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

abs_eval.hpp

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abs_eval Source Code

namespace CppAD { // BEGIN_CPPAD_NAMESPACE
// BEGIN PROTOTYPE
template <class Vector>
Vector abs_eval(
   size_t        n       ,
   size_t        m       ,
   size_t        s       ,
   const Vector& g_hat   ,
   const Vector& g_jac   ,
   const Vector& delta_x )
// END PROTOTYPE
{  using std::fabs;
   //
   CPPAD_ASSERT_KNOWN(
      size_t(delta_x.size()) == n,
      "abs_eval: size of delta_x not equal to n"
   );
   CPPAD_ASSERT_KNOWN(
      size_t(g_hat.size()) == m + s,
      "abs_eval: size of g_hat not equal to m + s"
   );
   CPPAD_ASSERT_KNOWN(
      size_t(g_jac.size()) == (m + s) * (n + s),
      "abs_eval: size of g_jac not equal to (m + s)*(n + s)"
   );
# ifndef NDEBUG
   // Check that partial_u z(x, u) is strictly lower triangular
   for(size_t i = 0; i < s; i++)
   {  for(size_t j = i; j < s; j++)
      {  // index in g_jac of partial of z_i w.r.t u_j
         // (note that g_jac has n + s elements in each row)
         size_t index = (m + i) * (n + s) + (n + j);
         CPPAD_ASSERT_KNOWN(
            g_jac[index] == 0.0,
            "abs_eval: partial z_i w.r.t u_j non-zero for i <= j"
         );
      }
   }
# endif
   // return value
   Vector g_tilde(m + s);
   //
   // compute z_tilde, the last s components of g_tilde
   for(size_t i = 0; i < s; i++)
   {  // start at z_hat_i
      g_tilde[m + i] = g_hat[m + i];
      // contribution for change x
      for(size_t j = 0; j < n; j++)
      {  // index in g_jac of partial of z_i w.r.t x_j
         size_t index = (m + i) * (n + s) + j;
         // add contribution for delta_x_j to z_tilde_i
         g_tilde[m + i] += g_jac[index] * delta_x[j];
      }
      // contribution for change in u_j for j < i
      for(size_t j = 0; j < i; j++)
      {  // approixmation for change in absolute value
         double delta_a_j = fabs(g_tilde[m + j]) - fabs(g_hat[m + j]);
         // index in g_jac of partial of z_i w.r.t u_j
         size_t index = (m + i) * (n + s) + n + j;
         // add constribution for delta_a_j to s_tilde_i
         g_tilde[m + i] += g_jac[index] * delta_a_j;
      }
   }
   //
   // compute y_tilde, the first m components of g_tilde
   for(size_t i = 0; i < m; i++)
   {  // start at y_hat_i
      g_tilde[i] = g_hat[i];
      // contribution for change x
      for(size_t j = 0; j < n; j++)
      {  // index in g_jac of partial of y_i w.r.t x_j
         size_t index = i * (n + s) + j;
         // add contribution for delta_x_j to y_tilde_i
         g_tilde[i] += g_jac[index] * delta_x[j];
      }
      // contribution for change in u_j
      for(size_t j = 0; j < s; j++)
      {  // approximation for change in absolute value
         double delta_a_j = fabs(g_tilde[m + j]) - fabs(g_hat[m + j]);
         // index in g_jac of partial of y_i w.r.t u_j
         size_t index = i * (n + s) + n + j;
         // add constribution for delta_a_j to s_tilde_i
         g_tilde[i] += g_jac[index] * delta_a_j;
      }
   }
   return g_tilde;
}
} // END_CPPAD_NAMESPACE