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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 reverse_two.cpp}
Second Order Reverse ModeExample and Test
#########################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end reverse_two.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>
namespace { // ----------------------------------------------------------
// define the template function reverse_two_cases<Vector> in empty namespace
template <class Vector>
bool reverse_two_cases(void)
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 2;
CPPAD_TESTVECTOR(AD<double>) X(n);
X[0] = 0.;
X[1] = 1.;
// declare independent variables and start recording
CppAD::Independent(X);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) Y(m);
Y[0] = X[0] * X[0] * X[1];
// create f : X -> Y and stop recording
CppAD::ADFun<double> f(X, Y);
// use zero order forward mode to evaluate y at x = (3, 4)
// use the template parameter Vector for the vector type
Vector x(n), y(m);
x[0] = 3.;
x[1] = 4.;
y = f.Forward(0, x);
ok &= NearEqual(y[0] , x[0]*x[0]*x[1], eps99, eps99);
// use first order forward mode in x[0] direction
// (all second order partials below involve x[0])
Vector dx(n), dy(m);
dx[0] = 1.;
dx[1] = 1.;
dy = f.Forward(1, dx);
double check = 2.*x[0]*x[1]*dx[0] + x[0]*x[0]*dx[1];
ok &= NearEqual(dy[0], check, eps99, eps99);
// use second order reverse mode to evalaute second partials of y[0]
// with respect to (x[0], x[0]) and with respect to (x[0], x[1])
Vector w(m), dw( n * 2 );
w[0] = 1.;
dw = f.Reverse(2, w);
// check derivative of f
ok &= NearEqual(dw[0*2+0] , 2.*x[0]*x[1], eps99, eps99);
ok &= NearEqual(dw[1*2+0] , x[0]*x[0], eps99, eps99);
// check derivative of f^{(1)} (x) * dx
check = 2.*x[1]*dx[1] + 2.*x[0]*dx[1];
ok &= NearEqual(dw[0*2+1] , check, eps99, eps99);
check = 2.*x[0]*dx[1];
ok &= NearEqual(dw[1*2+1] , check, eps99, eps99);
return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool reverse_two(void)
{ bool ok = true;
ok &= reverse_two_cases< CppAD::vector <double> >();
ok &= reverse_two_cases< std::vector <double> >();
ok &= reverse_two_cases< std::valarray <double> >();
return ok;
}
// END C++
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