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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, 234107 (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 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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#include "utils/NumericConstant.hpp" |
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|
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namespace OpenMD { |
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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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* \tparam Real the element type |
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* \tparam 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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typedef Real ElemType; |
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typedef Real* ElemPoinerType; |
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|
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/** default constructor */ |
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SquareMatrix() { |
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for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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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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SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){ |
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} |
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|
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/** Constructs and initializes from an array */ |
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SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){ |
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} |
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|
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|
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/** copy constructor */ |
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SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
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} |
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|
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/** 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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/** |
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* Retunrs the inversion of this matrix. |
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* @todo need implementation |
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*/ |
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SquareMatrix<Real, Dim> inverse() { |
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SquareMatrix<Real, Dim> result; |
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|
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return result; |
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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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* @todo need implementation |
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*/ |
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Real determinant() const { |
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Real det; |
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return det; |
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} |
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|
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/** Returns the trace of this matrix. */ |
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Real trace() const { |
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Real tmp = 0; |
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|
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for (unsigned int i = 0; i < Dim ; i++) |
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tmp += this->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(this->data_[i][j] - this->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 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(this->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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/** |
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* Returns a column vector that contains the elements from the |
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* diagonal of m in the order R(0) = m(0,0), R(1) = m(1,1), and so |
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* on. |
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*/ |
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Vector<Real, Dim> diagonals() const { |
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Vector<Real, Dim> result; |
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for (unsigned int i = 0; i < Dim; i++) { |
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result(i) = this->data_[i][i]; |
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} |
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return result; |
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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(this->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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/** Return the transpose of this matrix */ |
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SquareMatrix<Real, Dim> transpose() const{ |
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SquareMatrix<Real, Dim> result; |
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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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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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/** @todo need implementation */ |
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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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* 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 symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
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* overwritten |
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* @param d will contain the eigenvalues of the matrix On return of this function |
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* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
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* normalized and mutually orthogonal. |
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*/ |
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|
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static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d, |
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SquareMatrix<Real, Dim>& v); |
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};//end SquareMatrix |
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|
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|
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/*========================================================================= |
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|
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Program: Visualization Toolkit |
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Module: $RCSfile: SquareMatrix.hpp,v $ |
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|
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Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen |
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All rights reserved. |
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See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
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|
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This software is distributed WITHOUT ANY WARRANTY; without even |
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
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PURPOSE. See the above copyright notice for more information. |
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|
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=========================================================================*/ |
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|
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#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \ |
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a(k, l)=h+s*(g-h*tau) |
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|
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#define VTK_MAX_ROTATIONS 20 |
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|
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// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn |
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// real symmetric matrix. Square nxn matrix a; size of matrix in n; |
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// output eigenvalues in w; and output eigenvectors in v. Resulting |
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// eigenvalues/vectors are sorted in decreasing order; eigenvectors are |
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// normalized. |
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template<typename Real, int Dim> |
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int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, 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, numPos; |
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Real tresh, theta, tau, t, sm, s, h, g, c, tmp; |
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Real bspace[4], zspace[4]; |
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Real *b = bspace; |
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Real *z = zspace; |
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|
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// only allocate memory if the matrix is large |
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if (n > 4) { |
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b = new Real[n]; |
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z = new Real[n]; |
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} |
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|
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// initialize |
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for (ip=0; ip<n; ip++) { |
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for (iq=0; iq<n; iq++) { |
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v(ip, iq) = 0.0; |
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} |
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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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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<VTK_MAX_ROTATIONS; i++) { |
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sm = 0.0; |
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for (ip=0; ip<n-1; ip++) { |
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for (iq=ip+1; iq<n; iq++) { |
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sm += fabs(a(ip, iq)); |
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} |
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} |
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if (sm == 0.0) { |
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break; |
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} |
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|
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if (i < 3) { // first 3 sweeps |
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tresh = 0.2*sm/(n*n); |
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} else { |
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tresh = 0.0; |
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} |
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|
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for (ip=0; ip<n-1; ip++) { |
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for (iq=ip+1; iq<n; iq++) { |
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g = 100.0*fabs(a(ip, iq)); |
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|
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// after 4 sweeps |
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if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
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&& (fabs(w[iq])+g) == fabs(w[iq])) { |
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a(ip, iq) = 0.0; |
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} else if (fabs(a(ip, iq)) > tresh) { |
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h = w[iq] - w[ip]; |
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if ( (fabs(h)+g) == fabs(h)) { |
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t = (a(ip, iq)) / h; |
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} else { |
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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) { |
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t = -t; |
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} |
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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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|
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// ip already shifted left by 1 unit |
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for (j = 0;j <= ip-1;j++) { |
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VTK_ROTATE(a,j,ip,j,iq); |
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} |
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// ip and iq already shifted left by 1 unit |
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for (j = ip+1;j <= iq-1;j++) { |
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VTK_ROTATE(a,ip,j,j,iq); |
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} |
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// iq already shifted left by 1 unit |
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for (j=iq+1; j<n; j++) { |
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VTK_ROTATE(a,ip,j,iq,j); |
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} |
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for (j=0; j<n; j++) { |
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VTK_ROTATE(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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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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//// this is NEVER called |
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if ( i >= VTK_MAX_ROTATIONS ) { |
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std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; |
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if (n > 4) { |
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delete[] b; |
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delete[] z; |
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} |
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return 0; |
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} |
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|
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// sort eigenfunctions these changes do not affect accuracy |
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for (j=0; j<n-1; j++) { // boundary incorrect |
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k = j; |
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tmp = w[k]; |
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for (i=j+1; i<n; i++) { // boundary incorrect, shifted already |
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if (w[i] >= tmp) { // why exchage if same? |
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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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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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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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// insure eigenvector consistency (i.e., Jacobi can compute vectors that |
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// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can |
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// reek havoc in hyperstreamline/other stuff. We will select the most |
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// positive eigenvector. |
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int ceil_half_n = (n >> 1) + (n & 1); |
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for (j=0; j<n; j++) { |
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for (numPos=0, i=0; i<n; i++) { |
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if ( v(i, j) >= 0.0 ) { |
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numPos++; |
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} |
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} |
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// if ( numPos < ceil(RealType(n)/RealType(2.0)) ) |
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if ( numPos < ceil_half_n) { |
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for (i=0; i<n; i++) { |
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v(i, j) *= -1.0; |
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} |
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} |
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} |
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|
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if (n > 4) { |
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delete [] b; |
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delete [] z; |
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} |
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return 1; |
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} |
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|
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|
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typedef SquareMatrix<RealType, 6> Mat6x6d; |
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} |
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#endif //MATH_SQUAREMATRIX_HPP |
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|
