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Up-> CppAD ADFun abs_normal abs_eval abs_eval.hpp

ADFun-> record_adfun drivers Forward Reverse sparsity_pattern sparse_derivative optimize abs_normal FunCheck check_for_nan

abs_normal-> abs_normal_fun abs_print_mat abs_eval simplex_method lp_box abs_min_linear min_nso_linear qp_interior qp_box abs_min_quad min_nso_quad

abs_eval-> abs_eval.cpp abs_eval.hpp

abs_eval.hpp

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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