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Up-> CppAD ADFun optimize optimize_compare_op.cpp

optimize_compare_op.cpp

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# include <cppad/cppad.hpp>
namespace {
    struct tape_size { size_t n_var; size_t n_op; };

    template <class Vector> void fun(
        const std::string& options ,
        const Vector& x, Vector& y, tape_size& before, tape_size& after
    )
    {   typedef typename Vector::value_type scalar;

        // phantom variable with index 0 and independent variables
        // begin operator, independent variable operators and end operator
        before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
        after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

        // Create a variable that is is only used in the comparison operation
        // It is not used when the comparison operator is not included
        scalar one = 1. / x[0];
        before.n_var += 1; before.n_op += 1;
        after.n_var  += 0; after.n_op  += 0;
        // If we keep comparison operators, we must compute their operands
        if( options.find("no_compare_op") == std::string::npos )
        {   after.n_var += 1;  after.n_op += 1;
        }

        // Create a variable that is used by the result
        scalar two = x[0] * 5.;
        before.n_var += 1; before.n_op += 1;
        after.n_var  += 1; after.n_op += 1;

        // Only one variable created for this comparison operation
        // but the value depends on which branch is taken.
        scalar three;
        if( one < x[0] )        // comparison operator
            three = two / 2.0;  // division operator
        else
            three = 2.0 * two;  // multiplication operator
        // comparison and either division of multiplication operator
        before.n_var += 1; before.n_op += 2;
        // comparison operator depends on optimization options
        after.n_var += 1;  after.n_op += 1;
        // check if we are keeping the comparison operator
        if( options.find("no_compare_op") == std::string::npos )
            after.n_op += 1;

        // results for this operation sequence
        y[0] = three;
        before.n_var += 0; before.n_op  += 0;
        after.n_var  += 0; after.n_op   += 0;
    }
}

bool compare_op(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n  = 1;
    CPPAD_TESTVECTOR(AD<double>) ax(n);
    ax[0] = 0.5;

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

    for(size_t k = 0; k < 2; k++)
    {   // optimization options
        std::string options = "";
        if( k == 0 )
            options = "no_compare_op";

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

        // compute function value
        tape_size before, after;
        fun(options, ax, ay, before, after);

        // create f: x -> y and stop tape recording
        CppAD::ADFun<double> f(ax, ay);
        ok &= f.size_order() == 1; // this constructor does 0 order forward
        ok &= f.size_var() == before.n_var;
        ok &= f.size_op() == before.n_op;

        // Optimize the operation sequence
        f.optimize(options);
        ok &= f.size_order() == 0; // 0 order forward not present
        ok &= f.size_var() == after.n_var;
        ok &= f.size_op() == after.n_op;

        // Check result for a zero order calculation for a different x,
        // where the result of the comparison is he same.
        CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
        x[0] = 0.75;
        y    = f.Forward(0, x);
        if ( options == "" )
            ok  &= f.compare_change_number() == 0;
        fun(options, x, check, before, after);
        ok &= NearEqual(y[0], check[0], eps10, eps10);

        // Check case where result of the comparison is differnent
        // (hence one needs to re-tape to get correct result)
        x[0] = 2.0;
        y    = f.Forward(0, x);
        if ( options == "" )
            ok  &= f.compare_change_number() == 1;
        fun(options, x, check, before, after);
        ok  &= std::fabs(y[0] - check[0]) > 0.5;
    }
    return ok;
}