dynamic_sparsity_pattern.cc

// ---------------------------------------------------------------------
//
// Copyright (C) 2008 - 2017 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.
//
// ---------------------------------------------------------------------

#include <deal.II/lac/dynamic_sparsity_pattern.h>
#include <deal.II/lac/sparsity_pattern.h>
#include <deal.II/base/memory_consumption.h>

#include <algorithm>
#include <cmath>
#include <numeric>
#include <functional>

DEAL_II_NAMESPACE_OPEN



template <typename ForwardIterator>
void
DynamicSparsityPattern::Line::add_entries (ForwardIterator begin,
                                           ForwardIterator end,
                                           const bool      indices_are_sorted)
{
  const int n_elements = end - begin;
  if (n_elements <= 0)
    return;

  const size_type stop_size = entries.size() + n_elements;

  if (indices_are_sorted == true && n_elements > 3)
    {
      // in debug mode, check whether the
      // indices really are sorted.
#ifdef DEBUG
      {
        ForwardIterator test = begin, test1 = begin;
        ++test1;
        for ( ; test1 != end; ++test, ++test1)
          Assert (*test1 > *test, ExcInternalError());
      }
#endif

      if (entries.size() == 0 || entries.back() < *begin)
        {
          entries.insert(entries.end(), begin, end);
          return;
        }

      // find a possible insertion point for
      // the first entry. check whether the
      // first entry is a duplicate before
      // actually doing something.
      ForwardIterator my_it = begin;
      size_type col = *my_it;
      std::vector<size_type>::iterator it =
        Utilities::lower_bound(entries.begin(), entries.end(), col);
      while (*it == col)
        {
          ++my_it;
          if (my_it == end)
            break;
          col = *my_it;
          // check the very next entry in the
          // current array
          ++it;
          if (it == entries.end())
            break;
          if (*it > col)
            break;
          if (*it == col)
            continue;
          // ok, it wasn't the very next one, do a
          // binary search to find the insert point
          it = Utilities::lower_bound(it, entries.end(), col);
          if (it == entries.end())
            break;
        }
      // all input entries were duplicates.
      if (my_it == end)
        return;

      // resize vector by just inserting the
      // list
      const size_type pos1 = it - entries.begin();
      Assert (pos1 <= entries.size(), ExcInternalError());
      entries.insert (it, my_it, end);
      it = entries.begin() + pos1;
      Assert (entries.size() >= (size_type)(it-entries.begin()), ExcInternalError());

      // now merge the two lists.
      std::vector<size_type>::iterator it2 = it + (end-my_it);

      // as long as there are indices both in
      // the end of the entries list and in the
      // input list
      while (my_it != end && it2 != entries.end())
        {
          if (*my_it < *it2)
            *it++ = *my_it++;
          else if (*my_it == *it2)
            {
              *it++ = *it2++;
              ++my_it;
            }
          else
            *it++ = *it2++;
        }
      // in case there are indices left in the
      // input list
      while (my_it != end)
        *it++ = *my_it++;

      // in case there are indices left in the
      // end of entries
      while (it2 != entries.end())
        *it++ = *it2++;

      // resize and return
      const size_type new_size = it - entries.begin();
      Assert (new_size <= stop_size, ExcInternalError());
      entries.resize (new_size);
      return;
    }

  // unsorted case or case with too few
  // elements
  ForwardIterator my_it = begin;

  // If necessary, increase the size of the
  // array.
  if (stop_size > entries.capacity())
    entries.reserve (stop_size);

  size_type col = *my_it;
  std::vector<size_type>::iterator it, it2;
  // insert the first element as for one
  // entry only first check the last
  // element (or if line is still empty)
  if ( (entries.size()==0) || ( entries.back() < col) )
    {
      entries.push_back(col);
      it = entries.end()-1;
    }
  else
    {
      // do a binary search to find the place
      // where to insert:
      it2 = Utilities::lower_bound(entries.begin(), entries.end(), col);

      // If this entry is a duplicate, continue
      // immediately Insert at the right place
      // in the vector. Vector grows
      // automatically to fit elements. Always
      // doubles its size.
      if (*it2 != col)
        it = entries.insert(it2, col);
      else
        it = it2;
    }

  ++my_it;
  // Now try to be smart and insert with
  // bias in the direction we are
  // walking. This has the advantage that
  // for sorted lists, we always search in
  // the right direction, what should
  // decrease the work needed in here.
  for ( ; my_it != end; ++my_it)
    {
      col = *my_it;
      // need a special insertion command when
      // we're at the end of the list
      if (col > entries.back())
        {
          entries.push_back(col);
          it = entries.end()-1;
        }
      // search to the right (preferred search
      // direction)
      else if (col > *it)
        {
          it2 = Utilities::lower_bound(it++, entries.end(), col);
          if (*it2 != col)
            it = entries.insert(it2, col);
        }
      // search to the left
      else if (col < *it)
        {
          it2 = Utilities::lower_bound(entries.begin(), it, col);
          if (*it2 != col)
            it = entries.insert(it2, col);
        }
      // if we're neither larger nor smaller,
      // then this was a duplicate and we can
      // just continue.
    }
}


DynamicSparsityPattern::size_type
DynamicSparsityPattern::Line::memory_consumption () const
{
  return entries.capacity()*sizeof(size_type)+sizeof(Line);
}


DynamicSparsityPattern::DynamicSparsityPattern ()
  :
  have_entries (false),
  rows (0),
  cols (0),
  rowset (0)
{}



DynamicSparsityPattern::
DynamicSparsityPattern (const DynamicSparsityPattern &s)
  :
  Subscriptor(),
  have_entries (false),
  rows (0),
  cols (0),
  rowset (0)
{
  (void)s;
  Assert (s.rows==0 && s.cols==0,
          ExcMessage("This constructor can only be called if the provided argument "
                     "is the sparsity pattern for an empty matrix. This constructor can "
                     "not be used to copy-construct a non-empty sparsity pattern."));
}



DynamicSparsityPattern::DynamicSparsityPattern (const size_type m,
                                                const size_type n,
                                                const IndexSet &rowset_
                                               )
  :
  have_entries (false),
  rows (0),
  cols (0),
  rowset (0)
{
  reinit (m,n, rowset_);
}


DynamicSparsityPattern::DynamicSparsityPattern (const IndexSet &rowset_)
  :
  have_entries (false),
  rows(0),
  cols(0),
  rowset(0)
{
  reinit (rowset_.size(), rowset_.size(), rowset_);
}


DynamicSparsityPattern::DynamicSparsityPattern (const size_type n)
  :
  have_entries (false),
  rows(0),
  cols(0),
  rowset(0)
{
  reinit (n,n);
}



DynamicSparsityPattern &
DynamicSparsityPattern::operator = (const DynamicSparsityPattern &s)
{
  (void)s;
  Assert (s.rows==0 && s.cols==0,
          ExcMessage("This operator can only be called if the provided argument "
                     "is the sparsity pattern for an empty matrix. This operator can "
                     "not be used to copy a non-empty sparsity pattern."));

  Assert (rows==0 && cols==0,
          ExcMessage("This operator can only be called if the current object is"
                     "empty."));

  return *this;
}



void
DynamicSparsityPattern::reinit (const size_type m,
                                const size_type n,
                                const IndexSet &rowset_)
{
  have_entries = false;
  rows = m;
  cols = n;
  rowset=rowset_;

  Assert(rowset.size()==0 || rowset.size() == m,
         ExcMessage("The IndexSet argument to this function needs to either "
                    "be empty (indicating the complete set of rows), or have size "
                    "equal to the desired number of rows as specified by the "
                    "first argument to this function. (Of course, the number "
                    "of indices in this IndexSet may be less than the number "
                    "of rows, but the *size* of the IndexSet must be equal.)"));

  std::vector<Line> new_lines (rowset.size()==0 ? rows : rowset.n_elements());
  lines.swap (new_lines);
}



void
DynamicSparsityPattern::compress ()
{}



bool
DynamicSparsityPattern::empty () const
{
  return ((rows==0) && (cols==0));
}



DynamicSparsityPattern::size_type
DynamicSparsityPattern::max_entries_per_row () const
{
  if (!have_entries)
    return 0;

  size_type m = 0;
  for (size_type i=0; i<lines.size(); ++i)
    {
      m = std::max (m, static_cast<size_type>(lines[i].entries.size()));
    }

  return m;
}



bool
DynamicSparsityPattern::exists (const size_type i,
                                const size_type j) const
{
  Assert (i<rows, ExcIndexRange(i, 0, rows));
  Assert (j<cols, ExcIndexRange(j, 0, cols));
  Assert( rowset.size()==0 || rowset.is_element(i), ExcInternalError());

  if (!have_entries)
    return false;

  const size_type rowindex =
    rowset.size()==0 ? i : rowset.index_within_set(i);

  return std::binary_search (lines[rowindex].entries.begin(),
                             lines[rowindex].entries.end(),
                             j);
}



void
DynamicSparsityPattern::symmetrize ()
{
  Assert (rows==cols, ExcNotQuadratic());

  // loop over all elements presently
  // in the sparsity pattern and add
  // the transpose element. note:
  //
  // 1. that the sparsity pattern
  // changes which we work on, but
  // not the present row
  //
  // 2. that the @p{add} function can
  // be called on elements that
  // already exist without any harm
  for (size_type row=0; row<lines.size(); ++row)
    {
      const size_type rowindex =
        rowset.size()==0 ? row : rowset.nth_index_in_set(row);

      for (std::vector<size_type>::const_iterator
           j=lines[row].entries.begin();
           j != lines[row].entries.end();
           ++j)
        // add the transpose entry if
        // this is not the diagonal
        if (rowindex != *j)
          add (*j, rowindex);
    }
}



template <typename SparsityPatternTypeLeft, typename SparsityPatternTypeRight>
void
DynamicSparsityPattern::compute_mmult_pattern (
  const SparsityPatternTypeLeft &left,
  const SparsityPatternTypeRight &right)
{
  Assert (left.n_cols() == right.n_rows(),
          ExcDimensionMismatch(left.n_cols(), right.n_rows()));

  this->reinit(left.n_rows(),right.n_cols());

  typename SparsityPatternTypeLeft::iterator
  it_left = left.begin(),
  end_left = left.end();
  for (; it_left!=end_left; ++it_left)
    {
      const unsigned int j = it_left->column();

      // We are sitting on entry (i,j) of the left sparsity pattern. We then need
      // to add all entries (i,k) to the final sparsity pattern where (j,k) exists
      // in the right sparsity pattern -- i.e., we need to iterate over row j.
      typename SparsityPatternTypeRight::iterator
      it_right = right.begin(j),
      end_right = right.end(j);
      for (; it_right!=end_right; ++it_right)
        this->add(it_left->row(),it_right->column());
    }
}



void
DynamicSparsityPattern::print (std::ostream &out) const
{
  for (size_type row=0; row<lines.size(); ++row)
    {
      out << '[' << (rowset.size()==0 ? row : rowset.nth_index_in_set(row));

      for (std::vector<size_type >::const_iterator
           j=lines[row].entries.begin();
           j != lines[row].entries.end(); ++j)
        out << ',' << *j;

      out << ']' << std::endl;
    }

  AssertThrow (out, ExcIO());
}



void
DynamicSparsityPattern::print_gnuplot (std::ostream &out) const
{
  for (size_type row=0; row<lines.size(); ++row)
    {
      const size_type rowindex =
        rowset.size()==0 ? row : rowset.nth_index_in_set(row);

      for (std::vector<size_type >::const_iterator
           j=lines[row].entries.begin();
           j != lines[row].entries.end(); ++j)
        // while matrix entries are usually
        // written (i,j), with i vertical and
        // j horizontal, gnuplot output is
        // x-y, that is we have to exchange
        // the order of output
        out << *j << " "
            << -static_cast<signed int>(rowindex)
            << std::endl;
    }


  AssertThrow (out, ExcIO());
}



DynamicSparsityPattern::size_type
DynamicSparsityPattern::bandwidth () const
{
  size_type b=0;
  for (size_type row=0; row<lines.size(); ++row)
    {
      const size_type rowindex =
        rowset.size()==0 ? row : rowset.nth_index_in_set(row);

      for (std::vector<size_type>::const_iterator
           j=lines[row].entries.begin();
           j != lines[row].entries.end(); ++j)
        if (static_cast<size_type>(std::abs(static_cast<int>(rowindex-*j))) > b)
          b = std::abs(static_cast<signed int>(rowindex-*j));
    }

  return b;
}



DynamicSparsityPattern::size_type
DynamicSparsityPattern::n_nonzero_elements () const
{
  if (!have_entries)
    return 0;

  size_type n=0;
  for (size_type i=0; i<lines.size(); ++i)
    {
      n += lines[i].entries.size();
    }

  return n;
}


DynamicSparsityPattern::size_type
DynamicSparsityPattern::memory_consumption () const
{
  size_type mem = sizeof(DynamicSparsityPattern)
                  + MemoryConsumption::memory_consumption(rowset)
                  - sizeof(rowset);

  for (size_type i=0; i<lines.size(); ++i)
    mem += MemoryConsumption::memory_consumption (lines[i]);

  return mem;
}


// explicit instantiations
template void DynamicSparsityPattern::Line::add_entries(size_type *,
                                                        size_type *,
                                                        const bool);
template void DynamicSparsityPattern::Line::add_entries(const size_type *,
                                                        const size_type *,
                                                        const bool);
#ifndef DEAL_II_VECTOR_ITERATOR_IS_POINTER
template void DynamicSparsityPattern::Line::
add_entries(std::vector<size_type>::iterator,
            std::vector<size_type>::iterator,
            const bool);
#endif

template void DynamicSparsityPattern::compute_mmult_pattern(
  const DynamicSparsityPattern &,
  const DynamicSparsityPattern &);
template void DynamicSparsityPattern::compute_mmult_pattern(
  const DynamicSparsityPattern &,
  const SparsityPattern &);
template void DynamicSparsityPattern::compute_mmult_pattern(
  const SparsityPattern &,
  const DynamicSparsityPattern &);
template void DynamicSparsityPattern::compute_mmult_pattern(
  const SparsityPattern &,
  const SparsityPattern &);

DEAL_II_NAMESPACE_CLOSE