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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
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;
//
size_t(delta_x.size()) == n,
"abs_eval: size of delta_x not equal to n"
);
size_t(g_hat.size()) == m + s,
"abs_eval: size of g_hat not equal to m + s"
);
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);
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

Input File: example/abs_normal/abs_eval.omh