sparse_matrix.hpp
/*
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>
#ifdef _WIN32
# ifndef WIN32_LEAN_AND_MEAN
# define WIN32_LEAN_AND_MEAN
# endif // WIN32_LEAN_AND_MEAN
# ifndef NOMINMAX
# define NOMINMAX
# endif // NOMINMAX
# include <windows.h>
#endif //_WIN32
///////////////////
// SparseMatrix //
///////////////////
///////////////////////////////////////////
// Static Allocator Methods and Memebers //
///////////////////////////////////////////
namespace pcl
{
namespace poisson
{
template<class T> int SparseMatrix<T>::UseAlloc=0;
template<class T> Allocator<MatrixEntry<T> > SparseMatrix<T>::internalAllocator;
template<class T> int SparseMatrix<T>::UseAllocator(void){return UseAlloc;}
template<class T>
void SparseMatrix<T>::SetAllocator( int blockSize )
{
if(blockSize>0){
UseAlloc=1;
internalAllocator.set(blockSize);
}
else{UseAlloc=0;}
}
///////////////////////////////////////
// SparseMatrix Methods and Memebers //
///////////////////////////////////////
template< class T >
SparseMatrix< T >::SparseMatrix( void )
{
_contiguous = false;
_maxEntriesPerRow = 0;
rows = 0;
rowSizes = NULL;
m_ppElements = NULL;
}
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( !UseAlloc )
if( _contiguous ){ if( _maxEntriesPerRow ) free( m_ppElements[0] ); }
else for( int i=0 ; i<rows ; i++ ){ if( rowSizes[i] ) free( m_ppElements[i] ); }
free( m_ppElements );
free( rowSizes );
}
rows = r;
if( r )
{
rowSizes = ( int* )malloc( sizeof( int ) * r );
memset( rowSizes , 0 , sizeof( int ) * r );
m_ppElements = ( MatrixEntry< T >** )malloc( sizeof( MatrixEntry< T >* ) * r );
}
_contiguous = false;
_maxEntriesPerRow = 0;
}
template< class T >
void SparseMatrix< T >::Resize( int r , int e )
{
if( rows>0 )
{
if( !UseAlloc )
if( _contiguous ){ if( _maxEntriesPerRow ) free( m_ppElements[0] ); }
else for( int i=0 ; i<rows ; i++ ){ if( rowSizes[i] ) free( m_ppElements[i] ); }
free( m_ppElements );
free( rowSizes );
}
rows = r;
if( r )
{
rowSizes = ( int* )malloc( sizeof( int ) * r );
memset( rowSizes , 0 , sizeof( int ) * r );
m_ppElements = ( MatrixEntry< T >** )malloc( sizeof( MatrixEntry< T >* ) * r );
m_ppElements[0] = ( MatrixEntry< T >* )malloc( sizeof( MatrixEntry< T > ) * r * e );
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( UseAlloc ) m_ppElements[row] = internalAllocator.newElements(count);
else
{
if( rowSizes[row] ) free( m_ppElements[row] );
if( count>0 ) m_ppElements[row] = ( MatrixEntry< T >* )malloc( sizeof( 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>
Vector<T2> SparseMatrix<T>::Multiply( const Vector<T2>& V ) const
{
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 Vector<T2>& In , 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>
Vector<T2> SparseMatrix<T>::operator * (const 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 Vector<T2>& b , int iters , Vector<T2>& solution , const T2 eps , int reset , int threads )
{
if( reset )
{
solution.Resize( b.Dimensions() );
solution.SetZero();
}
Vector< T2 > r;
r.Resize( solution.Dimensions() );
M.Multiply( solution , r );
r = b - r;
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;
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 Vector<T>& b,int iters,Vector<T>& solution,const T eps){
SparseMatrix mTranspose=M.Transpose();
Vector<T> bb=mTranspose*b;
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>
Vector<T2> SparseSymmetricMatrix<T>::operator * (const Vector<T2>& V) const {return Multiply(V);}
template<class T>
template<class T2>
Vector<T2> SparseSymmetricMatrix<T>::Multiply( const Vector<T2>& V ) const
{
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 Vector<T2>& In , 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<this->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 Vector<T2>& In , 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];
for( const MatrixEntry< T > *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++ )
{
const T2& in_i_ = in[i];
T2& out_i_ = out[i];
for( const MatrixEntry< T > *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_;
}
}
}
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 Vector<T2>& In , 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];
}
}
#if defined _WIN32 && !defined __MINGW32__
#ifndef _AtomicIncrement_
#define _AtomicIncrement_
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 Vector< float >& In , 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 Vector< double >& In , 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 Vector< T2 >& b , int iters , Vector< T2 >& x , T2 eps , int reset , int threads , bool solveNormal )
{
eps *= eps;
int dim = b.Dimensions();
if( reset )
{
x.Resize( dim );
x.SetZero();
}
Vector< T2 > r( dim ) , d( dim ) , q( dim );
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 && !__MINGW32__
template< class T >
template< class T2 >
int SparseSymmetricMatrix< T >::Solve( const SparseSymmetricMatrix<T>& A , const Vector<T2>& b , int iters , 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() );
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 Vector<T2>& b , int iters , 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 );
Vector< T2 > r( dim ) , d( dim ) , q( dim );
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 Vector<T2>& diagonal , const Vector<T2>& b , int iters , Vector<T2>& solution , int reset )
{
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( 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;
}
}
}
}
pcl::poisson::SparseMatrix::SetIdentity
void SetIdentity()
Definition: sparse_matrix.hpp:233
pcl::poisson::SparseMatrix::internalAllocator
static Allocator< MatrixEntry< T > > internalAllocator
Definition: sparse_matrix.h:60
pcl::poisson::SparseMatrix::Resize
void Resize(int rows)
Definition: sparse_matrix.hpp:161
pcl::poisson::SparseMatrix::operator*
SparseMatrix< T > operator*(const T &V) const
Definition: sparse_matrix.hpp:241
pcl
Definition: cloud_iterator.h:46
pcl::poisson::MapReduceVector
Definition: sparse_matrix.h:116
pcl::poisson::Vector::Dimensions
size_t Dimensions() const
Definition: vector.hpp:89
pcl::poisson::MatrixEntry
Definition: sparse_matrix.h:45
pcl::poisson::SparseMatrix
Definition: sparse_matrix.h:53
pcl::poisson::SparseMatrix::operator*=
SparseMatrix< T > & operator*=(const T &V)
Definition: sparse_matrix.hpp:249
pcl::poisson::SparseMatrix::SetRowSize
void SetRowSize(int row, int count)
Definition: sparse_matrix.hpp:207
pcl::poisson::SparseMatrix::write
bool write(FILE *fp) const
Definition: sparse_matrix.hpp:135
pcl::poisson::Vector
Definition: vector.h:41
pcl::poisson::MatrixEntry::Value
T Value
Definition: sparse_matrix.h:50
pcl::poisson::MatrixEntry::N
int N
Definition: sparse_matrix.h:49
pcl::poisson::SparseMatrix::read
bool read(FILE *fp)
Definition: sparse_matrix.hpp:143
pcl::poisson::SparseMatrix::Multiply
SparseMatrix< T > Multiply(const SparseMatrix< T > &M) const
Definition: sparse_matrix.hpp:259
pcl::poisson::SparseMatrix::m_ppElements
MatrixEntry< T > ** m_ppElements
Definition: sparse_matrix.h:66
pcl::poisson::MapReduceVector::resize
void resize(int threads, int dim)
Definition: sparse_matrix.h:131
pcl::poisson::Vector::Resize
void Resize(size_t N)
Definition: vector.hpp:63
pcl::poisson::SparseMatrix::operator=
SparseMatrix< T > & operator=(const SparseMatrix< T > &M)
Definition: sparse_matrix.hpp:101
pcl::poisson::Vector::SetZero
void SetZero()
Definition: vector.hpp:91
pcl::poisson::SparseMatrix::SetZero
void SetZero()
Definition: sparse_matrix.hpp:227
pcl::poisson::SparseSymmetricMatrix::operator*
Vector< T2 > operator*(const Vector< T2 > &V) const
Definition: sparse_matrix.hpp:416
pcl::poisson::Vector::Dot
T Dot(const Vector &V) const
Definition: vector.hpp:237
pcl::poisson::SparseMatrix::SparseMatrix
SparseMatrix(void)
Definition: sparse_matrix.hpp:70
pcl::poisson::SparseSymmetricMatrix::Solve
static int Solve(const SparseSymmetricMatrix< T > &M, const Vector< T2 > &b, int iters, Vector< T2 > &solution, T2 eps=1e-8, int reset=1, int threads=0, bool addDCTerm=false, bool solveNormal=false)
Definition: sparse_matrix.hpp:846
pcl::poisson::SparseSymmetricMatrix::getDiagonal
void getDiagonal(Vector< T2 > &diagonal) const
Definition: sparse_matrix.hpp:959
pcl::poisson::SparseMatrix::rowSizes
int * rowSizes
Definition: sparse_matrix.h:65
pcl::poisson::SparseMatrix::SetAllocator
static void SetAllocator(int blockSize)
Definition: sparse_matrix.hpp:57
pcl::poisson::SparseMatrix::UseAllocator
static int UseAllocator(void)
Definition: sparse_matrix.hpp:55
pcl::poisson::SparseMatrix::Transpose
SparseMatrix< T > Transpose() const
Definition: sparse_matrix.hpp:318
pcl::poisson::SparseMatrix::Solve
static int Solve(const SparseMatrix< T > &M, const Vector< T > &b, int iters, Vector< T > &solution, const T eps=1e-8)
Definition: sparse_matrix.hpp:382
pcl::poisson::SparseMatrix::SolveSymmetric
static int SolveSymmetric(const SparseMatrix< T > &M, const Vector< T2 > &b, int iters, Vector< T2 > &solution, const T2 eps=1e-8, int reset=1, int threads=1)
Definition: sparse_matrix.hpp:333
pcl::poisson::SparseMatrix::Entries
int Entries(void) const
Definition: sparse_matrix.hpp:94
pcl::poisson::SparseMatrix::~SparseMatrix
~SparseMatrix()
Definition: sparse_matrix.hpp:114
pcl::poisson::SparseSymmetricMatrix::Multiply
Vector< T2 > Multiply(const Vector< T2 > &V) const
Definition: sparse_matrix.hpp:419
pcl::poisson::Vector::m_pV
T * m_pV
Definition: vector.h:91
pcl::poisson::SparseSymmetricMatrix
Definition: sparse_matrix.h:145
pcl::poisson::MapReduceVector::threads
int threads(void) const
Definition: sparse_matrix.h:130
pcl::poisson::SparseMatrix::rows
int rows
Definition: sparse_matrix.h:64