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<center><b><big><big>One Dimensional Romberg Integration: Example and Test</big></big></b></center>
<code><font color="blue"><pre style='display:inline'> 

# include &lt;cppad/romberg_one.hpp&gt;
# include &lt;cppad/vector.hpp&gt;
# include &lt;cppad/near_equal.hpp&gt;

namespace {
	class Fun {
	private:
		const size_t degree;
	public:
		// constructor
		Fun(size_t degree_) : degree(degree_) 
		{ }

		// function F(x) = x^degree
		template &lt;class Type&gt;
		Type operator () (const Type &amp;x)
		{	size_t i;
			Type   f = 1;
			for(i = 0; i &lt; 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 &lt;= degree; i++)
	{	bpow *= b;
		apow *= a;
	}  
	double check = (bpow - apow) / (degree+1);

	// step size corresponding to r
	double step = (b - a) / exp(log(2.)*(n-1));
	// step size corresponding to error estimate
	step *= 2.;
	// step size raised to a power
	double spow = 1;

	for(p = 0; p &lt; n; p++)
	{	spow = spow * step * step;

		r = CppAD::RombergOne(F, a, b, n, p, e);

		ok  &amp;= e &lt; (degree+1) * spow;
		ok  &amp;= CppAD::<a href="nearequal.xml" target="_top">NearEqual</a>(check, r, 0., e);	
	}

	return ok;
}

</pre>

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<hr/>Input File: example/romberg_one.cpp

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