interp_retape.cpp¶

Interpolation With Retaping: Example and Test¶

See Also¶

# include <cppad/cppad.hpp>
# include <cassert>
# include <cmath>

namespace {
    double ArgumentValue[] = {
        .0 ,
        .2 ,
        .4 ,
        .8 ,
        1.
    };
    double FunctionValue[] = {
        std::sin( ArgumentValue[0] ) ,
        std::sin( ArgumentValue[1] ) ,
        std::sin( ArgumentValue[2] ) ,
        std::sin( ArgumentValue[3] ) ,
        std::sin( ArgumentValue[4] )
    };
    size_t TableLength = 5;

    size_t Index(const CppAD::AD<double> &x)
    {   // determine the index j such that x is between
        // ArgumentValue[j] and ArgumentValue[j+1]
        static size_t j = 0;
        while ( x < ArgumentValue[j] && j > 0 )
            j--;
        while ( x > ArgumentValue[j+1] && j < TableLength - 2)
            j++;
        // assert conditions that must be true given logic above
        assert( j >= 0 && j < TableLength - 1 );
        return j;
    }
    double Argument(const CppAD::AD<double> &x)
    {   size_t j = Index(x);
        return ArgumentValue[j];
    }
    double Function(const CppAD::AD<double> &x)
    {   size_t j = Index(x);
        return FunctionValue[j];
    }
    double Slope(const CppAD::AD<double> &x)
    {   size_t j  = Index(x);
        double dx = ArgumentValue[j+1] - ArgumentValue[j];
        double dy = FunctionValue[j+1] - FunctionValue[j];
        return dy / dx;
    }
}

bool interp_retape(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;
    CPPAD_TESTVECTOR(AD<double>) X(n);

    // loop over argument values
    size_t k;
    for(k = 0; k < TableLength - 1; k++)
    {
        X[0] = .4 * ArgumentValue[k] + .6 * ArgumentValue[k+1];

        // declare independent variables and start tape recording
        // (use a different tape for each argument value)
        CppAD::Independent(X);

        // evaluate piecewise linear interpolant at X[0]
        AD<double> A = Argument(X[0]);
        AD<double> F = Function(X[0]);
        AD<double> S = Slope(X[0]);
        AD<double> I = F + (X[0] - A) * S;

        // range space vector
        size_t m = 1;
        CPPAD_TESTVECTOR(AD<double>) Y(m);
        Y[0] = I;

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

        // vectors for arguments to the function object f
        CPPAD_TESTVECTOR(double) x(n);   // argument values
        CPPAD_TESTVECTOR(double) y(m);   // function values
        CPPAD_TESTVECTOR(double) dx(n);  // differentials in x space
        CPPAD_TESTVECTOR(double) dy(m);  // differentials in y space

        // to check function value we use the fact that X[0] is between
        // ArgumentValue[k] and ArgumentValue[k+1]
        double delta, check;
        x[0]   = Value(X[0]);
        delta  = ArgumentValue[k+1] - ArgumentValue[k];
        check  = FunctionValue[k+1] * (x[0]-ArgumentValue[k]) / delta
                         + FunctionValue[k] * (ArgumentValue[k+1]-x[0]) / delta;
        ok    &= NearEqual(Y[0], check, eps99, eps99);

        // evaluate partials w.r.t. x[0]
        dx[0] = 1.;
        dy    = f.Forward(1, dx);

        // check that the derivative is the slope
        check = (FunctionValue[k+1] - FunctionValue[k])
                  / (ArgumentValue[k+1] - ArgumentValue[k]);
        ok   &= NearEqual(dy[0], check, eps99, eps99);
    }
    return ok;
}