\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

bool_fun.cpp

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AD Boolean Functions: Example and Test

# include <cppad/cppad.hpp>
# include <complex>


// define abbreviation for double precision complex
typedef std::complex<double> Complex;

namespace {
    // a unary bool function with Complex argument
    static bool IsReal(const Complex &x)
    {   return x.imag() == 0.; }

    // a binary bool function with Complex arguments
    static bool AbsGeq(const Complex &x, const Complex &y)
    {   double axsq = x.real() * x.real() + x.imag() * x.imag();
        double aysq = y.real() * y.real() + y.imag() * y.imag();

        return axsq >= aysq;
    }

    // Create version of IsReal with AD<Complex> argument
    // inside of namespace and outside of any other function.
    CPPAD_BOOL_UNARY(Complex, IsReal)

    // Create version of AbsGeq with AD<Complex> arguments
    // inside of namespace and outside of any other function.
    CPPAD_BOOL_BINARY(Complex, AbsGeq)

}
bool BoolFun(void)
{   bool ok = true;

    CppAD::AD<Complex> x = Complex(1.,  0.);
    CppAD::AD<Complex> y = Complex(1.,  1.);

    ok &= IsReal(x);
    ok &= ! AbsGeq(x, y);

    return ok;
}