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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 hes_times_dir.cpp}
Hessian Times Direction: Example and Test
#########################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end hes_times_dir.cpp}
*/
// BEGIN C++
// Example and test of computing the Hessian times a direction; i.e.,
// given F : R^n -> R and a direction dx in R^n, we compute F''(x) * dx
# include <cppad/cppad.hpp>
namespace { // put this function in the empty namespace
// F(x) = |x|^2 = x[0]^2 + ... + x[n-1]^2
template <class Type>
Type F(CPPAD_TESTVECTOR(Type) &x)
{ Type sum = 0;
size_t i = x.size();
while(i--)
sum += x[i] * x[i];
return sum;
}
}
bool HesTimesDir(void)
{ bool ok = true; // initialize test result
size_t j; // a domain variable variable
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
// domain space vector
size_t n = 5;
CPPAD_TESTVECTOR(AD<double>) X(n);
for(j = 0; j < n; j++)
X[j] = AD<double>(j);
// declare independent variables and start recording
CppAD::Independent(X);
// range space vector
size_t m = 1;
CPPAD_TESTVECTOR(AD<double>) Y(m);
Y[0] = F(X);
// create f : X -> Y and stop recording
CppAD::ADFun<double> f(X, Y);
// choose a direction dx and compute dy(x) = F'(x) * dx
CPPAD_TESTVECTOR(double) dx(n);
CPPAD_TESTVECTOR(double) dy(m);
for(j = 0; j < n; j++)
dx[j] = double(n - j);
dy = f.Forward(1, dx);
// compute ddw = F''(x) * dx
CPPAD_TESTVECTOR(double) w(m);
CPPAD_TESTVECTOR(double) ddw(2 * n);
w[0] = 1.;
ddw = f.Reverse(2, w);
// F(x) = x[0]^2 + x[1]^2 + ... + x[n-1]^2
// F''(x) = 2 * Identity_Matrix
// F''(x) * dx = 2 * dx
for(j = 0; j < n; j++)
ok &= NearEqual(ddw[j * 2 + 1], 2.*dx[j], eps99, eps99);
return ok;
}
// END C++
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