interp_onetape.cpp¶

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Interpolation With Out Retaping: Example and Test¶

See Also¶

interp_retape.cpp , atomic_four_bilinear.cpp

# 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 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 double &x)
    {   size_t j = Index(x);
        return ArgumentValue[j];
    }
    double Function(const double &x)
    {   size_t j = Index(x);
        return FunctionValue[j];
    }

    double Slope(const double &x)
    {   size_t j  = Index(x);
        double dx = ArgumentValue[j+1] - ArgumentValue[j];
        double dy = FunctionValue[j+1] - FunctionValue[j];
        return dy / dx;
    }
    CPPAD_DISCRETE_FUNCTION(double, Argument)
    CPPAD_DISCRETE_FUNCTION(double, Function)
    CPPAD_DISCRETE_FUNCTION(double, Slope)
}


bool interp_onetape(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>) ax(n);
    ax[0] = .4 * ArgumentValue[1] + .6 * ArgumentValue[2];

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

    // evaluate piecewise linear interpolant at ax[0]
    AD<double> ax_grid   = Argument(ax[0]);
    AD<double> af_grid   = Function(ax[0]);
    AD<double> as_grid   = Slope(ax[0]);
    AD<double> ay_linear = af_grid + (ax[0] - ax_grid) * as_grid;

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

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

    // 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 ax[0] is between
    // ArgumentValue[1] and ArgumentValue[2]
    x[0]          = Value(ax[0]);
    double delta  = ArgumentValue[2] - ArgumentValue[1];
    double check  = FunctionValue[2] * (x[0] - ArgumentValue[1]) / delta
                        + FunctionValue[1] * (ArgumentValue[2] - x[0]) / delta;
    ok  &= NearEqual(ay[0], check, eps99, eps99);

    // evaluate f where x has different value
    x[0]   = .7 * ArgumentValue[2] + .3 * ArgumentValue[3];
    y      = f.Forward(0, x);

    // check function value
    delta  = ArgumentValue[3] - ArgumentValue[2];
    check  = FunctionValue[3] * (x[0] - ArgumentValue[2]) / delta
                        + FunctionValue[2] * (ArgumentValue[3] - 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[3] - FunctionValue[2])
             / (ArgumentValue[3] - ArgumentValue[2]);
    ok   &= NearEqual(dy[0], check, eps99, eps99);

    return ok;
}