SparseMatrix.inl

/*
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
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CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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*/

#include <float.h>


///////////////////
//  SparseMatrix //
///////////////////

///////////////////////////////////////
// SparseMatrix Methods and Memebers //
///////////////////////////////////////

template<class T>
SparseMatrix<T>::SparseMatrix()
{
    rows=0;
    rowSizes=NULL;
    m_ppElements=NULL;
}

template<class T>
SparseMatrix<T>::SparseMatrix( int rows ){this->rows=0;Resize(rows);}

template<class T>
SparseMatrix<T>::SparseMatrix( const SparseMatrix& M )
{
    Resize(M.rows);
    for (int i=0; i<rows; i++){
        SetRowSize(i,M.rowSizes[i]);
        for(int j=0;j<rowSizes[i];j++){m_ppElements[i][j]=M.m_ppElements[i][j];}
    }
}
template<class T>
int SparseMatrix<T>::Entries(void){
    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)
{
    Resize(M.rows);
    for (int i=0; i<rows; i++){
        SetRowSize(i,M.rowSizes[i]);
        for (int j=0; j<rowSizes[i]; j++){m_ppElements[i][j]=M.m_ppElements[i][j];}
    }
    return *this;
}

template<class T>
SparseMatrix<T>::~SparseMatrix(){Resize(0);}

template<class T>
void SparseMatrix<T>::Resize( int r )
{
    int i;
    if(rows>0){
        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);
    }
}

template<class T>
void SparseMatrix<T>::SetRowSize(int row,int count){
    if(row>=0 && row<rows){
        if(rowSizes[row]){free(m_ppElements[row]);}
        if(count>0){m_ppElements[row]=(MatrixEntry<T>*)malloc(sizeof(MatrixEntry<T>)*count);}
        rowSizes[row]=count;
    }
}


template<class T>
void SparseMatrix<T>::SetZero()
{
    Resize(rows);
}

template<class T>
void SparseMatrix<T>::SetIdentity()
{
    SetZero();
//    for(int ij=0; ij < Min( this->Rows(), this->Columns() ); ij++)
//        (*this)(ij,ij) = T(1);
    for(int ij=0; ij < rows; ij++){
        SetRowSize(ij,1);
        m_ppElements[ij][0] = MatrixEntry<T>(ij);
        m_ppElements[ij][0].Value = 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();ii++){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) const
{
    for (int i=0; i<rows; i++){
        T2 temp=T2();
        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( rows );

    for (int i=0; i<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,const int& iters,Vector<T2>& solution,const T2 eps,const int& reset){
    Vector<T2> d,r,Md;
    T2 alpha,beta,rDotR;
    Md.Resize(b.Dimensions());
    if(reset){
        solution.Resize(b.Dimensions());
        solution.SetZero();
    }
    d=r=b-M.Multiply(solution);
    rDotR=r.Dot(r);
    if(b.Dot(b)<=eps){
        solution.SetZero();
        return 0;
    }

    int i;
    for(i=0;i<iters;i++){
        T2 temp;
        M.Multiply(d,Md);
        temp=d.Dot(Md);
        if(temp<=eps){break;}
        alpha=rDotR/temp;
        r.SubtractScaled(Md,alpha);
        temp=r.Dot(r);
        if(temp/b.Dot(b)<=eps){break;}
        beta=temp/rDotR;
        solution.AddScaled(d,alpha);
        if(beta<=eps){break;}
        rDotR=temp;
        Vector<T2>::Add(d,beta,r,d);
    }
    return i;
}

// 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,const 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;
}

////////////////////
//  SparseNMatrix //
////////////////////

////////////////////////////////////////
// SparseNMatrix Methods and Memebers //
////////////////////////////////////////

template<class T,int Dim>
SparseNMatrix<T,Dim>::SparseNMatrix()
{
    rows=0;
    rowSizes=NULL;
    m_ppElements=NULL;
}

template<class T,int Dim>
SparseNMatrix<T,Dim>::SparseNMatrix( int rows ){Resize(rows);}

template<class T,int Dim>
SparseNMatrix<T,Dim>::SparseNMatrix( const SparseNMatrix& M )
{
    Resize(M.rows);
    for (int i=0; i<rows; i++){
        SetRowSize(i,M.rowSizes[i]);
        for(int j=0;j<rowSizes[i];j++){m_ppElements[i][j]=M.m_ppElements[i][j];}
    }
}
template<class T,int Dim>
int SparseNMatrix<T,Dim>::Entries(void){
    int e=0;
    for(int i=0;i<rows;i++){e+=int(rowSizes[i]);}
    return e;
}
template<class T,int Dim>
SparseNMatrix<T,Dim>& SparseNMatrix<T,Dim>::operator = (const SparseNMatrix<T,Dim>& M)
{
    Resize(M.rows);
    for (int i=0; i<rows; i++){
        SetRowSize(i,M.rowSizes[i]);
        for (int j=0; j<rowSizes[i]; j++){m_ppElements[i][j]=M.m_ppElements[i][j];}
    }
    return *this;
}

template<class T,int Dim>
SparseNMatrix<T,Dim>::~SparseNMatrix(){Resize(0);}

template<class T,int Dim>
void SparseNMatrix<T,Dim>::Resize( int r )
{
    int i;
    if(rows>0){
        free(m_ppElements);
        free(rowSizes);
    }
    rows=r;
    if(r){
        rowSizes=(int*)malloc(sizeof(int)*r);
        memset(rowSizes,0,sizeof(int)*r);
        m_ppElements=(NMatrixEntry<T,Dim>**)malloc(sizeof(NMatrixEntry<T,Dim>*)*r);
    }
}

template<class T,int Dim>
void SparseNMatrix<T,Dim>::SetRowSize(int row,int count){
    if(row>=0 && row<rows){
        if(rowSizes[row]){free(m_ppElements[row]);}
        if(count>0){m_ppElements[row]=(NMatrixEntry<T,Dim>*)malloc(sizeof(NMatrixEntry<T,Dim>)*count);}
        rowSizes[row]=count;
    }
}

template<class T,int Dim>
SparseNMatrix<T,Dim> SparseNMatrix<T,Dim>::operator * (const T& V) const
{
    SparseNMatrix<T,Dim> M(*this);
    M *= V;
    return M;
}

template<class T,int Dim>
SparseNMatrix<T,Dim>& SparseNMatrix<T,Dim>::operator *= (const T& V)
{
    for (int i=0; i<rows; i++)
    {
        for(int ii=0;ii<m_ppElements[i].size();ii++){
            for(int jj=0;jj<Dim;jj++){
                m_ppElements[i][ii].Value[jj]*=V;
            }
        }
    }
    return *this;
}

template<class T,int Dim>
template<class T2>
NVector<T2,Dim> SparseNMatrix<T,Dim>::operator * (const Vector<T2>& V) const
{
    NVector<T2,Dim> R( rows );

    for (int i=0; i<rows; i++)
    {
        T2 temp[Dim];
        for(int ii=0;ii<Dim;ii++){temp[ii]=T2();}
        for(int ii=0;ii<rowSizes[i];ii++){
            for(int jj=0;jj<Dim;jj++){temp[jj]+=m_ppElements[i][ii].Value[jj]*V.m_pV[m_ppElements[i][jj].N];}
        }
        for(int ii=0;ii<Dim;ii++){R[i][ii]=temp[ii];}
    }
    return R;
}

template<class T,int Dim>
template<class T2>
Vector<T2> SparseNMatrix<T,Dim>::operator * (const NVector<T2,Dim>& V) const
{
    Vector<T2> R( rows );

    for (int i=0; i<rows; i++)
    {
        T2 temp(0);
        for(int ii=0;ii<rowSizes[i];ii++){
            for(int jj=0;jj<Dim;jj++){temp+=m_ppElements[i][ii].Value[jj]*V.m_pV[m_ppElements[i][ii].N][jj];}
        }
        R(i)=temp;
    }
    return R;
}

///////////////////////////
// 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( this->rows );

    for (int i=0; i<this->rows; i++){
        for(int ii=0;ii<this->rowSizes[i];ii++){
            int j=this->m_ppElements[i][ii].N;
            R(i)+=this->m_ppElements[i][ii].Value * V.m_pV[j];
            R(j)+=this->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) const
{
    Out.SetZero();
    for (int i=0; i<this->rows; i++){
        MatrixEntry<T>* temp=this->m_ppElements[i];
        T2& in1=In.m_pV[i];
        T2& out1=Out.m_pV[i];
        int rs=this->rowSizes[i];
        for(int ii=0;ii<rs;ii++){
            MatrixEntry<T>& temp2=temp[ii];
            int j=temp2.N;
            T2 v=temp2.Value;
            out1+=v * In.m_pV[j];
            Out.m_pV[j]+=v * in1;
        }
    }
}

template<class T>
template<class T2>
int SparseSymmetricMatrix<T>::Solve(const SparseSymmetricMatrix<T>& M,const Vector<T2>& b,const int& iters,Vector<T2>& solution,const T2 eps,const int& reset){
    Vector<T2> d,r,Md;
    T2 alpha,beta,rDotR,bDotB;
    Md.Resize(b.Dimensions());
    if(reset){
        solution.Resize(b.Dimensions());
        solution.SetZero();
    }
    d=r=b-M.Multiply(solution);     // error vector
    rDotR=r.Dot(r);                 // L2 distance of error vector
    bDotB=b.Dot(b);                 // L2 distance of b
    if(b.Dot(b)<=eps){
        solution.SetZero();
        return 0;
    }
    int i;
    for(i=0;i<iters;i++){
        T2 temp;
        M.Multiply(d,Md);           // vec Md = matrix M * vec d
        temp=d.Dot(Md);
        if(fabs(temp)<=eps){break;}
        alpha=rDotR/temp;
        r.SubtractScaled(Md,alpha);
        temp=r.Dot(r);
        if(temp/bDotB<=eps){break;}
        beta=temp/rDotR;
        solution.AddScaled(d,alpha);
        if(beta<=eps){break;}
        rDotR=temp;
        Vector<T2>::Add(d,beta,r,d);
    }
    return i;
}

template<class T>
template<class T2>
int SparseSymmetricMatrix<T>::Solve(const SparseSymmetricMatrix<T>& M,const Vector<T>& diagonal,const Vector<T2>& b,const int& iters,Vector<T2>& solution,const T2 eps,const 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;
        for(int j=0;j<int(M.rows);j++){solution[j]+=r[j]/diagonal[j];}
    }
    return iters;
}