$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
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 as left operand // in the comparision operation scalar left = 1. / x[0]; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // right operand in comparison operation scalar right = x[0]; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; // Note that the left and right operand in the CondExpLt comparison // are determined at this point. Hence the conditional skip operator // will be inserted here so that the operations mentioned below can // also be skipped during zero order foward mode. if( options.find("no_conditional_skip") == std::string::npos ) after.n_op += 1; // for conditional skip operation // Create a variable that is only used when comparison result is true // (can be skipped when the comparison result is false) scalar if_true = x[0] * 5.0; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // Create two variables only used when the comparison result is false // (can be skipped when the comparison result is true) scalar temp = 5.0 + x[0]; scalar if_false = temp * 3.0; before.n_var += 2; before.n_op += 2; after.n_var += 2; after.n_op += 2; // conditional comparision is 1 / x[0] < x[0] scalar value = CppAD::CondExpLt(left, right, if_true, if_false); before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; // results for this operation sequence y[0] = value; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; } } bool conditional_skip(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_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_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 case where result of the comparison is true (x[0] > 1.0). CPPAD_TESTVECTOR(double) x(n), y(m), check(m); x[0] = 1.75; 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() == 2; else ok &= f.number_skip() == 0; // Check case where result of the comparision is false (x[0] <= 1.0) x[0] = 0.5; 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; } return ok; }