tridiagonal_matrix.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2005 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, 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.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------

#ifndef dealii__tridiagonal_matrix_h
#define dealii__tridiagonal_matrix_h

#include <deal.II/base/config.h>
#include <deal.II/base/subscriptor.h>
#include <deal.II/lac/lapack_support.h>

#include <vector>
#include <iomanip>

DEAL_II_NAMESPACE_OPEN

// forward declarations
template<typename number> class Vector;


template<typename number>
class TridiagonalMatrix
{
public:


  typedef types::global_dof_index size_type;

  TridiagonalMatrix(size_type    n = 0,
                    bool symmetric = false);

  void reinit(size_type n,
              bool symmetric = false);




  size_type m () const;

  size_type n () const;

  bool all_zero () const;





  number operator()(size_type i, size_type j) const;

  number &operator()(size_type i, size_type j);



  void vmult (Vector<number>       &w,
              const Vector<number> &v,
              const bool            adding=false) const;

  void vmult_add (Vector<number>       &w,
                  const Vector<number> &v) const;

  void Tvmult (Vector<number>       &w,
               const Vector<number> &v,
               const bool            adding=false) const;

  void Tvmult_add (Vector<number>       &w,
                   const Vector<number> &v) const;

  number matrix_scalar_product (const Vector<number> &u,
                                const Vector<number> &v) const;

  number matrix_norm_square (const Vector<number> &v) const;



  number l1_norm () const;

  number linfty_norm () const;

  number frobenius_norm () const;

  number relative_symmetry_norm2 () const;


  void compute_eigenvalues();
  number eigenvalue(const size_type i) const;


  template <class OutputStream>
  void print(OutputStream &s,
             const unsigned int  width=5,
             const unsigned int  precision=2) const;

  std::size_t memory_consumption () const;

private:
  std::vector<number> diagonal;
  std::vector<number> left;
  std::vector<number> right;

  bool is_symmetric;

  LAPACKSupport::State state;
};

//---------------------------------------------------------------------------
#ifndef DOXYGEN

template<typename number>
types::global_dof_index
TridiagonalMatrix<number>::m() const
{
  return diagonal.size();
}



template<typename number>
types::global_dof_index
TridiagonalMatrix<number>::n() const
{
  return diagonal.size();
}


template<typename number>
inline
number
TridiagonalMatrix<number>::operator()(size_type i, size_type j) const
{
  Assert(i<n(), ExcIndexRange(i,0,n()));
  Assert(j<n(), ExcIndexRange(j,0,n()));
  Assert (i<=j+1, ExcIndexRange(i,j-1,j+2));
  Assert (j<=i+1, ExcIndexRange(j,i-1,i+2));

  if (j==i)
    return diagonal[i];
  if (j==i-1)
    {
      if (is_symmetric)
        return right[i-1];
      else
        return left[i];
    }

  if (j==i+1)
    return right[i];

  Assert (false, ExcInternalError());
  return 0;
}


template<typename number>
inline
number &
TridiagonalMatrix<number>::operator()(size_type i, size_type j)
{
  Assert(i<n(), ExcIndexRange(i,0,n()));
  Assert(j<n(), ExcIndexRange(j,0,n()));
  Assert (i<=j+1, ExcIndexRange(i,j-1,j+2));
  Assert (j<=i+1, ExcIndexRange(j,i-1,i+2));

  if (j==i)
    return diagonal[i];
  if (j==i-1)
    {
      if (is_symmetric)
        return right[i-1];
      else
        return left[i];
    }

  if (j==i+1)
    return right[i];

  Assert (false, ExcInternalError());
  return diagonal[0];
}


template <typename number>
template <class OutputStream>
void
TridiagonalMatrix<number>::print (
  OutputStream &s,
  const unsigned int width,
  const unsigned int) const
{
  for (size_type i=0; i<n(); ++i)
    {
      if (i>0)
        s << std::setw(width) << (*this)(i,i-1);
      else
        s << std::setw(width) << "";

      s << ' ' << (*this)(i,i) << ' ';

      if (i<n()-1)
        s << std::setw(width) << (*this)(i,i+1);

      s << std::endl;
    }
}


#endif // DOXYGEN

DEAL_II_NAMESPACE_CLOSE

#endif