$OpenXM: OpenXM/src/asir-contrib/packages/doc/nk_fb_gen_c/nk_fb_gen_c.oxg,v 1.3 2017/03/30 07:01:30 takayama Exp $
test1.c, test1.h はこのプログラムで生成された例. data, 初期値はすでに設定済.
/*  まだ書いてない.
begin: include|

@include nk_fb_gen_c_intro.ja

end:
*/

/* まだ書いてない.
begin: include|

@include nk_fb_gen_c_intro.en

end:
*/

/*&usage-ja
begin:  nk_fb_gen_c.gen_c(N)
  {N} 次元 Fisher-Bingham 分布についての最尤推定を HGD 法(holonomic gradient descent) でやるための C のプログラムを生成する.
description:
   この関数により, testN.c, testN.h なる二つの C のプログラムが生成される.
   testN.c にデータ, 最尤推定探索用のパラメータ初期値を設定する.
   コマンド
   @quotation
   @code{gcc testN.c $OpenXM_HOME/lib/libko_fb.a -lgsl -lblas }
   @end quotation
   で実行可能形式のファイルを作成する. @*
   なお,
   libko_fb.a は @file{OpenXM/src/hgm/fisher-bingham/src/} で @code{make install} することにより生成される.
   またシステムには gsl がインストールされていないといけない.
   @file{OpenXM/src/hgm/fisher-bingham/src/Testdata} にサンプルの
  データ, 最尤推定探索用のパラメータ初期値がある. @*
  testN.h の @code{#define MULTIMIN_FDFMINIMIZER_TYPE} で gsl のどの最適化関数を呼び出すか変更できる.
  testN.h の @code{#define ODEIV_STEP_TYPE} で gsl のどの常微分方程式数値解析関数を呼び出すか変更できる. @*
  アルゴリズムの詳細は,
  T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere, Computational Statistics (2013),
  @url{http://dx.doi.org/10.1007/s00180-013-0456-z} 
  を参照. @*
  Authors; T.Koyama, H.Nakayama, K.Nishiyama, N.Takayama.
example:
[1854] load("nk_fb_gen_c.rr");
[2186]  nk_fb_gen_c.gen_c(1);     S^1 の問題を解く program を生成.
generate test1.h
generate test1.c
1
[2187] quit;
$ emacs test1.c &


	 Write data here. 
とコメントに書かれているところの後
に $(OpenXM_HOME)/src/hgm/fisher-bingham/Testdata/s1_wind_data.h を挿入.
保存終了.

$ gcc test1.c $OpenXM_HOME/lib/libko_fb.a -lgsl -lblas 
$ ./a.out
  --- snip
points = [1.11945, 3.33044, -0.469454, 0.904504, -0.770373]
values = [3.4421, 1.13891, -0.0217944, 2.28474]
grad ; 0.005644 -0.033429 -0.005644 0.045820 0.047695 
norm(grad) ; 0.074535
  --- snip

ここで, points が parameter x11,x12,x22,y1,y2 の推定値.
Value 3.4421 が 尤度値の逆数で, これが最小化されている.
end:
*/

/*&usage-en
begin:  nk_fb_gen_c.gen_c(N)
  It generates a C program to make a MLE (maximal likelihood estimate)
  by the HGD (holonomic gradient descent)
 for {N} dimensional Fisher-Bingham distribution.
description:
   This function generates two C programs testN.c and testN.h.
   After setting data and an initial point to make MLE in testN.c,
   build an executable file by the command
   @quotation
   @code{gcc testN.c $OpenXM_HOME/lib/libko_fb.a -lgsl -lblas } 
   @end quotation
   The libray file libko_fb.a is generated by
   @code{make install} in the folder  @file{OpenXM/src/hgm/fisher-bingham/src/}
   The GSL (Gnu Scientific Library) should also be installed in the system.
   Sample data and initial points are in @file{OpenXM/src/hgm/fisher-bingham/src/Testdata}. 
   @*
  The definition @code{#define MULTIMIN_FDFMINIMIZER_TYPE} in testN.h specifies 
  an optimization problem solver of gsl.
  The definition @code{#define ODEIV_STEP_TYPE} in testN.h specifies a solver of the ordinary differential
  equation of gsl. @*
  As to the algorithm, refer to
  T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, Holonomic Gradient Descent for the Fisher-Bingham Distribution on the d-dimensional Sphere, Computational Statistics (2013),
  @url{http://dx.doi.org/10.1007/s00180-013-0456-z} @*
  Authors; T.Koyama, H.Nakayama, K.Nishiyama, N.Takayama.
example:
[1854] load("nk_fb_gen_c.rr");
[2186]  nk_fb_gen_c.gen_c(1);     Generate a program to solve MLE on S^1
generate test1.h
generate test1.c
1
[2187] quit;
$ emacs test1.c &

Find a line which contains
     Write data here
and insert $(OpenXM_HOME)/src/hgm/fisher-bingham/Testdata/s1_wind_data.h.
after this line.
Save and quit emacs.

$ gcc test1.c $OpenXM_HOME/lib/libko_fb.a -lgsl -lblas 
$ ./a.out
  --- snip
points = [1.11945, 3.33044, -0.469454, 0.904504, -0.770373]
values = [3.4421, 1.13891, -0.0217944, 2.28474]
grad ; 0.005644 -0.033429 -0.005644 0.045820 0.047695 
norm(grad) ; 0.074535
  --- snip

where ``points'' is the estimated value of the parameter x11,x12,x22,y1,y2.
Value 3.4421 is the inverse of the likelihood which is minimized.
end:
*/