\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

optimize_nest_conditional.cpp

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Optimize Nested Conditional Expressions: Example and Test

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 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;
}