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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
// ----------------------------------------------------------------------------
/*
old romberg_one.cpp example / test
$spell
Romberg
$$
$section One Dimensional Romberg Integration: Example and Test$$
$index Romberg, example$$
$index example, Romberg$$
$index test, Romberg$$
old verbatim%example/romberg_one.cpp%0%// BEGIN C++%// END C++%1%$$
$end
*/
// BEGIN C++
# include <cppad/cppad.hpp>
namespace {
class Fun {
private:
const size_t degree;
public:
// constructor
Fun(size_t degree_) : degree(degree_)
{ }
// function F(x) = x^degree
template <class Float>
Float operator () (const Float &x)
{ size_t i;
Float f(1);
for(i = 0; i < degree; i++)
f *= x;
return f;
}
};
template <class Float>
bool RombergOneCase(void)
{ bool ok = true;
size_t i;
size_t degree = 4;
Fun F(degree);
// arguments to RombergOne
Float a(0);
Float b(1);
Float r;
size_t n = 4;
Float e;
size_t p;
// int_a^b F(x) dx =
// [ b^(degree+1) - a^(degree+1) ] / (degree+1)
Float bpow(1);
Float apow(1);
for(i = 0; i <= degree; i++)
{ bpow *= b;
apow *= a;
}
Float check = (bpow - apow) / Float(degree+1);
// step size corresponding to r
Float step = (b - a) / exp(log(Float(2.))*Float(n-1));
// step size corresponding to error estimate
step *= Float(2.);
// step size raised to a power
Float spow = Float(1);
for(p = 0; p < n; p++)
{ spow = spow * step * step;
r = CppAD::RombergOne(F, a, b, n, p, e);
ok &= e < double(degree+1) * spow;
ok &= CppAD::NearEqual(check, r, Float(0.), e);
}
return ok;
}
}
bool RombergOne(void)
{ bool ok = true;
using CppAD::AD;
ok &= RombergOneCase<double>();
ok &= RombergOneCase< AD<double> >();
ok &= RombergOneCase< AD< AD<double> > >();
return ok;
}
// END C++
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