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RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v
retrieving revision 1.1
retrieving revision 1.10
diff -u -p -r1.1 -r1.10
--- OpenXM/src/hgm/doc/ref-hgm.html	2014/03/24 06:43:55	1.1
+++ OpenXM/src/hgm/doc/ref-hgm.html	2014/05/16 11:30:31	1.10
@@ -12,7 +12,15 @@ the Holonomic Gradient Descent Method  (HGD) </h1>
 
 <h2> Papers  and Tutorials</h2>
 <ol>
-<li> T.Koyama,
+<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>
 
@@ -30,11 +38,16 @@ T.Hibi et al, Groebner Bases : Statistics and Software
 Introduction to the Holonomic Gradient Method (movie), 2013. 
 <a href="http://www.youtube.com/watch?v=SgyDDLzWTyI"> movie at youtube </a>
 
+
 <li> T.Sei, A.Kume,
-Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method,
+Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method,
 Statistics and Computing, 2013,
 <a href="http://dx.doi.org/10.1007/s11222-013-9434-0">DOI</a>
 
+<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>
+
 <li>T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama,
 Holonomic Rank of the Fisher-Bingham System of Differential Equations,
 <!-- <a href="http://arxiv.org/abs/1205.6144"> arxiv:1205.6144 </a>-->
@@ -73,12 +86,51 @@ Advances in Applied Mathematics 47 (2011), 639--658,
 <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
 </ol>
 
+<h2> Three Steps of HGM </h2>
+<ol>
+<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> 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> 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.
+</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
+<a href="http://www.math.kobe-u.ac.jp/OpenXM/Current/doc/index-doc.html">
+OpenXM documents</a>
+or in <a href="./"> this folder</a>.
+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> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/"> hgm package for R </a>
-<li> yang (for Pfaffian systems) , nk_restriction (for D-module integrations), 
-tk_jack  (for Jack polynomials) are in the 
-<a href="http://www.math.kobe-u.ac.jp/Asir"> asir-contrib </a>
+<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> (hgm_*tar.gz, hgm-manual.pdf) for the step 3. 
+<li> The following packages are 
+for the computer algebra system 
+<a href="http://www.math.kobe-u.ac.jp/Asir"> Risa/Asir</a>.
+They are in the asir-contrib collection.
+<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).
+<li> ot_hgm_ahg.rr (HGM for A-distributions, very experimental).
+</ul>
 </ol>
 
 <h2> Programs to try examples of our papers </h2>
@@ -86,6 +138,6 @@ tk_jack  (for Jack polynomials) are 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> $OpenXM$ </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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