// Cannot make this work... need friend class !!!


#include <iostream.h>

// --------------------- Matrix3x3 declaration
class Matrix3x3;

// --------------------- Vector3 declaration
class Vector3;

// --------------------- Matrix3x3 definition
class Matrix3x3
{
private:
   double A[3][3];

   friend Vector3  Vector3::operator* ( Matrix3x3 & M );
   friend ostream & operator<< (ostream & output, Matrix3x3 & m);
   friend int main(int argc, char *argv[]);

public:
   Vector3  operator* ( Vector3 & v);
};



class Vector3
{
private:
   double d[3];       

   friend Vector3  Matrix3x3::operator* ( Vector3 & v );
   friend ostream & operator<< (ostream & output, Vector3 & v);
   friend int main(int argc, char *argv[]);

   Vector3  operator* (  Matrix3x3 & M );
};



// ---------------------- Implement Matrx * Vector
Vector3  Vector3::operator* (  Matrix3x3 & M )
{
   Vector3 out;
   int i, k;

   for (i = 0; i < 3; i = i + 1)
   {
      out.d[i] = 0.0;

      for (k = 0; k < 3; k = k + 1)
         out.d[i] = out.d[i] +  d[k] * M.A[k][i];
   }

   return(out);
}


// ---------------------- Implement Matrx * Vector
Vector3 Matrix3x3::operator* ( Vector3 & v)          
{
   Vector3 out;
   int i, k;

   for (i = 0; i < 3; i = i + 1)
   {
      out.d[i] = 0.0;

      for (k = 0; k < 3; k = k + 1)
         out.d[i] = out.d[i] +  A[i][k] * v.d[k];               
   }

   return(out);
};




ostream & operator<< (ostream & output, Vector3 & v)
{
   int i, j;

   for (i = 0; i < 3; i = i+1)
   {
      output << v.d[i];
   }
   output << endl;

   return(output);
}

ostream & operator<< (ostream & output, Matrix3x3 & m)
{
   int i, j;

   for (i = 0; i < 3; i = i+1)
   {
      for (j = 0; j < 3; j = j+1)
         output << m.A[i][j];
      output << endl;
   }

   return(output);
}

int main(int argc, char *argv[])
{
   Matrix3x3 A;
   Vector3   v, u;

   A.A[0][0] = 1.0; A.A[0][1] = 0.0; A.A[0][2] = 0.0;
   A.A[1][0] = 1.0; A.A[1][1] = 1.0; A.A[1][2] = 0.0;
   A.A[2][0] = 1.0; A.A[2][1] = 1.0; A.A[2][2] = 1.0;

   cout << "Initial matrix A:" << endl << endl;
   cout << A << endl;;

   v.d[0] = 1.0; v.d[1] = 2.0; v.d[2] = 3.0;

   cout << "Initial vector v:" << endl << endl;
   cout << v << endl;;

   u = A * v;

   cout << endl << "After  u = A * v, vector u:" << endl << endl;
   cout << v << endl;;
}