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

independent.cpp

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Independent and ADFun Constructor: Example and Test

# include <cppad/cppad.hpp>

namespace { // --------------------------------------------------------
// define the template function Test<ADVector>(void) in empty namespace
template <class ADVector>
bool Test(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // domain space vector
   size_t  n  = 2;
   ADVector X(n);  // ADVector is the template parameter in call to Test
   X[0] = 0.;
   X[1] = 1.;

   // declare independent variables and start recording
   // use the template parameter ADVector for the vector type
   CppAD::Independent(X);

   AD<double> a = X[0] + X[1];      // first AD operation
   AD<double> b = X[0] * X[1];      // second AD operation

   // range space vector
   size_t m = 2;
   ADVector Y(m);  // ADVector is the template paraemter in call to Test
   Y[0] = a;
   Y[1] = b;

   // create f: X -> Y and stop tape recording
   // use the template parameter ADVector for the vector type
   CppAD::ADFun<double> f(X, Y);

   // check value
   ok &= NearEqual(Y[0] , 1.,  eps99 , eps99);
   ok &= NearEqual(Y[1] , 0.,  eps99 , eps99);

   // compute f(1, 2)
   CPPAD_TESTVECTOR(double) x(n);
   CPPAD_TESTVECTOR(double) y(m);
   x[0] = 1.;
   x[1] = 2.;
   y    = f.Forward(0, x);
   ok &= NearEqual(y[0] , 3.,  eps99 , eps99);
   ok &= NearEqual(y[1] , 2.,  eps99 , eps99);

   // compute partial of f w.r.t x[0] at (1, 2)
   CPPAD_TESTVECTOR(double) dx(n);
   CPPAD_TESTVECTOR(double) dy(m);
   dx[0] = 1.;
   dx[1] = 0.;
   dy    = f.Forward(1, dx);
   ok &= NearEqual(dy[0] ,   1.,  eps99 , eps99);
   ok &= NearEqual(dy[1] , x[1],  eps99 , eps99);

   // compute partial of f w.r.t x[1] at (1, 2)
   dx[0] = 0.;
   dx[1] = 1.;
   dy    = f.Forward(1, dx);
   ok &= NearEqual(dy[0] ,   1.,  eps99 , eps99);
   ok &= NearEqual(dy[1] , x[0],  eps99 , eps99);

   return ok;
}
} // End of empty namespace -------------------------------------------

# include <vector>
# include <valarray>
bool Independent(void)
{  bool ok = true;
   typedef CppAD::AD<double> ADdouble;
   // Run with ADVector equal to three different cases
   // all of which are Simple Vectors with elements of type AD<double>.
   ok &= Test< CppAD::vector  <ADdouble> >();
   ok &= Test< std::vector    <ADdouble> >();
   ok &= Test< std::valarray  <ADdouble> >();
   return ok;
}