=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.9 retrieving revision 1.11 diff -u -p -r1.9 -r1.11 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/05/15 07:34:05 1.9 +++ OpenXM/src/hgm/doc/ref-hgm.html 2014/05/20 02:12:18 1.11 @@ -12,6 +12,10 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

    +
  1. N.Marumo, T.Oaku, A.Takemura, +Properties of powers of functions satisfying second-order linear differential equations with applications to statistics, + arxiv:1405.4451 +
  2. J.Hayakawa, A.Takemura, Estimation of exponential-polynomial distribution by holonomic gradient descent arxiv:1403.7852 @@ -51,7 +55,8 @@ Calculation of Orthant Probabilities by the Holonomic
  3. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, Holonomic Rank of the Fisher-Bingham System of Differential Equations, -to appear in Journal of Pure and Applied Algebra +Journal of Pure and Applied Algebra (online), + DOI
  4. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, @@ -74,8 +79,8 @@ Journal of Multivariate Analysis, 116 (2013), 440--455
  5. T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral, Funkcialaj Ekvacioj 56 (2013), 51--61. - -jstage +DOI +
  6. Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, @@ -88,14 +93,14 @@ Advances in Applied Mathematics 47 (2011), 639--658,

    Three Steps of HGM

      -
    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. @@ -109,22 +114,32 @@ of the OpenXM documents or in this folder. -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 cvsweb page.
      1. Command line interfaces are in the folder OpenXM/src/hgm in the OpenXM source tree. See OpenXM distribution page . -
      2. hgm package for R for the step 3. -
      3. yang (for Pfaffian systems) , nk_restriction (for D-module integrations), -tk_jack (for Jack polynomials), ko_fb_pfaffian (Pfaffian system for the Fisher-Bingham system) -are for the steps 1 or 2 and in the - asir-contrib. -
      4. nk_fb_gen_c is a package to generate a C program to perform +
      5. hgm package for R (hgm_*tar.gz, hgm-manual.pdf) for the step 3. +To install this package in R, type in +
        +R CMD install hgm_*.tar.gz
+
        +
      6. The following packages are +for the computer algebra system + Risa/Asir. +They are in the asir-contrib collection. +
          +
        • 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). -It is in the - asir-contrib. +
        • ot_hgm_ahg.rr (HGM for A-distributions, very experimental). +

      Programs to try examples of our papers

      @@ -132,6 +147,6 @@ It is in the
    7. d-dimensional Fisher-Bingham System
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