div_eq.cpp

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AD Compound Assignment Division: Example and Test

# include <cppad/cppad.hpp>

bool DivEq(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t  n = 1;
    double x0 = .5;
    CPPAD_TESTVECTOR(AD<double>) x(n);
    x[0]      = x0;

    // declare independent variables and start tape recording
    CppAD::Independent(x);

    // range space vector
    size_t m = 2;
    CPPAD_TESTVECTOR(AD<double>) y(m);
    y[0] = x[0] * x[0];  // initial value
    y[0] /= 2;           // AD<double> /= int
    y[0] /= 4.;          // AD<double> /= double
    y[1] = y[0] /= x[0]; // use the result of a compound assignment

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

    // check value
    ok &= NearEqual(y[0] , x0*x0/(2.*4.*x0), eps99, eps99);
    ok &= NearEqual(y[1] ,             y[0], eps99, eps99);

    // forward computation of partials w.r.t. x[0]
    CPPAD_TESTVECTOR(double) dx(n);
    CPPAD_TESTVECTOR(double) dy(m);
    dx[0] = 1.;
    dy    = f.Forward(1, dx);
    ok   &= NearEqual(dy[0], 1./8., eps99, eps99);
    ok   &= NearEqual(dy[1], 1./8., eps99, eps99);

    // reverse computation of derivative of y[0]
    CPPAD_TESTVECTOR(double)  w(m);
    CPPAD_TESTVECTOR(double) dw(n);
    w[0]  = 1.;
    w[1]  = 0.;
    dw    = f.Reverse(1, w);
    ok   &= NearEqual(dw[0], 1./8., eps99, eps99);

    // use a VecAD<Base>::reference object with computed division
    CppAD::VecAD<double> v(1);
    AD<double> zero(0);
    AD<double> result = 2;
    v[zero] = 1;
    result /= v[zero];
    ok     &= (result == 2);

    return ok;
}