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# include <cppad/cppad.hpp>
# include <cmath>
bool Erf(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TEST_VECTOR< AD<double> > x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// a temporary value
// range space vector
size_t m = 1;
CPPAD_TEST_VECTOR< AD<double> > y(m);
y[0] = CppAD::erf(x[0]);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
double erf_x0 = 0.5205;
ok &= NearEqual(y[0] , erf_x0, 1e-4 , 1e-4);
// value of derivative of erf at x0
double pi = 4. * std::atan(1.);
double factor = 2. / sqrt(pi);
double check = factor * std::exp(-x0 * x0);
// forward computation of first partial w.r.t. x[0]
CPPAD_TEST_VECTOR<double> dx(n);
CPPAD_TEST_VECTOR<double> dy(m);
dx[0] = 1.;
dy = f.Forward(1, dx);
ok &= NearEqual(dy[0], check, 1e-10, 1e-10);
// reverse computation of derivative of y[0]
CPPAD_TEST_VECTOR<double> w(m);
CPPAD_TEST_VECTOR<double> dw(n);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], check, 1e-10, 1e-10);
// use a VecAD<Base>::reference object with erf
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = x0;
AD<double> result = CppAD::erf(v[zero]);
ok &= NearEqual(result, y[0], 1e-10, 1e-10);
// use a double with erf
ok &= NearEqual(CppAD::erf(x0), y[0], 1e-10, 1e-10);
return ok;
}