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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 romberg_one.cpp}
One Dimensional Romberg Integration: Example and Test
#####################################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end romberg_one.cpp}
*/
// BEGIN C++
# include <cppad/utility/romberg_one.hpp>
# include <cppad/utility/vector.hpp>
# include <cppad/utility/near_equal.hpp>
namespace {
class Fun {
private:
const size_t degree;
public:
// constructor
Fun(size_t degree_) : degree(degree_)
{ }
// function F(x) = x^degree
template <class Type>
Type operator () (const Type &x)
{ size_t i;
Type f = 1;
for(i = 0; i < degree; i++)
f *= x;
return f;
}
};
}
bool RombergOne(void)
{ bool ok = true;
size_t i;
size_t degree = 4;
Fun F(degree);
// arguments to RombergOne
double a = 0.;
double b = 1.;
size_t n = 4;
size_t p;
double r, e;
// int_a^b F(x) dx = [ b^(degree+1) - a^(degree+1) ] / (degree+1)
double bpow = 1.;
double apow = 1.;
for(i = 0; i <= degree; i++)
{ bpow *= b;
apow *= a;
}
double check = (bpow - apow) / double(degree+1);
// step size corresponding to r
double step = (b - a) / exp(log(2.)*double(n-1));
// step size corresponding to error estimate
step *= 2.;
// step size raised to a power
double spow = 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, 0., e);
}
return ok;
}
// END C++
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