# include <cppad/cppad.hpp>

bool Eq(void)
{	bool ok = true;
	using CppAD::AD;

	// domain space vector
	size_t n = 3;
	CPPAD_TEST_VECTOR< AD<double> > x(n);
	x[0]     = 2;      // AD<double> = int
	x[1]     = 3.;     // AD<double> = double
	x[2]     = x[1];   // AD<double> = AD<double>

	// declare independent variables and start tape recording
	CppAD::Independent(x);
	
	// range space vector 
	size_t m = 3;
	CPPAD_TEST_VECTOR< AD<double> > y(m);

	// assign an AD<Base> object equal to an independent variable
	// (choose the first independent variable to check a special case)
	// use the value returned by the assignment (for another assignment)
	y[0] = y[1] = x[0];  

	// assign an AD<Base> object equal to an expression 
	y[1] = x[1] + 1.;
	y[2] = x[2] + 2.;

	// check that all the resulting components of y depend on x
	ok &= Variable(y[0]);  // y[0] = x[0]
	ok &= Variable(y[1]);  // y[1] = x[1] + 1
	ok &= Variable(y[2]);  // y[2] = x[2] + 2

	// construct f : x -> y and stop the tape recording
	CppAD::ADFun<double> f(x, y);

	// check variable values
	ok &= ( y[0] == 2.);
	ok &= ( y[1] == 4.);
	ok &= ( y[2] == 5.);

	// compute partials w.r.t x[1]
	CPPAD_TEST_VECTOR<double> dx(n);
	CPPAD_TEST_VECTOR<double> dy(m);
	dx[0] = 0.;
	dx[1] = 1.;
	dx[2] = 0.;
	dy   = f.Forward(1, dx);
	ok  &= (dy[0] == 0.);  // dy[0] / dx[1]
	ok  &= (dy[1] == 1.);  // dy[1] / dx[1]
	ok  &= (dy[2] == 0.);  // dy[2] / dx[1]

	// compute the derivative y[2]
	CPPAD_TEST_VECTOR<double>  w(m);
	CPPAD_TEST_VECTOR<double> dw(n);
	w[0] = 0.;
	w[1] = 0.;
	w[2] = 1.;
	dw   = f.Reverse(1, w);
	ok  &= (dw[0] == 0.);  // dy[2] / dx[0]
	ok  &= (dw[1] == 0.);  // dy[2] / dx[1]
	ok  &= (dw[2] == 1.);  // dy[2] / dx[2]

	// assign a VecAD<Base>::reference
	CppAD::VecAD<double> v(1);
	AD<double> zero(0);
	v[zero] = 5.;
	ok     &= (v[0] == 5.);

	return ok;
}