math_symmetric_matrix.h

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/*
 * Copyright (c) 2013-2015:  G-CSC, Goethe University Frankfurt
 * Author: Christian Wehner
 * 
 * This file is part of UG4.
 * 
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 * 
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 * 
 * This program 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.
 */
 
#ifndef SYM_MATRIX_H_
#define SYM_MATRIX_H_
 
#include <cstddef>
#include <ostream>
#include <iomanip>
#include "../../types.h"
#include "math_vector.h"
#include "common/assert.h"
 
namespace ug
{
 
//template <std::size_t N, std::size_t M, typename T = number> class MathSymmetricMatrix;
 
template <std::size_t N, typename T = number>
class MathSymmetricMatrix
{
  public:
    typedef T value_type;
    typedef std::size_t size_type;
    static const std::size_t RowSize = N;
    static const std::size_t ColSize = N;
 
  public:
    MathSymmetricMatrix() {}
    MathSymmetricMatrix(const MathSymmetricMatrix& v) {assign(v);}
    
    MathSymmetricMatrix& operator=  (const MathSymmetricMatrix& v)
    {
      assign(v);
      return *this;
    }
 
    MathSymmetricMatrix& operator+= (const MathSymmetricMatrix& B)
    {
      for(std::size_t i = 0; i < m_size; ++i)
      {
        m_data[i] += B[i];
      }
      return *this;
    }
 
    MathSymmetricMatrix& operator-= (const MathSymmetricMatrix& B)
    {
      for(std::size_t i = 0; i < m_size; ++i)
      {
        m_data[i] -= B[i];
      }
      return *this;
    }
 
    MathSymmetricMatrix& operator= (const value_type& val)
    {
      for(std::size_t i = 0; i < m_size; ++i)
      {
        m_data[i] = val;
      }
      return *this;
    }
 
    MathSymmetricMatrix& operator+= (const value_type& val)
    {
      for(std::size_t i = 0; i < m_size; ++i)
      {
        m_data[i] += val;
      }
      return *this;
    }
 
    MathSymmetricMatrix& operator-= (const value_type& val)
    {
      for(std::size_t i = 0; i < m_size; ++i)
      {
        m_data[i] -= val;
      }
      return *this;
    }
 
    MathSymmetricMatrix& operator/= (const value_type& val)
    {
      for(std::size_t i = 0; i < m_size; ++i)
      {
        m_data[i] /= val;
      }
      return *this;
    }
 
    MathSymmetricMatrix& operator*= (const value_type& val)
    {
      for(std::size_t i = 0; i < m_size; ++i)
      {
        m_data[i] *= val;
      }
      return *this;
    }
    
    value_type operator* (const MathSymmetricMatrix& v) const
    {
      value_type res = 0.0;
      for(std::size_t i = 0; i < N; ++i)
      {
        for(std::size_t j = 0; j < N; ++j)
        {
          res += this->entry(i,j) * v(i,j);
        }
      }
      return res;
    }
 
    inline std::size_t num_rows() const {return N;}
    inline std::size_t num_cols() const {return N;}
 
    inline value_type& entry(std::size_t row, std::size_t col)        
    {
      UG_ASSERT(row < N && col < N, "Accessing "<<N<<"x"<<N<<"Matrix at entry ("<<row<<","<<col<<")"); 
      if (row<col) return m_data[row * N - (row - 1) * row / 2 + col - row];
        else return m_data[col * N - (col - 1) * col / 2 + row - col];
    }
    
    inline const value_type& entry(std::size_t row, std::size_t col) const
    {
      UG_ASSERT(row < N && col < N, "Accessing "<<N<<"x"<<N<<"Matrix at entry ("<<row<<","<<col<<")"); 
      if (row<col) return m_data[row * N - (row - 1) * row / 2 + col - row];
        else return m_data[col * N - (col - 1) * col / 2 + row - col];
    }
 
    inline value_type& operator[](std::size_t index)        {UG_ASSERT(index < m_size, "Invalid index"); return m_data[index];}
    inline const value_type& operator[](std::size_t index) const  {UG_ASSERT(index < m_size, "Invalid index"); return m_data[index];}
 
    inline value_type& operator() (std::size_t row, std::size_t col)        
    {
      UG_ASSERT(row < N && col < N, "Accessing "<<N<<"x"<<N<<"Matrix at entry ("<<row<<","<<col<<")"); 
      if (row<col) return m_data[row * N - (row - 1) * row / 2 + col - row];
        else return m_data[col * N - (col - 1) * col / 2 + row - col];
    }
    
    inline const value_type& operator() (std::size_t row, std::size_t col) const
    {
      UG_ASSERT(row < N && col < N, "Accessing "<<N<<"x"<<N<<"Matrix at entry ("<<row<<","<<col<<")"); 
      if (row<col) return m_data[row * N - (row - 1) * row / 2 + col - row];
        else return m_data[col * N - (col - 1) * col / 2 + row - col];
    }
 
    // frobenius norm |A|_{F} = \sqrt{ 2 \sum_{i,j} A_{i,j} } 
    inline value_type fnorm(){
      value_type norm=m_data[0]*m_data[0];
      for (size_t i=1;i<m_size-1;i++){
        norm += 2*m_data[i]*m_data[i];
      }
      norm+=m_data[m_size-1]*m_data[m_size-1];
      if (N>2)
        for (size_t diag=1;diag<N-1;diag++)
          norm -= m_data[diag * N - (diag - 1) * diag / 2]*m_data[diag * N - (diag - 1) * diag / 2];
      return sqrt(2.0*norm);
    }
    
    // scale matrix by frobenius norm
    void scale_by_fnorm(){
      number norm=fnorm();
      for (size_t i=0;i<m_size;i++) m_data[i]*=norm;
    }
    
  protected:
    static const size_t m_size = (size_t)((N*N+N)/2);
    
    value_type m_data[m_size];
 
    inline void assign(const MathSymmetricMatrix& v)
    {
      for(std::size_t i = 0; i < m_size; ++i)
      {
        m_data[i] = v[i];
      }
    }
};
  
 
template <std::size_t N>
std::ostream& operator<< (std::ostream& outStream, const ug::MathSymmetricMatrix<N>& m)
{
  for(std::size_t i = 0; i < N; ++i)
  {
    for(std::size_t j = 0; j < N; ++j)
    {
      outStream << "[" << i << "][" << j << "]: " << std::scientific << std::setprecision(8) << std::setw(15) << m.entry(i, j) << std::endl;
    }
  }
  return outStream;
}
 
std::ostream& operator<< (std::ostream& outStream, const ug::MathSymmetricMatrix<2>& m);
std::ostream& operator<< (std::ostream& outStream, const ug::MathSymmetricMatrix<3>& m);
 
 
} //end of namespace: lgmath
 
 
#endif /* SYM_Matrix_H_ */