=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.3 retrieving revision 1.10 diff -u -p -r1.3 -r1.10 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/03/24 07:54:51 1.3 +++ 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)

Papers and Tutorials

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  1. T.Koyama, A.Takemura, +
  2. J.Hayakawa, A.Takemura, +Estimation of exponential-polynomial distribution by holonomic gradient descent + arxiv:1403.7852 + +
  3. C.Siriteanu, A.Takemura, S.Kuriki, +MIMO Zero-Forcing Detection Performance Evaluation by Holonomic Gradient Method + arxiv:1403.3788 + +
  4. T.Koyama, Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra, arxiv:1311.6905 @@ -36,7 +44,7 @@ Calculating the Normalising Constant of the Bingham Di Statistics and Computing, 2013, DOI -
  5. T.Koyama, +
  6. T.Koyama, A.Takemura, Calculation of Orthant Probabilities by the Holonomic Gradient Method, arxiv:1211.6822 @@ -80,25 +88,49 @@ Advances in Applied Mathematics 47 (2011), 639--658,

    Three Steps of HGM

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    1. Find a holonomic system satisfied by the normalizing constant. +
    2. 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. -
    3. Find an initial value vector for the holonomic system. +
    4. 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. -
    5. Solve the holonomic system numerically. We use several methods +
    6. 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.

    Software Packages for HGM

    +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 +or in this folder. +The nightly snapshot of the asir-contrib can be found in the asir page below, +or look up our +cvsweb page.
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    1. hgm package for R for the step 3. -
    2. 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 - asir-contrib +
    3. Command line interfaces are in the folder OpenXM/src/hgm +in the OpenXM source tree. See +OpenXM distribution page . +
    4. hgm package for R (hgm_*tar.gz, hgm-manual.pdf) for the step 3. +
    5. The following packages are +for the computer algebra system + Risa/Asir. +They are in the asir-contrib collection. +
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      • 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. +
      • 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). +
      • ot_hgm_ahg.rr (HGM for A-distributions, very experimental). +

    Programs to try examples of our papers

    @@ -106,6 +138,6 @@ tk_jack (for Jack polynomials) are for the steps 1 or
  7. d-dimensional Fisher-Bingham System
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