 420 |
|
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/** Negate the value of every element of this matrix. */ |
| 422 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 423 |
inline RectMatrix<Real, Row, Col> operator -(const RectMatrix<Real, Row, Col>& m) { |
| 424 |
RectMatrix<Real, Row, Col> result(m); |
| 425 |
|
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result.negate(); |
| 427 |
|
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return result; |
| 429 |
} |
| 430 |
|
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/** |
| 432 |
* Return the sum of two matrixes (m1 + m2). |
| 433 |
* @return the sum of two matrixes |
| 434 |
* @param m1 the first matrix |
| 435 |
* @param m2 the second matrix |
| 436 |
*/ |
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template<typename Real, unsigned int Row, unsigned int Col> |
| 438 |
inline RectMatrix<Real, Row, Col> operator + (const RectMatrix<Real, Row, Col>& m1,const RectMatrix<Real, Row, Col>& m2) { |
| 439 |
RectMatrix<Real, Row, Col> result; |
| 440 |
|
| 441 |
result.add(m1, m2); |
| 442 |
|
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return result; |
| 444 |
} |
| 445 |
|
| 446 |
/** |
| 447 |
* Return the difference of two matrixes (m1 - m2). |
| 448 |
* @return the sum of two matrixes |
| 449 |
* @param m1 the first matrix |
| 450 |
* @param m2 the second matrix |
| 451 |
*/ |
| 452 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 453 |
inline RectMatrix<Real, Row, Col> operator - (const RectMatrix<Real, Row, Col>& m1, const RectMatrix<Real, Row, Col>& m2) { |
| 454 |
RectMatrix<Real, Row, Col> result; |
| 455 |
|
| 456 |
result.sub(m1, m2); |
| 457 |
|
| 458 |
return result; |
| 459 |
} |
| 460 |
|
| 461 |
/** |
| 462 |
* Return the multiplication of scalra and matrix (m * s). |
| 463 |
* @return the multiplication of a scalra and a matrix |
| 464 |
* @param m the matrix |
| 465 |
* @param s the scalar |
| 466 |
*/ |
| 467 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 468 |
inline RectMatrix<Real, Row, Col> operator *(const RectMatrix<Real, Row, Col>& m, Real s) { |
| 469 |
RectMatrix<Real, Row, Col> result; |
| 470 |
|
| 471 |
result.mul(s, m); |
| 472 |
|
| 473 |
return result; |
| 474 |
} |
| 475 |
|
| 476 |
/** |
| 477 |
* Return the multiplication of a scalra and a matrix (s * m). |
| 478 |
* @return the multiplication of a scalra and a matrix |
| 479 |
* @param s the scalar |
| 480 |
* @param m the matrix |
| 481 |
*/ |
| 482 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 483 |
inline RectMatrix<Real, Row, Col> operator *(Real s, const RectMatrix<Real, Row, Col>& m) { |
| 484 |
RectMatrix<Real, Row, Col> result; |
| 485 |
|
| 486 |
result.mul(s, m); |
| 487 |
|
| 488 |
return result; |
| 489 |
} |
| 490 |
|
| 491 |
/** |
| 492 |
* Return the multiplication of two matrixes (m1 * m2). |
| 493 |
* @return the multiplication of two matrixes |
| 494 |
* @param m1 the first matrix |
| 495 |
* @param m2 the second matrix |
| 496 |
*/ |
| 497 |
template<typename Real, unsigned int Row, unsigned int Col, unsigned int SameDim> |
| 498 |
inline RectMatrix<Real, Row, Col> operator *(const RectMatrix<Real, Row, SameDim>& m1, const RectMatrix<Real, SameDim, Col>& m2) { |
| 499 |
RectMatrix<Real, Row, Col> result; |
| 500 |
|
| 501 |
for (unsigned int i = 0; i < Row; i++) |
| 502 |
for (unsigned int j = 0; j < Col; j++) |
| 503 |
for (unsigned int k = 0; k < SameDim; k++) |
| 504 |
result(i, j) += m1(i, k) * m2(k, j); |
| 505 |
|
| 506 |
return result; |
| 507 |
} |
| 508 |
|
| 509 |
/** |
| 510 |
* Returns the multiplication of a matrix and a vector (m * v). |
| 511 |
* @return the multiplication of a matrix and a vector |
| 512 |
* @param m the matrix |
| 513 |
* @param v the vector |
| 514 |
*/ |
| 515 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 516 |
inline Vector<Real, Row> operator *(const RectMatrix<Real, Row, Col>& m, const Vector<Real, Col>& v) { |
| 517 |
Vector<Real, Row> result; |
| 518 |
|
| 519 |
for (unsigned int i = 0; i < Row ; i++) |
| 520 |
for (unsigned int j = 0; j < Col ; j++) |
| 521 |
result[i] += m(i, j) * v[j]; |
| 522 |
|
| 523 |
return result; |
| 524 |
} |
| 525 |
|
| 526 |
/** |
| 527 |
* Returns the multiplication of a vector transpose and a matrix (v^T * m). |
| 528 |
* @return the multiplication of a vector transpose and a matrix |
| 529 |
* @param v the vector |
| 530 |
* @param m the matrix |
| 531 |
*/ |
| 532 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 533 |
inline Vector<Real, Col> operator *(const Vector<Real, Row>& v, const RectMatrix<Real, Row, Col>& m) { |
| 534 |
Vector<Real, Row> result; |
| 535 |
|
| 536 |
for (unsigned int i = 0; i < Col ; i++) |
| 537 |
for (unsigned int j = 0; j < Row ; j++) |
| 538 |
result[i] += v[j] * m(j, i); |
| 539 |
|
| 540 |
return result; |
| 541 |
} |
| 542 |
|
| 543 |
/** |
| 544 |
* Return the scalar division of matrix (m / s). |
| 545 |
* @return the scalar division of matrix |
| 546 |
* @param m the matrix |
| 547 |
* @param s the scalar |
| 548 |
*/ |
| 549 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 550 |
inline RectMatrix<Real, Row, Col> operator /(const RectMatrix<Real, Row, Col>& m, Real s) { |
| 551 |
RectMatrix<Real, Row, Col> result; |
| 552 |
|
| 553 |
result.div(s, m); |
| 554 |
|
| 555 |
return result; |
| 556 |
} |
| 557 |
|
| 558 |
|
| 559 |
/** |
| 560 |
* Returns the vector (cross) product of two matrices. This |
| 561 |
* operation is defined in: |
| 562 |
* |
| 563 |
* W. Smith, "Point Multipoles in the Ewald Summation (Revisited)," |
| 564 |
* CCP5 Newsletter No 46., pp. 18-30. |
| 565 |
* |
| 566 |
* Equation 21 defines: |
| 567 |
* \f[ |
| 568 |
* V_alpha = \sum_\beta \left[ A_{\alpha+1,\beta} * B_{\alpha+2,\beta} |
| 569 |
-A_{\alpha+2,\beta} * B_{\alpha+2,\beta} \right] |
| 570 |
* \f] |
| 571 |
* where \f[\alpha+1\f] and \f[\alpha+2\f] are regarded as cyclic permuations of the |
| 572 |
* matrix indices (i.e. for a 3x3 matrix, when \f[\alpha = 2\f], \f[\alpha + 1 = 3 \f], |
| 573 |
* and \f[\alpha + 2 = 1 \f] ). |
| 574 |
* |
| 575 |
* @param t1 first matrix |
| 576 |
* @param t2 second matrix |
| 577 |
* @return the cross product (vector product) of t1 and t2 |
| 578 |
*/ |
| 579 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 580 |
inline Vector<Real, Row> cross( const RectMatrix<Real, Row, Col>& t1, const RectMatrix<Real, Row, Col>& t2 ) { |
| 581 |
Vector<Real, Row> result; |
| 582 |
unsigned int i1; |
| 583 |
unsigned int i2; |
| 584 |
|
| 585 |
for (unsigned int i = 0; i < Row; i++) { |
| 586 |
//for (unsigned int i = 0; i < Col; i++) { |
| 587 |
i1 = (i+1)%Row; |
| 588 |
i2 = (i+2)%Row; |
| 589 |
//i1 = (i+1)%Col; |
| 590 |
//i2 = (i+2)%Col; |
| 591 |
for (unsigned int j =0; j < Col; j++) { |
| 592 |
//for (unsigned int j =0; j < Row; j++) { |
| 593 |
result[i] = t1(i1,j) * t2(i2,j) - t1(i2,j) * t2(i1,j); |
| 594 |
//result[i] = t1(j,i1) * t2(j,i2) - t1(j,i2) * t2(j,i1); |
| 595 |
} |
| 596 |
} |
| 597 |
|
| 598 |
return result; |
| 599 |
} |
| 600 |
|
| 601 |
|
| 602 |
/** |
| 603 |
* Write to an output stream |
| 604 |
*/ |
| 605 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 606 |
std::ostream &operator<< ( std::ostream& o, const RectMatrix<Real, Row, Col>& m) { |
| 607 |
for (unsigned int i = 0; i < Row ; i++) { |
| 608 |
o << "("; |
| 609 |
for (unsigned int j = 0; j < Col ; j++) { |
| 610 |
o << m(i, j); |
| 611 |
if (j != Col -1) |
| 612 |
o << "\t"; |
| 613 |
} |
| 614 |
o << ")" << std::endl; |
| 615 |
} |
| 616 |
return o; |
| 617 |
} |
| 618 |
} |
| 619 |
#endif //MATH_RECTMATRIX_HPP |
