tridiagonal_matrix.cc

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//
// Copyright (C) 2005 - 2020 by the deal.II authors
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#include <deal.II/lac/lapack_templates.h>
#include <deal.II/lac/tridiagonal_matrix.h>
#include <deal.II/lac/vector.h>

#include <complex>

DEAL_II_NAMESPACE_OPEN

using namespace LAPACKSupport;

template <typename number>
TridiagonalMatrix<number>::TridiagonalMatrix(size_type size, bool symmetric)
  : diagonal(size, 0.)
  , left((symmetric ? 0 : size), 0.)
  , right(size, 0.)
  , is_symmetric(symmetric)
  , state(matrix)
{}



template <typename number>
void
TridiagonalMatrix<number>::reinit(size_type size, bool symmetric)
{
  is_symmetric = symmetric;
  diagonal.resize(size);
  right.resize(size);
  left.resize(symmetric ? 0 : size);
  state = matrix;
}



template <typename number>
bool
TridiagonalMatrix<number>::all_zero() const
{
  Assert(state == matrix, ExcState(state));

  typename std::vector<number>::const_iterator i;
  typename std::vector<number>::const_iterator e;

  e = diagonal.end();
  for (i = diagonal.begin(); i != e; ++i)
    if (std::abs(*i) != 0.)
      return false;

  e = left.end();
  for (i = left.begin(); i != e; ++i)
    if (std::abs(*i) != 0.)
      return false;

  e = right.end();
  for (i = right.begin(); i != e; ++i)
    if (std::abs(*i) != 0.)
      return false;
  return true;
}



template <typename number>
void
TridiagonalMatrix<number>::vmult(Vector<number> &      w,
                                 const Vector<number> &v,
                                 const bool            adding) const
{
  Assert(state == matrix, ExcState(state));

  Assert(w.size() == n(), ExcDimensionMismatch(w.size(), n()));
  Assert(v.size() == n(), ExcDimensionMismatch(v.size(), n()));

  if (n() == 0)
    return;

  // The actual loop skips the first
  // and last row
  const size_type e = n() - 1;
  // Let iterators point to the first
  // entry of each diagonal
  typename std::vector<number>::const_iterator d = diagonal.begin();
  typename std::vector<number>::const_iterator r = right.begin();
  // The left diagonal starts one
  // later or is equal to the right
  // one for symmetric storage
  typename std::vector<number>::const_iterator l = left.begin();
  if (is_symmetric)
    l = r;
  else
    ++l;

  if (adding)
    {
      // Treat first row separately
      w(0) += (*d) * v(0) + (*r) * v(1);
      ++d;
      ++r;
      // All rows with three entries
      for (size_type i = 1; i < e; ++i, ++d, ++r, ++l)
        w(i) += (*l) * v(i - 1) + (*d) * v(i) + (*r) * v(i + 1);
      // Last row is special again
      w(e) += (*l) * v(e - 1) + (*d) * v(e);
    }
  else
    {
      w(0) = (*d) * v(0) + (*r) * v(1);
      ++d;
      ++r;
      for (size_type i = 1; i < e; ++i, ++d, ++r, ++l)
        w(i) = (*l) * v(i - 1) + (*d) * v(i) + (*r) * v(i + 1);
      w(e) = (*l) * v(e - 1) + (*d) * v(e);
    }
}


template <typename number>
void
TridiagonalMatrix<number>::vmult_add(Vector<number> &      w,
                                     const Vector<number> &v) const
{
  vmult(w, v, true);
}



template <typename number>
void
TridiagonalMatrix<number>::Tvmult(Vector<number> &      w,
                                  const Vector<number> &v,
                                  const bool            adding) const
{
  Assert(state == matrix, ExcState(state));

  Assert(w.size() == n(), ExcDimensionMismatch(w.size(), n()));
  Assert(v.size() == n(), ExcDimensionMismatch(v.size(), n()));

  if (n() == 0)
    return;

  const size_type                              e = n() - 1;
  typename std::vector<number>::const_iterator d = diagonal.begin();
  typename std::vector<number>::const_iterator r = right.begin();
  typename std::vector<number>::const_iterator l = left.begin();
  if (is_symmetric)
    l = r;
  else
    ++l;

  if (adding)
    {
      w(0) += (*d) * v(0) + (*l) * v(1);
      ++d;
      ++l;
      for (size_type i = 1; i < e; ++i, ++d, ++r, ++l)
        w(i) += (*l) * v(i + 1) + (*d) * v(i) + (*r) * v(i - 1);
      w(e) += (*d) * v(e) + (*r) * v(e - 1);
    }
  else
    {
      w(0) = (*d) * v(0) + (*l) * v(1);
      ++d;
      ++l;
      for (size_type i = 1; i < e; ++i, ++d, ++r, ++l)
        w(i) = (*l) * v(i + 1) + (*d) * v(i) + (*r) * v(i - 1);
      w(e) = (*d) * v(e) + (*r) * v(e - 1);
    }
}



template <typename number>
void
TridiagonalMatrix<number>::Tvmult_add(Vector<number> &      w,
                                      const Vector<number> &v) const
{
  Tvmult(w, v, true);
}



template <typename number>
number
TridiagonalMatrix<number>::matrix_scalar_product(const Vector<number> &w,
                                                 const Vector<number> &v) const
{
  Assert(state == matrix, ExcState(state));

  const size_type                              e = n() - 1;
  typename std::vector<number>::const_iterator d = diagonal.begin();
  typename std::vector<number>::const_iterator r = right.begin();
  typename std::vector<number>::const_iterator l = left.begin();
  if (is_symmetric)
    l = r;
  else
    ++l;

  number result = w(0) * ((*d) * v(0) + (*r) * v(1));
  ++d;
  ++r;
  for (size_type i = 1; i < e; ++i, ++d, ++r, ++l)
    result += w(i) * ((*l) * v(i - 1) + (*d) * v(i) + (*r) * v(i + 1));
  result += w(e) * ((*l) * v(e - 1) + (*d) * v(e));
  return result;
}



template <typename number>
number
TridiagonalMatrix<number>::matrix_norm_square(const Vector<number> &v) const
{
  return matrix_scalar_product(v, v);
}



template <typename number>
void
TridiagonalMatrix<number>::compute_eigenvalues()
{
#ifdef DEAL_II_WITH_LAPACK
  Assert(state == matrix, ExcState(state));
  Assert(is_symmetric, ExcNotImplemented());

  const types::blas_int nn = n();
  types::blas_int       info;
  stev(&N,
       &nn,
       diagonal.data(),
       right.data(),
       static_cast<number *>(nullptr),
       &one,
       static_cast<number *>(nullptr),
       &info);
  Assert(info == 0, ExcInternalError());

  state = LAPACKSupport::eigenvalues;
#else
  AssertThrow(false, ExcNeedsLAPACK());
#endif
}



template <typename number>
number
TridiagonalMatrix<number>::eigenvalue(const size_type i) const
{
  Assert(state == LAPACKSupport::eigenvalues, ExcState(state));
  AssertIndexRange(i, n());
  return diagonal[i];
}


/*
template <typename number>
TridiagonalMatrix<number>::
{
}


*/

template class TridiagonalMatrix<float>;
template class TridiagonalMatrix<double>;
#ifdef DEAL_II_WITH_COMPLEX_VALUES
template class TridiagonalMatrix<std::complex<float>>;
template class TridiagonalMatrix<std::complex<double>>;
#endif

DEAL_II_NAMESPACE_CLOSE