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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_trapezoid_integral.html">TrapezoidIntegral</a></div>
<h1>TrapezoidIntegral Class Reference</h1><!-- doxytag: class="QuantLib::TrapezoidIntegral" --><code>#include <ql/Math/trapezoidintegral.hpp></code>
<p>
Inheritance diagram for TrapezoidIntegral:<p><center><img src="class_quant_lib_1_1_trapezoid_integral__inherit__graph.png" border="0" usemap="#_trapezoid_integral__inherit__map" alt="Inheritance graph"></center>
<map name="_trapezoid_integral__inherit__map">
<area href="class_quant_lib_1_1_simpson_integral.html" shape="rect" coords="9,81,140,105" alt="">
</map>
<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center><a href="class_quant_lib_1_1_trapezoid_integral-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
Integral of a one-dimensional function.
<p>
Given a target accuracy <img class="formulaInl" alt="$ \epsilon $" src="form_129.png">, the integral of a function <img class="formulaInl" alt="$ f $" src="form_41.png"> between <img class="formulaInl" alt="$ a $" src="form_143.png"> and <img class="formulaInl" alt="$ b $" src="form_144.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_145.png">
<p>
where <img class="formulaInl" alt="$ x_0 = a $" src="form_146.png">, <img class="formulaInl" alt="$ x_N = b $" src="form_147.png">, and <img class="formulaInl" alt="$ x_i = a+i \Delta x $" src="form_148.png"> with <img class="formulaInl" alt="$ \Delta x = (b-a)/N $" src="form_149.png">. The number <img class="formulaInl" alt="$ N $" src="form_36.png"> of intervals is repeatedly increased until the target accuracy is reached.<p>
<dl compact><dt><b><a class="el" href="test.html#_test000054">Tests:</a></b></dt><dd>the correctness of the result is tested by checking it against known good values. </dd></dl>
<p>
<table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Types</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">enum </td><td class="memItemRight" valign="bottom"><b>Method</b> { <b>Default</b>,
<b>MidPoint</b>
}</td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9c7308d0565380b43bab0abb085336f4"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::TrapezoidIntegral" ref="9c7308d0565380b43bab0abb085336f4" args="(Real accuracy, Method method=Default, Size maxIterations=Null< Size >())" -->
</td><td class="memItemRight" valign="bottom"><b>TrapezoidIntegral</b> (Real accuracy, Method method=Default, Size maxIterations=<a class="el" href="class_quant_lib_1_1_null.html">Null</a>< Size >())</td></tr>
<tr><td class="memTemplParams" nowrap colspan="2"><a class="anchor" name="77589e5d2d6e98c9423f971f82e569fb"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::operator()" ref="77589e5d2d6e98c9423f971f82e569fb" args="(const F &f, Real a, Real b) const" -->
template<class F> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">Real </td><td class="memTemplItemRight" valign="bottom"><b>operator()</b> (const F &f, Real a, Real b) const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="85c86e1ed0ac0113cd90eb6726271bf2"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::accuracy" ref="85c86e1ed0ac0113cd90eb6726271bf2" args="() const" -->
Real </td><td class="memItemRight" valign="bottom"><b>accuracy</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c9dd87824f2a0b47b3b8de2fe586be60"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::accuracy" ref="c9dd87824f2a0b47b3b8de2fe586be60" args="()" -->
Real & </td><td class="memItemRight" valign="bottom"><b>accuracy</b> ()</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="41065317f311efb2f1798e3a988919b1"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::method" ref="41065317f311efb2f1798e3a988919b1" args="() const" -->
Method </td><td class="memItemRight" valign="bottom"><b>method</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2409d604c9d6490364641db156e6a33b"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::method" ref="2409d604c9d6490364641db156e6a33b" args="()" -->
Method & </td><td class="memItemRight" valign="bottom"><b>method</b> ()</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8577348a4efd6f58c50dc54ca79ed54e"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::maxIterations" ref="8577348a4efd6f58c50dc54ca79ed54e" args="() const" -->
Size </td><td class="memItemRight" valign="bottom"><b>maxIterations</b> () const</td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d7e73e7819d87ce8bdeabb391be14cc5"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::maxIterations" ref="d7e73e7819d87ce8bdeabb391be14cc5" args="()" -->
Size & </td><td class="memItemRight" valign="bottom"><b>maxIterations</b> ()</td></tr>
<tr><td colspan="2"><br><h2>Protected Member Functions</h2></td></tr>
<tr><td class="memTemplParams" nowrap colspan="2"><a class="anchor" name="6300416a0d6980fe53e0a29216abbc52"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::defaultIteration" ref="6300416a0d6980fe53e0a29216abbc52" args="(const F &f, Real a, Real b, Real I, Size N) const" -->
template<class F> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">Real </td><td class="memTemplItemRight" valign="bottom"><b>defaultIteration</b> (const F &f, Real a, Real b, Real I, Size N) const</td></tr>
<tr><td class="memTemplParams" nowrap colspan="2"><a class="anchor" name="35e081cfe001015716cf692aeda1dbad"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::midPointIteration" ref="35e081cfe001015716cf692aeda1dbad" args="(const F &f, Real a, Real b, Real I, Size N) const" -->
template<class F> </td></tr>
<tr><td class="memTemplItemLeft" nowrap align="right" valign="top">Real </td><td class="memTemplItemRight" valign="bottom"><b>midPointIteration</b> (const F &f, Real a, Real b, Real I, Size N) const</td></tr>
<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9ee5ac7e44b518c6da03615672cb6e9b"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::accuracy_" ref="9ee5ac7e44b518c6da03615672cb6e9b" args="" -->
Real </td><td class="memItemRight" valign="bottom"><b>accuracy_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="976da067e26411726fa98bb844e15a12"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::method_" ref="976da067e26411726fa98bb844e15a12" args="" -->
Method </td><td class="memItemRight" valign="bottom"><b>method_</b></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f75d2bb304cdff446e507879467b2582"></a><!-- doxytag: member="QuantLib::TrapezoidIntegral::maxIterations_" ref="f75d2bb304cdff446e507879467b2582" args="" -->
Size </td><td class="memItemRight" valign="bottom"><b>maxIterations_</b></td></tr>
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