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<a class="el" href="namespace_quant_lib.html">QuantLib</a>::<a class="el" href="class_quant_lib_1_1_segment_integral.html">SegmentIntegral</a></div>
<h1>SegmentIntegral Class Reference</h1><!-- doxytag: class="QuantLib::SegmentIntegral" --><!-- doxytag: inherits="QuantLib::Integrator" --><code>#include <ql/math/integrals/segmentintegral.hpp></code>
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Inherits Integrator.
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<a href="class_quant_lib_1_1_segment_integral-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Integral of a one-dimensional function.
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Given a number <img class="formulaInl" alt="$ N $" src="form_36.png"> of intervals, the integral of a function <img class="formulaInl" alt="$ f $" src="form_41.png"> between <img class="formulaInl" alt="$ a $" src="form_51.png"> and <img class="formulaInl" alt="$ b $" src="form_52.png"> is calculated by means of the trapezoid formula <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_132.png">
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where <img class="formulaInl" alt="$ x_0 = a $" src="form_133.png">, <img class="formulaInl" alt="$ x_N = b $" src="form_134.png">, and <img class="formulaInl" alt="$ x_i = a+i \Delta x $" src="form_135.png"> with <img class="formulaInl" alt="$ \Delta x = (b-a)/N $" src="form_136.png">.<p>
<dl compact><dt><b><a class="el" href="test.html#_test000029">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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<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3bc5927b1280d2893f72b40b9e817bc7"></a><!-- doxytag: member="QuantLib::SegmentIntegral::SegmentIntegral" ref="3bc5927b1280d2893f72b40b9e817bc7" args="(Size intervals)" -->
</td><td class="memItemRight" valign="bottom"><b>SegmentIntegral</b> (<a class="el" href="group__types.html#gf38bdb4c54463b1f456655efa95b5c77">Size</a> intervals)</td></tr>
<tr><td colspan="2"><br><h2>Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5a7b69e9c96cb1f7b182caef74747c6c"></a><!-- doxytag: member="QuantLib::SegmentIntegral::integrate" ref="5a7b69e9c96cb1f7b182caef74747c6c" args="(const boost::function< Real(Real)> &f, Real a, Real b) const " -->
virtual <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>integrate</b> (const boost::function< <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>(<a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a>)> &f, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> a, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> b) const </td></tr>
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