/* $Id: not_complex_ad.cpp 2506 2012-10-24 19:36:49Z bradbell $ */
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 Bradley M. Bell
CppAD is distributed under multiple licenses. This distribution is under
the terms of the
GNU General Public License Version 3.
A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */
/*
$begin not_complex_ad.cpp$$
$spell
imag
Cpp
$$
$section Not Complex Differentiable: Example and Test$$
$index complex, polynomial$$
$index polynomial, complex$$
$index imag()$$
$index real()$$
$index example, not complex differentiable$$
$index test, not complex differentiable$$
$head Not Complex Differentiable$$
If $icode x$$ is complex, the functions
$codei%real(%x%)%$$,
$codei%imag(%x%)%$$,
$codei%conj(%x%)%$$, and
$codei%abs(%x%)%$$
are examples of functions that are not complex differentiable.
$head See Also$$
$cref complex_poly.cpp$$
$head Poly$$
Select this link to view specifications for $cref Poly$$:
$code
$verbatim%example/not_complex_ad.cpp%0%// BEGIN C++%// END C++%1%$$
$$
$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# include <complex>
bool not_complex_ad(void)
{ bool ok = true;
size_t deg = 4;
using CppAD::AD;
using CppAD::Poly;
typedef std::complex<double> Complex;
typedef std::complex< AD<double> > ComplexAD;
// The imaginary part in the following assignment will use
// the CppAD::AD<double> default constructor. Make sure it is zero.
AD<double> ad_zero = AD<double>(0);
AD<double> ad_two = AD<double>(2);
ComplexAD cad_two = ad_two;
ok &= cad_two == ComplexAD(ad_two, ad_zero);
// polynomial coefficients
CPPAD_TESTVECTOR( Complex ) a (deg + 1); // coefficients for p(z)
CPPAD_TESTVECTOR( ComplexAD ) A (deg + 1);
size_t i;
for(i = 0; i <= deg; i++)
{ a[i] = Complex(i, i);
A[i] = ComplexAD( AD<double>(i) , AD<double>(i) );
}
// declare independent variables and start taping
CPPAD_TESTVECTOR(AD<double>) Z_real(1);
double z_real = 1.;
Z_real[0] = z_real;
Independent(Z_real);
// complex calculations
double z_imag = 2.;
ComplexAD Z = ComplexAD( Z_real[0], AD<double>(z_imag) );
ComplexAD P = Poly(0, A, Z);
// range space vector
CPPAD_TESTVECTOR(AD<double>) P_real(1);
P_real[0] = P.real(); // real() is not complex differentiable
// create f: Z_real -> P_real and stop taping
CppAD::ADFun<double> f(Z_real, P_real);
// check first derivative w.r.t z
CPPAD_TESTVECTOR(double) v( f.Domain() );
CPPAD_TESTVECTOR(double) w( f.Range() );
v[0] = 1.;
w = f.Forward(1, v);
Complex z = Complex(z_real, z_imag);
Complex p = Poly(1, a, z);
ok &= ( w[0] == p.real() );
// 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.real() );
return ok;
}
// END C++