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// $Id$
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-16 Bradley M. Bell
CppAD is distributed under multiple licenses. This distribution is under
the terms of the
GNU General Public License Version 3.
A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */
/*
$begin asinh.cpp$$
$spell
sinh
asinh
$$
$section The AD asinh Function: Example and Test$$
$code
$srcfile%example/asinh.cpp%0%// BEGIN C++%// END C++%1%$$
$$
$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>
bool asinh(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
// 10 times machine epsilon
double eps = 10. * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 1;
double x0 = 0.5;
CPPAD_TESTVECTOR(AD<double>) x(n);
x[0] = x0;
// declare independent variables and start tape recording
CppAD::Independent(x);
// a temporary value
AD<double> sinh_of_x0 = CppAD::sinh(x[0]);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) y(m);
y[0] = CppAD::asinh(sinh_of_x0);
// create f: x -> y and stop tape recording
CppAD::ADFun<double> f(x, y);
// check value
ok &= NearEqual(y[0] , x0, eps, eps);
// 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], 1., eps, eps);
// 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], 1., eps, eps);
// use a VecAD<Base>::reference object with asinh
CppAD::VecAD<double> v(1);
AD<double> zero(0);
v[zero] = sinh_of_x0;
AD<double> result = CppAD::asinh(v[zero]);
ok &= NearEqual(result, x0, eps, eps);
return ok;
}
// END C++
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