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Annotation of OpenXM/src/R/r-packages/hgm/man/hgm.Rhgm.Rd, Revision 1.2

1.2     ! takayama    1: % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.Rhgm.Rd,v 1.1 2014/03/25 02:25:26 takayama Exp $
1.1       takayama    2: \name{hgm.Rhgm}
                      3: \alias{hgm.Rhgm}
                      4: %- Also NEED an '\alias' for EACH other topic documented here.
                      5: \title{
                      6:     The function hgm.Rhgm performs the holonomic gradient method (HGM)
                      7:    for a given Pfaffian system and an initial value vector.
                      8: }
                      9: \description{
                     10:    The function hgm.Rhgm performs the holonomic gradient method (HGM)
                     11:    for a given Pfaffian system and an initial value vector
                     12:    with the deSolve package in R.
                     13: }
                     14: \usage{
                     15:  hgm.Rhgm(th0, G0, th1, dG.fun, times=NULL, fn.params=NULL)
                     16: }
                     17: %- maybe also 'usage' for other objects documented here.
                     18: \arguments{
                     19:   \item{th0}{ A d-dimensional vector which is an initial point of the parameter vector th (theta).}
                     20:   \item{G0}{
                     21:     A r-dimensional vector which is the initial value of the vector G
                     22:     of the normalizing constant and its derivatives.
                     23:   }
                     24:   \item{th1}{
                     25:     A d-dimensional vector which is the target point of th.
                     26:   }
                     27:   \item{dG.fun}{
                     28:      dG.fun is the ``right hand sides'' of the Pfaffian system.
                     29:      It is a d*r-dimensional array.
                     30:   }
                     31:   \item{times}{a vector; times in [0,1] at which explicit estimates for G are desired.
                     32:          If time = NULL, the set {0,1} is used, and only the final value is returned.
                     33:   }
                     34:   \item{fn.params}{
                     35:   fn.params: a list of parameters passed to the function dG.fun.
                     36:          If fn.params = NULL, no parameter is passed to dG.fun.
                     37:   }
                     38: }
                     39: \details{
                     40:   The function hgm.Rhgm computes the value of a holonomic function
                     41:   at a given point, using HGM.
                     42:   This is a ``Step 3'' function (see the reference below),
                     43:   which can be used for an arbitrary input, in the HGM framework.
                     44:   Efficient ``Step 3'' functions are given for some distributions
                     45:   in this package.
                     46:
                     47:   The Pfaffian system assumed is
                     48:     d G_j / d th_i = (dG.fun(th, G))_{i,j}
                     49:
                     50:   The inputs of hgm.Rhgm are the initial point th0, initial value G0, final point th1,
                     51:   and Pfaffian system dG.fun. The output is the final value G1.
                     52:
                     53:   If the argument `times' is specified, the function returns a matrix,
                     54:   where the first column denotes time, the following d-vector denotes th,
                     55:   and the remaining r-vector denotes G.
                     56: %  \code{\link[RCurl]{postForm}}.
                     57: }
                     58: \value{
                     59: The output is the value of G at th1. The first element of G is the normalizing
                     60: constant.
                     61: }
                     62: \references{
                     63: \url{http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/ref-hgm.html}
                     64: }
                     65: \author{
                     66: Tomonari Sei
                     67: }
1.2     ! takayama   68: %\note{
        !            69: %%%  ~~further notes~~
        !            70: %}
1.1       takayama   71:
                     72: %% ~Make other sections like Warning with \section{Warning }{....} ~
                     73:
1.2     ! takayama   74: %\seealso{
        !            75: %%%\code{\link{oxm.matrix_r2tfb}}
        !            76: %}
1.1       takayama   77: \examples{
                     78: # Example 1.
                     79: # A demo program; von Mises--Fisher on S^{3-1}
                     80:
                     81: G.exact = function(th){  # exact value by built-in function
                     82:   c( sinh(th[1])/th[1], cosh(th[1])/th[1] - sinh(th[1])/th[1]^2 )
                     83: }
                     84:
                     85: dG.fun = function(th, G, fn.params=NULL){  # Pfaffian
                     86:   dG = array(0, c(1, 2))
                     87:   sh = G[1] * th[1]
                     88:   ch = G[2] * th[1] + G[1]
                     89:   dG[1,1] = G[2] # Pfaffian eq's
                     90:   dG[1,2] = sh/th[1] - 2*ch/th[1]^2 + 2*sh/th[1]^3
                     91:   dG
                     92: }
                     93:
                     94: th0 = 0.5
                     95: th1 = 15
                     96:
                     97: G0 = G.exact(th0)
                     98: G0
                     99:
                    100: G1 = hgm.Rhgm(th0, G0, th1, dG.fun)  # HGM
                    101: G1
                    102:
                    103: G1.exact = G.exact(th1)
                    104: G1.exact
                    105:
                    106: #
                    107: # Example 2.
                    108: #
                    109: hgm.Rhgm.demo1()
                    110:
                    111: }
                    112: % Add one or more standard keywords, see file 'KEYWORDS' in the
                    113: % R documentation directory.
                    114: \keyword{ Normalization constant }
                    115: \keyword{ Holonomic gradient method }
                    116: \keyword{ HGM }
                    117:
                    118: