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<!-- doxytag: class="QuantLib::GaussLobattoIntegral" --><!-- doxytag: inherits="QuantLib::Integrator" -->
<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>
<p><a href="class_quant_lib_1_1_gauss_lobatto_integral-members.html">List of all members.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a22e1010dd30105e19d6f6b777128f45a"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::GaussLobattoIntegral" ref="a22e1010dd30105e19d6f6b777128f45a" args="(Size maxIterations, Real absAccuracy, Real relAccuracy=Null< Real >(), bool useConvergenceEstimate=true)" -->
 </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=Null< <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> >(), bool useConvergenceEstimate=true)</td></tr>
<tr><td colspan="2"><h2><a name="pro-methods"></a>
Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a5a7b69e9c96cb1f7b182caef74747c6c"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::integrate" ref="a5a7b69e9c96cb1f7b182caef74747c6c" args="(const boost::function< Real(Real)> &f, Real a, Real b) const " -->
<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>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aa65734e98a9fabf86cfb2e8ba6d90fb7"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::adaptivGaussLobattoStep" ref="aa65734e98a9fabf86cfb2e8ba6d90fb7" args="(const boost::function< Real(Real)> &f, Real a, Real b, Real fa, Real fb, Real is) const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>adaptivGaussLobattoStep</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, <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>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a7dac00925faa00ccecc1541d3aad5a5a"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::calculateAbsTolerance" ref="a7dac00925faa00ccecc1541d3aad5a5a" args="(const boost::function< Real(Real)> &f, Real a, Real b) const " -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>calculateAbsTolerance</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>
<tr><td colspan="2"><h2><a name="pro-attribs"></a>
Protected Attributes</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a749796204ab17a5427deb9062ce57cc4"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::relAccuracy_" ref="a749796204ab17a5427deb9062ce57cc4" args="" -->
<a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>relAccuracy_</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="abe7b6eda37c4288c5a827b0c6c1bcbb6"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::useConvergenceEstimate_" ref="abe7b6eda37c4288c5a827b0c6c1bcbb6" args="" -->
const bool </td><td class="memItemRight" valign="bottom"><b>useConvergenceEstimate_</b></td></tr>
<tr><td colspan="2"><h2><a name="pro-static-attribs"></a>
Static Protected Attributes</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a3a5f60670b1c3273333467ce33939204"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::alpha_" ref="a3a5f60670b1c3273333467ce33939204" args="" -->
static const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>alpha_</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a208eaa0a2d6a36ccb65c022c3485363b"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::beta_" ref="a208eaa0a2d6a36ccb65c022c3485363b" args="" -->
static const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>beta_</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a98b2b596e0d186346a067d8411833cfe"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::x1_" ref="a98b2b596e0d186346a067d8411833cfe" args="" -->
static const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>x1_</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a70d791405e28cf163895351eba87a26d"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::x2_" ref="a70d791405e28cf163895351eba87a26d" args="" -->
static const <a class="el" href="group__types.html#ga4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><b>x2_</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a2841be2337b04a9d0be7deaa6df9add2"></a><!-- doxytag: member="QuantLib::GaussLobattoIntegral::x3_" ref="a2841be2337b04a9d0be7deaa6df9add2" args="" -->
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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<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><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 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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