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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. Acknowledgement of the program authors must be made in any | 
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 *    publication of scientific results based in part on use of the | 
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 *    program.  An acceptable form of acknowledgement is citation of | 
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 *    the article in which the program was described (Matthew | 
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 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher | 
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 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented | 
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 *    Parallel Simulation Engine for Molecular Dynamics," | 
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 *    J. Comput. Chem. 26, pp. 252-271 (2005)) | 
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 * | 
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 * 2. Redistributions of source code must retain the above copyright | 
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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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 * 3. Redistributions in binary form must reproduce the above copyright | 
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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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 * 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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#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 oopse { | 
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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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   * @template Real the element type | 
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   * @template Dim the dimension of the square matrix | 
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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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      Real det; | 
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      return det; | 
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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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    Real trace() const { | 
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      Real tmp = 0; | 
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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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    /** | 
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     * Returns the tensor contraction (double dot product) of two rank 2 | 
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     * tensors (or Matrices) | 
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     * @param t1 first tensor | 
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     * @param t2 second tensor | 
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     * @return the tensor contraction (double dot product) of t1 and t2 | 
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     */ | 
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    Real doubleDot( const SquareMatrix<Real, Dim>& t1, const SquareMatrix<Real, Dim>& t2 ) { | 
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      Real tmp; | 
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      tmp = 0; | 
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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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          tmp += t1[i][j] * t2[i][j]; | 
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       | 
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      return tmp; | 
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    } | 
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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]) > oopse::epsilon)  | 
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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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    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]) > oopse::epsilon)  | 
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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) > oopse::epsilon) | 
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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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     * @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 w will contain the eigenvalues of the matrix On return of this function | 
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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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    //// 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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          numPos++; | 
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  | 
        } | 
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  | 
      } | 
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      //    if ( numPos < ceil(double(n)/double(2.0)) ) | 
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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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< | 
  typedef SquareMatrix<double, 6> Mat6x6d; | 
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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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