$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
cond_exp.cpp  # 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 comparision 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 comparision 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_var() == before.n_var; ok &= f.size_op() == before.n_op; // Optimize the operation sequence f.optimize(options); 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 comparision 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; }