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<p>Integral of a one-dimensional function.
<a href="class_quant_lib_1_1_gauss_lobatto_integral.html#details">More...</a></p>
<p><code>#include <ql/math/integrals/gausslobattointegral.hpp></code></p>
<p>Inherits Integrator.</p>
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Public Member Functions</h2></td></tr>
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 </td><td class="memItemRight" valign="bottom"><b>GaussLobattoIntegral</b> (<a class="el" href="group__types.html#gaf38bdb4c54463b1f456655efa95b5c77">Size</a> maxIterations, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> absAccuracy, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> relAccuracy=<a class="el" href="class_quant_lib_1_1_null.html">Null</a>< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> >(), bool useConvergenceEstimate=true)</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 ext::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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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>adaptivGaussLobattoStep</b> (const ext::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, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> fa, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> fb, <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> is) const</td></tr>
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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>calculateAbsTolerance</b> (const ext::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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<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>relAccuracy_</b></td></tr>
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const bool </td><td class="memItemRight" valign="bottom"><b>useConvergenceEstimate_</b></td></tr>
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static const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>alpha_</b></td></tr>
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static const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>x1_</b></td></tr>
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static const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>x2_</b></td></tr>
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static const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>x3_</b></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Integral of a one-dimensional function. </p>
<p>Given a target accuracy \( \epsilon \), the integral of a function \( f \) between \( a \) and \( b \) is calculated by means of the Gauss-Lobatto formula</p>
<p>References: This algorithm is a C++ implementation of the algorithm outlined in</p>
<p>W. Gander and W. Gautschi, Adaptive Quadrature - Revisited. BIT, 40(1):84-101, March 2000. CS technical report: ftp.inf.ethz.ch/pub/publications/tech-reports/3xx/306.ps.gz</p>
<p>The original MATLAB version can be downloaded here <a href="http://www.inf.ethz.ch/personal/gander/adaptlob.m">http://www.inf.ethz.ch/personal/gander/adaptlob.m</a> </p>
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