#include	<iostream>
#include	<string>
#include	<sstream>
using std::cout;
using std::string;
using std::ostream;
using std::ostringstream;

class MyMat;
class MyVec;
class Vadd;
class MVmul;
class MVmuladd; 

struct Vadd {  // represents v1+v2
  const MyVec *v1, *v2;

  Vadd(const MyVec &_v1, const MyVec &_v2)
  { v1 = &_v1; v2 = &_v2; }

  operator MyVec(); // This computes v1+v2
};

struct MVmul {  // represents m*v
  const MyMat *m; // use references
  const MyVec *v; // to avoid copying

  MVmul(const MyMat &_m, const MyVec &_v)
  { m = &_m; v = &_v; }

  operator MyVec(); // This computes m*v
};

struct MVmuladd {  // represents m*v1+v2
  const MyMat *m;
  const MyVec *v1, *v2;

  MVmuladd(const MVmul &mv, const MyVec &_v2)
  { m = mv.m; v1 = mv.v; v2 = &_v2; }

  operator MyVec(); // This computes m*v1+v2
};

class MyMat {
  string name;
 public:
  friend class MyVec;
  friend MyVec &mul_assign(const MyMat &A, 
                           const MyVec &x, MyVec &out);
  friend MyVec &mul_add_assign(const MyMat &A, const MyVec &x, 
                               const MyVec &y, MyVec &out);

  MyMat(string _name) : name(_name) 
  { cout << "Creating MyMat " << _name << "\n"; }
  ~MyMat() { cout << "Destroying MyMat " << name << "\n"; }
  friend ostream &operator<<(ostream &s, const MyMat &x)
  { return s << x.name; }
};

class MyVec {
  string name;
 public:
  friend class MyMat;
  friend MyVec &add_assign(const MyVec &x, const MyVec &y, 
                           MyVec &out);
  friend MyVec &mul_assign(const MyMat &A, const MyVec &x, 
                           MyVec &out);
  friend MyVec &mul_add_assign(const MyMat &A, const MyVec &x, 
                               const MyVec &y, MyVec &out);

  MyVec(string _name) : name(_name) 
  { cout << "Creating MyVec " << _name << "\n"; }
  ~MyVec() { cout << "Destroying MyVec " << name << "\n"; }
  MyVec(const Vadd &vv)
  { add_assign(*vv.v1,*vv.v2,*this); }
  MyVec(const MVmul &mv)
  { mul_assign(*mv.m,*mv.v,*this); }
  MyVec(const MVmuladd &mv)
  { mul_add_assign(*mv.m,*mv.v1,*mv.v2,*this); }
  MyVec &operator=(const Vadd &vv)
  { return add_assign(*vv.v1,*vv.v2,*this); }
  MyVec &operator=(const MVmul &mv)
  { return mul_assign(*mv.m,*mv.v,*this); }
  MyVec &operator=(const MVmuladd &mv)
  { return mul_add_assign(*mv.m,*mv.v1,*mv.v2,*this); }

  friend ostream &operator<<(ostream &s, const MyVec &x)
  { return s << x.name; }
};


inline MVmul operator*(const MyMat &mm, const MyVec &vv)
{ return MVmul(mm,vv); }

inline MVmuladd operator+(const MVmul &mv, const MyVec &vv)
{ return MVmuladd(mv,vv); }

inline Vadd operator+(const MyVec &v1, const MyVec &v2)
{ return Vadd(v1,v2); }

Vadd::operator MyVec()
{
  ostringstream oss;
  oss << "(" << *v1 << "+" << *v2 << ")";
  MyVec *out = new MyVec(oss.str());
  return add_assign(*v1,*v2,*out);
}

MVmul::operator MyVec()
{
  ostringstream oss;
  oss << "(" << *m << "*" << *v << ")";
  MyVec *out = new MyVec(oss.str());
  return mul_assign(*m,*v,*out);
}

MVmuladd::operator MyVec()
{
  ostringstream oss;
  oss << "(" << *m << "*" << *v1 << "+" << *v2 << ")";
  MyVec *out = new MyVec(oss.str());
  return mul_add_assign(*m,*v1,*v2,*out);
}

MyVec &add_assign(const MyVec &v1, const MyVec &v2, MyVec &out)
{
  cout << "add_assign(" << v1 << "," << v2 << "," << out << ")\n";
  return out;
}

MyVec &mul_assign(const MyMat &A, const MyVec &x, MyVec &out)
{
  cout << "mul_assign(" << A << "," << x << "," << out << ")\n";
  return out;
}


MyVec &mul_add_assign(const MyMat &A, const MyVec &x, 
                      const MyVec &y, MyVec &out)
{
  cout << "mul_add_assign(" << A << "," << x << "," << y << "," << out << ")\n";
  return out;
}



int main(int argc, char *argv[])
{
  MyVec	u("u"), v("v"), w("w"), z("z");
  MyMat	A("A");

  cout << "operation: w = u+v;\n";
  w = u+v;
  cout << "operation: z = A*u+v;\n";
  z = A*u+v;
  cout << "operation: z = A*(A*u+v)+z;\n";
  z = A*(A*u+v)+z;
  cout << "operation: z = A*u + A*v + w + z;\n";
  z = A*u + A*v + w + z;
  cout << "operation: A*(u+v) + w + z\n";
  z = A*(u+v) + w + z;
  
  cout << "Done!\n";
}