bool complex_poly(void)
{ bool ok = true;
size_t deg = 4;
using CppAD::AD;
using CppAD::Poly;
typedef std::complex<double> Complex;
// polynomial coefficients
CPPAD_TESTVECTOR( Complex ) a (deg + 1); // coefficients for p(z)
CPPAD_TESTVECTOR(AD<Complex>) A (deg + 1);
size_t i;
for(i = 0; i <= deg; i++)
A[i] = a[i] = Complex(double(i), double(i));
// independent variable vector
CPPAD_TESTVECTOR(AD<Complex>) Z(1);
Complex z = Complex(1., 2.);
Z[0] = z;
Independent(Z);
// dependent variable vector and indices
CPPAD_TESTVECTOR(AD<Complex>) P(1);
// dependent variable values
P[0] = Poly(0, A, Z[0]);
// create f: Z -> P and vectors used for derivative calculations
CppAD::ADFun<Complex> f(Z, P);
CPPAD_TESTVECTOR(Complex) v( f.Domain() );
CPPAD_TESTVECTOR(Complex) w( f.Range() );
// check first derivative w.r.t z
v[0] = 1.;
w = f.Forward(1, v);
Complex p = Poly(1, a, z);
ok &= ( w[0] == p );
// second derivative w.r.t z is 2 times its second order Taylor coeff
v[0] = 0.;
w = f.Forward(2, v);
p = Poly(2, a, z);
ok &= ( 2. * w[0] == p );
return ok;
}
