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<div><a class="htmltoc" href="../FRONTMATTER/manconts.xml">NAG Library Manual</a></div><hr/><h1 class="libdoc">NAG Library Chapter Contents<br/><br/>D01 &#8211; Quadrature</h1>
<h3 class="standard"><a class="chapint" href="../D01/d01intro.xml">D01 Chapter Introduction</a></h3>
<div class="left-tablediv"><table class="contents"><tbody>
<tr>
<td class="contents" valign="top" align="left"><b>Routine<br/>Name</b></td>
<td class="contents" valign="top" align="center"><b>Mark of<br/>Introduction</b></td>
<td class="contents" valign="top" align="left"><br/><b>Purpose</b></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01ahf.xml">D01AHF</a>
<br/><a class="tocexample" href="../../examples/source/d01ahfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, finite interval, strategy due to Patterson, suitable for well-behaved integrands</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01ajf.xml">D01AJF</a>
<br/><a class="tocexample" href="../../examples/source/d01ajfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, finite interval, strategy due to Piessens and de Doncker, allowing for badly behaved integrands</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01akf.xml">D01AKF</a>
<br/><a class="tocexample" href="../../examples/source/d01akfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, finite interval, method suitable for oscillating functions</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01alf.xml">D01ALF</a>
<br/><a class="tocexample" href="../../examples/source/d01alfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, finite interval, allowing for singularities at user-specified break-points</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01amf.xml">D01AMF</a>
<br/><a class="tocexample" href="../../examples/source/d01amfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, infinite or semi-infinite interval</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01anf.xml">D01ANF</a>
<br/><a class="tocexample" href="../../examples/source/d01anfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, finite interval, weight function <m:math><m:mrow><m:mi>cos</m:mi><m:mfenced separators=""><m:mi>&#969;</m:mi><m:mi>x</m:mi></m:mfenced></m:mrow></m:math>&#160;or <m:math><m:mrow><m:mi>sin</m:mi><m:mfenced separators=""><m:mi>&#969;</m:mi><m:mi>x</m:mi></m:mfenced></m:mrow></m:math></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01apf.xml">D01APF</a>
<br/><a class="tocexample" href="../../examples/source/d01apfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, finite interval, weight function with end-point singularities of algebraico-logarithmic type</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01aqf.xml">D01AQF</a>
<br/><a class="tocexample" href="../../examples/source/d01aqfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, finite interval, weight function <m:math><m:mn>1</m:mn><m:mo>/</m:mo><m:mfenced separators=""><m:mi>x</m:mi><m:mo>-</m:mo><m:mi>c</m:mi></m:mfenced></m:math>, Cauchy principal value (Hilbert transform)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01arf.xml">D01ARF</a>
<br/><a class="tocexample" href="../../examples/source/d01arfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, non-adaptive, finite interval with provision for indefinite integrals</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01asf.xml">D01ASF</a>
<br/><a class="tocexample" href="../../examples/source/d01asfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, semi-infinite interval, weight function <m:math><m:mrow><m:mi>cos</m:mi><m:mfenced separators=""><m:mi>&#969;</m:mi><m:mi>x</m:mi></m:mfenced></m:mrow></m:math>&#160;or <m:math><m:mrow><m:mi>sin</m:mi><m:mfenced separators=""><m:mi>&#969;</m:mi><m:mi>x</m:mi></m:mfenced></m:mrow></m:math></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01atf.xml">D01ATF</a>
<br/><a class="tocexample" href="../../examples/source/d01atfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, finite interval, variant of <a class="rout" href="../D01/d01ajf.xml">D01AJF</a> efficient on vector machines</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01auf.xml">D01AUF</a>
<br/><a class="tocexample" href="../../examples/source/d01aufe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, adaptive, finite interval, variant of <a class="rout" href="../D01/d01akf.xml">D01AKF</a> efficient on vector machines</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01baf.xml">D01BAF</a>
<br/><a class="tocexample" href="../../examples/source/d01bafe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">7</td>
<td class="contentsdoc" valign="top">One-dimensional Gaussian quadrature</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01bbf.xml">D01BBF</a>
<br/><a class="tocexample" href="../../examples/source/d01bbfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">7</td>
<td class="contentsdoc" valign="top">Pre-computed weights and abscissae for Gaussian quadrature rules, restricted choice of rule</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01bcf.xml">D01BCF</a>
<br/><a class="tocexample" href="../../examples/source/d01bcfe.f">Example&#160;Text</a><br/><a class="plot" href="../D01/d01bcf.xml#examresults">Example Plot</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Calculation of weights and abscissae for Gaussian quadrature rules, general choice of rule</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01bdf.xml">D01BDF</a>
<br/><a class="tocexample" href="../../examples/source/d01bdfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, non-adaptive, finite interval</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01daf.xml">D01DAF</a>
<br/><a class="tocexample" href="../../examples/source/d01dafe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">5</td>
<td class="contentsdoc" valign="top">Two-dimensional quadrature, finite region</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01eaf.xml">D01EAF</a>
<br/><a class="tocexample" href="../../examples/source/d01eafe.f">Example&#160;Text</a><br/><a class="plot" href="../D01/d01eaf.xml#examresults">Example Plot</a></td>
<td class="contentsdoc" valign="top" align="center">12</td>
<td class="contentsdoc" valign="top">Multi-dimensional adaptive quadrature over hyper-rectangle, multiple integrands</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01fbf.xml">D01FBF</a>
<br/><a class="tocexample" href="../../examples/source/d01fbfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Multi-dimensional Gaussian quadrature over hyper-rectangle</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01fcf.xml">D01FCF</a>
<br/><a class="tocexample" href="../../examples/source/d01fcfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Multi-dimensional adaptive quadrature over hyper-rectangle</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01fdf.xml">D01FDF</a>
<br/><a class="tocexample" href="../../examples/source/d01fdfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multi-dimensional quadrature, Sag&#8211;Szekeres method, general product region or <m:math><m:mi>n</m:mi></m:math>-sphere</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01gaf.xml">D01GAF</a>
<br/><a class="tocexample" href="../../examples/source/d01gafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/d01gafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">5</td>
<td class="contentsdoc" valign="top">One-dimensional quadrature, integration of function defined by data values, Gill&#8211;Miller method</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01gbf.xml">D01GBF</a>
<br/><a class="tocexample" href="../../examples/source/d01gbfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multi-dimensional quadrature over hyper-rectangle, Monte Carlo method</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01gcf.xml">D01GCF</a>
<br/><a class="tocexample" href="../../examples/source/d01gcfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multi-dimensional quadrature, general product region, number-theoretic method</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01gdf.xml">D01GDF</a>
<br/><a class="tocexample" href="../../examples/source/d01gdfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">14</td>
<td class="contentsdoc" valign="top">Multi-dimensional quadrature, general product region, number-theoretic method, variant of <a class="rout" href="../D01/d01gcf.xml">D01GCF</a> efficient on vector machines</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01gyf.xml">D01GYF</a>
<br/><a class="tocexample" href="../../examples/source/d01gyfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Korobov optimal coefficients for use in <a class="rout" href="../D01/d01gcf.xml">D01GCF</a> or <a class="rout" href="../D01/d01gdf.xml">D01GDF</a>, when number of points is prime</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01gzf.xml">D01GZF</a>
<br/><a class="tocexample" href="../../examples/source/d01gzfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Korobov optimal coefficients for use in <a class="rout" href="../D01/d01gcf.xml">D01GCF</a> or <a class="rout" href="../D01/d01gdf.xml">D01GDF</a>, when number of points is product of two primes</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01jaf.xml">D01JAF</a>
<br/><a class="tocexample" href="../../examples/source/d01jafe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multi-dimensional quadrature over an <m:math><m:mi>n</m:mi></m:math>-sphere, allowing for badly behaved integrands</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../D01/d01paf.xml">D01PAF</a>
<br/><a class="tocexample" href="../../examples/source/d01pafe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multi-dimensional quadrature over an <m:math><m:mi>n</m:mi></m:math>-simplex</td>
</tr>
</tbody>
</table></div><hr/><div><a class="chap" href="../../pdf/D01/d01conts.pdf">D01 Chapter Contents (PDF version)</a></div><div><a class="chapint" href="d01intro.xml">D01 Chapter Introduction</a></div>
<div><a class="htmltoc" href="../FRONTMATTER/manconts.xml">NAG Library Manual</a></div>
<div><hr/><a class="genint" href="../FRONTMATTER/copyright.xml">&#169; The Numerical Algorithms Group Ltd, Oxford, UK. 2009</a></div></body></html>