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Line 12 the Holonomic Gradient Descent Method (HGD) </h1>

<h2> Papers and Tutorials</h2>

<ol>

<li> T.Koyama, A.Takemura,

<li> J.Hayakawa, A.Takemura,

Estimation of exponential-polynomial distribution by holonomic gradient descent

<a href="http://arxiv.org/abs/1403.7852"> arxiv:1403.7852</a>

<li> C.Siriteanu, A.Takemura, S.Kuriki,

MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method

<a href="http://arxiv.org/abs/1403.3788"> arxiv:1403.3788</a>

<li> T.Koyama,

Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra,

<a href="http://arxiv.org/abs/1311.6905"> arxiv:1311.6905 </a>

Line 36 Calculating the Normalising Constant of the Bingham Di

Line 44 Calculating the Normalising Constant of the Bingham Di

Statistics and Computing, 2013,

<li> T.Koyama,

<li> T.Koyama, A.Takemura,

Calculation of Orthant Probabilities by the Holonomic Gradient Method,

<a href="http://arxiv.org/abs/1211.6822"> arxiv:1211.6822</a>

Line 94 equations.

Line 102 equations.

</ol>

<h2> Software Packages for HGM</h2>

Most software packages are experimental and temporary documents are found in

"asir-contrib manual" (auto-autogenerated part), or

"Experimental Functions in Asir", or "miscellaneous and other documents"

of the

OpenXM documents</a>

or in <a href="./"> this folder</a>.

The nightly snapshot of the asir-contrib can be found in the Asir-Contrib page below,

or look up our <a href="http://www.math.sci.kobe-u.ac.jp/cgi/cvsweb.cgi/">

cvsweb page</a>.

<ol>

<li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/"> hgm package for R </a> for the step 3.

<li> yang (for Pfaffian systems) , nk_restriction (for D-module integrations),

tk_jack (for Jack polynomials) are for the steps 1 or 2 and in the

tk_jack (for Jack polynomials), ko_fb_pfaffian (Pfaffian system for the Fisher-Bingham system)

<a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib </a>

are for the steps 1 or 2 and in the

<a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib</a>.

<li> nk_fb_gen_c is a package to generate a C program to perform

maximal Likehood estimates for the Fisher-Bingham distribution by HGD (holonomic gradient descent).

It is in the

<a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib</a>.

</ol>

<h2> Programs to try examples of our papers </h2>

Line 106 tk_jack (for Jack polynomials) are for the steps 1 or

Line 129 tk_jack (for Jack polynomials) are for the steps 1 or

<li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>

</ol>

<pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.2 2014/03/24 06:58:31 takayama Exp $ </pre>

<pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.7 2014/03/31 07:23:09 takayama Exp $ </pre>

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