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@(@\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}} }@)@
Example Optimization and Conditional Expressions

See Also
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;
}

Input File: example/optimize/conditional_skip.cpp