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// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin atan2.cpp}
The AD atan2 Function: Example and Test
#######################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end atan2.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
# define N_THETA 20
bool atan2(void)
{ bool ok = true;
//
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
double pi = 2.0 * std::atan(1.0);
//
for(size_t k = 0; k < N_THETA; ++k)
{ // theta
double theta = 2.0 * pi * double(k+1) / double(N_THETA) - pi;
//
// radius
double radius = 1.0 + double(k) / double(N_THETA);
//
// x, y
double x = radius * std::cos(theta);
double y = radius * std::sin(theta);
//
// au
CPPAD_TESTVECTOR(AD<double>) au(2);
au[0] = x;
au[1] = y;
CppAD::Independent(au);
//
// av
CPPAD_TESTVECTOR(AD<double>) av(1);
av[0] = CppAD::atan2(au[1], au[0]);
//
// f(x, y) = atan2(y, x)
CppAD::ADFun<double> f(au, av);
//
// check value
ok &= NearEqual(av[0] , theta, eps99, eps99);
//
// partial_x, partial_y
// see https://en.wikipedia.org/wiki/Atan2#Derivative
double partial_x = - y / (radius * radius);
double partial_y = x / (radius * radius);
//
// check forward mode
CPPAD_TESTVECTOR(double) du(2), dv(1);
du[0] = 1.0;
du[1] = 0.0;
dv = f.Forward(1, du);
ok &= NearEqual(dv[0], partial_x, eps99, eps99);
du[0] = 0.0;
du[1] = 1.0;
dv = f.Forward(1, du);
ok &= NearEqual(dv[0], partial_y, eps99, eps99);
//
// check reverse mode
CPPAD_TESTVECTOR(double) w(1);
CPPAD_TESTVECTOR(double) dw(2);
w[0] = 1.;
dw = f.Reverse(1, w);
ok &= NearEqual(dw[0], partial_x, eps99, eps99);
ok &= NearEqual(dw[1], partial_y, eps99, eps99);
//
}
return ok;
}
// END C++
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