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Line 88 Advances in Applied Mathematics 47 (2011), 639--658,

<h2> Three Steps of HGM </h2>

<ol>

<li> Find a holonomic system satisfied by the normalizing constant.

<li> Finding a holonomic system satisfied by the normalizing constant.

We may use computational or theoretical methods to find it.

Groebner basis and related methods are used.

<li> Find an initial value vector for the holonomic system.

<li> Finding an initial value vector for the holonomic system.

This is equivalent to evaluating the normalizing constant and its derivatives

at a point.

This step is usually performed by a series expansion.

<li> Solve the holonomic system numerically. We use several methods

<li> Solving the holonomic system numerically. We use several methods

in numerical analysis such as the Runge-Kutta method of solving

ordinary differential equations and efficient solvers of systems of linear

equations.

Line 109 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,

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

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

cvsweb page</a>.

<ol>

<li> Command line interfaces are in the folder OpenXM/src/hgm

in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">

OpenXM distribution page </a>.

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

<li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/"> hgm package for R </a> (hgm_*tar.gz, hgm-manual.pdf) for the step 3.

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

<li> The following packages are

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

for the computer algebra system

are for the steps 1 or 2 and in the

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

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

They are in the asir-contrib collection.

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

<ul>

<li> yang.rr (for Pfaffian systems) ,

nk_restriction.rr (for D-module integrations),

tk_jack.rr (for Jack polynomials),

ko_fb_pfaffian.rr (Pfaffian system for the Fisher-Bingham system),

are for the steps 1 or 2.

<li> nk_fb_gen_c.rr 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

<li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).

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

</ul>

</ol>

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

Line 132 It is in the

Line 138 It is in the

<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 1.8 2014/04/03 07:34:31 takayama Exp $ </pre>

<pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.9 2014/05/15 07:34:05 takayama Exp $ </pre>

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