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If Dp == 0, no intermediate data is stored.
If Dp < 0, Dp is automatically set.

$OpenXM: OpenXM/src/hgm/mh/src/usage-w-n.txt,v 1.2 2016/03/01 07:13:30 takayama Exp $

hgm_w-n
     [--idata input_data_file] [--gnuplotf gnuplot_file_name]
     [--dataf output_data_file] [--raw]  [--xmax xmax] [--test m] [--step h]
     [ --95 --verbose]
     [ --strategy s --abserr ae --relerr re]
s:0 rk, s:1 adaptive, s:2 adaptive&multiply, see rk.c for the default value of ae and re.
!oxprintfe("strategy default = %d\n",MH_strategy);
--raw does not add data parameters to the output_data_file.
The command hgm_w-n [options] evaluates the matrix hypergeometric function pFq by 
the HGM (holonomic gradient method) from the initial value generated by hgm_jack-n.

Parameters are specified by the input_data_file. Otherwise, default values are used.
By executing ./hgm_jack-n without argument, a sample input file is output.
The format of the input_data_file specified by --idata: 
# or %% are used for a comment line.
The value of a parameter xyz is specified by %xyz=value
!oxprintfe("Input data file should start with the line for the latest input data format: %s\n",VSTRING);

  p_pFq : p of pFq, a_1, ..., a_p
  q_pFq : q of pFq, b_1, ..., b_q
  Mg: m (the number of variables).
  Beta: vector of length m. Evaluation is done on the line Beta*x
        All Beta[i] must be different and must not be 0.
  X0g:  starting point of x >0. The initial value Iv must be given at X0g
  Iv: initial values at X0g*Beta evaluated by this program.
  Ef: a scalar factor to the initial value evaluated by this program.
  ef_type: exponential or scalar factor type.
    case 0: rare pFq  (Todo, not implemented)
    case 1: It is for the case of evaluating 
        Pr({y | y<xmax}), which is the cumulative distribution function of the largest root 
        of the m by m Wishart matrices with n degrees of freedom and the covariantce matrix 
        sigma where 
        Beta=sigma^(-1)/2 (diagonized) and  n must be given by Ng.
        p_pFq, q_pFq are automatically set for 1F1.
        Ef must be set properly.
    case 2: 
        Pr({y | y<xmax}), which is the cumulative distribution function of the largest root
        of P Q^(-1) where P and Q are Wishart matrices. It uses 2F1 and Beta, p_pFq, q_pFq
        should be properly given.
        Ef must be set properly.

  Hg: h (step size) for hgm_w-n.
  Dp: output data is stored in every Dp steps when output_data_file is specified. 
      If it is 0, output data is not stored. If it is negative, Dp is automatically set to floor(1/Hg). Note that small Dp value makes the program slow. 
  Xng: terminating value of x for hgm_w-n.

"--95: output the 95%% point. --verbose: verbose mode.
When --idata option is used, this command is quiet. Use --verbose option if you want to see some messages

Examples:
[1] ./hgm_w-n 
[2] ./hgm_w-n --xmax 20
[3] ./hgm_w-n --test 6
A test run in Mg=6.
[4] ./hgm_jack-n --idata Testdata/tmp-idata3.txt >t.txt
    ./hgm_w-n --idata t.txt --gnuplotf test-g --verbose
    gnuplot -persist <test-g-gp.txt
    tmp-idata3.txt is a sample input data distributed with this file.
    test-g-gp.txt is an input file of the gnuplot
    test-g is the table of x and the values of Pr({y | y<x}).
[5] ./hgm_jack-n --idata Testdata/new-2016-02-04-4.txt --verbose