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optimize_nest_conditional.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 second comparison
        scalar two = 1. + x[0];
        before.n_var += 1; before.n_op += 1;
        after.n_var  += 1; after.n_op  += 1;

        // Conditional skip for second comparison will be inserted here.
        if( options.find("no_conditional_skip") == std::string::npos )
            after.n_op += 1; // for conditional skip operation

        // Create a variable that is is only used in the first comparison
        // (can be skipped when second comparison result is false)
        scalar one = 1. / x[0];
        before.n_var += 1; before.n_op += 1;
        after.n_var  += 1; after.n_op  += 1;

        // Conditional skip for first comparison will be inserted here.
        if( options.find("no_conditional_skip") == std::string::npos )
            after.n_op += 1; // for conditional skip operation

        // value when first comparison if false
        scalar one_false = 5.0;

        // Create a variable that is only used when second comparison is true
        // (can be skipped when it is false)
        scalar one_true = x[0] / 5.0;
        before.n_var += 1; before.n_op += 1;
        after.n_var  += 1; after.n_op  += 1;

        // value when second comparison is false
        scalar two_false = 3.0;

        // First conditional compaison is 1 / x[0] < x[0]
        // is only used when second conditional expression is true
        // (can be skipped when it is false)
        scalar two_true  = CppAD::CondExpLt(one, x[0], one_true, one_false);
        before.n_var += 1; before.n_op += 1;
        after.n_var  += 1; after.n_op  += 1;

        // Second conditional compaison is 1 + x[0] < x[1]
        scalar two_value = CppAD::CondExpLt(two, x[1], two_true, two_false);
        before.n_var += 1; before.n_op += 1;
        after.n_var  += 1; after.n_op  += 1;

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

bool nest_conditional(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  = 2;
    CPPAD_TESTVECTOR(AD<double>) ax(n);
    ax[0] = 0.5;
    ax[1] = 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_conditional_skip";

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

        // compute function computation
        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 case where result of the second comparison is true
        // and first comparison is true
        CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
        x[0] = 1.75;
        x[1] = 4.0;
        y    = f.Forward(0, x);
        fun(options, x, check, before, after);
        ok &= NearEqual(y[0], check[0], eps10, eps10);
        ok  &= f.number_skip() == 0;

        // Check case where result of the second comparison is true
        // and first comparison is false
        x[0] = 0.5;
        x[1] = 4.0;
        y    = f.Forward(0, x);
        fun(options, x, check, before, after);
        ok &= NearEqual(y[0], check[0], eps10, eps10);
        if( options == "" )
            ok  &= f.number_skip() == 1;
        else
            ok &= f.number_skip() == 0;

        // Check case where result of the second comparison is false
        // and first comparison is true
        x[0] = 1.75;
        x[1] = 0.0;
        y    = f.Forward(0, x);
        fun(options, x, check, before, after);
        ok &= NearEqual(y[0], check[0], eps10, eps10);
        if( options == "" )
            ok  &= f.number_skip() == 3;
        else
            ok &= f.number_skip() == 0;

        // Check case where result of the second comparison is false
        // and first comparison is false
        x[0] = 0.5;
        x[1] = 0.0;
        y    = f.Forward(0, x);
        fun(options, x, check, before, after);
        ok &= NearEqual(y[0], check[0], eps10, eps10);
        if( options == "" )
            ok  &= f.number_skip() == 3;
        else
            ok &= f.number_skip() == 0;
    }
    return ok;
}