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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_mul.cpp}
Multi-Dimensional Romberg Integration: Example and Test
#######################################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end romberg_mul.cpp}
*/
// BEGIN C++
# include <cppad/utility/romberg_mul.hpp>
# include <cppad/utility/vector.hpp>
# include <cppad/utility/near_equal.hpp>
namespace {
class TestFun {
private:
const CppAD::vector<size_t> deg;
public:
// constructor
TestFun(const CppAD::vector<size_t> deg_)
: deg(deg_)
{ }
// function F(x) = x[0]^deg[0] * x[1]^deg[1]
double operator () (const CppAD::vector<double> &x)
{ size_t i;
double f = 1;
for(i = 0; i < deg[0]; i++)
f *= x[0];
for(i = 0; i < deg[1]; i++)
f *= x[1];
return f;
}
};
}
bool RombergMul(void)
{ bool ok = true;
size_t i;
size_t k;
CppAD::vector<size_t> deg(2);
deg[0] = 5;
deg[1] = 3;
TestFun F(deg);
CppAD::RombergMul<
TestFun ,
CppAD::vector<size_t>,
CppAD::vector<double>,
2 > RombergMulTest;
// arguments to RombergMul
CppAD::vector<double> a(2);
CppAD::vector<double> b(2);
CppAD::vector<size_t> n(2);
CppAD::vector<size_t> p(2);
for(i = 0; i < 2; i++)
{ a[i] = 0.;
b[i] = 1.;
}
n[0] = 4;
n[1] = 3;
double r, e;
// int_a1^b1 dx1 int_a0^b0 F(x0,x1) dx0
// = [ b0^(deg[0]+1) - a0^(deg[0]+1) ] / (deg[0]+1)
// * [ b1^(deg[1]+1) - a1^(deg[1]+1) ] / (deg[1]+1)
double bpow = 1.;
double apow = 1.;
for(i = 0; i <= deg[0]; i++)
{ bpow *= b[0];
apow *= a[0];
}
double check = (bpow - apow) / double(deg[0]+1);
bpow = 1.;
apow = 1.;
for(i = 0; i <= deg[1]; i++)
{ bpow *= b[1];
apow *= a[1];
}
check *= (bpow - apow) / double(deg[1]+1);
double step = (b[1] - a[1]) / exp(log(2.)*double(n[1]-1));
double spow = 1;
for(k = 0; k <= n[1]; k++)
{ spow = spow * step * step;
double bnd = 3 * double(deg[1] + 1) * spow;
for(i = 0; i < 2; i++)
p[i] = k;
r = RombergMulTest(F, a, b, n, p, e);
ok &= e < bnd;
ok &= CppAD::NearEqual(check, r, 0., e);
}
return ok;
}
// END C++
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