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

complex_poly.cpp

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Complex Polynomial: Example and Test

Poly

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// Complex examples should suppress conversion warnings
# include <cppad/wno_conversion.hpp>

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

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;
}