linrcomb.h

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//
// $Source: /home/gambit/CVS/gambit/sources/numerical/linrcomb.h,v $
// $Date: 2002/09/26 17:50:54 $
// $Revision: 1.1.2.1 $
//
// DESCRIPTION:
// Find linear weights for dependencies between rows of a matrix
//
// This file is part of Gambit
// Copyright (c) 2002, The Gambit Project
//
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
//

/*
   This file contains the file for a class that performs a very specific
computation, namely asking whether the last row of a matrix is a linear
combination of the other rows, and if so computing the coefficients of
a linear dependence.
   All computation is done in the constructor.  The constructor should
only be called when there is a guarantee (which this class may be used
to compute!) that the rows other than the last are linearly
independent.
*/

#ifndef LINRCOMB_H
#define LINRCOMB_H

#include "math/rational.h"
#include "math/gmatrix.h"

template <class T> class LinearCombination  {
  private:
    gMatrix<T> scrambled;
    gVector<T> weights;
    bool       last_row_is_spanned;

    void AddMultipleOfRowiToRowj(const int& i, 
				 const int& j, 
				 const T& scalar);
    void AddMultipleOfRowiToRowj(const int& i, 
				 const int& j, 
				 const T& scalar,
				 gMatrix<T>& B);

  // This function is left unimplemented to avoid copying
    LinearCombination<T>& operator=(const LinearCombination<T> &);
  
  public:
       // Constructors, Destructor, Constructive Operators
    LinearCombination(const gMatrix<T> &);
    LinearCombination(const LinearCombination<T> &);

    virtual ~LinearCombination();


       // Comparison Operators
    bool operator==(const LinearCombination<T> &) const;
    bool operator!=(const LinearCombination<T> &) const;

       // Information
    bool       LastRowIsSpanned() const;
    gVector<T> LinearDependence() const;
 
    void Output(gOutput &) const;
};

template <class T> gOutput &operator<<(gOutput &,
				       const LinearCombination<T> &);


#endif     // LinearCombination_H