text: /*
   * This file is part of the GROMACS molecular simulation package.
   *
   * Copyright (c) 2019,2020, by the GROMACS development team, led by
   * Mark Abraham, David van der Spoel, Berk Hess, and Erik Lindahl,
   * and including many others, as listed in the AUTHORS file in the
   * top-level source directory and at http://www.gromacs.org.
   *
   * GROMACS is free software; you can redistribute it and/or
   * modify it under the terms of the GNU Lesser General Public License
   * as published by the Free Software Foundation; either version 2.1
   * of the License, or (at your option) any later version.
   *
   * GROMACS is distributed in the hope that it will be useful,
   * but WITHOUT ANY WARRANTY; without even the implied warranty of
   * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   * Lesser General Public License for more details.
   *
   * You should have received a copy of the GNU Lesser General Public
   * License along with GROMACS; if not, see
   * http://www.gnu.org/licenses, or write to the Free Software Foundation,
   * Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA.
   *
   * If you want to redistribute modifications to GROMACS, please
   * consider that scientific software is very special. Version
   * control is crucial - bugs must be traceable. We will be happy to
   * consider code for inclusion in the official distribution, but
   * derived work must not be called official GROMACS. Details are found
   * in the README & COPYING files - if they are missing, get the
   * official version at http://www.gromacs.org.
   *
   * To help us fund GROMACS development, we humbly ask that you cite
   * the research papers on the package. Check out http://www.gromacs.org.
   */
  /*! \libinternal
   * \file
   * \brief Declares special case of 3x3 matrix frequently used, and associated functions.
   *
   * \author Christian Blau <cblau@gwdg.de>
   * \ingroup module_math
   */
  
  #ifndef GMX_MATH_MATRIX_H_
  #define GMX_MATH_MATRIX_H_
  
  #include <array>
  
  #include "gromacs/math/multidimarray.h"
  #include "gromacs/math/utilities.h"
  #include "gromacs/math/vec.h"
  #include "gromacs/utility/real.h"
  
  namespace gmx
  {
  
  /*! \brief Three-by-three matrix of ElementType.
   * \tparam ElementType type of element to be stored in matrix
   */
  template<class ElementType>
  using BasicMatrix3x3 = MultiDimArray<std::array<ElementType, 3 * 3>, extents<3, 3>>;
  
  /*! \brief Three-by-three real number matrix.
   * \note will replace the C-style real[3][3] "matrix"
   */
  using Matrix3x3 = BasicMatrix3x3<real>;
  //! Convenience alias for a matrix view
  using Matrix3x3Span = Matrix3x3::view_type;
  //! Convenience alias for a const matrix view
  using Matrix3x3ConstSpan = Matrix3x3::const_view_type;
  
  //! Determinant of a 3x3 matrix
  constexpr real determinant(Matrix3x3ConstSpan matrix)
  {
      return (matrix(0, 0) * (matrix(1, 1) * matrix(2, 2) - matrix(2, 1) * matrix(1, 2))
              - matrix(1, 0) * (matrix(0, 1) * matrix(2, 2) - matrix(2, 1) * matrix(0, 2))
              + matrix(2, 0) * (matrix(0, 1) * matrix(1, 2) - matrix(1, 1) * matrix(0, 2)));
  }
  
  //! Calculates the trace of a 3x3 matrix view
  constexpr real trace(Matrix3x3ConstSpan matrixView)
  {
      return matrixView(0, 0) + matrixView(1, 1) + matrixView(2, 2);
  }
  
  /*! \brief Create an identity matrix of ElementType with N * M elements.
   *
   * \tparam ElementType type of matrix elements
   * \tparam N number of rows
   * \tparam M number of columns, defaults to number of rows if not set
   *
   * \returns a matrix with values one where row equals column index and null
   *          where row does not equal column index
   */
  template<typename ElementType, int N, int M = N>
  MultiDimArray<std::array<ElementType, N * M>, extents<N, M>> identityMatrix()
  {
      std::array<ElementType, N * M>                               matrixEntries{};
      MultiDimArray<std::array<ElementType, N * M>, extents<N, M>> idMatrix(matrixEntries);
      for (int i = 0; i < std::min(N, M); i++)
      {
          idMatrix(i, i) = 1;
      }
      return idMatrix;
  }
  
  //! Calculate the transpose of a 3x3 matrix, from its view
  Matrix3x3 transpose(Matrix3x3ConstSpan matrixView);
  
  //! Multiply matrix with vector.
  void matrixVectorMultiply(Matrix3x3ConstSpan matrix, RVec* v);
  
  //! Create new matrix type from legacy type.
  static inline Matrix3x3 createMatrix3x3FromLegacyMatrix(const matrix legacyMatrix)
  {
      GMX_RELEASE_ASSERT(legacyMatrix, "Need valid legacy matrix");
      Matrix3x3 newMatrix;
      for (int i = 0; i < DIM; i++)
      {
          for (int j = 0; j < DIM; j++)
          {
              newMatrix(i, j) = legacyMatrix[i][j];
          }
      }
      return newMatrix;
  }
  
  //! Fill legacy matrix from new matrix type.
  static inline void fillLegacyMatrix(Matrix3x3ConstSpan newMatrix, matrix legacyMatrix)
  {
      GMX_RELEASE_ASSERT(legacyMatrix, "Need valid legacy matrix");
      for (int i = 0; i < DIM; i++)
      {
          for (int j = 0; j < DIM; j++)
          {
              legacyMatrix[i][j] = newMatrix(i, j);
          }
      }
  }
  
  } // namespace gmx
  
  #endif
  