AD Absolute Value Function: Example and Test

fabs.cpp

Headings

@(@\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}} }@)@ This is cppad-20221105 documentation. Here is a link to its current documentation . AD Absolute Value Function: Example and Test


# include <cppad/cppad.hpp>

bool fabs(void)
{   bool ok = true;

    using CppAD::AD;
    using CppAD::NearEqual;

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

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

    // range space vector
    size_t m = 3;
    CPPAD_TESTVECTOR(AD<double>) ay(m);
    ay[0]     = fabs(ax[0] - 1.);
    ay[1]     = fabs(ax[0]);
    ay[2]     = fabs(ax[0] + 1.);
    //
    // create f: x -> y and stop tape recording
    CppAD::ADFun<double> f(ax, ay);

    // check values
    ok &= (ay[0] == 1.);
    ok &= (ay[1] == 0.);
    ok &= (ay[2] == 1.);
    //
    // forward computation of partials w.r.t. a positive x[0] direction
    size_t p = 1;
    CPPAD_TESTVECTOR(double) dx(n), dy(m);
    dx[0] = 1.;
    dy    = f.Forward(p, dx);
    ok  &= (dy[0] == - dx[0]);
    ok  &= (dy[1] ==   0.   );
    ok  &= (dy[2] == + dx[0]);
    //
    // forward computation of partials w.r.t. a negative x[0] direction
    dx[0] = -1.;
    dy    = f.Forward(p, dx);
    ok  &= (dy[0] == - dx[0]);
    ok  &= (dy[1] ==   0.   );
    ok  &= (dy[2] == + dx[0]);
    //
    // reverse computation of derivative of y[0]
    p    = 1;
    CPPAD_TESTVECTOR(double)  w(m), dw(n);
    w[0] = 1.; w[1] = 0.; w[2] = 0;
    dw   = f.Reverse(p, w);
    ok  &= (dw[0] == -1.);

    // reverse computation of derivative of y[1]
    w[0] = 0.; w[1] = 1.; w[2] = 0;
    dw   = f.Reverse(p, w);
    ok  &= (dw[0] == 0.);

    // reverse computation of derivative of y[3]
    w[0] = 0.; w[1] = 0.; w[2] = 1;
    dw   = f.Reverse(p, w);
    ok  &= (dw[0] == 1.);

    // use a VecAD<Base>::reference object with fabs
    CppAD::VecAD<double> av(1);
    AD<double> az(0);
    av[az]   = -1;
    AD<double> a_result = fabs(av[az]);
    ok  &= a_result == 1.0;

    return ok;
}

Input File: example/general/fabs.cpp