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<html xmlns="http://www.w3.org/1999/xhtml" xmlns:dsi="http://www.w3.org/1999/xlink" xmlns:m="http://www.w3.org/1998/Math/MathML" xml:space="preserve"><head><meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"/><title>C06 Chapter Contents : NAG Library Manual, Mark 22</title><link rel="stylesheet" href="../styles/libdoc.css" type="text/css"/></head><body><hr/><div><a class="chap" href="../../pdf/C06/c06conts.pdf">C06 Chapter Contents (PDF version)</a></div><div><a class="chapint" href="c06intro.xml">C06 Chapter Introduction</a></div>
<div><a class="htmltoc" href="../FRONTMATTER/manconts.xml">NAG Library Manual</a></div><hr/><h1 class="libdoc">NAG Library Chapter Contents<br/><br/>C06 &#8211; Summation of Series</h1>
<h3 class="standard"><a class="chapint" href="../C06/c06intro.xml">C06 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="../C06/c06baf.xml">C06BAF</a>
<br/><a class="tocexample" href="../../examples/source/c06bafe.f">Example&#160;Text</a><br/><a class="plot" href="../C06/c06baf.xml#examresults">Example Plot</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Acceleration of convergence of sequence, Shanks' transformation and epsilon algorithm</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06dbf.xml">C06DBF</a>
<br/><a class="tocexample" href="../../examples/source/c06dbfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">6</td>
<td class="contentsdoc" valign="top">Sum of a Chebyshev series</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06eaf.xml">C06EAF</a>
<br/><a class="tocexample" href="../../examples/source/c06eafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06eafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Single one-dimensional real discrete Fourier transform, no extra workspace</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06ebf.xml">C06EBF</a>
<br/><a class="tocexample" href="../../examples/source/c06ebfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06ebfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Single one-dimensional Hermitian discrete Fourier transform, no extra workspace</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06ecf.xml">C06ECF</a>
<br/><a class="tocexample" href="../../examples/source/c06ecfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06ecfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Single one-dimensional complex discrete Fourier transform, no extra workspace</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06ekf.xml">C06EKF</a>
<br/><a class="tocexample" href="../../examples/source/c06ekfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06ekfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Circular convolution or correlation of two real vectors, no extra workspace</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06faf.xml">C06FAF</a>
<br/><a class="tocexample" href="../../examples/source/c06fafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Single one-dimensional real discrete Fourier transform, extra workspace for greater speed</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06fbf.xml">C06FBF</a>
<br/><a class="tocexample" href="../../examples/source/c06fbfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fbfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Single one-dimensional Hermitian discrete Fourier transform, extra workspace for greater speed</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06fcf.xml">C06FCF</a>
<br/><a class="tocexample" href="../../examples/source/c06fcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Single one-dimensional complex discrete Fourier transform, extra workspace for greater speed</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06fff.xml">C06FFF</a>
<br/><a class="tocexample" href="../../examples/source/c06fffe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fffe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">One-dimensional complex discrete Fourier transform of multi-dimensional data</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06fjf.xml">C06FJF</a>
<br/><a class="tocexample" href="../../examples/source/c06fjfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fjfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Multi-dimensional complex discrete Fourier transform of multi-dimensional data</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06fkf.xml">C06FKF</a>
<br/><a class="tocexample" href="../../examples/source/c06fkfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fkfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Circular convolution or correlation of two real vectors, extra workspace for greater speed</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06fpf.xml">C06FPF</a>
<br/><a class="tocexample" href="../../examples/source/c06fpfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fpfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">12</td>
<td class="contentsdoc" valign="top">Multiple one-dimensional real discrete Fourier transforms</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06fqf.xml">C06FQF</a>
<br/><a class="tocexample" href="../../examples/source/c06fqfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fqfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">12</td>
<td class="contentsdoc" valign="top">Multiple one-dimensional Hermitian discrete Fourier transforms</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06frf.xml">C06FRF</a>
<br/><a class="tocexample" href="../../examples/source/c06frfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06frfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">12</td>
<td class="contentsdoc" valign="top">Multiple one-dimensional complex discrete Fourier transforms</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06fuf.xml">C06FUF</a>
<br/><a class="tocexample" href="../../examples/source/c06fufe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fufe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Two-dimensional complex discrete Fourier transform</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06fxf.xml">C06FXF</a>
<br/><a class="tocexample" href="../../examples/source/c06fxfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06fxfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">17</td>
<td class="contentsdoc" valign="top">Three-dimensional complex discrete Fourier transform</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06gbf.xml">C06GBF</a>
<br/><a class="tocexample" href="../../examples/source/c06gbfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06gbfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Complex conjugate of Hermitian sequence</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06gcf.xml">C06GCF</a>
<br/><a class="tocexample" href="../../examples/source/c06gcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06gcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Complex conjugate of complex sequence</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06gqf.xml">C06GQF</a>
<br/><a class="tocexample" href="../../examples/source/c06gqfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06gqfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">12</td>
<td class="contentsdoc" valign="top">Complex conjugate of multiple Hermitian sequences</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06gsf.xml">C06GSF</a>
<br/><a class="tocexample" href="../../examples/source/c06gsfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06gsfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">12</td>
<td class="contentsdoc" valign="top">Convert Hermitian sequences to general complex sequences</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06haf.xml">C06HAF</a>
<br/><a class="tocexample" href="../../examples/source/c06hafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06hafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Discrete sine transform</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06hbf.xml">C06HBF</a>
<br/><a class="tocexample" href="../../examples/source/c06hbfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06hbfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Discrete cosine transform</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06hcf.xml">C06HCF</a>
<br/><a class="tocexample" href="../../examples/source/c06hcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06hcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Discrete quarter-wave sine transform</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06hdf.xml">C06HDF</a>
<br/><a class="tocexample" href="../../examples/source/c06hdfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06hdfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Discrete quarter-wave cosine transform</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06laf.xml">C06LAF</a>
<br/><a class="tocexample" href="../../examples/source/c06lafe.f">Example&#160;Text</a><br/><a class="plot" href="../C06/c06laf.xml#examresults">Example Plot</a></td>
<td class="contentsdoc" valign="top" align="center">12</td>
<td class="contentsdoc" valign="top">Inverse Laplace transform, Crump's method</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06lbf.xml">C06LBF</a>
<br/><a class="tocexample" href="../../examples/source/c06lbfe.f">Example&#160;Text</a><br/><a class="plot" href="../C06/c06lbf.xml#examresults">Example Plot</a></td>
<td class="contentsdoc" valign="top" align="center">14</td>
<td class="contentsdoc" valign="top">Inverse Laplace transform, modified Weeks' method</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06lcf.xml">C06LCF</a></td>
<td class="contentsdoc" valign="top" align="center">14</td>
<td class="contentsdoc" valign="top">Evaluate inverse Laplace transform as computed by <a class="rout" href="../C06/c06lbf.xml">C06LBF</a></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06paf.xml">C06PAF</a>
<br/><a class="tocexample" href="../../examples/source/c06pafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06pafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Single one-dimensional real and Hermitian complex discrete Fourier transform, using complex storage format for Hermitian sequences</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06pcf.xml">C06PCF</a>
<br/><a class="tocexample" href="../../examples/source/c06pcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06pcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Single one-dimensional complex discrete Fourier transform, complex data type</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06pff.xml">C06PFF</a>
<br/><a class="tocexample" href="../../examples/source/c06pffe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06pffe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">One-dimensional complex discrete Fourier transform of multi-dimensional data (using Complex data type)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06pjf.xml">C06PJF</a>
<br/><a class="tocexample" href="../../examples/source/c06pjfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06pjfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Multi-dimensional complex discrete Fourier transform of multi-dimensional data (using Complex data type)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06pkf.xml">C06PKF</a>
<br/><a class="tocexample" href="../../examples/source/c06pkfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06pkfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Circular convolution or correlation of two complex vectors</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06ppf.xml">C06PPF</a>
<br/><a class="tocexample" href="../../examples/source/c06ppfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06ppfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex storage format for Hermitian sequences</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06pqf.xml">C06PQF</a>
<br/><a class="tocexample" href="../../examples/source/c06pqfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06pqfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Multiple one-dimensional real and Hermitian complex discrete Fourier transforms, using complex storage format  for Hermitian sequences</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06prf.xml">C06PRF</a>
<br/><a class="tocexample" href="../../examples/source/c06prfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06prfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Multiple one-dimensional complex discrete Fourier transforms using complex data type</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06psf.xml">C06PSF</a>
<br/><a class="tocexample" href="../../examples/source/c06psfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06psfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Multiple one-dimensional complex discrete Fourier transforms using complex data type and sequences stored as columns</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06puf.xml">C06PUF</a>
<br/><a class="tocexample" href="../../examples/source/c06pufe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06pufe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Two-dimensional complex discrete Fourier transform, complex data type</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06pxf.xml">C06PXF</a>
<br/><a class="tocexample" href="../../examples/source/c06pxfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06pxfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Three-dimensional complex discrete Fourier transform, Complex data type</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06raf.xml">C06RAF</a>
<br/><a class="tocexample" href="../../examples/source/c06rafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06rafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Discrete sine transform (easy-to-use)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06rbf.xml">C06RBF</a>
<br/><a class="tocexample" href="../../examples/source/c06rbfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06rbfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Discrete cosine transform (easy-to-use)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06rcf.xml">C06RCF</a>
<br/><a class="tocexample" href="../../examples/source/c06rcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06rcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Discrete quarter-wave sine transform (easy-to-use)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../C06/c06rdf.xml">C06RDF</a>
<br/><a class="tocexample" href="../../examples/source/c06rdfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/c06rdfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">19</td>
<td class="contentsdoc" valign="top">Discrete quarter-wave cosine transform (easy-to-use)</td>
</tr>
</tbody>
</table></div><hr/><div><a class="chap" href="../../pdf/C06/c06conts.pdf">C06 Chapter Contents (PDF version)</a></div><div><a class="chapint" href="c06intro.xml">C06 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>
