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

rev_one.cpp

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First Order Derivative Driver: Example and Test

# include <cppad/cppad.hpp>
namespace { // -------------------------------------------------------
// define the template function RevOneCases<Vector> in empty namespace
template <class Vector>
bool RevOneCases()
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
    using CppAD::exp;
    using CppAD::sin;
    using CppAD::cos;

    // domain space vector
    size_t n = 2;
    CPPAD_TESTVECTOR(AD<double>)  X(n);
    X[0] = 1.;
    X[1] = 2.;

    // declare independent variables and starting recording
    CppAD::Independent(X);

    // range space vector
    size_t m = 3;
    CPPAD_TESTVECTOR(AD<double>)  Y(m);
    Y[0] = X[0] * exp( X[1] );
    Y[1] = X[0] * sin( X[1] );
    Y[2] = X[0] * cos( X[1] );

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

    // new value for the independent variable vector
    Vector x(n);
    x[0] = 2.;
    x[1] = 1.;

    // compute and check derivative of y[0]
    Vector dw(n);
    dw  = f.RevOne(x, 0);
    ok &= NearEqual(dw[0],      exp(x[1]), eps99, eps99); // w.r.t x[0]
    ok &= NearEqual(dw[1], x[0]*exp(x[1]), eps99, eps99); // w.r.t x[1]

    // compute and check derivative of y[1]
    dw  = f.RevOne(x, 1);
    ok &= NearEqual(dw[0],      sin(x[1]), eps99, eps99);
    ok &= NearEqual(dw[1], x[0]*cos(x[1]), eps99, eps99);

    // compute and check derivative of y[2]
    dw  = f.RevOne(x, 2);
    ok &= NearEqual(dw[0],        cos(x[1]), eps99, eps99);
    ok &= NearEqual(dw[1], - x[0]*sin(x[1]), eps99, eps99);

    return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool RevOne(void)
{   bool ok = true;
    // Run with Vector equal to three different cases
    // all of which are Simple Vectors with elements of type double.
    ok &= RevOneCases< CppAD::vector  <double> >();
    ok &= RevOneCases< std::vector    <double> >();
    ok &= RevOneCases< std::valarray  <double> >();
    return ok;
}