//
// Matrix * Vector using ordinary function

#include <iostream.h>

class Vector3
{
public:
   double d[3];       
};

class Matrix3x3
{
public:
   double A[3][3];
};


// ----------------------------------------------
// Here is the Matrix * Vector operator
// ----------------------------------------------
Vector3  operator* ( Matrix3x3 & M, 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] +  M.A[i][k] * v.d[k];               
   }

   return(out);
}


void printV(Vector3 *v)
{
   int i, j;

   for (i = 0; i < 3; i = i+1)
   {
      printf("%5.2lf ", v->d[i]);
   }
   cout << endl;
}

void printM(Matrix3x3 *m)
{
   int i, j;

   for (i = 0; i < 3; i = i+1)
   {
      for (j = 0; j < 3; j = j+1)
         printf("%5.2lf ", m->A[i][j]);
      cout << endl;
   }
}

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;
   printM(&A);

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

   cout << "Initial vector v:" << endl << endl;
   printV(&v);

   u = A * v;

   cout << endl << "After  u = A * v, vector u:" << endl << endl;
   printV(&u);
}