The AD erf Function: Example and Test
Keywords: the ad erf function: example test

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The AD erf Function: Example and Test
`

    # include <cppad/cppad.hpp>
    # include <cmath>
    # include <limits>

    bool Erf(void)
    {	bool ok = true;

    	using CppAD::AD;
    	using CppAD::NearEqual;
    	double eps = 10. * CppAD::numeric_limits<double>::epsilon();

    	// domain space vector
    	size_t n  = 1;
    	double x0 = 0.5;
    	CPPAD_TESTVECTOR(AD<double>) ax(n);
    	ax[0]     = x0;

    	// declare independent variables and start tape recording
    	CppAD::Independent(ax);

    	// range space vector
    	size_t m = 1;
    	CPPAD_TESTVECTOR(AD<double>) ay(m);
    	ay[0] = CppAD::erf(ax[0]);

    	// create f: x -> y and stop tape recording
    	CppAD::ADFun<double> f(ax, ay);

    	// check relative erorr
    	double erf_x0 = 0.52050;
    	ok &= NearEqual(ay[0] , erf_x0,  0.,    4e-4);
    # if CPPAD_USE_CPLUSPLUS_2011
    	ok &= NearEqual(ay[0] , erf_x0,  0.,    1e-5);
    # endif

    	// 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_TESTVECTOR(double) dx(n);
    	CPPAD_TESTVECTOR(double) dy(m);
    	dx[0] = 1.;
    	dy    = f.Forward(1, dx);
    	ok   &= NearEqual(dy[0], check,  0.,  1e-3);
    # if CPPAD_USE_CPLUSPLUS_2011
    	ok   &= NearEqual(dy[0], check,  0.,  eps);
    # endif

    	// reverse computation of derivative of y[0]
    	CPPAD_TESTVECTOR(double)  w(m);
    	CPPAD_TESTVECTOR(double) dw(n);
    	w[0]  = 1.;
    	dw    = f.Reverse(1, w);
    	ok   &= NearEqual(dw[0], check,  0., 1e-1);
    # if CPPAD_USE_CPLUSPLUS_2011
    	ok   &= NearEqual(dw[0], check,  0., eps);
    # endif

    	// 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, ay[0], eps, eps);

    	// use a double with erf
    	ok   &= NearEqual(CppAD::erf(x0), ay[0], eps, eps);

    	return ok;
    }

`

Input File: example/erf.cpp