#include <iostream.h>


class Matrix3x3
{
private:
   double A[3][3];

friend void operator<<( ostream & output, Matrix3x3 &x );         

public:
   int isSymmetric(double m[3][3])
   {
      int i, j;
      int sym = 1;

      for ( i = 0; i < 2; i = i + 1 )
         for ( j = i+1; j < 3; j = j + 1 )
	     if ( m[i][j] != m[j][i] )
		return(0);	// No

      // The input matrix passed the symmetry test
      return(1);
   }


   int init(double m[3][3])
   {
      int i, j;

      if ( ! isSymmetric(m) )
      {
	 cout << "Input matrix is NOT symmetric" << endl;

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

      return(1);
   }

   Matrix3x3 operator*(Matrix3x3 &m)
   {
      Matrix3x3 out;
      int i, j, k;

      if ( ! isSymmetric(m.A) )
      {
	 cout << "Input matrix is NOT symmetric" << endl;

         for (i = 0; i < 3; i = i + 1)
            for (j = 0; j < 3; j = j + 1)
	        out.A[i][j] = 0;
	 return(out);
      }
      
   
      for (i = 0; i < 3; i = i + 1)
      {
         for (j = 0; j < 3; j = j + 1)
         {
   	 out.A[i][j] = 0.0;
   
   	 for (k = 0; k < 3; k = k + 1)
               out.A[i][j] = out.A[i][j] + A[i][k]*m.A[k][j];
         }
      }
   
      return(out);
   }
};



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

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


int main(int argc, char *argv[])
{
   Matrix3x3 A, B, C;
   double    p[3][3];

   p[0][0] = 1.0; p[0][1] = 0.0; p[0][2] = 1.0;
   p[1][0] = 0.0; p[1][1] = 1.0; p[1][2] = 1.0;
   p[2][0] = 1.0; p[2][1] = 1.0; p[2][2] = 0.0;

   if ( A.init(p) == 0 )
   {
      cout << "Input error, exiting..." << endl;
      exit(1);
   }

   cout << "\nInitial matrix A:" << endl;
   cout << A;
   cout << endl;

   p[0][0] = 1.0; p[0][1] = 0.0; p[0][2] = 2.0;
   p[1][0] = 0.0; p[1][1] = 1.0; p[1][2] = 1.0;
   p[2][0] = 2.0; p[2][1] = 1.0; p[2][2] = 0.0;

   if ( B.init(p) == 0 )
   {
      cout << "Input error, exiting..." << endl;
      exit(1);
   }

   cout << "\nInitial matrix B:" << endl;
   cout << B;
   cout << endl;



   C = A * B;
   cout << endl << "\nAfter C = A * B, matrix C:" << endl << endl;
   cout << C;
   cout << endl;
}