#include <iostream.h>


// ======================================  Vector3
class Vector3
{
private:
   float x[3];
public:
   /* --------------------
      Default constructor
      -------------------- */
   Vector3()
   {  int i;

      for (i = 0; i < 3; i=i+1)
         x[i] = i + 10;
   }

   friend ostream & operator<<(ostream &, Vector3 &);

   friend class Matrix3;
};

// ======================================  Matrix3
class Matrix3
{
private:
   float A[3][3];

public:
   /* --------------------
      Default constructor
      -------------------- */
   Matrix3()
   {  int i, j;

      for (i = 0; i < 3; i=i+1)
         for (j = 0; j < 3; j=j+1)
            A[i][j] = i + j;
   }

   /************************************************
     Matrix vector multiply member FRIEND function
    *************************************************/
   Vector3 operator*(Vector3 & v)
   {
      Vector3 z;
      int i, j;

      for (i = 0; i < 3; i=i+1)
         z.x[i] = 0;

      for (i = 0; i < 3; i=i+1)
         for (j = 0; j < 3; j=j+1)
            z.x[i] = z.x[i] + A[i][j]*v.x[j];

      return z;
   }

   friend ostream & operator<<(ostream &, Matrix3 &);
};


// ================================================ Print functions
ostream & operator<<(ostream & cout, Vector3 & v)
{  int i;

   for (i = 0; i < 3; i=i+1)
      cout << v.x[i] << "\t";
   cout << endl;

   return(cout);
}


ostream & operator<<(ostream & cout, Matrix3 & M)
{
   int i, j;

   for (i = 0; i < 3; i=i+1)
   {
      for (j = 0; j < 3; j=j+1)
         cout << M.A[i][j] << "\t";
      cout << endl;
   }

   return(cout);
}


// ================================================ Main


int main(int argc, char *argv[])
{
   Matrix3 M;
   Vector3 v1, v2;

   cout << "Matrix M:" << endl << M << endl;
   cout << "Vector v1:" << endl << v1 << endl;
   cout << "Vector v2:" << endl << v2 << endl;

   // Matrix-vector multiply
   v2 = M * v1;

   cout << "After v2 = M * v1:" << endl << endl;

   cout << "Vector v1:" << endl << v1 << endl;
   cout << "Vector v2:" << endl << v2 << endl;
}