===================================================================
RCS file: /home/cvs/OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v
retrieving revision 1.2
retrieving revision 1.10
diff -u -p -r1.2 -r1.10
--- OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd	2013/03/01 05:27:08	1.2
+++ OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd	2015/03/27 02:36:30	1.10
@@ -1,26 +1,28 @@
-% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.1 2013/02/23 07:00:21 takayama Exp $
-\name{hgm.cwishart}
-\alias{hgm.cwishart}
+% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.9 2015/03/26 11:54:13 takayama Exp $
+\name{hgm.pwishart}
+\alias{hgm.pwishart}
 %- Also NEED an '\alias' for EACH other topic documented here.
 \title{
-    The function hgm.cwishart evaluates the cumulative distribution function
-  of random wishart matrix.
+    The function hgm.pwishart evaluates the cumulative distribution function
+  of random wishart matrices.
 }
 \description{
-    The function hgm.cwishart evaluates the cumulative distribution function
-  of random wishart matrix of size m times m.
+    The function hgm.pwishart evaluates the cumulative distribution function
+  of random wishart matrices of size m times m.
 }
 \usage{
-hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x)
+hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
+            err,automatic,assigned_series_error,verbose)
 }
 %- maybe also 'usage' for other objects documented here.
 \arguments{
   \item{m}{The dimension of the Wishart matrix.}
   \item{n}{The degree of freedome (a parameter of the Wishart distribution)}
-  \item{beta}{The eigenvalues of the inverse of the covariant matrix
-(a parameter of the Wishart distribution)
+  \item{beta}{The eigenvalues of the inverse of the covariant matrix /2
+(a parameter of the Wishart distribution).
+    The beta is equal to inverse(sigma)/2.
   }
-  \item{x0}{The point to evaluate the matrix hypergeometric series. x0>0}
+  \item{q0}{The point to evaluate the matrix hypergeometric series. q0>0}
   \item{approxdeg}{
     Zonal polynomials upto the approxdeg are calculated to evaluate
    values near the origin. A zonal polynomial is determined by a given
@@ -32,47 +34,95 @@ hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x)
   \item{dp}{
     Sampling interval of solutions by the Runge-Kutta method.
   }
-  \item{x}{
-    The first value of this function is the Prob(L1 < x)
+  \item{q}{
+    The second value y[0] of this function is the Prob(L1 < q)
     where L1 is the first eigenvalue of the Wishart matrix.
   }
+  \item{mode}{
+    When mode=c(1,0,0), it returns the evaluation 
+    of the matrix hypergeometric series and its derivatives at x0.
+    When mode=c(1,1,(m^2+1)*p), intermediate values of P(L1 < x) with respect to
+    p-steps of x are also returned.  Sampling interval is controled by dp.
+  }
+  \item{method}{
+    a-rk4 is the default value. 
+    When method="a-rk4", the adaptive Runge-Kutta method is used.
+    Steps are automatically adjusted by err.
+  }
+  \item{err}{
+    When err=c(e1,e2), e1 is the absolute error and e2 is the relative error.
+    As long as NaN is not returned, it is recommended to set to
+    err=c(0.0, 1e-10), because initial values are usually very small. 
+  }  
+  \item{automatic}{
+    automatic=1 is the default value.
+    If it is 1, the degree of the series approximation will be increased until 
+    |(F(i)-F(i-1))/F(i-1)| < assigned_series_error where
+    F(i) is the degree i approximation of the hypergeometric series
+    with matrix argument.
+    Step sizes for the Runge-Kutta method are also set automatically from
+    the assigned_series_error if it is 1.
+  }  
+  \item{assigned_series_error}{
+    assigned_series_error=0.00001 is the default value.
+  }  
+  \item{verbose}{
+    verbose=0 is the default value.
+    If it is 1, then steps of automatic degree updates and several parameters
+    are output to stdout and stderr.
+  }  
 }
 \details{
   It is evaluated by the Koev-Edelman algorithm when x is near the origin and
   by the HGM when x is far from the origin.
-  We can obtain more accurate result when the variables h, x0 are smaller
+  We can obtain more accurate result when the variables h is smaller,
+  x0 is relevant value (not very big, not very small),
   and the approxdeg is more larger.
+  A heuristic method to set parameters x0, h, approxdeg properly
+  is to make x larger and to check if the y[0] approaches to 1.
 %  \code{\link[RCurl]{postForm}}.
 }
 \value{
-The output is x, y[0], ..., y[2^m],  
+The output is x, y[0], ..., y[2^m] in the default mode,  
 y[0] is the value of the cumulative distribution
 function P(L1 < x) at x.  y[1],...,y[2^m] are some derivatives.
 See the reference below.
 }
 \references{
 H.Hashiguchi, Y.Numata, N.Takayama, A.Takemura,
-Holonomic gradient method for the distribution function of the largest root of a Wishart matrix
-\url{http://arxiv.org/abs/1201.0472},
+Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
+Journal of Multivariate Analysis, 117, (2013) 296-312, 
+\url{http://dx.doi.org/10.1016/j.jmva.2013.03.011},
 }
 \author{
 Nobuki Takayama
 }
 \note{
-%%  ~~further notes~~
+This function does not work well under the following cases:
+1. The beta (the set of eigenvalues)
+is degenerated or is almost degenerated.
+2. The beta is very skew, in other words, there is a big eigenvalue
+and there is also a small eigenvalue.
+The error control is done by a heuristic method. 
+The obtained value is not validated automatically.
 }
 
 %% ~Make other sections like Warning with \section{Warning }{....} ~
 
-\seealso{
-%%\code{\link{oxm.matrix_r2tfb}}
-}
+%\seealso{
+%%%\code{\link{oxm.matrix_r2tfb}}
+%}
 \examples{
 ## =====================================================
-## Example 1. Computing normalization constant of the Fisher distribution on SO(3)
+## Example 1. 
 ## =====================================================
-hgm.cwishart(m=3,n=5,beta=c(1,2,3),x=10)
-
+hgm.pwishart(m=3,n=5,beta=c(1,2,3),q=10)
+## =====================================================
+## Example 2. 
+## =====================================================
+b<-hgm.pwishart(m=4,n=10,beta=c(1,2,3,4),q0=1,q=10,approxdeg=20,mode=c(1,1,(16+1)*100));
+c<-matrix(b,ncol=16+1,byrow=1);
+#plot(c)
 }
 % Add one or more standard keywords, see file 'KEYWORDS' in the
 % R documentation directory.