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<h3 class="subtitle">A free/open-source library for quantitative finance</h3>
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<div class="title">TrapezoidIntegral< IntegrationPolicy > Class Template Reference</div> </div>
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<!-- doxytag: class="QuantLib::TrapezoidIntegral" --><!-- doxytag: inherits="QuantLib::Integrator" -->
<p>Integral of a one-dimensional function.
<a href="class_quant_lib_1_1_trapezoid_integral.html#details">More...</a></p>
<p><code>#include <ql/math/integrals/trapezoidintegral.hpp></code></p>
<p>Inherits Integrator.</p>
<p><a href="class_quant_lib_1_1_trapezoid_integral-members.html">List of all members.</a></p>
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Public Member Functions</h2></td></tr>
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 </td><td class="memItemRight" valign="bottom"><b>TrapezoidIntegral</b> (<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> accuracy, <a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> maxIterations)</td></tr>
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Protected Member Functions</h2></td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>integrate</b> (const boost::function< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>(<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>)> &f, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> a, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> b) const </td></tr>
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<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><h3>template<class IntegrationPolicy><br/>
class QuantLib::TrapezoidIntegral< IntegrationPolicy ></h3>
<p>Integral of a one-dimensional function. </p>
<p>Given a target accuracy <img class="formulaInl" alt="$ \epsilon $" src="form_203.png"/>, the integral of a function <img class="formulaInl" alt="$ f $" src="form_37.png"/> between <img class="formulaInl" alt="$ a $" src="form_47.png"/> and <img class="formulaInl" alt="$ b $" src="form_48.png"/> is calculated by means of the trapezoid formula </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \int_{a}^{b} f \mathrm{d}x = \frac{1}{2} f(x_{0}) + f(x_{1}) + f(x_{2}) + \dots + f(x_{N-1}) + \frac{1}{2} f(x_{N}) \]" src="form_204.png"/>
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<p> where <img class="formulaInl" alt="$ x_0 = a $" src="form_205.png"/>, <img class="formulaInl" alt="$ x_N = b $" src="form_206.png"/>, and <img class="formulaInl" alt="$ x_i = a+i \Delta x $" src="form_207.png"/> with <img class="formulaInl" alt="$ \Delta x = (b-a)/N $" src="form_208.png"/>. The number <img class="formulaInl" alt="$ N $" src="form_32.png"/> of intervals is repeatedly increased until the target accuracy is reached.</p>
<dl class="test"><dt><b><a class="el" href="test.html#_test000041">Tests:</a></b></dt><dd>the correctness of the result is tested by checking it against known good values. </dd></dl>
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