fmat.h

Go to the documentation of this file.

/*

*
* Template Numerical Toolkit (TNT): Linear Algebra Module
*
* 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.  The Template Numerical Toolkit (TNT) is
* an experimental system.  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.
*
* BETA VERSION INCOMPLETE AND SUBJECT TO CHANGE
* see http://math.nist.gov/tnt for latest updates.
*
*/



// Fortran-compatible matrix: column oriented, 1-based (i,j) indexing

#ifndef FMAT_H
#define FMAT_H

#include "subscript.h"
#include "vec.h"
#include <cstdlib>
#include <cassert>
#include <iostream>
#ifdef TNT_USE_REGIONS
#include "region2d.h"
#endif

// simple 1-based, column oriented Matrix class

namespace TNT
{

template <class T>
class Fortran_Matrix 
{


  public:

    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;}
 
  protected:
    T* v_;                  // these are adjusted to simulate 1-offset
    Subscript m_;
    Subscript n_;
    T** col_;           // these are adjusted to simulate 1-offset

    // internal helper function to create the array
    // of row pointers

    void initialize(Subscript M, Subscript N)
    {
        // adjust col_[] pointers so that they are 1-offset:
        //   col_[j][i] is really col_[j-1][i-1];
        //
        // v_[] is the internal contiguous array, it is still 0-offset
        //
        v_ = new T[M*N];
        col_ = new T*[N];

        assert(v_  != NULL);
        assert(col_ != NULL);


        m_ = M;
        n_ = N;
        T* p = v_ - 1;              
        for (Subscript i=0; i<N; i++)
        {
            col_[i] = p;
            p += M ;
            
        }
        col_ --; 
    }
   
    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 */
        delete [] (v_);     
        col_ ++;                // changed back to 0-offset
        delete [] (col_);
    }


  public:

    T* begin() { return v_; }
    const T* begin() const { return v_;}

    T* end() { return v_ + m_*n_; }
    const T* end() const { return v_ + m_*n_; }


    // constructors

    Fortran_Matrix() : v_(0), m_(0), n_(0), col_(0)  {};
    Fortran_Matrix(const Fortran_Matrix<T> &A)
    {
        initialize(A.m_, A.n_);
        copy(A.v_);
    }

    Fortran_Matrix(Subscript M, Subscript N, const T& value = T())
    {
        initialize(M,N);
        set(value);
    }

    Fortran_Matrix(Subscript M, Subscript N, const T* v)
    {
        initialize(M,N);
        copy(v);
    }


    // destructor
    ~Fortran_Matrix()
    {
        destroy();
    }


    // assignments
    //
    Fortran_Matrix<T>& operator=(const Fortran_Matrix<T> &A)
    {
        if (v_ == A.v_)
            return *this;

        if (m_ == A.m_  && n_ == A.n_)      // no need to re-alloc
            copy(A.v_);

        else
        {
            destroy();
            initialize(A.m_, A.n_);
            copy(A.v_);
        }

        return *this;
    }
        
    Fortran_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_; }

    Fortran_Matrix<T>& newsize(Subscript M, Subscript N)
    {
        if (num_rows() == M && num_cols() == N)
            return *this;

        destroy();
        initialize(M,N);

        return *this;
    }



    // 1-based element access
    //
    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 col_[j][i]; 
    }

    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 col_[j][i]; 
    }


#ifdef TNT_USE_REGIONS

    typedef Region2D<Fortran_Matrix<T> > Region;
    typedef const_Region2D< Fortran_Matrix<T> > const_Region;

    Region operator()(const Index1D &I, const Index1D &J)
    {
        return Region(*this, I,J);
    }

    const_Region operator()(const Index1D &I, const Index1D &J) const
    {
        return const_Region(*this, I,J);
    }

#endif


};


/* ***************************  I/O  ********************************/

template <class T>
std::ostream& operator<<(std::ostream &s, const Fortran_Matrix<T> &A)
{
    Subscript M=A.num_rows();
    Subscript N=A.num_cols();

    s << M << " " << N << "\n";

    for (Subscript i=1; i<=M; i++)
    {
        for (Subscript j=1; j<=N; j++)
        {
            s << A(i,j) << " ";
        }
        s << "\n";
    }


    return s;
}

template <class T>
std::istream& operator>>(std::istream &s, Fortran_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=1; i<=M; i++)
        for (Subscript j=1; j<=N; j++)
        {
            s >>  A(i,j);
        }


    return s;
}

// *******************[ basic matrix algorithms ]***************************


template <class T>
Fortran_Matrix<T> operator+(const Fortran_Matrix<T> &A, 
    const Fortran_Matrix<T> &B)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();

    assert(M==B.num_rows());
    assert(N==B.num_cols());

    Fortran_Matrix<T> tmp(M,N);
    Subscript i,j;

    for (i=1; i<=M; i++)
        for (j=1; j<=N; j++)
            tmp(i,j) = A(i,j) + B(i,j);

    return tmp;
}

template <class T>
Fortran_Matrix<T> operator-(const Fortran_Matrix<T> &A, 
    const Fortran_Matrix<T> &B)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();

    assert(M==B.num_rows());
    assert(N==B.num_cols());

    Fortran_Matrix<T> tmp(M,N);
    Subscript i,j;

    for (i=1; i<=M; i++)
        for (j=1; j<=N; j++)
            tmp(i,j) = A(i,j) - B(i,j);

    return tmp;
}

// element-wise multiplication  (use matmult() below for matrix
// multiplication in the linear algebra sense.)
//
//
template <class T>
Fortran_Matrix<T> mult_element(const Fortran_Matrix<T> &A, 
    const Fortran_Matrix<T> &B)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();

    assert(M==B.num_rows());
    assert(N==B.num_cols());

    Fortran_Matrix<T> tmp(M,N);
    Subscript i,j;

    for (i=1; i<=M; i++)
        for (j=1; j<=N; j++)
            tmp(i,j) = A(i,j) * B(i,j);

    return tmp;
}


template <class T>
Fortran_Matrix<T> transpose(const Fortran_Matrix<T> &A)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();

    Fortran_Matrix<T> S(N,M);
    Subscript i, j;

    for (i=1; i<=M; i++)
        for (j=1; j<=N; j++)
            S(j,i) = A(i,j);

    return S;
}


    
template <class T>
inline Fortran_Matrix<T> matmult(const Fortran_Matrix<T>  &A, 
    const Fortran_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();

    Fortran_Matrix<T> tmp(M,K);
    T sum;

    for (Subscript i=1; i<=M; i++)
    for (Subscript k=1; k<=K; k++)
    {
        sum = 0;
        for (Subscript j=1; j<=N; j++)
            sum = sum +  A(i,j) * B(j,k);

        tmp(i,k) = sum; 
    }

    return tmp;
}

template <class T>
inline Fortran_Matrix<T> operator*(const Fortran_Matrix<T> &A, 
    const Fortran_Matrix<T> &B)
{
    return matmult(A,B);
}

template <class T>
inline int matmult(Fortran_Matrix<T>& C, const Fortran_Matrix<T>  &A, 
    const Fortran_Matrix<T> &B)
{

    assert(A.num_cols() == B.num_rows());

    Subscript M = A.num_rows();
    Subscript N = A.num_cols();
    Subscript K = B.num_cols();

    C.newsize(M,K);         // adjust shape of C, if necessary


    T sum; 

    const T* row_i;
    const T* col_k;

    for (Subscript i=1; i<=M; i++)
    {
        for (Subscript k=1; k<=K; k++)
        {
            row_i = &A(i,1);
            col_k = &B(1,k);
            sum = 0;
            for (Subscript j=1; j<=N; j++)
            {
                sum +=  *row_i * *col_k;
                row_i += M;
                col_k ++;
            }
        
            C(i,k) = sum; 
        }

    }

    return 0;
}


template <class T>
Vector<T> matmult(const Fortran_Matrix<T>  &A, const Vector<T> &x)
{

#ifdef TNT_BOUNDS_CHECK
    assert(A.num_cols() == x.dim());
#endif

    Subscript M = A.num_rows();
    Subscript N = A.num_cols();

    Vector<T> tmp(M);
    T sum;

    for (Subscript i=1; i<=M; i++)
    {
        sum = 0;
        for (Subscript j=1; j<=N; j++)
            sum = sum +  A(i,j) * x(j);

        tmp(i) = sum; 
    }

    return tmp;
}

template <class T>
inline Vector<T> operator*(const Fortran_Matrix<T>  &A, const Vector<T> &x)
{
    return matmult(A,x);
}

template <class T>
inline Fortran_Matrix<T> operator*(const Fortran_Matrix<T>  &A, const T &x)
{
    Subscript M = A.num_rows();
    Subscript N = A.num_cols();

    Subscript MN = M*N; 

    Fortran_Matrix<T> res(M,N);
    const T* a = A.begin();
    T* t = res.begin();
    T* tend = res.end();

    for (t=res.begin(); t < tend; t++, a++)
        *t = *a * x;

    return res;
} 

}  // namespace TNT

#endif // FMAT_H