#include <iostream.h>

// ======================================  Data types
class Matrix3x3
{
public:
   float A[3][3];
};

class Vector3
{
public:
   float x[3];
};


// ================================================ Matrix-matrix multiply
Matrix3x3 operator*(Matrix3x3 & M1, Matrix3x3 & M2)
{
   Matrix3x3 r;

   int i, j, k;

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

   for (i = 0; i < 3; i=i+1)
      for (j = 0; j < 3; j=j+1)
	 for (k = 0; k < 3; k=k+1)
            r.A[i][j] = r.A[i][j] + M1.A[i][k]*M2.A[k][j];

   return r;
}

// ================================================ Matrix-vector multiply
Vector3 operator*(Matrix3x3 &M, 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] + M.A[i][j]*v.x[j];

   return z;
}



// ================================================ Print functions
ostream & operator<<(ostream & cout, Matrix3x3 & 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);
}

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

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

   return(cout);
}

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


int main(int argc, char *argv[])
{
   int i, j, z;
   Matrix3x3 M1, M2, M3;
   Vector3 v1, v2;

   for (i = 0; i < 3; i=i+1)
      for (j = 0; j < 3; j=j+1)
         M1.A[i][j] = i + j;
   cout << "Matrix M1:" << M1 << endl;
   cout << endl;

   for (i = 0; i < 3; i=i+1)
      for (j = 0; j < 3; j=j+1)
         M2.A[i][j] = i + j + 1;
   cout << "Matrix M2:" << M2 << endl;
   cout << endl;

   for (i = 0; i < 3; i=i+1)
      v1.x[i] = i + 10;
   cout << "Vector v1:" << v1 << endl;
   cout << endl;

   // Operator * overload....

   // Matrix-matrix multiply
   M3 = M1 * M2;
   cout << "M3 = M1 * M2:" << M3 << endl;
   cout << endl;

   // Matrix-vector multiply
   v2 = M2 * v1;
   cout << "v2 = M2 * v1:" << v2 << endl;
   cout << endl;
}