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# include <cppad/cppad.hpp>
# include <cmath>
bool Pow(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 2;
double x = 0.5;
double y = 2.;
CPPAD_TEST_VECTOR< AD<double> > XY(n);
XY[0] = x;
XY[1] = y;
// declare independent variables and start tape recording
CppAD::Independent(XY);
// range space vector
size_t m = 3;
CPPAD_TEST_VECTOR< AD<double> > Z(m);
Z[0] = CppAD::pow(XY[0], XY[1]); // pow(variable, variable)
Z[1] = CppAD::pow(XY[0], y); // pow(variable, parameter)
Z[2] = CppAD::pow(x, XY[1]); // pow(parameter, variable)
// create f: XY -> Z and stop tape recording
CppAD::ADFun<double> f(XY, Z);
// check value
double check = std::pow(x, y);
size_t i;
for(i = 0; i < m; i++)
ok &= NearEqual(Z[i] , check, 1e-10 , 1e-10);
// forward computation of first partial w.r.t. x
CPPAD_TEST_VECTOR<double> dxy(n);
CPPAD_TEST_VECTOR<double> dz(m);
dxy[0] = 1.;
dxy[1] = 0.;
dz = f.Forward(1, dxy);
check = y * std::pow(x, y-1.);
ok &= NearEqual(dz[0], check, 1e-10, 1e-10);
ok &= NearEqual(dz[1], check, 1e-10, 1e-10);
ok &= NearEqual(dz[2], 0., 1e-10, 1e-10);
// forward computation of first partial w.r.t. y
dxy[0] = 0.;
dxy[1] = 1.;
dz = f.Forward(1, dxy);
check = std::log(x) * std::pow(x, y);
ok &= NearEqual(dz[0], check, 1e-10, 1e-10);
ok &= NearEqual(dz[1], 0., 1e-10, 1e-10);
ok &= NearEqual(dz[2], check, 1e-10, 1e-10);
// reverse computation of derivative of z[0] + z[1] + z[2]
CPPAD_TEST_VECTOR<double> w(m);
CPPAD_TEST_VECTOR<double> dw(n);
w[0] = 1.;
w[1] = 1.;
w[2] = 1.;
dw = f.Reverse(1, w);
check = y * std::pow(x, y-1.);
ok &= NearEqual(dw[0], 2. * check, 1e-10, 1e-10);
check = std::log(x) * std::pow(x, y);
ok &= NearEqual(dw[1], 2. * check, 1e-10, 1e-10);
// use a VecAD<Base>::reference object with pow
CppAD::VecAD<double> v(2);
AD<double> zero(0);
AD<double> one(1);
v[zero] = XY[0];
v[one] = XY[1];
AD<double> result = CppAD::pow(v[zero], v[one]);
ok &= NearEqual(result, Z[0], 1e-10, 1e-10);
return ok;
}