CLASSE MATRIX

/*
 * 			TMatrix c++ class
 *		
 *			Author: Simon Charlier
 *							  2002
 *
 *		This class implement an object with 2 dimensional array
 *		like a matrix. Elements are stored into a simple array. Another
 *		array contain a pointer on each row.
 *      When you build a matrix, like "TMatrix<float> a(6,4);", you must
 *      de-allocate memory using the function "a.destroy();". The destructor
 *      TMatrix::~Tmatrix(); cause malfunctions... sorry :( 
 *      If you give only one dimension, like "TMatrix<float> a(3);", you
 *      create a square matrix 3x3. Default is 2x2.
 *		To put data on a matrix, create before an array of float with
 *		values and use the function "M.in(DATAARRAY);" if M is the matrix.
 *      If DATAARRAY size not correspond at the size of matrix, the result
 *      is not guaranteed.
 *		Next, use functions and operators classically: 		
 *			M.reverse();
 *			M.determinant();
 *			M0=M1*M2;
 *			...etc.
 *		For more, contact me at s.c@oreka.com
*/

#ifndef __TMATRIX H__
#define __TMATRIX H__

#include <iostream.h>
#include <math.h>

// Uses this declaTn for C ONLY
// version of memory allocation
// #include <alloc.h>

class TMatrixException        /* Exception class for TFloatMatix */
{
    public:
      enum Exception
      {
           DIM_TOO_SMALL ,
           NOT_SAME_DIM  ,
           NOT_SQUARE    ,
           NOT_MULTIPLICABLE
      };

      TMatrixException(Exception);
      Exception Err;
};

template <class T> class TMatrix
{
    public:
      /* ---------------------- Attributes --------------------------- */
      T *M;							     /* Linear matrix data storage */
      T **P;						          /* Pointers on each rows */
      int dimR;						 /* Number of rows ( column size ) */
      int dimC;						 /* Number of columns ( row size ) */
		
	  /*  ----------------------- Builders --------------------------- */
      TMatrix(int dim=2);                /* Default, for square matrix */
      TMatrix(int,int);                              /* For NxM matrix */
      TMatrix(const TMatrix<T>&);                              /* Copy */
      ~TMatrix();								 /* de-allocate memory */

      /* -------------------- Utils procedures ----------------------- */
      void clear();							/* Reset to 0 all elements */
      void destroy();                            /* de-allocate memory */
      void resize(int,int);                     /* Set a new dimension */
      void resize(int dim=2);                  /* The same, for square */
      void in(T*);						     /* Input data in a matrix */
      ostream& out(ostream&) const;	     /* Display matrix on std::out */

	  /*  ------------- Functions and procedure on this object ------- */
      TMatrix cofactor();				 	 /* Return cofactor matrix */
      T cofactor(int, int);					 	 /* 1 element cofactor */
      T minor(int, int);				   			/* 1 element minor */
      T determinant();						/* Determinant of a matrix */
      void transpose();							 /* Transpose a matrix */
      void reverse();							   /* Reverse a matrix */
      void TC();					  /* Transpose and cofactor matrix */

	  /* ---------------------- Operators ---------------------------- */
      TMatrix<T>& operator=(const TMatrix<T>&);
	
	  TMatrix<T> operator-() 				  ;
      TMatrix<T> operator+(const TMatrix<T>&) ;
      TMatrix<T> operator-(const TMatrix<T>&) ;
      TMatrix<T> operator*(const TMatrix<T>&) ;
      TMatrix<T> operator*(const T);
      TMatrix<T> operator*=(const T);

    private:
      T det3x3();			/* return the determinant of a 3x3 matrix */
      T det2x2();			/* return the determinant of a 2x2 matrix */
      TMatrix<T> matrix4minor(int,int);   	/* Return matrix of minor */
      TMatrix<T> mul(const TMatrix<T>&);  	 /* Multiply two matrices */
};

template <class T>
ostream& operator<< (ostream& o, const TMatrix<T>& m)
{return m.out(o);}

template <class T>
istream& operator>> (istream&, TMatrix<T>&);
#endif
//===========================================================================

TMatrixException::TMatrixException(Exception e) : Err(e)
{
    if (e==DIM_TOO_SMALL)
    {
        cout <<"ERR: DIM TOO SMALL"<<endl<<endl;
        system("pause");
        return;//exit(0);
    }
    if (e==NOT_SAME_DIM)
    {
        cout <<"ERR: NOT SAME DIM"<<endl;
        cout <<"US: Add or substract only same size matrix."<<endl;
        cout <<"FR: Additionner ou soustraire uniquement des ";
        cout <<"matrices de meme taille"<<endl;
        system("pause");
        return;//exit(0);
    }
    if (e==NOT_SQUARE)
    {
        cout <<"ERR: NOT SQUARE"<<endl<<endl;
        cout <<"US: Attempt to use a function reserved to square matrix ";
        cout <<"on a not-square matrix."<<endl;
        cout <<"FR: Tentative d'utilisation d'une fonction reservee aux ";
        cout <<"matrices carrees sur une matrice non-carree."<<endl;
        system("pause");
        return;//exit(0);
    }
    if (e==NOT_MULTIPLICABLE)
    {
        cout <<"ERR: NOT MULTIPLICABLE"<<endl<<endl;
        cout <<"US: To multiply, the number of columns in first matrix ";
        cout <<"must be equal to number of rows in the second."<<endl;
        cout <<"FR: Pour multiplier, le nombre de colonnes de la ";
        cout <<"premiere matrice doit etre egal au nombre de lignes ";
        cout <<"de la deuxieme."<<endl;
        system("pause");
        return;//exit(0);
    }
    else
    {
        cout <<"UNKNOW EXCEPTION"<<endl;
        system("pause");
        return ;//exit(0);
    }
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T>::TMatrix(int dimRow, int dimCol)
{
    if (dimRow<1 || dimCol<1)
        throw TMatrixException(TMatrixException::DIM_TOO_SMALL);

    dimR=dimRow;
	dimC=dimCol;
	
    // C ONLY VERSION
    // M=(float*) malloc (dimR*dimR*sizeof(float));
    // P=(float**) malloc (dimR*sizeof(float*));

    // C++ VERSION
    M=new T[dimR*dimC*sizeof(T)];
    P=new T*[dimR*sizeof(T*)];

    T *ref;
    ref=M;
    for (int i=0; i<dimR; i++)
    {
        P[i]=ref;
        ref+=dimC;
    }
    clear();
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T>::TMatrix(int dim)
{
    if (dim<1)
        throw TMatrixException(TMatrixException::DIM_TOO_SMALL);

    dimR=dim;
	dimC=dim;
	
    // C ONLY VERSION
    // M=(float*) malloc (dimR*dimR*sizeof(float));
    // P=(float**) malloc (dimR*sizeof(float*));

    // C++ VERSION
    M=new T[dimR*dimC*sizeof(T)];
    P=new T*[dimR*sizeof(T*)];

    T *ref;
    ref=M;
    for (int i=0; i<dimR; i++)
    {
        P[i]=ref;
        ref+=dimC;
    }
    clear();
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T>::TMatrix(const TMatrix<T>& m)
{
    dimR=m.dimR;
    dimC=m.dimC;
    M=m.M;
    P=m.P;
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T>::~TMatrix()
{
    /* use the function destroy() after use. */
    /* This destructor cause exceptions ...  */
}
//---------------------------------------------------------------------------

template <class T>
void TMatrix<T>::destroy()
{
	// C ONLY VERSION
    // free(M);
    // free(P);

    // C++ VERSION
    for (int i=0; i<dimR; i++)
        delete [] P[i];
    delete[] P;
    delete[] M;
}
//---------------------------------------------------------------------------

template <class T>
void TMatrix<T>::clear()
{
    for (int i=0; i<dimR; i++)
        for (int j=0; j<dimC; j++)
            P[i][j]=0;
}
//---------------------------------------------------------------------------

template <class T>
void TMatrix<T>::resize(int rw, int cl)
{
    TMatrix<T> m(rw,cl);
    if (dimR*dimC <= rw*cl)
    {
        for (int i=0; i<dimR;i++)
            for (int j=0; j<dimC; j++)
                m.P[i][j]=P[i][j];
        for (int i2=dimR; i2<rw; i2++)
            for (int j2=dimC; j2<cl; j2++)
                m.P[i2][j2]=0;
    }
    else
    {
        for (int i=0; i<rw;i++)
            for (int j=0; j<cl; j++)
                m.P[i][j]=P[i][j];
    }
    *this=m;
}
//---------------------------------------------------------------------------

template <class T>
void TMatrix<T>::resize(int dim)
{
    TMatrix<T> m(dim);
    if (dimR*dimC <= dim*dim)
    {
        for (int i=0; i<dimR;i++)
            for (int j=0; j<dimC; j++)
                m.P[i][j]=P[i][j];
        for (int i2=dimR; i2<dim; i2++)
            for (int j2=dimC; j2<dim; j2++)
                m.P[i2][j2]=0;
    }
    else
    {
        for (int i=0; i<dim;i++)
            for (int j=0; j<dim; j++)
                m.P[i][j]=P[i][j];
    }
    *this=m;
}
//---------------------------------------------------------------------------

template <class T>
void TMatrix<T>::in(T *data)
{
    for (int i=0; i<dimR;i++)
        for (int j=0; j<dimC; j++)
            P[i][j]=data[dimC*i+j];
}
//---------------------------------------------------------------------------

template <class T>
ostream& TMatrix<T>::out(ostream& o) const
{
    for (int i=0; i<dimR; i++)
    {
        for (int j=0; j<dimC; j++)
            o <<P[i][j]<<" ";
        o <<endl;
    }
    return o;
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T>& TMatrix<T>::operator=(const TMatrix<T>& m)
{
    dimR=m.dimR;
    dimC=m.dimC;
    M=m.M;
    P=m.P;
    return *this;
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T> TMatrix<T>::operator-()
{
    TMatrix<T> r(dimR,dimC);
    r=*this * T(-1);
    return r;
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T> TMatrix<T>::operator+(const TMatrix<T>& m)
{
	if (dimR!=m.dimR || dimC!=m.dimC)
        throw TMatrixException(TMatrixException::NOT_SAME_DIM);

    TMatrix<T> r(dimR,dimC);
    for (int i=0; i<dimR; i++)
        for (int j=0; j<dimC; j++)
            r.P[i][j]=P[i][j]+m.P[i][j];
    return r;
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T> TMatrix<T>::operator-(const TMatrix<T>& m)
{
	if (dimR!=m.dimR || dimC!=m.dimC)
        throw TMatrixException(TMatrixException::NOT_SAME_DIM);

    TMatrix<T> r(dimR,dimC);
    for (int i=0; i<dimR; i++)
        for (int j=0; j<dimC; j++)
            r.P[i][j]=P[i][j]-m.P[i][j];
    return r;
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T> TMatrix<T>::operator*(const TMatrix<T>& m)
{
	if (dimC!=m.dimR)
        throw TMatrixException(TMatrixException::NOT_MULTIPLICABLE);

    TMatrix<T> r(dimR,m.dimC);
    r=this->mul(m);
    return r;
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T> TMatrix<T>::operator*(const T f)
{
    for (int i=0; i<dimR; i++)
        for (int j=0; j<dimC; j++)
            P[i][j]*=f;
    return *this;
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T> TMatrix<T>::operator*=(const T f)
{
    *this=*this*f;
    return *this;
}
//---------------------------------------------------------------------------

template <class T>
TMatrix<T> TMatrix<T>::mul(const TMatrix<T>& m)
{
    TMatrix<T> r(dimR,m.dimC);
    T e=0;
    for (int i=0; i<dimR; i++)
        for (int j=0; j<m.dimC; j++)
        {
            for (int k=0; k<dimC; k++)
                e+=P[i][k]*m.P[k][j];
            r.P[i][j]=e;
            e=0;
        }
    return r;
}
//---------------------------------------------------------------------------

template <class T>
void TMatrix<T>::reverse()
{
	if (dimR!=dimC)
        throw TMatrixException(TMatrixException::NOT_SQUARE);

    TMatrix<T> r(dimR,dimC);
    r=cofactor();
    r.transpose();
    for (int i=0; i<dimR; i++)
        for (int j=0; j<dimR; j++)
            r.P[i][j]=r.P[i][j]*pow(-1,i+j+2);
    r*=T(1)/determinant();
    *this=r;
}
//---------------------------------------------------------------------------

template <class T>
void TMatrix<T>::TC()
{
	if (dimR!=dimC)
        throw TMatrixException(TMatrixException::NOT_SQUARE);

    TMatrix<T> r(dimR,dimC);
    r=cofactor();
    r.transpose();
    for (int i=0; i<dimR; i++)
        for (int j=0; j<dimR; j++)
            r.P[i][j]=r.P[i][j]*pow(-1,i+j+2);
    *this=r;
}
//---------------------------------------------------------------------------

template <class T>
void TMatrix<T>::transpose()
{
    TMatrix<T> m(dimC,dimR);
    for (int i=0; i<dimR; i++)
        for (int j=0; j<dimC; j++)
        {      m.P[i][j]=P[j][i];}
    *this=m;
}
//---------------------------------------------------------------------------

template <class T>
T TMatrix<T>::det3x3()
{
    return   P[0][0] * ( (P[1][1]*P[2][2])-(P[1][2]*P[2][1]) )
           - P[1][0] * ( (P[0][1]*P[2][2])-(P[0][2]*P[2][1]) )
           + P[2][0] * ( (P[0][1]*P[1][2])-(P[0][2]*P[1][1]) );
}
//---------------------------------------------------------------------------

template <class T>
T TMatrix<T>::det2x2()
{
    return   P[0][0]*P[1][1] - P[0][1]*P[1][0];
}
//---------------------------------------------------------------------------

template <class T>
T TMatrix<T>::determinant()
{
	if (dimR!=dimC)
        throw TMatrixException(TMatrixException::NOT_SQUARE);

    if (dimR==2) return det2x2();
    if (dimR==3) return det3x3();
    T d=0;
    for (int i=0; i<dimR; i++)
        d+=P[i][0] * cofactor(i,0);
    return d;
}
//---------------------------------------------------------------------------

template <class T>
T TMatrix<T>::cofactor(int ir, int ic)
{
	if (dimR!=dimC)
        throw TMatrixException(TMatrixException::NOT_SQUARE);

    return minor(ir,ic) * pow(-1, ir+ic+2);
}
//---------------------------------------------------------------------------
 
template <class T>
T TMatrix<T>::minor(int ir, int ic)
{
	if (dimR!=dimC)
        throw TMatrixException(TMatrixException::NOT_SQUARE);

    TMatrix<T> m4m(dimR-1);
    m4m=matrix4minor(ir,ic);
    return m4m.determinant();
}
//---------------------------------------------------------------------------
 
template <class T>
TMatrix<T> TMatrix<T>::cofactor()
{
	if (dimR!=dimC)
        throw TMatrixException(TMatrixException::NOT_SQUARE);

    TMatrix<T> r(dimR);
    for (int i=0; i<dimR; i++)
        for (int j=0; j<dimR; j++)
            r.P[i][j]=cofactor(i,j);
    return r;
}
//---------------------------------------------------------------------------
 
template <class T>
TMatrix<T> TMatrix<T>::matrix4minor(int ir, int ic)
{
	if (dimR!=dimC)
        throw TMatrixException(TMatrixException::NOT_SQUARE);
    
    int indexR=0;
    int indexC=0;
    TMatrix<T> r(dimR-1);
    for (int i=0; i<dimR; i++)
        for (int j=0; j<dimR; j++)
        {
            if (i!=ir && j!=ic)
            {
                r.P[indexR][indexC]=P[i][j];
                indexC++;
            }
            if (indexC==r.dimR)
            {
                indexC=0;
                indexR++;
            }
            if (indexR==r.dimR)
                return r;
        }
    return r;
}
//---------------------------------------------------------------------------

template <class T>
istream& operator>> (istream& in, TMatrix<T> &m)
{
	int rw,cl;
	cout << "DIM ROW: ";
	in   >> rw;
	cout << "DIM COL: ";
	in   >> cl;
	
	if (rw<1 && cl<1)
		throw TMatrixException(TMatrixException::DIM_TOO_SMALL);

	m.resize(rw,cl);
    T *data=new T[rw*cl];
    T element;
	for (int i=0; i<rw; i++)
        for (int j=0; j<cl; j++)
        {
			cout << i <<','<<j<<':';
			in   >> element;
            data[cl*i+j]=element;
        }
     for (int x=0; x<rw; x++)
        for (int y=0; y<cl; y++)
            m.P[x][y]=data[cl*x+y];
    delete [] data;
	return in;
}
//---------------------------------------------------------------------------				

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