$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
# ifndef CPPAD_DET_GRAD_33_HPP # define CPPAD_DET_GRAD_33_HPP # include <limits> # include <cppad/utility/near_equal.hpp> namespace CppAD { template <class Vector> bool det_grad_33(const Vector &x, const Vector &g) { bool ok = true; typedef typename Vector::value_type Float; Float eps = 10. * Float( std::numeric_limits<double>::epsilon() ); // use expansion by minors to compute the derivative by hand double check[9]; check[0] = + ( x[4] * x[8] - x[5] * x[7] ); check[1] = - ( x[3] * x[8] - x[5] * x[6] ); check[2] = + ( x[3] * x[7] - x[4] * x[6] ); // check[3] = - ( x[1] * x[8] - x[2] * x[7] ); check[4] = + ( x[0] * x[8] - x[2] * x[6] ); check[5] = - ( x[0] * x[7] - x[1] * x[6] ); // check[6] = + ( x[1] * x[5] - x[2] * x[4] ); check[7] = - ( x[0] * x[5] - x[2] * x[3] ); check[8] = + ( x[0] * x[4] - x[1] * x[3] ); // for(size_t i = 0; i < 3 * 3; i++) ok &= CppAD::NearEqual(check[i], g[i], eps, eps); return ok; } } # endif