sparse.cpp 43.3 KB
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#define _CRT_SECURE_NO_WARNINGS
#include "inmost_sparse.h"
#include <fstream>
#include <sstream>

namespace INMOST
{
  namespace Sparse
  {
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    const std::string stubstring = "";
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    bool _hasRowEntryType = false;
    INMOST_MPI_Type RowEntryType = INMOST_MPI_DATATYPE_NULL;


    INMOST_MPI_Type GetRowEntryType() {return RowEntryType;}

    bool HaveRowEntryType() {return _hasRowEntryType;}

    void CreateRowEntryType()
    {
#if defined(USE_MPI)
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      if( !HaveRowEntryType() )
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      {
        int ierr;
        MPI_Datatype type[3] = { INMOST_MPI_DATA_ENUM_TYPE, INMOST_MPI_DATA_REAL_TYPE, MPI_UB};
		    int blocklen[3] = { 1, 1, 1 };
		    MPI_Aint disp[3];
		    disp[0] = offsetof(Sparse::Row::entry,first);
		    disp[1] = offsetof(Sparse::Row::entry,second);
		    disp[2] = sizeof(Sparse::Row::entry);
		    ierr = MPI_Type_create_struct(3, blocklen, disp, type, &RowEntryType);
		    if( ierr != MPI_SUCCESS )
		    {
			    std::cout << __FILE__ << ":" << __LINE__ << "problem in MPI_Type_create_struct" << std::endl;
		    }
		    ierr = MPI_Type_commit(&RowEntryType);
		    if( ierr != MPI_SUCCESS )
		    {
			    std::cout << __FILE__ << ":" << __LINE__ << "problem in MPI_Type_commit" << std::endl;
		    }
      }
#endif
      _hasRowEntryType = true;
    }

    void DestroyRowEntryType()
    {
#if defined(USE_MPI)
      if( HaveRowEntryType() )
      {
		    MPI_Type_free(&RowEntryType);
        RowEntryType = INMOST_MPI_DATATYPE_NULL;
      }
#endif
      _hasRowEntryType = false;
    }

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    RowMerger::RowMerger() : Sorted(true), Nonzeros(0) {}

    INMOST_DATA_REAL_TYPE & RowMerger::operator[] (INMOST_DATA_ENUM_TYPE pos)
    {
      if( LinkedList[pos+1].first != UNDEF ) return LinkedList[pos+1].second;
      else 
      {
        INMOST_DATA_ENUM_TYPE index = LinkedList.get_interval_beg(), next;
        if( Sorted )
        {
          next = index;
          while(next < pos+1)
          {
            index = next;
            next = LinkedList[index].first;
          }
          assert(index < pos+1);
          assert(pos+1 < next);
          ++Nonzeros;
          LinkedList[index].first = pos+1;
          LinkedList[pos+1].first = next;
          return LinkedList[pos+1].second;
        }
        else
        {
          INMOST_DATA_ENUM_TYPE index = LinkedList.get_interval_beg();
          ++Nonzeros;
          LinkedList[pos+1].first = LinkedList[index].first;
          LinkedList[index].first = pos+1;
          return LinkedList[pos+1].second;
        }
      }
    }

    INMOST_DATA_REAL_TYPE RowMerger::operator[] (INMOST_DATA_ENUM_TYPE pos) const
    {
      if( LinkedList[pos+1].first != UNDEF ) return LinkedList[pos+1].second;
      else throw -1;
    }

	  RowMerger::RowMerger(INMOST_DATA_ENUM_TYPE interval_begin, INMOST_DATA_ENUM_TYPE interval_end, bool Sorted) 
				  : Sorted(Sorted), Nonzeros(0), LinkedList(interval_begin,interval_end+1,Row::make_entry(UNDEF,0.0)) 
	  {
		  LinkedList.begin()->first = EOL;
	  }

	  void RowMerger::Resize(INMOST_DATA_ENUM_TYPE interval_begin, INMOST_DATA_ENUM_TYPE interval_end, bool _Sorted) 
	  {
		  LinkedList.set_interval_beg(interval_begin);
		  LinkedList.set_interval_end(interval_end+1);
		  std::fill(LinkedList.begin(),LinkedList.end(),Row::make_entry(UNDEF,0.0));
		  LinkedList.begin()->first = EOL;
		  Nonzeros = 0;
		  Sorted = _Sorted;
	  }

	  void RowMerger::Resize(Matrix & A, bool _Sorted)
	  {
		  INMOST_DATA_ENUM_TYPE mbeg, mend;
		  A.GetInterval(mbeg,mend);
		  Resize(mbeg,mend,_Sorted);
	  }

	  RowMerger::RowMerger(Matrix & A, bool Sorted) : Sorted(Sorted), Nonzeros(0)
	  {
		  INMOST_DATA_ENUM_TYPE mbeg, mend;
		  A.GetInterval(mbeg,mend);
		  LinkedList.set_interval_beg(mbeg);
		  LinkedList.set_interval_end(mend+1);
		  std::fill(LinkedList.begin(),LinkedList.end(),Row::make_entry(UNDEF,0.0));
		  LinkedList.begin()->first = EOL;
	  }

	  RowMerger::~RowMerger() {}

	  void RowMerger::Clear()
	  {
		  INMOST_DATA_ENUM_TYPE i = LinkedList.begin()->first, j;
		  LinkedList.begin()->first = EOL;
		  while( i != EOL )
		  {
			  j = LinkedList[i].first;
			  LinkedList[i].first = UNDEF;
        LinkedList[i].second = 0.0;
			  i = j;
		  }
		  Nonzeros = 0;
	  }

	  void RowMerger::PushRow(INMOST_DATA_REAL_TYPE coef, Row & r, bool PreSortRow)
	  {
		  if( Sorted && PreSortRow ) std::sort(r.Begin(),r.End());
      //if( Nonzeros != 0 ) printf("nnz %d link %p proc %d\n",Nonzeros,this,omp_get_thread_num());
		  assert(Nonzeros == 0); //Linked list should be empty
		  assert(LinkedList.begin()->first == EOL); //again check that list is empty
		  INMOST_DATA_ENUM_TYPE index = LinkedList.get_interval_beg();
		  Row::iterator it = r.Begin(), jt;
		  while( it != r.End() )
		  {
			  LinkedList[index].first = it->first+1;
			  LinkedList[it->first+1].first = EOL;
			  LinkedList[it->first+1].second = it->second*coef;
			  index = it->first+1;
			  ++Nonzeros;
			  jt = it;
			  ++it;
			  assert(!Sorted || it == r.End() || jt->first < it->first);
		  }
	  }

	  void RowMerger::AddRow(INMOST_DATA_REAL_TYPE coef, Row & r, bool PreSortRow)
	  {
		  if( Sorted && PreSortRow ) std::sort(r.Begin(),r.End());
		  INMOST_DATA_ENUM_TYPE index = LinkedList.get_interval_beg(), next;
		  Row::iterator it = r.Begin(), jt;
		  while( it != r.End() )
		  {
			  if( LinkedList[it->first+1].first != UNDEF )
				  LinkedList[it->first+1].second += coef*it->second;
			  else if( Sorted )
			  {
				  next = index;
				  while(next < it->first+1)
				  {
					  index = next;
					  next = LinkedList[index].first;
				  }
				  assert(index < it->first+1);
				  assert(it->first+1 < next);
				  LinkedList[index].first = it->first+1;
				  LinkedList[it->first+1].first = next;
				  LinkedList[it->first+1].second = coef*it->second;
				  ++Nonzeros;
			  }
			  else
			  {
				  LinkedList[it->first+1].first = LinkedList[index].first;
				  LinkedList[it->first+1].second = coef*it->second;
				  LinkedList[index].first = it->first+1;
				  ++Nonzeros;
			  }
			  jt = it;
			  ++it;
			  assert(!Sorted || it == r.End() || jt->first < it->first);
		  }
	  }

	  void RowMerger::RetriveRow(Row & r)
	  {
		  r.Resize(Nonzeros);
		  INMOST_DATA_ENUM_TYPE i = LinkedList.begin()->first, k = 0;
		  while( i != EOL )
		  {
			  if( LinkedList[i].second )
			  {
				  r.GetIndex(k) = i-1;
				  r.GetValue(k) = LinkedList[i].second;
				  ++k;
			  }
			  i = LinkedList[i].first;
		  }
		  r.Resize(k);
	  }









    Vector::Vector(std::string _name, INMOST_DATA_ENUM_TYPE start, INMOST_DATA_ENUM_TYPE end, INMOST_MPI_Comm _comm) :data(start,end) 
	  {
		  comm = _comm;
		  name = _name;
		  is_parallel = false;
	  }
	
	  Vector::Vector(const Vector & other) : data(other.data) 
	  {
		  comm = other.comm;
		  name = other.name;
		  is_parallel = other.is_parallel;
	  }
	
	  Vector & Vector::operator =(Vector const & other) 
	  {
		  comm = other.comm;
		  data = other.data; 
		  name = other.name; 
		  is_parallel = other.is_parallel;
		  return *this;
	  }
	
	  Vector::~Vector() 
	  {
	  }

    INMOST_DATA_REAL_TYPE   Row::RowVec(Vector & x) const
	  {
		  INMOST_DATA_REAL_TYPE ret = 0;
		  INMOST_DATA_ENUM_TYPE end = Size();
		  for(INMOST_DATA_ENUM_TYPE i = 0; i < end; i++) ret = ret + x[GetIndex(i)]*GetValue(i);
		  return ret;
	  }
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    void   HessianRow::RowVec(INMOST_DATA_REAL_TYPE alpha, const Row & rU, INMOST_DATA_REAL_TYPE beta, Row & rJ) const
	  {
		  INMOST_DATA_ENUM_TYPE end = rU.Size();
      for(INMOST_DATA_ENUM_TYPE i = 0; i < end; i++) rJ.GetValue(i) *= beta;
		  for(INMOST_DATA_ENUM_TYPE i = 0; i < end; i++) 
      {
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        const index & ind = GetIndex(i);
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        if( ind.first == ind.second )
          rJ[ind.first] += alpha*rU.get_safe(ind.first)*GetValue(i);
        else
        {
          rJ[ind.first ] += alpha*rU.get_safe(ind.second)*GetValue(i);
          rJ[ind.second] += alpha*rU.get_safe(ind.first )*GetValue(i);
        }
      }
	  }
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	  void Matrix::MatVec(INMOST_DATA_REAL_TYPE alpha, Vector & x, INMOST_DATA_REAL_TYPE beta, Vector & out) const //y = alpha*A*x + beta * y
	  {
		  INMOST_DATA_ENUM_TYPE mbeg, mend;
		  INMOST_DATA_INTEGER_TYPE ind, imbeg, imend;
		  if( out.Empty() )
		  {
			  INMOST_DATA_ENUM_TYPE vbeg,vend;
			  GetInterval(vbeg,vend);
			  out.SetInterval(vbeg,vend);
		  }
		  //CHECK SOMEHOW FOR DEBUG THAT PROVIDED VECTORS ARE OK
		  //~ assert(GetFirstIndex() == out.GetFirstIndex());
		  //~ assert(Size() == out.Size());
		  GetInterval(mbeg,mend);
		  imbeg = mbeg;
		  imend = mend;
  #if defined(USE_OMP)
  #pragma omp for private(ind)
  #endif
		  for(ind = imbeg; ind < imend; ++ind) //iterate rows of matrix
			  out[ind] = beta * out[ind] + alpha * (*this)[ind].RowVec(x);
		  // outer procedure should update out vector, if needed
	  }

    
	  void Matrix::MatVecTranspose(INMOST_DATA_REAL_TYPE alpha, Vector & x, INMOST_DATA_REAL_TYPE beta, Vector & out) const //y = alpha*A*x + beta * y
	  {
		  INMOST_DATA_ENUM_TYPE mbeg, mend;
		  INMOST_DATA_INTEGER_TYPE ind, imbeg, imend;
		  if( out.Empty() )
		  {
			  INMOST_DATA_ENUM_TYPE vbeg,vend;
			  GetInterval(vbeg,vend);
			  out.SetInterval(vbeg,vend);
		  }
		  //CHECK SOMEHOW FOR DEBUG THAT PROVIDED VECTORS ARE OK
		  //~ assert(GetFirstIndex() == out.GetFirstIndex());
		  //~ assert(Size() == out.Size());
		  GetInterval(mbeg,mend);
		  imbeg = mbeg;
		  imend = mend;
		  if( beta ) for(Vector::iterator it = out.Begin(); it != out.End(); ++it) (*it) *= beta;
  #if defined(USE_OMP)
  #pragma omp for private(ind)
  #endif
		  for(ind = imbeg; ind < imend; ++ind)
		  {
			  for(Row::const_iterator it = (*this)[ind].Begin(); it != (*this)[ind].End(); ++it)
				  out[it->first] += alpha * x[ind] * it->second;
		  }
		  // outer procedure should update out vector, if needed
	  }
	

	  Matrix::Matrix(std::string _name, INMOST_DATA_ENUM_TYPE start, INMOST_DATA_ENUM_TYPE end, INMOST_MPI_Comm _comm) 
	  :data(start,end) 
	  {
		  is_parallel = false;
		  comm = _comm;
		  SetInterval(start,end);
		  name = _name;
	  }
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    HessianMatrix::HessianMatrix(std::string _name, INMOST_DATA_ENUM_TYPE start, INMOST_DATA_ENUM_TYPE end, INMOST_MPI_Comm _comm) 
	  :data(start,end) 
	  {
		  is_parallel = false;
		  comm = _comm;
		  SetInterval(start,end);
		  name = _name;
	  }
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	  Matrix::Matrix(const Matrix & other) :data(other.data)
	  {
		  comm = other.comm;
		  name = other.name;
	  }

    HessianMatrix::HessianMatrix(const HessianMatrix & other) :data(other.data)
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	  {
		  comm = other.comm;
		  name = other.name;
	  }
	
	  Matrix & Matrix::operator =(Matrix const & other) 
	  {
		  comm = other.comm;
		  data = other.data; 
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      name = other.name; 
      return *this;
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	  }
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    HessianMatrix & HessianMatrix::operator =(HessianMatrix const & other) 
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	  {
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		  comm = other.comm;
		  data = other.data; 
      name = other.name; 
      return *this;
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	  }
	
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	  Matrix::~Matrix() {}

    HessianMatrix::~HessianMatrix() {}
	
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    void      Matrix::MoveRows(INMOST_DATA_ENUM_TYPE from, INMOST_DATA_ENUM_TYPE to, INMOST_DATA_ENUM_TYPE size)
	  {
		  INMOST_DATA_ENUM_TYPE i = to + size, j = from + size;
		  if( size > 0 && to != from )
			  while( j != from ) data[--j].MoveRow(data[--i]);
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	  }

    void      HessianMatrix::MoveRows(INMOST_DATA_ENUM_TYPE from, INMOST_DATA_ENUM_TYPE to, INMOST_DATA_ENUM_TYPE size)
	  {
		  INMOST_DATA_ENUM_TYPE i = to + size, j = from + size;
		  if( size > 0 && to != from )
			  while( j != from ) data[--j].MoveRow(data[--i]);
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	  }

    
	  void     Matrix::Load(std::string file, INMOST_DATA_ENUM_TYPE mbeg, INMOST_DATA_ENUM_TYPE mend)
	  {
		  char str[16384];
		  std::ifstream input(file.c_str());
		  if( input.fail() ) throw -1;
		  int state = 0, k;
		  INMOST_DATA_ENUM_TYPE mat_size, max_lines, row, col, mat_block;
		  INMOST_DATA_REAL_TYPE val;
		  int size = 1, rank = 0;
  #if defined(USE_MPI)
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      int flag = 0;
      MPI_Initialized(&flag);
		  if( flag && mend == ENUMUNDEF && mbeg == ENUMUNDEF )
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		  {
			  MPI_Comm_rank(GetCommunicator(),&rank);
			  MPI_Comm_size(GetCommunicator(),&size);
		  }
  #endif
		  int line = 0;
		  while( !input.getline(str,16384).eof() )
		  {
			  line++;
			  k = 0; while( isspace(str[k]) ) k++;
			  if( str[k] == '%' || str[k] == '\0' ) continue;
			  std::istringstream istr(str+k);
			  switch(state)
			  {
			  case 0: 
				  istr >> mat_size >> mat_size >> max_lines; state = 1; 
				  mat_block = mat_size/size;
				  if( mbeg == ENUMUNDEF ) mbeg = rank*mat_block;
				  if( mend == ENUMUNDEF ) 
				  {
					  if( rank == size-1 ) mend = mat_size;
					  else mend = mbeg+mat_block;
				  }
				  SetInterval(mbeg,mend);
				  //~ std::cout << rank << " my interval " << mbeg << ":" << mend << std::endl;
			  break;
			  case 1: 
				  istr >> row >> col >> val;
				  row--; col--;
				  if( row >= mbeg && row < mend ) data[row][col] = val; 
			  break;
			  }
		  }
		  int nonzero = 0;
		  for(iterator it = Begin(); it != End(); ++it) nonzero += it->Size();
		  //~ std::cout << rank << " total nonzero " << max_lines << " my nonzero " << nonzero << std::endl;
		  input.close();
	  }

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    void     HessianMatrix::Load(std::string file, INMOST_DATA_ENUM_TYPE mbeg, INMOST_DATA_ENUM_TYPE mend)
	  {
		  char str[16384];
		  std::ifstream input(file.c_str());
		  if( input.fail() ) throw -1;
		  int state = 0, k;
		  INMOST_DATA_ENUM_TYPE mat_size, max_lines, row, coli, colj, mat_block;
		  INMOST_DATA_REAL_TYPE val;
		  int size = 1, rank = 0;
  #if defined(USE_MPI)
      int flag = 0;
      MPI_Initialized(&flag);
		  if( flag && mend == ENUMUNDEF && mbeg == ENUMUNDEF )
		  {
			  MPI_Comm_rank(GetCommunicator(),&rank);
			  MPI_Comm_size(GetCommunicator(),&size);
		  }
  #endif
		  int line = 0;
		  while( !input.getline(str,16384).eof() )
		  {
			  line++;
			  k = 0; while( isspace(str[k]) ) k++;
			  if( str[k] == '%' || str[k] == '\0' ) continue;
			  std::istringstream istr(str+k);
			  switch(state)
			  {
			  case 0: 
				  istr >> mat_size >> mat_size >> max_lines; state = 1; 
				  mat_block = mat_size/size;
				  if( mbeg == ENUMUNDEF ) mbeg = rank*mat_block;
				  if( mend == ENUMUNDEF ) 
				  {
					  if( rank == size-1 ) mend = mat_size;
					  else mend = mbeg+mat_block;
				  }
				  SetInterval(mbeg,mend);
				  //~ std::cout << rank << " my interval " << mbeg << ":" << mend << std::endl;
			  break;
			  case 1: 
				  istr >> row >> coli >> colj >> val;
				  row--; coli--; colj--;
				  if( row >= mbeg && row < mend ) data[row][HessianRow::make_index(coli,colj)] = val; 
			  break;
			  }
		  }
		  int nonzero = 0;
		  for(iterator it = Begin(); it != End(); ++it) nonzero += it->Size();
		  //~ std::cout << rank << " total nonzero " << max_lines << " my nonzero " << nonzero << std::endl;
		  input.close();
	  }

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    void     Vector::Load(std::string file, INMOST_DATA_ENUM_TYPE mbeg, INMOST_DATA_ENUM_TYPE mend)
	  {
		  char str[16384];
		  std::ifstream input(file.c_str());
		  if( input.fail() ) throw -1;
		  int state = 0, k;
		  INMOST_DATA_ENUM_TYPE vec_size, vec_block, ind = 0;
		  INMOST_DATA_REAL_TYPE val;
		  int size = 1, rank = 0;
  #if defined(USE_MPI)
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      int flag = 0;
      MPI_Initialized(&flag);
		  if( flag && mend == ENUMUNDEF && mbeg == ENUMUNDEF )
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		  {
			  MPI_Comm_rank(GetCommunicator(),&rank);
			  MPI_Comm_size(GetCommunicator(),&size);
		  }
  #endif
		  while( !input.getline(str,16384).eof() )
		  {
			  k = 0; while( isspace(str[k]) ) k++;
			  if( str[k] == '%' || str[k] == '\0' ) continue;
			  std::istringstream istr(str+k);
			  switch(state)
			  {
			  case 0: 
				  istr >> vec_size; state = 1; 
				  vec_block = vec_size/size;
				  if( mbeg == ENUMUNDEF ) mbeg = rank*vec_block;
				  if( mend == ENUMUNDEF ) 
				  {
					  if( rank == size-1 ) mend = vec_size;
					  else mend = mbeg+vec_block;
				  }
				  SetInterval(mbeg,mend);
			  break;
			  case 1: 
				  istr >> val;
				  if( ind >= mbeg && ind < mend ) data[ind] = val;
				  ind++;
			  break;
			  }
		  }
		  input.close();
	  }

    
	  void     Vector::Save(std::string file)
	  {
		  INMOST_DATA_ENUM_TYPE vecsize = Size();
		
#if defined(USE_MPI)
		  int rank = 0, size = 1;
		  {
			  MPI_Comm_rank(GetCommunicator(),&rank);
			  MPI_Comm_size(GetCommunicator(),&size);
			  INMOST_DATA_ENUM_TYPE temp = vecsize;
			  MPI_Allreduce(&temp,&vecsize,1,INMOST_MPI_DATA_ENUM_TYPE,MPI_SUM,GetCommunicator());
		  }
#endif
		  std::stringstream rhs(std::ios::in | std::ios::out);
		  rhs << std::scientific;
		  rhs.precision(15);
		  for(iterator it = Begin(); it != End(); ++it) rhs << *it << std::endl;
#if defined(USE_MPI) && defined(USE_MPI_FILE) // Use mpi files
		  { 
			  int ierr;
			  MPI_File fh;
			  MPI_Status stat;
			  ierr = MPI_File_open(GetCommunicator(),const_cast<char *>(file.c_str()), MPI_MODE_CREATE | MPI_MODE_DELETE_ON_CLOSE | MPI_MODE_WRONLY, MPI_INFO_NULL, &fh);
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        if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  ierr = MPI_File_close(&fh);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  ierr = MPI_File_open(GetCommunicator(),const_cast<char *>(file.c_str()),MPI_MODE_WRONLY | MPI_MODE_CREATE,MPI_INFO_NULL,&fh);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  if( rank == 0 )
			  {
				  std::stringstream header;
				  //header << "% vector " << name << std::endl;
				  //header << "% is written by INMOST" << std::endl;
				  //header << "% by MPI_File_* api" << std::endl;
				  header << vecsize << std::endl;
				  ierr = MPI_File_write_shared(fh,const_cast<char *>(header.str().c_str()),static_cast<int>(header.str().size()),MPI_CHAR,&stat);
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				  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  }
			  ierr = MPI_File_write_ordered(fh,const_cast<char *>(rhs.str().c_str()),static_cast<int>(rhs.str().size()),MPI_CHAR,&stat);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  ierr = MPI_File_close(&fh);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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		  }
#elif defined(USE_MPI) //USE_MPI alternative
		  std::string senddata = rhs.str(), recvdata;
		  int sendsize = static_cast<int>(senddata.size());
		  std::vector<int> recvsize(size), displ(size);
		  MPI_Gather(&sendsize,1,MPI_INT,&recvsize[0],1,MPI_INT,0,GetCommunicator());
		  if( rank == 0 )
		  {
			  int totsize = recvsize[0];
			
			  displ[0] = 0;
			  for(int i = 1; i < size; i++) 
			  {
				  totsize += recvsize[i];
				  displ[i] = displ[i-1]+recvsize[i-1];
			  }
			  recvdata.resize(totsize);
		  }
		  else recvdata.resize(1); //protect from dereferencing null
		  MPI_Gatherv(&senddata[0],sendsize,MPI_CHAR,&recvdata[0],&recvsize[0],&displ[0],MPI_CHAR,0,GetCommunicator());
		  if( rank == 0 )
		  {
			  std::fstream output(file.c_str(),std::ios::out);
			  output << vecsize << std::endl;
			  output << recvdata;
		  }
#else
		  std::fstream output(file.c_str(),std::ios::out);
		  //output << "% vector " << name << std::endl;
		  //output << "% is written by INMOST" << std::endl;
		  //output << "% by sequential write" << std::endl;
		  output << vecsize << std::endl;
		  output << rhs.rdbuf();
#endif
	  }


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    void     Matrix::Save(std::string file, const AnnotationService * text)
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	  {
		  INMOST_DATA_ENUM_TYPE matsize = Size(), nonzero = 0, row = GetFirstIndex()+1;
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		  bool have_annotation = false;
      if( text && !text->Empty() )
      {
        if( text->GetFirstIndex() == GetFirstIndex() &&
            text->GetLastIndex() == GetLastIndex())
            have_annotation = true;
        else
        {
          std::cout << "Size of provided annotation (" << text->GetFirstIndex() << "," << text->GetLastIndex() << ")" << std::endl;
          std::cout << "differs from the size of the matrix (" << GetFirstIndex() << "," << GetLastIndex() << ")" << std::endl;
        }
      }
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		  for(iterator it = Begin(); it != End(); ++it) nonzero += it->Size();
#if defined(USE_MPI)
		  int rank = 0, size = 1;
		  {
			  MPI_Comm_rank(GetCommunicator(),&rank);
			  MPI_Comm_size(GetCommunicator(),&size);
			  INMOST_DATA_ENUM_TYPE temp_two[2] = {matsize,nonzero}, two[2];
			  MPI_Allreduce(temp_two,two,2,INMOST_MPI_DATA_ENUM_TYPE,MPI_SUM,GetCommunicator());
			  matsize = two[0];
			  nonzero = two[1];
		  }
#endif
		  std::stringstream mtx(std::ios::in | std::ios::out);
		  mtx << std::scientific;
		  mtx.precision(15);
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		  for(INMOST_DATA_ENUM_TYPE k = GetFirstIndex(); k < GetLastIndex(); ++k)
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		  {
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        if( have_annotation ) 
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        {
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          const std::string & str = text->GetAnnotation(k);
          if( !str.empty() ) mtx << "% " << str << "\n";
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        }
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			  for(Row::iterator jt = (*this)[k].Begin(); jt != (*this)[k].End(); ++jt)
          mtx << row << " " << jt->first+1 << " " << jt->second << "\n";
        ++row;
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		  }
#if defined(USE_MPI) && defined(USE_MPI_FILE) // USE_MPI2?
		  {
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              char estring[MPI_MAX_ERROR_STRING];
			  int ierr, len;
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			  MPI_File fh;
			  MPI_Status stat;
			  ierr = MPI_File_open(GetCommunicator(),const_cast<char *>(file.c_str()), MPI_MODE_CREATE | MPI_MODE_DELETE_ON_CLOSE | MPI_MODE_WRONLY, MPI_INFO_NULL, &fh);
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        if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  ierr = MPI_File_close(&fh);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
              ierr = MPI_Barrier(GetCommunicator());
              if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  ierr = MPI_File_open(GetCommunicator(),const_cast<char *>(file.c_str()),MPI_MODE_WRONLY | MPI_MODE_CREATE,MPI_INFO_NULL,&fh);
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			  if( ierr != MPI_SUCCESS ) 
              {
                  MPI_Error_string(ierr,estring,&len);
                  std::cout << estring << std::endl;
                  MPI_Abort(GetCommunicator(),__LINE__);
              }
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			  if( rank == 0 )
			  {
				  std::stringstream header;
				  header << "%%MatrixMarket matrix coordinate real general" << std::endl;
				  header << "% matrix " << name << std::endl;
				  header << "% is written by INMOST" << std::endl;
				  header << "% by MPI_File_* api" << std::endl;
				  header << matsize << " " << matsize << " " << nonzero << std::endl;
				  //std::string header_data(header.str());
				  ierr = MPI_File_write_shared(fh,const_cast<char *>(header.str().c_str()),static_cast<int>(header.str().size()),MPI_CHAR,&stat);
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				  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  }
			  ierr = MPI_File_write_ordered(fh,const_cast<char *>(mtx.str().c_str()),static_cast<int>(mtx.str().size()),MPI_CHAR,&stat);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  ierr = MPI_File_close(&fh);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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		  }
#elif defined(USE_MPI)//USE_MPI alternative
		  std::string senddata = mtx.str(), recvdata;
		  int sendsize = static_cast<int>(senddata.size());
		  std::vector<int> recvsize(size), displ(size);
		  MPI_Gather(&sendsize,1,MPI_INT,&recvsize[0],1,MPI_INT,0,GetCommunicator());
		  if( rank == 0 )
		  {
			  int totsize = recvsize[0];
			
			  displ[0] = 0;
			  for(int i = 1; i < size; i++) 
			  {
				  totsize += recvsize[i];
				  displ[i] = displ[i-1]+recvsize[i-1];
			  }
			  recvdata.resize(totsize);
		  }
		  else recvdata.resize(1); //protect from dereferencing null
		  MPI_Gatherv(&senddata[0],sendsize,MPI_CHAR,&recvdata[0],&recvsize[0],&displ[0],MPI_CHAR,0,GetCommunicator());
		  if( rank == 0 )
		  {
			  std::fstream output(file.c_str(),std::ios::out);
			  output << "%%MatrixMarket matrix coordinate real general" << std::endl;
			  output << "% matrix " << name << std::endl;
			  output << "% is written by INMOST" << std::endl;
			  output << "% by MPI_Gather* api and sequential write" << std::endl;
			  output << matsize << " " << matsize << " " << nonzero << std::endl;
			  output << recvdata;
		  }
#else
		  std::fstream output(file.c_str(),std::ios::out);
		  output << "%%MatrixMarket matrix coordinate real general" << std::endl;
		  output << "% matrix " << name << std::endl;
		  output << "% is written by INMOST" << std::endl;
		  output << "% by sequential write " << std::endl;
		  output << matsize << " " << matsize << " " << nonzero << std::endl;
		  output << mtx.rdbuf();
#endif
	  }
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    void     HessianMatrix::Save(std::string file, const AnnotationService * text)
	  {
		  INMOST_DATA_ENUM_TYPE matsize = Size(), nonzero = 0, row = GetFirstIndex()+1;
		  bool have_annotation = false;
      if( text && !text->Empty() )
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      {
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        if( text->GetFirstIndex() == GetFirstIndex() &&
            text->GetLastIndex() == GetLastIndex())
            have_annotation = true;
        else
        {
          std::cout << "Size of provided annotation (" << text->GetFirstIndex() << "," << text->GetLastIndex() << ")" << std::endl;
          std::cout << "differs from the size of the matrix (" << GetFirstIndex() << "," << GetLastIndex() << ")" << std::endl;
        }
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      }
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		  for(iterator it = Begin(); it != End(); ++it) nonzero += it->Size();
#if defined(USE_MPI)
		  int rank = 0, size = 1;
		  {
			  MPI_Comm_rank(GetCommunicator(),&rank);
			  MPI_Comm_size(GetCommunicator(),&size);
			  INMOST_DATA_ENUM_TYPE temp_two[2] = {matsize,nonzero}, two[2];
			  MPI_Allreduce(temp_two,two,2,INMOST_MPI_DATA_ENUM_TYPE,MPI_SUM,GetCommunicator());
			  matsize = two[0];
			  nonzero = two[1];
		  }
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#endif
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		  std::stringstream mtx(std::ios::in | std::ios::out);
		  mtx << std::scientific;
		  mtx.precision(15);
		  for(INMOST_DATA_ENUM_TYPE k = GetFirstIndex(); k < GetLastIndex(); ++k)
		  {
        if( have_annotation ) 
        {
          const std::string & str = text->GetAnnotation(k);
          if( !str.empty() ) mtx << "% " << str << "\n";
        }
			  for(HessianRow::iterator jt = (*this)[k].Begin(); jt != (*this)[k].End(); ++jt)
          mtx << row << " " << jt->first.first+1 << " " << jt->first.second+1 << " " << jt->second << "\n";
        ++row;
		  }
#if defined(USE_MPI) && defined(USE_MPI_FILE) // USE_MPI2?
		  {
			  int ierr;
			  MPI_File fh;
			  MPI_Status stat;
			  ierr = MPI_File_open(GetCommunicator(),const_cast<char *>(file.c_str()), MPI_MODE_CREATE | MPI_MODE_DELETE_ON_CLOSE | MPI_MODE_WRONLY, MPI_INFO_NULL, &fh);
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        if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  ierr = MPI_File_close(&fh);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  ierr = MPI_File_open(GetCommunicator(),const_cast<char *>(file.c_str()),MPI_MODE_WRONLY | MPI_MODE_CREATE,MPI_INFO_NULL,&fh);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  if( rank == 0 )
			  {
				  std::stringstream header;
				  header << "%%MatrixMarket matrix coordinate real general" << std::endl;
				  header << "% matrix " << name << std::endl;
				  header << "% is written by INMOST" << std::endl;
				  header << "% by MPI_File_* api" << std::endl;
				  header << matsize << " " << matsize << " " << nonzero << std::endl;
				  //std::string header_data(header.str());
				  ierr = MPI_File_write_shared(fh,const_cast<char *>(header.str().c_str()),static_cast<int>(header.str().size()),MPI_CHAR,&stat);
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				  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  }
			  ierr = MPI_File_write_ordered(fh,const_cast<char *>(mtx.str().c_str()),static_cast<int>(mtx.str().size()),MPI_CHAR,&stat);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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			  ierr = MPI_File_close(&fh);
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			  if( ierr != MPI_SUCCESS ) MPI_Abort(GetCommunicator(),__LINE__);
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		  }
#elif defined(USE_MPI)//USE_MPI alternative
		  std::string senddata = mtx.str(), recvdata;
		  int sendsize = static_cast<int>(senddata.size());
		  std::vector<int> recvsize(size), displ(size);
		  MPI_Gather(&sendsize,1,MPI_INT,&recvsize[0],1,MPI_INT,0,GetCommunicator());
		  if( rank == 0 )
		  {
			  int totsize = recvsize[0];
			
			  displ[0] = 0;
			  for(int i = 1; i < size; i++) 
			  {
				  totsize += recvsize[i];
				  displ[i] = displ[i-1]+recvsize[i-1];
			  }
			  recvdata.resize(totsize);
		  }
		  else recvdata.resize(1); //protect from dereferencing null
		  MPI_Gatherv(&senddata[0],sendsize,MPI_CHAR,&recvdata[0],&recvsize[0],&displ[0],MPI_CHAR,0,GetCommunicator());
		  if( rank == 0 )
		  {
			  std::fstream output(file.c_str(),std::ios::out);
			  output << "%%MatrixMarket matrix coordinate real general" << std::endl;
			  output << "% matrix " << name << std::endl;
			  output << "% is written by INMOST" << std::endl;
			  output << "% by MPI_Gather* api and sequential write" << std::endl;
			  output << matsize << " " << matsize << " " << nonzero << std::endl;
			  output << recvdata;
		  }
#else
		  std::fstream output(file.c_str(),std::ios::out);
		  output << "%%MatrixMarket matrix coordinate real general" << std::endl;
		  output << "% matrix " << name << std::endl;
		  output << "% is written by INMOST" << std::endl;
		  output << "% by sequential write " << std::endl;
		  output << matsize << " " << matsize << " " << nonzero << std::endl;
		  output << mtx.rdbuf();
#endif
	  }

    
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      void Matrix::Swap(Matrix & other)
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      {
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          data.swap(other.data);
          name.swap(other.name);
          std::swap(comm,other.comm);
          std::swap(is_parallel,other.is_parallel);
      }
      
      void HessianMatrix::Swap(HessianMatrix & other)
      {
          data.swap(other.data);
          name.swap(other.name);
          std::swap(comm,other.comm);
          std::swap(is_parallel,other.is_parallel);
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      }
#if defined(USE_OMP)
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      bool LockService::HaveLocks() const
      {
          return !locks.empty();
      }
      bool LockService::Lock(INMOST_DATA_ENUM_TYPE row)
      {
          assert( !locks.empty() );
          omp_set_lock(&locks[row]);
          return true;
      }
      bool LockService::TestLock(INMOST_DATA_ENUM_TYPE row)
      {
          assert( !locks.empty() );
          if( omp_test_lock(&locks[row]) )
              return true;
          else
              return false;
      }
      bool LockService::UnLock(INMOST_DATA_ENUM_TYPE row)
      {
          assert( !locks.empty() );
          omp_unset_lock(&locks[row]);
          return true;
      }
      void LockService::SetInterval(INMOST_DATA_ENUM_TYPE beg, INMOST_DATA_ENUM_TYPE end)
      {
          if( !locks.empty() ) DestroyLocks();
          if( end != beg )
          {
              locks.set_interval_beg(beg);
              locks.set_interval_end(end);
              for(INMOST_DATA_ENUM_TYPE k = beg; k < end; ++k)
                  omp_init_lock(&locks[k]);
          }
      }
      void LockService::DestroyLocks()
      {
          INMOST_DATA_ENUM_TYPE kbeg,kend;
          kbeg = locks.get_interval_beg();
          kend = locks.get_interval_end();
          for(INMOST_DATA_ENUM_TYPE k = kbeg; k < kend; ++k)
              omp_destroy_lock(&locks[k]);
      }
      INMOST_DATA_ENUM_TYPE  LockService::GetFirstIndex() const {return locks.get_interval_beg();}
      INMOST_DATA_ENUM_TYPE  LockService::GetLastIndex() const {return locks.get_interval_end();}
      bool LockService::Empty() const {return locks.empty();}
      void LockService::GetInterval(INMOST_DATA_ENUM_TYPE & start, INMOST_DATA_ENUM_TYPE & end) const {start = locks.get_interval_beg(); end = locks.get_interval_end();}
#else
      bool LockService::HaveLocks() const {return false;}
      bool LockService::Lock(INMOST_DATA_ENUM_TYPE row) {return true;}
      bool LockService::TestLock(INMOST_DATA_ENUM_TYPE row) {return true;}
      bool LockService::UnLock(INMOST_DATA_ENUM_TYPE row) {return true;}
      void LockService::SetInterval(INMOST_DATA_ENUM_TYPE beg, INMOST_DATA_ENUM_TYPE end) {}
      void LockService::DestroyLocks() {}
      INMOST_DATA_ENUM_TYPE  LockService::GetFirstIndex() const {return 0;}
      INMOST_DATA_ENUM_TYPE  LockService::GetLastIndex() const {return 0;}
      bool LockService::Empty() const {return true;}
      void LockService::GetInterval(INMOST_DATA_ENUM_TYPE & start, INMOST_DATA_ENUM_TYPE & end) const {start = 0; end = 0;}
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#endif
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      void HessianMatrix::MatVec(INMOST_DATA_REAL_TYPE alpha, const Matrix & U, INMOST_DATA_REAL_TYPE beta, Matrix & J) const //y = alpha*A*x + beta * y
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      {
          INMOST_DATA_ENUM_TYPE mbeg, mend;
          INMOST_DATA_INTEGER_TYPE ind, imbeg, imend;
          if( J.Empty() )
          {
              INMOST_DATA_ENUM_TYPE vbeg,vend;
              GetInterval(vbeg,vend);
              J.SetInterval(vbeg,vend);
          }
          //CHECK SOMEHOW FOR DEBUG THAT PROVIDED VECTORS ARE OK
          //~ assert(GetFirstIndex() == out.GetFirstIndex());
          //~ assert(Size() == out.Size());
          GetInterval(mbeg,mend);
          imbeg = mbeg;
          imend = mend;
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#if defined(USE_OMP)
#pragma omp for private(ind)
#endif
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          for(ind = imbeg; ind < imend; ++ind) //iterate rows of matrix
              (*this)[ind].RowVec(alpha,U[ind],beta,J[ind]);
          // outer procedure should update J Matrix, if needed
      }
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      bool Row::isSorted() const
      {
          for(INMOST_DATA_ENUM_TYPE k = 1; k < Size(); ++k)
              if( GetIndex(k) < GetIndex(k-1) ) return false;
          return true;
      }
      void Row::MergeSortedRows(INMOST_DATA_REAL_TYPE alpha, const Row & left, INMOST_DATA_REAL_TYPE beta, const Row & right, Row & output)
      {
          assert(left.isSorted());
          assert(right.isSorted());
          output.Resize(left.Size()+right.Size());
          INMOST_DATA_ENUM_TYPE i = 0, j = 0, q = 0;
          while( i < left.Size() && j < right.Size() )
          {
              if( left.GetIndex(i) < right.GetIndex(j) )
              {
                  output.GetIndex(q) = left.GetIndex(i);
                  output.GetValue(q) = alpha*left.GetValue(i);
                  ++q;
                  ++i;
              }
              else if( left.GetIndex(i) == right.GetIndex(j) )
              {
                  output.GetIndex(q) = left.GetIndex(i);
                  output.GetValue(q) = alpha*left.GetValue(i) + beta*right.GetValue(j);
                  ++q;
                  ++i;
                  ++j;
              }
              else //right is smaller
              {
                  output.GetIndex(q) = right.GetIndex(j);
                  output.GetValue(q) = beta*right.GetValue(j);
                  ++q;
                  ++j;
              }
          }
          while( i < left.Size() )
          {
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              if( q > 0 && (output.GetIndex(q-1) == left.GetIndex(i)) )
                  output.GetValue(q-1) += alpha*left.GetValue(i);
              else
              {
                  output.GetIndex(q) = left.GetIndex(i);
                  output.GetValue(q) = alpha*left.GetValue(i);
                  ++q;
              }
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              ++i;
          }
          while( j < right.Size() )
          {
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              if( q > 0 && (output.GetIndex(q-1) == right.GetIndex(j)) )
                  output.GetValue(q-1) += beta*right.GetValue(j);
              else
              {
                  output.GetIndex(q) = right.GetIndex(j);
                  output.GetValue(q) = beta*right.GetValue(j);
                  ++q;
              }
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              ++j;
          }
          output.Resize(q);
      }

      bool HessianRow::isSorted() const
      {
        for(INMOST_DATA_ENUM_TYPE k = 1; k < Size(); ++k)
          if( GetIndex(k) < GetIndex(k-1) ) return false;
        return true;
      }
      void HessianRow::MergeSortedRows(INMOST_DATA_REAL_TYPE alpha, const HessianRow & left, INMOST_DATA_REAL_TYPE beta, const HessianRow & right, HessianRow & output)
      {
          assert(left.isSorted());
          assert(right.isSorted());
          output.Resize(left.Size()+right.Size());
          INMOST_DATA_ENUM_TYPE i = 0, j = 0, q = 0;
          while( i < left.Size() && j < right.Size() )
          {
              if( left.GetIndex(i) < right.GetIndex(j) )
              {
                  output.GetIndex(q) = left.GetIndex(i);
                  output.GetValue(q) = alpha*left.GetValue(i);
                  ++q;
                  ++i;
              }
              else if( left.GetIndex(i) == right.GetIndex(j) )
              {
                  output.GetIndex(q) = left.GetIndex(i);
                  output.GetValue(q) = alpha*left.GetValue(i) + beta*right.GetValue(j);
                  ++q;
                  ++i;
                  ++j;
              }
              else //right is smaller
              {
                  output.GetIndex(q) = right.GetIndex(j);
                  output.GetValue(q) = beta*right.GetValue(j);
                  ++q;
                  ++j;
              }
          }
          while( i < left.Size() )
          {
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              if( q > 0 && (output.GetIndex(q-1) == left.GetIndex(i)) )
                  output.GetValue(q-1) += alpha*left.GetValue(i);
              else
              {
                  output.GetIndex(q) = left.GetIndex(i);
                  output.GetValue(q) = alpha*left.GetValue(i);
                  ++q;
              }
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              ++i;
          }
          while( j < right.Size() )
          {
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              if( q > 0 && (output.GetIndex(q-1) == right.GetIndex(j)) )
                  output.GetValue(q-1) += beta*right.GetValue(j);
              else
              {
                  output.GetIndex(q) = right.GetIndex(j);
                  output.GetValue(q) = beta*right.GetValue(j);
                  ++q;
              }
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              ++j;
          }
          output.Resize(q);
      }
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      void HessianRow::MergeJacobianHessian(INMOST_DATA_REAL_TYPE a, const Row & JL, const Row & JR, INMOST_DATA_REAL_TYPE b, const HessianRow & HL, INMOST_DATA_REAL_TYPE c, const HessianRow & HR, HessianRow & output)
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      {
          // merge three sorted arrays at once
          // one of the array is synthesized from JL and JR on the go
          static const entry stub_entry = make_entry(make_index(ENUMUNDEF,ENUMUNDEF),0.0);
          assert(JL.isSorted());
          assert(JR.isSorted());
          assert(HL.isSorted());
          assert(HR.isSorted());
          output.Resize(HL.Size()+HR.Size()+JL.Size()*JR.Size());
          INMOST_DATA_ENUM_TYPE i = 0, j = 0, k = 0, l = 0, q = 0, kk = 0, ll = 0, r;
          entry candidate[3] = {stub_entry,stub_entry,stub_entry};
          if( i < HL.Size() ) 
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              candidate[0] = make_entry(HL.GetIndex(i),b*HL.GetValue(i));
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          if( j < HR.Size() ) 
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              candidate[1] = make_entry(HR.GetIndex(j),c*HR.GetValue(j));
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          if( k < JL.Size() && l < JR.Size() ) 
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              candidate[2] = make_entry(make_index(JL.GetIndex(kk),JR.GetIndex(ll)),a*JL.GetValue(kk)*JR.GetValue(ll));
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          do
          {
              //pick smallest
              r = 0;
              if( candidate[1].first < candidate[r].first ) r = 1;
              if( candidate[2].first < candidate[r].first ) r = 2;
              //all candidates are stub - exit
              if( candidate[r].first == stub_entry.first ) break;
              //record selected entry
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              if( q > 0 && (output.GetIndex(q-1) == candidate[r].first) )
                  output.GetValue(q-1) += candidate[r].second;
              else
              {
                  output.GetIndex(q) = candidate[r].first;
                  output.GetValue(q) = candidate[r].second;
                  ++q;
              }
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              if( r == 0 ) //update left hessian index
              {
                  if( ++i < HL.Size() )
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                      candidate[0] = make_entry(HL.GetIndex(i),b*HL.GetValue(i));
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                  else candidate[0] = stub_entry;
              }
              else if( r == 1 ) //update right hessian index
              {
                  if( ++j < HR.Size() )
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                      candidate[1] = make_entry(HR.GetIndex(j),c*HR.GetValue(j));
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                  else candidate[1] = stub_entry;
              }
              else //update jacobians indexes
              {
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                  if( JR.GetIndex(l) < JL.GetIndex(k) )
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                  {
                      if( ++kk == JL.Size() )
                      {
                          ++l;
                          kk = k;
                          ll = l;
                      }
                  }
                  else if( JL.GetIndex(k) < JR.GetIndex(l) )
                  {
                      if( ++ll == JR.Size() )
                      {
                          ++k;
                          kk = k;
                          ll = l;
                      }
                  }
                  else //values are equal
                  {
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                      if( ++ll == JR.Size() )
                      {
                          ++k;
                          kk = k;
                          ll = l;
                      }
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                  }
                  if( kk < JL.Size() && ll < JR.Size() )
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                      candidate[2] = make_entry(make_index(JL.GetIndex(kk),JR.GetIndex(ll)),a*JL.GetValue(kk)*JR.GetValue(ll));
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                  else
                      candidate[2] = stub_entry;
              }
          }
          while(true);
          output.Resize(q);
      }
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      void HessianRow::MergeJacobianHessian(INMOST_DATA_REAL_TYPE a, const Row & JL, const Row & JR, INMOST_DATA_REAL_TYPE b, const HessianRow & H, HessianRow & output)
      {
          // merge three sorted arrays at once
          // one of the array is synthesized from JL and JR on the go
          static const entry stub_entry = make_entry(make_index(ENUMUNDEF,ENUMUNDEF),0.0);
          assert(JL.isSorted());
          assert(JR.isSorted());
          assert(H.isSorted());
          output.Resize(H.Size()+JL.Size()*JR.Size());
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          INMOST_DATA_ENUM_TYPE i = 0, k = 0, l = 0, q = 0, kk = 0, ll = 0, r;
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          entry candidate[2] = {stub_entry,stub_entry};
          if( i < H.Size() )
              candidate[0] = make_entry(H.GetIndex(i),b*H.GetValue(i));
          if( k < JL.Size() && l < JR.Size() )
              candidate[1] = make_entry(make_index(JL.GetIndex(kk),JR.GetIndex(ll)),a*JL.GetValue(kk)*JR.GetValue(ll));
          do
          {
              //pick smallest
              r = 0;
              if( candidate[1].first < candidate[r].first ) r = 1;
              //all candidates are stub - exit
              if( candidate[r].first == stub_entry.first ) break;
              //record selected entry
              if( q > 0 && (output.GetIndex(q-1) == candidate[r].first) )
                  output.GetValue(q-1) += candidate[r].second;
              else
              {
                  output.GetIndex(q) = candidate[r].first;
                  output.GetValue(q) = candidate[r].second;
                  ++q;
              }
              if( r == 0 ) //update left hessian index
              {
                  if( ++i < H.Size() )
                      candidate[0] = make_entry(H.GetIndex(i),b*H.GetValue(i));
                  else candidate[0] = stub_entry;
              }
              else //update jacobians indexes
              {
                  if( JR.GetIndex(l) < JL.GetIndex(k) )
                  {
                      if( ++kk == JL.Size() )
                      {
                          ++l;
                          kk = k;
                          ll = l;
                      }
                  }
                  else if( JL.GetIndex(k) < JR.GetIndex(l) )
                  {
                      if( ++ll == JR.Size() )
                      {
                          ++k;
                          kk = k;
                          ll = l;
                      }
                  }
                  else //values are equal
                  {
                      if( ++ll == JR.Size() )
                      {
                          ++k;
                          kk = k;
                          ll = l;
                      }
                  }
                  if( kk < JL.Size() && ll < JR.Size() )
                      candidate[1] = make_entry(make_index(JL.GetIndex(kk),JR.GetIndex(ll)),a*JL.GetValue(kk)*JR.GetValue(ll));
                  else
                      candidate[1] = stub_entry;
              }
          }
          while(true);
          output.Resize(q);
      }
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  }
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}