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library-> py_lib cpp_lib

cpp_lib-> a_double vector cpp_fun sparse cpp_utility more_cpp

cpp_fun-> cpp_independent cpp_abort_recording cpp_fun_ctor cpp_fun_property cpp_fun_new_dynamic cpp_fun_jacobian cpp_fun_hessian cpp_fun_forward cpp_fun_reverse cpp_fun_optimize

cpp_fun_forward-> fun_forward_xam.cpp

fun_forward_xam.cpp

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# include <cstdio>
# include <cppad/py/cppad_py.hpp>

bool fun_forward_xam(void) {
     using cppad_py::a_double;
     using cppad_py::vec_double;
     using cppad_py::vec_a_double;
     using cppad_py::d_fun;
     using cppad_py::a_fun;
     //
     // initialize return variable
     bool ok = true;
     // ----------------------------------------------------------------------
     // number of dependent and independent variables
     int n_dep = 1;
     int n_ind = 2;
     //
     // create the independent variables ax
     vec_double xp(n_ind);
     for(int i = 0; i < n_ind ; i++) {
          xp[i] = i + 1.0;
     }
     vec_a_double ax = cppad_py::independent(xp);
     //
     // create dependent varialbes ay with ay0 = ax0 * ax1
     a_double ax0 = ax[0];
     a_double ax1 = ax[1];
     vec_a_double ay(n_dep);
     ay[0] = ax0 * ax1;
     //
     // define af corresponding to f(x) = x0 * x1
     d_fun f(ax, ay);
     ok &= f.size_order() == 0;
     //
     // define X(t) = (3 + t, 2 + t)
     // it follows that Y(t) = f(X(t)) = (3 + t) * (2 + t)
     //
     // Y(0) = 6 and p ! = 1
     int p = 0;
     xp[0] = 3.0;
     xp[1] = 2.0;
     vec_double yp = f.forward(p, xp);
     ok  = ok && yp[0] == 6.0;
     ok &= f.size_order() == 1;
     //
     // first order Taylor coefficients for X(t)
     p = 1;
     xp[0] = 1.0;
     xp[1] = 1.0;
     //
     // first order Taylor coefficient for Y(t)
     // Y'(0) = 3 + 2 = 5 and p ! = 1
     yp = f.forward(p, xp);
     ok = ok && yp[0] == 5.0;
     ok &= f.size_order() == 2;
     //
     // second order Taylor coefficients for X(t)
     p = 2;
     xp[0] = 0.0;
     xp[1] = 0.0;
     //
     // second order Taylor coefficient for Y(t)
     // Y''(0) = 2.0 and p ! = 2
     yp = f.forward(p, xp);
     ok = ok && yp[0] == 1.0;
     ok &= f.size_order() == 3;
     // ----------------------------------------------------------------------
     a_fun af(f);
     ok &= af.size_order() == 0;
     //
     // zero order forward
     vec_a_double axp(n_ind), ayp(n_dep);
     p      = 0;
     axp[0] = 3.0;
     axp[1] = 2.0;
     ayp    = af.forward(p, axp);
     ok     = ok && ayp[0] == 6.0;
     ok    &= af.size_order() == 1;
     //
     return( ok );
}