/* $Id: rev_two.cpp 2506 2012-10-24 19:36:49Z bradbell $ */
/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-12 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 rev_two.cpp$$
$spell
Cpp
$$
$section Second Partials Reverse Driver: Example and Test$$
$index second, partial$$
$index partial, second$$
$index example, second partial$$
$index test, second partial$$
$code
$verbatim%example/rev_two.cpp%0%// BEGIN C++%// END C++%1%$$
$$
$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>
namespace { // -----------------------------------------------------
// define the template function in empty namespace
// bool RevTwoCases<VectorBase, VectorSize_t>(void)
template <class VectorBase, class VectorSize_t>
bool RevTwoCases()
{ bool ok = true;
using CppAD::AD;
using CppAD::NearEqual;
using CppAD::exp;
using CppAD::sin;
using CppAD::cos;
// domain space vector
size_t n = 2;
CPPAD_TESTVECTOR(AD<double>) X(n);
X[0] = 1.;
X[1] = 2.;
// declare independent variables and starting recording
CppAD::Independent(X);
// a calculation between the domain and range values
AD<double> Square = X[0] * X[0];
// range space vector
size_t m = 3;
CPPAD_TESTVECTOR(AD<double>) Y(m);
Y[0] = Square * exp( X[1] );
Y[1] = Square * sin( X[1] );
Y[2] = Square * cos( X[1] );
// create f: X -> Y and stop tape recording
CppAD::ADFun<double> f(X, Y);
// new value for the independent variable vector
VectorBase x(n);
x[0] = 2.;
x[1] = 1.;
// set i and j to compute specific second partials of y
size_t p = 2;
VectorSize_t i(p);
VectorSize_t j(p);
i[0] = 0; j[0] = 0; // for partials y[0] w.r.t x[0] and x[k]
i[1] = 1; j[1] = 1; // for partials y[1] w.r.t x[1] and x[k]
// compute the second partials
VectorBase ddw(n * p);
ddw = f.RevTwo(x, i, j);
// partials of y[0] w.r.t x[0] is 2 * x[0] * exp(x[1])
// check partials of y[0] w.r.t x[0] and x[k] for k = 0, 1
ok &= NearEqual( 2.*exp(x[1]), ddw[0*p+0], 1e-10, 1e-10 );
ok &= NearEqual( 2.*x[0]*exp(x[1]), ddw[1*p+0], 1e-10, 1e-10 );
// partials of y[1] w.r.t x[1] is x[0] * x[0] * cos(x[1])
// check partials of F_1 w.r.t x[1] and x[k] for k = 0, 1
ok &= NearEqual( 2.*x[0]*cos(x[1]), ddw[0*p+1], 1e-10, 1e-10 );
ok &= NearEqual( -x[0]*x[0]*sin(x[1]), ddw[1*p+1], 1e-10, 1e-10 );
return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool RevTwo(void)
{ bool ok = true;
// Run with VectorBase equal to three different cases
// all of which are Simple Vectors with elements of type double.
ok &= RevTwoCases< CppAD::vector <double>, std::vector<size_t> >();
ok &= RevTwoCases< std::vector <double>, std::vector<size_t> >();
ok &= RevTwoCases< std::valarray <double>, std::vector<size_t> >();
// Run with VectorSize_t equal to two other cases
// which are Simple Vectors with elements of type size_t.
ok &= RevTwoCases< std::vector <double>, CppAD::vector<size_t> >();
ok &= RevTwoCases< std::vector <double>, std::valarray<size_t> >();
return ok;
}
// END C++