tnt_matrix.h

/*
*
* Template Numerical Toolkit (TNT)
*
* Mathematical and Computational Sciences Division
* National Institute of Technology,
* Gaithersburg, MD USA
*
*
* This software was developed at the National Institute of Standards and
* Technology (NIST) by employees of the Federal Government in the course
* of their official duties. Pursuant to title 17 Section 105 of the
* United States Code, this software is not subject to copyright protection
* and is in the public domain. NIST assumes no responsibility whatsoever for
* its use by other parties, and makes no guarantees, expressed or implied,
* about its quality, reliability, or any other characteristic.
*
*/
 
 
// C compatible matrix: row-oriented, 0-based [i][j] and 1-based (i,j) indexing
//
 
#ifndef TNT_MATRIX_H
#define TNT_MATRIX_H
 
#include "tnt_subscript.h"
#include "tnt_vector.h"
#include <cstdlib>
#include <cassert>
#include <iostream>
#include <sstream>
#include <fstream>
 
namespace TNT
{
 
//namespace Linear_Algebra {
 
 
template <class T>
class Matrix 
{
 
  private:
    Subscript m_;
    Subscript n_;
    Subscript mn_;      // total size
    T* v_;                  
    T** row_;           
    T* vm1_ ;       // these point to the same data, but are 1-based 
    T** rowm1_;
 
    // internal helper function to create the array
    // of row pointers
 
    void initialize(Subscript M, Subscript N)
    {
        mn_ = M*N;
        m_ = M;
        n_ = N;
 
        v_ = new T[mn_]; 
        row_ = new T*[M];
        rowm1_ = new T*[M];
 
        assert(v_  != NULL);
        assert(row_  != NULL);
        assert(rowm1_ != NULL);
 
        T* p = v_;              
        vm1_ = v_ - 1;
        for (Subscript i=0; i<M; i++)
        {
            row_[i] = p;
            rowm1_[i] = p-1;
            p += N ;
            
        }
 
        rowm1_ -- ;     // compensate for 1-based offset
    }
   
    void copy(const T*  v)
    {
        Subscript N = m_ * n_;
        Subscript i;
 
#ifdef TNT_UNROLL_LOOPS
        Subscript Nmod4 = N & 3;
        Subscript N4 = N - Nmod4;
 
        for (i=0; i<N4; i+=4)
        {
            v_[i] = v[i];
            v_[i+1] = v[i+1];
            v_[i+2] = v[i+2];
            v_[i+3] = v[i+3];
        }
 
        for (i=N4; i< N; i++)
            v_[i] = v[i];
#else
 
        for (i=0; i< N; i++)
            v_[i] = v[i];
#endif      
    }
 
    void set(const T& val)
    {
        Subscript N = m_ * n_;
        Subscript i;
 
#ifdef TNT_UNROLL_LOOPS
        Subscript Nmod4 = N & 3;
        Subscript N4 = N - Nmod4;
 
        for (i=0; i<N4; i+=4)
        {
            v_[i] = val;
            v_[i+1] = val;
            v_[i+2] = val;
            v_[i+3] = val; 
        }
 
        for (i=N4; i< N; i++)
            v_[i] = val;
#else
 
        for (i=0; i< N; i++)
            v_[i] = val;
        
#endif      
    }
    
 
    
    void destroy()
    {     
        /* do nothing, if no memory has been previously allocated */
        if (v_ == NULL) return ;
 
        /* if we are here, then matrix was previously allocated */
        if (v_ != NULL) delete [] (v_);     
        if (row_ != NULL) delete [] (row_);
 
        /* return rowm1_ back to original value */
        rowm1_ ++;
        if (rowm1_ != NULL ) delete [] (rowm1_);
    }
 
  public:
 
    typedef Subscript   size_type;
    typedef         T   value_type;
    typedef         T   element_type;
    typedef         T*  pointer;
    typedef         T*  iterator;
    typedef         T&  reference;
    typedef const   T*  const_iterator;
    typedef const   T&  const_reference;
 
    Subscript lbound() const { return 1;}
 
 
 
 
    operator T**(){ return  row_; }
    operator const T**() const { return row_; }
 
 
    Subscript size() const { return mn_; }
 
    // constructors
 
    Matrix() : m_(0), n_(0), mn_(0), v_(0), row_(0), vm1_(0), rowm1_(0) {};
 
    Matrix(const Matrix<T> &A)
    {
        initialize(A.m_, A.n_);
        copy(A.v_);
    }
 
    Matrix(Subscript M, Subscript N, const T& value = T(0))
    {
        initialize(M,N);
        set(value);
    }
 
    Matrix(Subscript M, Subscript N, const T* v)
    {
        initialize(M,N);
        copy(v);
    }
 
    Matrix(Subscript M, Subscript N, const char *s)
    {
        initialize(M,N);
        //std::istrstream ins(s);
        std::istringstream ins(s);
 
        Subscript i, j;
 
        for (i=0; i<M; i++)
            for (j=0; j<N; j++)
                ins >> row_[i][j];
    }
 
    // destructor
    //
    ~Matrix()
    {
        destroy();
    }
 
 
    Matrix<T>& newsize(Subscript M, Subscript N)
    {
        if (num_rows() == M && num_cols() == N)
            return *this;
 
        destroy();
        initialize(M,N);
        
        return *this;
    }
 
 
 
 
    Matrix<T>& operator=(const Matrix<T> &B)
    {
        if (v_ == B.v_)
            return *this;
 
        if (m_ == B.m_  && n_ == B.n_)      // no need to re-alloc
            copy(B.v_);
 
        else
        {
            destroy();
            initialize(B.m_, B.n_);
            copy(B.v_);
        }
 
        return *this;
    }
        
    Matrix<T>& operator=(const T& scalar)
    { 
        set(scalar); 
        return *this;
    }
 
 
    Subscript dim(Subscript d) const 
    {
#ifdef TNT_BOUNDS_CHECK
        assert( d >= 1);
        assert( d <= 2);
#endif
        return (d==1) ? m_ : ((d==2) ? n_ : 0); 
    }
 
    Subscript num_rows() const { return m_; }
    Subscript num_cols() const { return n_; }
 
 
 
 
    inline T* operator[](Subscript i)
    {
#ifdef TNT_BOUNDS_CHECK
        assert(0<=i);
        assert(i < m_) ;
#endif
        return row_[i];
    }
 
    inline const T* operator[](Subscript i) const
    {
#ifdef TNT_BOUNDS_CHECK
        assert(0<=i);
        assert(i < m_) ;
#endif
        return row_[i];
    }
 
    inline reference operator()(Subscript i)
    { 
#ifdef TNT_BOUNDS_CHECK
        assert(1<=i);
        assert(i <= mn_) ;
#endif
        return vm1_[i]; 
    }
 
    inline const_reference operator()(Subscript i) const
    { 
#ifdef TNT_BOUNDS_CHECK
        assert(1<=i);
        assert(i <= mn_) ;
#endif
        return vm1_[i]; 
    }
 
 
 
    inline reference operator()(Subscript i, Subscript j)
    { 
#ifdef TNT_BOUNDS_CHECK
        assert(1<=i);
        assert(i <= m_) ;
        assert(1<=j);
        assert(j <= n_);
#endif
        return  rowm1_[i][j]; 
    }
 
 
    
    inline const_reference operator() (Subscript i, Subscript j) const
    {
#ifdef TNT_BOUNDS_CHECK
        assert(1<=i);
        assert(i <= m_) ;
        assert(1<=j);
        assert(j <= n_);
#endif
        return rowm1_[i][j]; 
    }
 
 
 
        Vector<T> diag() const
        {
            Subscript N = n_ < m_ ? n_ : m_; 
            Vector<T> d(N);
 
            for (int i=0; i<N; i++)
                d[i] = row_[i][i];
 
          return d;
        }
 
      Matrix<T> upper_triangular() const;
        Matrix<T> lower_triangular() const;
 
    /* basic computations */
 
};
 
 
/* ***************************  I/O  ********************************/
 
 
template <class T>
std::ostream& operator<<(std::ostream &s, const Matrix<T> &A)
{
    Subscript M=A.num_rows();
    Subscript N=A.num_cols();
 
    s << M << " " << N << "\n";
    for (Subscript i=0; i<M; i++)
    {
        for (Subscript j=0; j<N; j++)
        {
            s << A[i][j] << " ";
        }
        s << "\n";
    }
 
 
    return s;
}
 
 
template <class T>
std::istream& operator>>(std::istream &s, Matrix<T> &A)
{
 
    Subscript M, N;
 
    s >> M >> N;
 
    if ( !(M == A.num_rows() && N == A.num_cols() ))
    {
        A.newsize(M,N);
    }
 
 
    for (Subscript i=0; i<M; i++)
        for (Subscript j=0; j<N; j++)
        {
            s >>  A[i][j];
        }
 
 
    return s;
}
 
 
 
// *******************[ basic matrix algorithms ]***************************
 
template <class T>
Matrix<T> & mult(Matrix<T>& C, const Matrix<T>  &A, const Matrix<T> &B)
{
 
#ifdef TNT_BOUNDS_CHECK
    assert(A.num_cols() == B.num_rows());
#endif
 
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
    Subscript K = B.num_cols();
 
#ifdef TNT_BOUNDS_CHECK
        assert(C.num_rows() == M);
        assert(C.num_cols() == K);
#endif  
 
    T sum;
 
    const T* row_i;
    const T* col_k;
 
    for (Subscript i=0; i<M; i++)
    for (Subscript k=0; k<K; k++)
    {
        row_i  = &(A[i][0]);
        col_k  = &(B[0][k]);
        sum = 0;
        for (Subscript j=0; j<N; j++)
        {
            sum  += *row_i * *col_k;
            row_i++;
            col_k += K;
        }
        C[i][k] = sum; 
    }
 
    return C;
}
 
 
template <class T>
inline Matrix<T> mult(const Matrix<T>  &A, const Matrix<T> &B)
{
 
#ifdef TNT_BOUNDS_CHECK
    assert(A.num_cols() == B.num_rows());
#endif
 
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
    Subscript K = B.num_cols();
 
    Matrix<T> tmp(M,K);
 
    // for (Subscript i=0; i<M; i++)
        // {
    // for (Subscript k=0; k<K; k++)
    //      {
    //      T sum = 0;
    //          for (Subscript j=0; j<N; j++)
    //          sum = sum +  A[i][j] * B[j][k];
        //  
        //         tmp[i][k] = sum; 
      //   }
        // }
 
        mult(tmp, A, B);        // tmp = A*B
 
    return tmp;
}
 
template <class T>
inline Matrix<T> operator*(const Matrix<T>  &A, const Matrix<T> &B)
{
    return mult(A,B);
}
 
template <class T>
inline Vector<T> mult(const Matrix<T>  &A, const Vector<T> &b)
{
 
#ifdef TNT_BOUNDS_CHECK
    assert(A.num_cols() == b.dim());
#endif
 
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
    Vector<T> tmp(M);
    T sum;
 
    for (Subscript i=0; i<M; i++)
    {
        sum = 0;
        for (Subscript j=0; j<N; j++)
            sum = sum +  A[i][j] * b[j];
 
        tmp[i] = sum; 
    }
 
    return tmp;
}
 
template <class T>
inline Vector<T> operator*(const Matrix<T>  &A, const Vector<T> &b)
{
    return mult(A,b);
}
 
 
template <class T>
inline Matrix<T> mult(const T& s, const Matrix<T> &A)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
        Matrix<T> R(M,N);
        for (int i=0; i<M; i++)
            for (int j=0; j<N; j++)
                R[i][j] = s * A[i][j];
                 
        return R;
}
 
template <class T>
inline Matrix<T> mult(const Matrix<T> &A, const T& s)
{
    return mult(s, A);
}
 
 
template <class T>
inline Matrix<T> mult_eq(const T& s, Matrix<T> &A)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
        for (int i=0; i<M; i++)
            for (int j=0; j<N; j++)
                A[i][j] *= s;
}
 
template <class T>
inline Matrix<T> mult_eq(Matrix<T> &A, const T&a)
{
    return mult_eq(a, A);
}
 
 
template <class T>
inline Matrix<T> transpose_mult(const Matrix<T>  &A, const Matrix<T> &B)
{
 
#ifdef TNT_BOUNDS_CHECK
    assert(A.num_rows() == B.num_rows());
#endif
 
    Subscript M = A.num_cols();
    Subscript N = A.num_rows();
    Subscript K = B.num_cols();
 
    Matrix<T> tmp(M,K);
    T sum;
 
    for (Subscript i=0; i<N; i++)
    for (Subscript k=0; k<K; k++)
    {
        sum = 0;
        for (Subscript j=0; j<M; j++)
            sum = sum +  A[j][i] * B[j][k];
 
        tmp[i][k] = sum; 
    }
 
    return tmp;
}
 
template <class T>
inline Vector<T> transpose_mult(const Matrix<T>  &A, const Vector<T> &b)
{
 
#ifdef TNT_BOUNDS_CHECK
    assert(A.num_rows() == b.dim());
#endif
 
    Subscript M = A.num_cols();
    Subscript N = A.num_rows();
    
    Vector<T> tmp(M);
 
    for (Subscript i=0; i<M; i++)
    {
        T sum = 0;
        for (Subscript j=0; j<N; j++)
            sum = sum +  A[j][i] * b[j];
 
        tmp[i] = sum; 
    }
 
    return tmp;
}
 
 
template <class T>
Matrix<T> add(const Matrix<T> &A, const Matrix<T> &B)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
    assert(M==B.num_rows());
    assert(N==B.num_cols());
 
    Matrix<T> tmp(M,N);
    Subscript i,j;
 
    for (i=0; i<M; i++)
        for (j=0; j<N; j++)
            tmp[i][j] = A[i][j] + B[i][j];
 
    return tmp;
}
 
template <class T>
inline Matrix<T> operator+(const Matrix<T> &A, const Matrix<T> &B)
{
    return add(A,B);
}
 
 
 
template <class T>
Matrix<T>& add_eq(Matrix<T> &A, const Matrix<T> &B)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
    assert(M==B.num_rows());
    assert(N==B.num_cols());
 
    Matrix<T> tmp(M,N);
    Subscript i,j;
 
    for (i=0; i<M; i++)
        for (j=0; j<N; j++)
            tmp[i][j] = A[i][j] + B[i][j];
 
    return A += tmp;
}
 
template <class T> 
inline Matrix<T> operator+=(Matrix<T> &A, const Matrix<T> &B)
{
    return add_eq(A,B);
}
 
template <class T>
Matrix<T> minus(const Matrix <T>& A, const Matrix<T> &B)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
    assert(M==B.num_rows());
    assert(N==B.num_cols());
 
    Matrix<T> tmp(M,N);
    Subscript i,j;
 
    for (i=0; i<M; i++)
        for (j=0; j<N; j++)
            tmp[i][j] = A[i][j] - B[i][j];
 
    return tmp;
 
}
 
template <class T>
inline Matrix<T> operator-(const Matrix<T> &A, 
    const Matrix<T> &B)
{
    return minus(A,B);
}
 
 
template <class T>
Matrix<T> mult_element(const Matrix<T> &A, const Matrix<T> &B)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
    assert(M==B.num_rows());
    assert(N==B.num_cols());
 
    Matrix<T> tmp(M,N);
    Subscript i,j;
 
    for (i=0; i<M; i++)
        for (j=0; j<N; j++)
            tmp[i][j] = A[i][j] * B[i][j];
 
    return tmp;
}
 
template <class T>
Matrix<T>&  mult_element_eq(Matrix<T> &A, const Matrix<T> &B)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
    assert(M==B.num_rows());
    assert(N==B.num_cols());
 
    Subscript i,j;
 
    for (i=0; i<M; i++)
        for (j=0; j<N; j++)
            A[i][j] *= B[i][j];
 
        return A;
}
 
 
template <class T>
double norm(const Matrix<T> &A)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
    T sum = 0.0;
    for (int i=1; i<=M; i++)
        for (int j=1; j<=N; j++)
                    sum += A(i,j) * A(i,j);
    return sqrt(sum);
 
}
 
template <class T>
Matrix<T> transpose(const Matrix<T> &A)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
 
    Matrix<T> S(N,M);
    Subscript i, j;
 
    for (i=0; i<M; i++)
        for (j=0; j<N; j++)
            S[j][i] = A[i][j];
 
    return S;
}
 
 
 
 
 
 
 
template <class T>
Vector<T> upper_triangular_solve(const Matrix<T> &A, const Vector<T> &b) 
{
    int n = A.num_rows() < A.num_cols() ? A.num_rows() : A.num_cols();
    Vector<T> x(b);
    for (int k=n; k >= 1; k--)
    {
        x(k) /= A(k,k);
        for (int i=1; i< k; i++ )
            x(i) -= x(k) * A(i,k);
        }
 
        return x;
}
        
template <class T>
Vector<T> lower_triangular_solve(const Matrix<T> &A, const Vector<T> &b) 
{
    int n = A.num_rows() < A.num_cols() ? A.num_rows() : A.num_cols();
    Vector<T> x(b);
    for (int k=1; k <= n; k++)
    {
        x(k) /= A(k,k);
        for (int i=k+1; i<= n; i++ )
            x(i) -= x(k) * A(i,k);
        }
 
        return x;
}
        
 
//}     /*  namespace TNT::Linear_Algebra; */
}   /* namespace TNT  */
 
#endif
// TNT_MATRIX_H