text: /*
  Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
  All rights reserved.
  
  Redistribution and use in source and binary forms, with or without modification,
  are permitted provided that the following conditions are met:
  
  Redistributions of source code must retain the above copyright notice, this list of
  conditions and the following disclaimer. Redistributions in binary form must reproduce
  the above copyright notice, this list of conditions and the following disclaimer
  in the documentation and/or other materials provided with the distribution. 
  
  Neither the name of the Johns Hopkins University nor the names of its contributors
  may be used to endorse or promote products derived from this software without specific
  prior written permission. 
  
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO THE IMPLIED WARRANTIES 
  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
  SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
  TO, PROCUREMENT OF SUBSTITUTE  GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  DAMAGE.
  */
  
  #include <float.h>
  
  
  ///////////////////
  //  SparseMatrix //
  ///////////////////
  ///////////////////////////////////////
  // SparseMatrix Methods and Memebers //
  ///////////////////////////////////////
  
  template< class T >
  SparseMatrix< T >::SparseMatrix( void )
  {
  	_contiguous = false;
  	_maxEntriesPerRow = 0;
  	rows = 0;
  	rowSizes = NullPointer< int >( );
  	m_ppElements = NullPointer< Pointer( MatrixEntry< T > ) >( );
  }
  
  template< class T > SparseMatrix< T >::SparseMatrix( int rows                        ) : SparseMatrix< T >() { Resize( rows ); }
  template< class T > SparseMatrix< T >::SparseMatrix( int rows , int maxEntriesPerRow ) : SparseMatrix< T >() { Resize( rows , maxEntriesPerRow ); }
  
  template< class T >
  SparseMatrix< T >::SparseMatrix( const SparseMatrix& M ) : SparseMatrix< T >()
  {
  	if( M._contiguous ) Resize( M.rows , M._maxEntriesPerRow );
  	else                Resize( M.rows );
  	for( int i=0 ; i<rows ; i++ )
  	{
  		SetRowSize( i , M.rowSizes[i] );
  		memcpy( (*this)[i] , M[i] , sizeof( MatrixEntry< T > ) * rowSizes[i] );
  	}
  }
  template<class T>
  int SparseMatrix<T>::Entries( void ) const
  {
  	int e = 0;
  	for( int i=0 ; i<rows ; i++ ) e += int( rowSizes[i] );
  	return e;
  }
  template<class T>
  SparseMatrix<T>& SparseMatrix<T>::operator = (const SparseMatrix<T>& M)
  {
  	if( M._contiguous ) Resize( M.rows , M._maxEntriesPerRow );
  	else                Resize( M.rows );
  	for( int i=0 ; i<rows ; i++ )
  	{
  		SetRowSize( i , M.rowSizes[i] );
  		memcpy( (*this)[i] , M[i] , sizeof( MatrixEntry< T > ) * rowSizes[i] );
  	}
  	return *this;
  }
  
  template<class T>
  SparseMatrix<T>::~SparseMatrix( void ){ Resize( 0 ); }
  
  template< class T >
  bool SparseMatrix< T >::write( const char* fileName ) const
  {
  	FILE* fp = fopen( fileName , "wb" );
  	if( !fp ) return false;
  	bool ret = write( fp );
  	fclose( fp );
  	return ret;
  }
  template< class T >
  bool SparseMatrix< T >::read( const char* fileName )
  {
  	FILE* fp = fopen( fileName , "rb" );
  	if( !fp ) return false;
  	bool ret = read( fp );
  	fclose( fp );
  	return ret;
  }
  template< class T >
  bool SparseMatrix< T >::write( FILE* fp ) const
  {
  	if( fwrite( &rows , sizeof( int ) , 1 , fp )!=1 ) return false;
  	if( fwrite( rowSizes , sizeof( int ) , rows , fp )!=rows ) return false;
  	for( int i=0 ; i<rows ; i++ ) if( fwrite( (*this)[i] , sizeof( MatrixEntry< T > ) , rowSizes[i] , fp )!=rowSizes[i] ) return false;
  	return true;
  }
  template< class T >
  bool SparseMatrix< T >::read( FILE* fp )
  {
  	int r;
  	if( fread( &r , sizeof( int ) , 1 , fp )!=1 ) return false;
  	Resize( r );
  	if( fread( rowSizes , sizeof( int ) , rows , fp )!=rows ) return false;
  	for( int i=0 ; i<rows ; i++ )
  	{
  		r = rowSizes[i];
  		rowSizes[i] = 0;
  		SetRowSize( i , r );
  		if( fread( (*this)[i] , sizeof( MatrixEntry< T > ) , rowSizes[i] , fp )!=rowSizes[i] ) return false;
  	}
  	return true;
  }
  
  
  template< class T >
  void SparseMatrix< T >::Resize( int r )
  {
  	if( rows>0 )
  	{
  		if( _contiguous ){ if( _maxEntriesPerRow ) FreePointer( m_ppElements[0] ); }
  		else for( int i=0 ; i<rows ; i++ ){ if( rowSizes[i] ) FreePointer( m_ppElements[i] ); }
  		FreePointer( m_ppElements );
  		FreePointer( rowSizes );
  	}
  	rows = r;
  	if( r )
  	{
  		rowSizes = AllocPointer< int >( r );
  		m_ppElements = AllocPointer< Pointer( MatrixEntry< T > ) >( r );
  		memset( rowSizes , 0 , sizeof( int ) * r );
  	}
  	_contiguous = false;
  	_maxEntriesPerRow = 0;
  }
  template< class T >
  void SparseMatrix< T >::Resize( int r , int e )
  {
  	if( rows>0 )
  	{
  		if( _contiguous ){ if( _maxEntriesPerRow ) FreePointer( m_ppElements[0] ); }
  		else for( int i=0 ; i<rows ; i++ ){ if( rowSizes[i] ) FreePointer( m_ppElements[i] ); }
  		FreePointer( m_ppElements );
  		FreePointer( rowSizes );
  	}
  	rows = r;
  	if( r )
  	{
  		rowSizes = AllocPointer< int >( r );
  		m_ppElements = AllocPointer< Pointer( MatrixEntry< T > ) >( r );
  		m_ppElements[0] = AllocPointer< MatrixEntry< T > >( r * e );
  		memset( rowSizes , 0 , sizeof( int ) * r );
  		for( int i=1 ; i<r ; i++ ) m_ppElements[i] = m_ppElements[i-1] + e;
  	}
  	_contiguous = true;
  	_maxEntriesPerRow = e;
  }
  
  template<class T>
  void SparseMatrix< T >::SetRowSize( int row , int count )
  {
  	if( _contiguous )
  	{
  		if( count>_maxEntriesPerRow ) fprintf( stderr , "[ERROR] Cannot set row size on contiguous matrix: %d<=%d\n" , count , _maxEntriesPerRow ) , exit( 0 );
  		rowSizes[row] = count;
  	}
  	else if( row>=0 && row<rows )
  	{
  		if( rowSizes[row] ) FreePointer( m_ppElements[row] );
  		if( count>0 ) m_ppElements[row] = AllocPointer< MatrixEntry< T > >( count );
  	}
  }
  
  
  template<class T>
  void SparseMatrix<T>::SetZero()
  {
  	Resize(this->m_N, this->m_M);
  }
  
  template<class T>
  void SparseMatrix<T>::SetIdentity()
  {
  	SetZero();
  	for(int ij=0; ij < Min( this->Rows(), this->Columns() ); ij++)
  		(*this)(ij,ij) = T(1);
  }
  
  template<class T>
  SparseMatrix<T> SparseMatrix<T>::operator * (const T& V) const
  {
  	SparseMatrix<T> M(*this);
  	M *= V;
  	return M;
  }
  
  template<class T>
  SparseMatrix<T>& SparseMatrix<T>::operator *= (const T& V)
  {
  	for (int i=0; i<this->Rows(); i++)
  	{
  		for(int ii=0;ii<m_ppElements[i].size();i++){m_ppElements[i][ii].Value*=V;}
  	}
  	return *this;
  }
  
  template<class T>
  SparseMatrix<T> SparseMatrix<T>::Multiply( const SparseMatrix<T>& M ) const
  {
  	SparseMatrix<T> R( this->Rows(), M.Columns() );
  	for(int i=0; i<R.Rows(); i++){
  		for(int ii=0;ii<m_ppElements[i].size();ii++){
  			int N=m_ppElements[i][ii].N;
  			T Value=m_ppElements[i][ii].Value;
  			for(int jj=0;jj<M.m_ppElements[N].size();jj++){
  				R(i,M.m_ppElements[N][jj].N) += Value * M.m_ppElements[N][jj].Value;
  			}
  		}
  	}
  	return R;		
  }
  
  template<class T>
  template<class T2>
  pr::Vector<T2> SparseMatrix<T>::Multiply( const pr::Vector<T2>& V ) const
  {
      pr::Vector<T2> R( rows );
  	
  	for (int i=0; i<rows; i++)
  	{
  		T2 temp=T2();
  		for(int ii=0;ii<rowSizes[i];ii++){
  			temp+=m_ppElements[i][ii].Value * V.m_pV[m_ppElements[i][ii].N];
  		}
  		R(i)=temp;
  	}
  	return R;
  }
  
  template<class T>
  template<class T2>
  void SparseMatrix<T>::Multiply( const pr::Vector<T2>& In , pr::Vector<T2>& Out , int threads ) const
  {
  #pragma omp parallel for num_threads( threads ) schedule( static )
  	for( int i=0 ; i<rows ; i++ )
  	{
  		T2 temp = T2();
  		temp *= 0;
  		for( int j=0 ; j<rowSizes[i] ; j++ ) temp += m_ppElements[i][j].Value * In.m_pV[m_ppElements[i][j].N];
  		Out.m_pV[i] = temp;
  	}
  }
  
  template<class T>
  SparseMatrix<T> SparseMatrix<T>::operator * (const SparseMatrix<T>& M) const
  {
  	return Multiply(M);
  }
  template<class T>
  template<class T2>
  pr::Vector<T2> SparseMatrix<T>::operator * (const pr::Vector<T2>& V) const
  {
  	return Multiply(V);
  }
  
  template<class T>
  SparseMatrix<T> SparseMatrix<T>::Transpose() const
  {
      SparseMatrix<T> M( this->Columns(), this->Rows() );
  
      for (int i=0; i<this->Rows(); i++)
  	{
  		for(int ii=0;ii<m_ppElements[i].size();ii++){
  			M(m_ppElements[i][ii].N,i) = m_ppElements[i][ii].Value;
  		}
  	}
  	return M;
  }
  
  template<class T>
  template<class T2>
  int SparseMatrix<T>::SolveSymmetric( const SparseMatrix<T>& M , const pr::Vector<T2>& b , int iters , pr::Vector<T2>& solution , const T2 eps , int reset , int threads )
  {
  	if( reset )
  	{
  		solution.Resize( b.Dimensions() );
  		solution.SetZero();
  	}
      pr::Vector< T2 > r;
  	r.Resize( solution.Dimensions() );
  	M.Multiply( solution , r );
  	r = b - r;
      pr::Vector< T2 > d = r;
  	double delta_new , delta_0;
  	for( int i=0 ; i<r.Dimensions() ; i++ ) delta_new += r.m_pV[i] * r.m_pV[i];
  	delta_0 = delta_new;
  	if( delta_new<eps ) return 0;
  	int ii;
      pr::Vector< T2 > q;
  	q.Resize( d.Dimensions() );
  	for( ii=0; ii<iters && delta_new>eps*delta_0 ; ii++ )
  	{
  		M.Multiply( d , q , threads );
          double dDotQ = 0 , alpha = 0;
  		for( int i=0 ; i<d.Dimensions() ; i++ ) dDotQ += d.m_pV[i] * q.m_pV[i];
  		alpha = delta_new / dDotQ;
  #pragma omp parallel for num_threads( threads ) schedule( static )
  		for( int i=0 ; i<r.Dimensions() ; i++ ) solution.m_pV[i] += d.m_pV[i] * T2( alpha );
  		if( !(ii%50) )
  		{
  			r.Resize( solution.Dimensions() );
  			M.Multiply( solution , r , threads );
  			r = b - r;
  		}
  		else
  #pragma omp parallel for num_threads( threads ) schedule( static )
  			for( int i=0 ; i<r.Dimensions() ; i++ ) r.m_pV[i] = r.m_pV[i] - q.m_pV[i] * T2(alpha);
  
  		double delta_old = delta_new , beta;
  		delta_new = 0;
  		for( int i=0 ; i<r.Dimensions() ; i++ ) delta_new += r.m_pV[i]*r.m_pV[i];
  		beta = delta_new / delta_old;
  #pragma omp parallel for num_threads( threads ) schedule( static )
  		for( int i=0 ; i<d.Dimensions() ; i++ ) d.m_pV[i] = r.m_pV[i] + d.m_pV[i] * T2( beta );
  	}
  	return ii;
  }
  
  // Solve for x s.t. M(x)=b by solving for x s.t. M^tM(x)=M^t(b)
  template<class T>
  int SparseMatrix<T>::Solve(const SparseMatrix<T>& M,const pr::Vector<T>& b,int iters,pr::Vector<T>& solution,const T eps){
  	SparseMatrix mTranspose=M.Transpose();
      pr::Vector<T> bb=mTranspose*b;
      pr::Vector<T> d,r,Md;
  	T alpha,beta,rDotR;
  	int i;
  
  	solution.Resize(M.Columns());
  	solution.SetZero();
  
  	d=r=bb;
  	rDotR=r.Dot(r);
  	for(i=0;i<iters && rDotR>eps;i++){
  		T temp;
  		Md=mTranspose*(M*d);
  		alpha=rDotR/d.Dot(Md);
  		solution+=d*alpha;
  		r-=Md*alpha;
  		temp=r.Dot(r);
  		beta=temp/rDotR;
  		rDotR=temp;
  		d=r+d*beta;
  	}
  	return i;
  }
  
  
  
  
  ///////////////////////////
  // SparseSymmetricMatrix //
  ///////////////////////////
  template<class T>
  template<class T2>
  pr::Vector<T2> SparseSymmetricMatrix<T>::operator * (const pr::Vector<T2>& V) const {return Multiply(V);}
  template<class T>
  template<class T2>
  pr::Vector<T2> SparseSymmetricMatrix<T>::Multiply( const pr::Vector<T2>& V ) const
  {
      pr::Vector<T2> R( SparseMatrix< T >::rows );
  
  	for(int i=0; i<SparseMatrix< T >::rows; i++){
  		for(int ii=0;ii<SparseMatrix< T >::rowSizes[i];ii++)
  		{
  			int j=SparseMatrix< T >::m_ppElements[i][ii].N;
  			R(i)+=SparseMatrix< T >::m_ppElements[i][ii].Value * V.m_pV[j];
  			R(j)+=SparseMatrix< T >::m_ppElements[i][ii].Value * V.m_pV[i];
  		}
  	}
  	return R;
  }
  
  template<class T>
  template<class T2>
  void SparseSymmetricMatrix<T>::Multiply( const pr::Vector<T2>& In , pr::Vector<T2>& Out , bool addDCTerm ) const
  {
  	Out.SetZero();
  	const T2* in = &In[0];
  	T2* out = &Out[0];
  	T2 dcTerm = T2( 0 );
  	if( addDCTerm )
  	{
  		for( int i=0 ; i<SparseMatrix< T >::rows ; i++ ) dcTerm += in[i];
  		dcTerm /= SparseMatrix< T >::rows;
  	}
  	for( int i=0 ; i<SparseMatrix< T >::rows ; i++ )
  	{
  		const MatrixEntry<T>* temp = SparseMatrix< T >::m_ppElements[i];
  		const MatrixEntry<T>* end = temp + SparseMatrix< T >::rowSizes[i];
  		const T2& in_i_ = in[i];
  		T2 out_i = T2(0);
  		for( ; temp!=end ; temp++ )
  		{
  			int j=temp->N;
  			T2 v=temp->Value;
  			out_i += v * in[j];
  			out[j] += v * in_i_;
  		}
  		out[i] += out_i;
  	}
  	if( addDCTerm ) for( int i=0 ; i<SparseMatrix< T >::rows ; i++ ) out[i] += dcTerm;
  }
  template<class T>
  template<class T2>
  void SparseSymmetricMatrix<T>::Multiply( const pr::Vector<T2>& In , pr::Vector<T2>& Out , MapReduceVector< T2 >& OutScratch , bool addDCTerm ) const
  {
  	int dim = int( In.Dimensions() );
  	const T2* in = &In[0];
  	int threads = OutScratch.threads();
  	if( addDCTerm )
  	{
  		T2 dcTerm = 0;
  #pragma omp parallel for num_threads( threads ) reduction ( + : dcTerm )
  		for( int t=0 ; t<threads ; t++ ) 
  		{
  			T2* out = OutScratch[t];
  			memset( out , 0 , sizeof( T2 ) * dim );
  			for( int i=(SparseMatrix< T >::rows*t)/threads ; i<(SparseMatrix< T >::rows*(t+1))/threads ; i++ )
  			{
  				const T2& in_i_ = in[i];
  				T2& out_i_ = out[i];
  				ConstPointer( MatrixEntry< T > ) temp;
  				ConstPointer( MatrixEntry< T > ) end;
  				for( temp = SparseMatrix< T >::m_ppElements[i] , end = temp+SparseMatrix< T >::rowSizes[i] ; temp!=end ; temp++ )
  				{
  					int j = temp->N;
  					T2 v = temp->Value;
  					out_i_ += v * in[j];
  					out[j] += v * in_i_;
  				}
  				dcTerm += in_i_;
  			}
  		}
  		dcTerm /= dim;
  		dim = int( Out.Dimensions() );
  		T2* out = &Out[0];
  #pragma omp parallel for num_threads( threads ) schedule( static )
  		for( int i=0 ; i<dim ; i++ )
  		{
  			T2 _out = dcTerm;
  			for( int t=0 ; t<threads ; t++ ) _out += OutScratch[t][i];
  			out[i] = _out;
  		}
  	}
  	else
  	{
  #pragma omp parallel for num_threads( threads )
  		for( int t=0 ; t<threads ; t++ ) 
  		{
  			T2* out = OutScratch[t];
  			memset( out , 0 , sizeof( T2 ) * dim );
  			for( int i=(SparseMatrix< T >::rows*t)/threads ; i<(SparseMatrix< T >::rows*(t+1))/threads ; i++ )
  			{
  				T2 in_i_ = in[i];
  				T2 out_i_ = T2();
  				ConstPointer( MatrixEntry< T > ) temp;
  				ConstPointer( MatrixEntry< T > ) end;
  				for( temp = SparseMatrix< T >::m_ppElements[i] , end = temp+SparseMatrix< T >::rowSizes[i] ; temp!=end ; temp++ )
  				{
  					int j = temp->N;
  					T2 v = temp->Value;
  					out_i_ += v * in[j];
  					out[j] += v * in_i_;
  				}
  				out[i] += out_i_;
  			}
  		}
  		dim = int( Out.Dimensions() );
  		T2* out = &Out[0];
  #pragma omp parallel for num_threads( threads ) schedule( static )
  		for( int i=0 ; i<dim ; i++ )
  		{
  			T2 _out = T2(0);
  			for( int t=0 ; t<threads ; t++ ) _out += OutScratch[t][i];
  			out[i] = _out;
  		}
  	}
  }
  template<class T>
  template<class T2>
  void SparseSymmetricMatrix<T>::Multiply( const pr::Vector<T2>& In , pr::Vector<T2>& Out , std::vector< T2* >& OutScratch , const std::vector< int >& bounds ) const
  {
  	int dim = In.Dimensions();
  	const T2* in = &In[0];
  	int threads = OutScratch.size();
  #pragma omp parallel for num_threads( threads )
  	for( int t=0 ; t<threads ; t++ )
  		for( int i=0 ; i<dim ; i++ ) OutScratch[t][i] = T2(0);
  #pragma omp parallel for num_threads( threads )
  	for( int t=0 ; t<threads ; t++ ) 
  	{
  		T2* out = OutScratch[t];
  		for( int i=bounds[t] ; i<bounds[t+1] ; i++ )
  		{
  			const MatrixEntry<T>* temp = SparseMatrix< T >::m_ppElements[i];
  			const MatrixEntry<T>* end = temp + SparseMatrix< T >::rowSizes[i];
  			const T2& in_i_ = in[i];
  			T2& out_i_ = out[i];
  			for(  ; temp!=end ; temp++ )
  			{
  				int j = temp->N;
  				T2 v = temp->Value;
  				out_i_ += v * in[j];
  				out[j] += v * in_i_;
  			}
  		}
  	}
  	T2* out = &Out[0];
  #pragma omp parallel for num_threads( threads ) schedule( static )
  	for( int i=0 ; i<Out.Dimensions() ; i++ )
  	{
  		T2& _out = out[i];
  		_out = T2(0);
  		for( int t=0 ; t<threads ; t++ ) _out += OutScratch[t][i];
  	}
  }
  #ifdef WIN32
  #ifndef _AtomicIncrement_
  #define _AtomicIncrement_
  #include <WinBase.h>
  inline void AtomicIncrement( volatile float* ptr , float addend )
  {
  	float newValue = *ptr;
  	LONG& _newValue = *( (LONG*)&newValue );
  	LONG  _oldValue;
  	for( ;; )
  	{
  		_oldValue = _newValue;
  		newValue += addend;
  		_newValue = InterlockedCompareExchange( (LONG*) ptr , _newValue , _oldValue );
  		if( _newValue==_oldValue ) break;
  	}
  }
  inline void AtomicIncrement( volatile double* ptr , double addend )
  //inline void AtomicIncrement( double* ptr , double addend )
  {
  	double newValue = *ptr;
  	LONGLONG& _newValue = *( (LONGLONG*)&newValue );
  	LONGLONG  _oldValue;
  	do
  	{
  		_oldValue = _newValue;
  		newValue += addend;
  		_newValue = InterlockedCompareExchange64( (LONGLONG*) ptr , _newValue , _oldValue );
  	}
  	while( _newValue!=_oldValue );
  }
  #endif // _AtomicIncrement_
  template< class T >
  void MultiplyAtomic( const SparseSymmetricMatrix< T >& A , const pr::Vector< float >& In , pr::Vector< float >& Out , int threads , const int* partition=NULL )
  {
  	Out.SetZero();
  	const float* in = &In[0];
  	float* out = &Out[0];
  	if( partition )
  #pragma omp parallel for num_threads( threads )
  		for( int t=0 ; t<threads ; t++ )
  			for( int i=partition[t] ; i<partition[t+1] ; i++ )
  			{
  				const MatrixEntry< T >* temp = A[i];
  				const MatrixEntry< T >* end = temp + A.rowSizes[i];
  				const float& in_i = in[i];
  				float out_i = 0.;
  				for( ; temp!=end ; temp++ )
  				{
  					int j = temp->N;
  					float v = temp->Value;
  					out_i += v * in[j];
  					AtomicIncrement( out+j , v * in_i );
  				}
  				AtomicIncrement( out+i , out_i );
  			}
  	else
  #pragma omp parallel for num_threads( threads )
  		for( int i=0 ; i<A.rows ; i++ )
  		{
  			const MatrixEntry< T >* temp = A[i];
  			const MatrixEntry< T >* end = temp + A.rowSizes[i];
  			const float& in_i = in[i];
  			float out_i = 0.f;
  			for( ; temp!=end ; temp++ )
  			{
  				int j = temp->N;
  				float v = temp->Value;
  				out_i += v * in[j];
  				AtomicIncrement( out+j , v * in_i );
  			}
  			AtomicIncrement( out+i , out_i );
  		}
  }
  template< class T >
  void MultiplyAtomic( const SparseSymmetricMatrix< T >& A , const pr::Vector< double >& In , pr::Vector< double >& Out , int threads , const int* partition=NULL )
  {
  	Out.SetZero();
  	const double* in = &In[0];
  	double* out = &Out[0];
  
  	if( partition )
  #pragma omp parallel for num_threads( threads )
  		for( int t=0 ; t<threads ; t++ )
  			for( int i=partition[t] ; i<partition[t+1] ; i++ )
  			{
  				const MatrixEntry< T >* temp = A[i];
  				const MatrixEntry< T >* end = temp + A.rowSizes[i];
  				const double& in_i = in[i];
  				double out_i = 0.;
  				for( ; temp!=end ; temp++ )
  				{
  					int j = temp->N;
  					T v = temp->Value;
  					out_i += v * in[j];
  					AtomicIncrement( out+j , v * in_i );
  				}
  				AtomicIncrement( out+i , out_i );
  			}
  	else
  #pragma omp parallel for num_threads( threads )
  		for( int i=0 ; i<A.rows ; i++ )
  		{
  			const MatrixEntry< T >* temp = A[i];
  			const MatrixEntry< T >* end = temp + A.rowSizes[i];
  			const double& in_i = in[i];
  			double out_i = 0.;
  			for( ; temp!=end ; temp++ )
  			{
  				int j = temp->N;
  				T v = temp->Value;
  				out_i += v * in[j];
  				AtomicIncrement( out+j , v * in_i );
  			}
  			AtomicIncrement( out+i , out_i );
  		}
  }
  
  template< class T >
  template< class T2 >
  int SparseSymmetricMatrix< T >::SolveAtomic( const SparseSymmetricMatrix< T >& A , const pr::Vector< T2 >& b , int iters , pr::Vector< T2 >& x , T2 eps , int reset , int threads , bool solveNormal )
  {
  	eps *= eps;
  	int dim = b.Dimensions();
  	if( reset )
  	{
  		x.Resize( dim );
  		x.SetZero();
  	}
      pr::Vector< T2 > r( dim ) , d( dim ) , q( dim );
      pr::Vector< T2 > temp;
  	if( solveNormal ) temp.Resize( dim );
  	T2 *_x = &x[0] , *_r = &r[0] , *_d = &d[0] , *_q = &q[0];
  	const T2* _b = &b[0];
  
  	std::vector< int > partition( threads+1 );
  	{
  		int eCount = 0;
  		for( int i=0 ; i<A.rows ; i++ ) eCount += A.rowSizes[i];
  		partition[0] = 0;
  #pragma omp parallel for num_threads( threads )
  		for( int t=0 ; t<threads ; t++ )
  		{
  			int _eCount = 0;
  			for( int i=0 ; i<A.rows ; i++ )
  			{
  				_eCount += A.rowSizes[i];
  				if( _eCount*threads>=eCount*(t+1) )
  				{
  					partition[t+1] = i;
  					break;
  				}
  			}
  		}
  		partition[threads] = A.rows;
  	}
  	if( solveNormal )
  	{
  		MultiplyAtomic( A , x , temp , threads , &partition[0] );
  		MultiplyAtomic( A , temp , r , threads , &partition[0] );
  		MultiplyAtomic( A , b , temp , threads , &partition[0] );
  #pragma omp parallel for num_threads( threads ) schedule( static )
  		for( int i=0 ; i<dim ; i++ ) _d[i] = _r[i] = temp[i] - _r[i];
  	}
  	else
  	{
  		MultiplyAtomic( A , x , r , threads , &partition[0] );
  #pragma omp parallel for num_threads( threads ) schedule( static )
  		for( int i=0 ; i<dim ; i++ ) _d[i] = _r[i] = _b[i] - _r[i];
  	}
  	double delta_new = 0 , delta_0;
  	for( size_t i=0 ; i<dim ; i++ ) delta_new += _r[i] * _r[i];
  	delta_0 = delta_new;
  	if( delta_new<eps )
  	{
  		fprintf( stderr , "[WARNING] Initial residual too low: %g < %f\n" , delta_new , eps );
  		return 0;
  	}
  	int ii;
  	for( ii=0; ii<iters && delta_new>eps*delta_0 ; ii++ )
  	{
  		if( solveNormal ) MultiplyAtomic( A , d , temp , threads , &partition[0] ) , MultiplyAtomic( A , temp , q , threads , &partition[0] );
  		else              MultiplyAtomic( A , d , q , threads , &partition[0] );
          double dDotQ = 0;
  		for( int i=0 ; i<dim ; i++ ) dDotQ += _d[i] * _q[i];
  		T2 alpha = T2( delta_new / dDotQ );
  #pragma omp parallel for num_threads( threads ) schedule( static )
  		for( int i=0 ; i<dim ; i++ ) _x[i] += _d[i] * alpha;
  		if( (ii%50)==(50-1) )
  		{
  			r.Resize( dim );
  			if( solveNormal ) MultiplyAtomic( A , x , temp , threads , &partition[0] ) , MultiplyAtomic( A , temp , r , threads , &partition[0] );
  			else              MultiplyAtomic( A , x , r , threads , &partition[0] );
  #pragma omp parallel for num_threads( threads ) schedule( static )
  			for( int i=0 ; i<dim ; i++ ) _r[i] = _b[i] - _r[i];
  		}
  		else
  #pragma omp parallel for num_threads( threads ) schedule( static )
  			for( int i=0 ; i<dim ; i++ ) _r[i] -= _q[i] * alpha;
  
  		double delta_old = delta_new;
  		delta_new = 0;
  		for( size_t i=0 ; i<dim ; i++ ) delta_new += _r[i] * _r[i];
  		T2 beta = T2( delta_new / delta_old );
  #pragma omp parallel for num_threads( threads ) schedule( static )
  		for( int i=0 ; i<dim ; i++ ) _d[i] = _r[i] + _d[i] * beta;
  	}
  	return ii;
  }
  #endif // WIN32
  template< class T >
  template< class T2 >
  int SparseSymmetricMatrix< T >::Solve( const SparseSymmetricMatrix<T>& A , const pr::Vector<T2>& b , int iters , pr::Vector<T2>& x , MapReduceVector< T2 >& scratch , T2 eps , int reset , bool addDCTerm , bool solveNormal )
  {
  	int threads = scratch.threads();
  	eps *= eps;
  	int dim = int( b.Dimensions() );
      pr::Vector< T2 > r( dim ) , d( dim ) , q( dim ) , temp;
  	if( reset ) x.Resize( dim );
  	if( solveNormal ) temp.Resize( dim );
  	T2 *_x = &x[0] , *_r = &r[0] , *_d = &d[0] , *_q = &q[0];
  	const T2* _b = &b[0];
  
  	double delta_new = 0 , delta_0;
  	if( solveNormal )
  	{
  		A.Multiply( x , temp , scratch , addDCTerm ) , A.Multiply( temp , r , scratch , addDCTerm ) , A.Multiply( b , temp , scratch , addDCTerm );
  #pragma omp parallel for num_threads( threads ) reduction( + : delta_new )
  		for( int i=0 ; i<dim ; i++ ) _d[i] = _r[i] = temp[i] - _r[i] , delta_new += _r[i] * _r[i];
  	}
  	else
  	{
  		 A.Multiply( x , r , scratch , addDCTerm );
  #pragma omp parallel for num_threads( threads )  reduction ( + : delta_new )
  		for( int i=0 ; i<dim ; i++ ) _d[i] = _r[i] = _b[i] - _r[i] , delta_new += _r[i] * _r[i];
  	}
  	delta_0 = delta_new;
  	if( delta_new<eps )
  	{
  		fprintf( stderr , "[WARNING] Initial residual too low: %g < %f\n" , delta_new , eps );
  		return 0;
  	}
  	int ii;
  	for( ii=0 ; ii<iters && delta_new>eps*delta_0 ; ii++ )
  	{
  		if( solveNormal ) A.Multiply( d , temp , scratch , addDCTerm ) , A.Multiply( temp , q , scratch , addDCTerm );
  		else              A.Multiply( d , q , scratch , addDCTerm );
          double dDotQ = 0;
  #pragma omp parallel for num_threads( threads ) reduction( + : dDotQ )
  		for( int i=0 ; i<dim ; i++ ) dDotQ += _d[i] * _q[i];
  		T2 alpha = T2( delta_new / dDotQ );
  		double delta_old = delta_new;
  		delta_new = 0;
  		if( (ii%50)==(50-1) )
  		{
  #pragma omp parallel for num_threads( threads )
  			for( int i=0 ; i<dim ; i++ ) _x[i] += _d[i] * alpha;
  			r.Resize( dim );
  			if( solveNormal ) A.Multiply( x , temp , scratch , addDCTerm ) , A.Multiply( temp , r , scratch , addDCTerm );
  			else              A.Multiply( x , r , scratch , addDCTerm );
  #pragma omp parallel for num_threads( threads ) reduction( + : delta_new )
  			for( int i=0 ; i<dim ; i++ ) _r[i] = _b[i] - _r[i] , delta_new += _r[i] * _r[i] , _x[i] += _d[i] * alpha;
  		}
  		else
  #pragma omp parallel for num_threads( threads ) reduction( + : delta_new )
  			for( int i=0 ; i<dim ; i++ ) _r[i] -= _q[i] * alpha , delta_new += _r[i] * _r[i] ,  _x[i] += _d[i] * alpha;
  
  		T2 beta = T2( delta_new / delta_old );
  #pragma omp parallel for num_threads( threads )
  		for( int i=0 ; i<dim ; i++ ) _d[i] = _r[i] + _d[i] * beta;
  	}
  	return ii;
  }
  template< class T >
  template< class T2 >
  int SparseSymmetricMatrix<T>::Solve( const SparseSymmetricMatrix<T>& A , const pr::Vector<T2>& b , int iters , pr::Vector<T2>& x , T2 eps , int reset , int threads , bool addDCTerm , bool solveNormal )
  {
  	eps *= eps;
  	int dim = int( b.Dimensions() );
  	MapReduceVector< T2 > outScratch;
  	if( threads<1 ) threads = 1;
  	if( threads>1 ) outScratch.resize( threads , dim );
  	if( reset ) x.Resize( dim );
      pr::Vector< T2 > r( dim ) , d( dim ) , q( dim );
      pr::Vector< T2 > temp;
  	if( solveNormal ) temp.Resize( dim );
  	T2 *_x = &x[0] , *_r = &r[0] , *_d = &d[0] , *_q = &q[0];
  	const T2* _b = &b[0];
  
  	double delta_new = 0 , delta_0;
  
  	if( solveNormal )
  	{
  		if( threads>1 ) A.Multiply( x , temp , outScratch , addDCTerm ) , A.Multiply( temp , r , outScratch , addDCTerm ) , A.Multiply( b , temp , outScratch , addDCTerm );
  		else            A.Multiply( x , temp , addDCTerm )              , A.Multiply( temp , r , addDCTerm )              , A.Multiply( b , temp , addDCTerm );
  #pragma omp parallel for num_threads( threads ) reduction( + : delta_new )
  		for( int i=0 ; i<dim ; i++ ) _d[i] = _r[i] = temp[i] - _r[i] , delta_new += _r[i] * _r[i];
  	}
  	else
  	{
  		if( threads>1 ) A.Multiply( x , r , outScratch , addDCTerm );
  		else            A.Multiply( x , r , addDCTerm );
  #pragma omp parallel for num_threads( threads ) reduction( + : delta_new )
  		for( int i=0 ; i<dim ; i++ ) _d[i] = _r[i] = _b[i] - _r[i] , delta_new += _r[i] * _r[i];
  	}
  
  	delta_0 = delta_new;
  	if( delta_new<eps )
  	{
  		fprintf( stderr , "[WARNING] Initial residual too low: %g < %f\n" , delta_new , eps );
  		return 0;
  	}
  	int ii;
  	for( ii=0 ; ii<iters && delta_new>eps*delta_0 ; ii++ )
  	{
  		if( solveNormal )
  		{
  			if( threads>1 ) A.Multiply( d , temp , outScratch , addDCTerm ) , A.Multiply( temp , q , outScratch , addDCTerm );
  			else            A.Multiply( d , temp , addDCTerm )              , A.Multiply( temp , q , addDCTerm );
  		}
  		else
  		{
  			if( threads>1 ) A.Multiply( d , q , outScratch , addDCTerm );
  			else            A.Multiply( d , q , addDCTerm );
  		}
          double dDotQ = 0;
  #pragma omp parallel for num_threads( threads ) reduction( + : dDotQ )
  		for( int i=0 ; i<dim ; i++ ) dDotQ += _d[i] * _q[i];
  		T2 alpha = T2( delta_new / dDotQ );
  		double delta_old = delta_new;
  		delta_new = 0;
  
  		if( (ii%50)==(50-1) )
  		{
  #pragma omp parallel for num_threads( threads )
  			for( int i=0 ; i<dim ; i++ ) _x[i] += _d[i] * alpha;
  			r.SetZero();
  			if( solveNormal )
  			{
  				if( threads>1 ) A.Multiply( x , temp , outScratch , addDCTerm ) , A.Multiply( temp , r , outScratch , addDCTerm );
  				else            A.Multiply( x , temp , addDCTerm )              , A.Multiply( temp , r , addDCTerm );
  			}
  			else
  			{
  				if( threads>1 ) A.Multiply( x , r , outScratch , addDCTerm );
  				else            A.Multiply( x , r , addDCTerm );
  			}
  #pragma omp parallel for num_threads( threads ) reduction ( + : delta_new )
  			for( int i=0 ; i<dim ; i++ ) _r[i] = _b[i] - _r[i] , delta_new += _r[i] * _r[i] , _x[i] += _d[i] * alpha;
  		}
  		else
  		{
  #pragma omp parallel for num_threads( threads ) reduction( + : delta_new )
  			for( int i=0 ; i<dim ; i++ ) _r[i] -= _q[i] * alpha , delta_new += _r[i] * _r[i] , _x[i] += _d[i] * alpha;
  		}
  
  		T2 beta = T2( delta_new / delta_old );
  #pragma omp parallel for num_threads( threads )
  		for( int i=0 ; i<dim ; i++ ) _d[i] = _r[i] + _d[i] * beta;
  	}
  	return ii;
  }
  
  template<class T>
  template<class T2>
  int SparseSymmetricMatrix<T>::Solve( const SparseSymmetricMatrix<T>& M , const pr::Vector<T2>& diagonal , const pr::Vector<T2>& b , int iters , pr::Vector<T2>& solution , int reset )
  {
      pr::Vector<T2> d,r,Md;
  
  	if(reset)
  	{
  		solution.Resize(b.Dimensions());
  		solution.SetZero();
  	}
  	Md.Resize(M.rows);
  	for( int i=0 ; i<iters ; i++ )
  	{
  		M.Multiply( solution , Md );
  		r = b-Md;
  		// solution_new[j] * diagonal[j] + ( Md[j] - solution_old[j] * diagonal[j] ) = b[j]
  		// solution_new[j] = ( b[j] - ( Md[j] - solution_old[j] * diagonal[j] ) ) / diagonal[j]
  		// solution_new[j] = ( b[j] - Md[j] ) / diagonal[j] + solution_old[j]
  		for( int j=0 ; j<int(M.rows) ; j++ ) solution[j] += (b[j]-Md[j])/diagonal[j];
  	}
  	return iters;
  }
  template< class T >
  template< class T2 >
  void SparseSymmetricMatrix< T >::getDiagonal( pr::Vector< T2 >& diagonal ) const
  {
  	diagonal.Resize( SparseMatrix< T >::rows );
  	for( int i=0 ; i<SparseMatrix< T >::rows ; i++ )
  	{
  		diagonal[i] = 0.;
  		for( int j=0 ; j<SparseMatrix< T >::rowSizes[i] ; j++ ) if( SparseMatrix< T >::m_ppElements[i][j].N==i ) diagonal[i] += SparseMatrix< T >::m_ppElements[i][j].Value * 2;
  	}
  }
  