===================================================================
RCS file: /home/cvs/OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v
retrieving revision 1.3
retrieving revision 1.13
diff -u -p -r1.3 -r1.13
--- OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd	2013/03/08 07:32:28	1.3
+++ OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd	2016/02/15 07:42:07	1.13
@@ -1,17 +1,18 @@
-% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.2 2013/03/01 05:27:08 takayama Exp $
-\name{hgm.cwishart}
-\alias{hgm.cwishart}
+% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.12 2016/02/14 00:21:50 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,mode,method,err)
+hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
+            err,automatic,assigned_series_error,verbose,autoplot)
 }
 %- maybe also 'usage' for other objects documented here.
 \arguments{
@@ -21,7 +22,7 @@ hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,mode,method,
 (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
@@ -32,35 +33,60 @@ hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,mode,method,
   }
   \item{dp}{
     Sampling interval of solutions by the Runge-Kutta method.
+    When autoplot=1, it is automatically set.
   }
-  \item{x}{
-    The second value y[0] 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
+    of the matrix hypergeometric series and its derivatives at q0.
+    When mode=c(1,1,(2^m+1)*p), intermediate values of P(L1 < x) with respect to
     p-steps of x are also returned.  Sampling interval is controled by dp.
+    When autoplot=1, it is automatically set.
   }
   \item{method}{
-    rk4 is the default value. 
+    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. 
+    This parameter controls the adative Runge-Kutta method.
+    If the output is absurd, you may get a correct answer by setting,  e.g.,
+    err=c(1e-(xy+5), 1e-10) when initial value at q0 is very small as 1e-xy. 
   }  
+  \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.
+  }  
+  \item{autoplot}{
+    autoplot=0 is the default value.
+    If it is 1, then it outputs an input for plot.
+    When ans is the output, ans[1,] is c(q,prob at q,...), ans[2,] is c(q0,prob at q0,...), and ans[3,] is c(q0+q/100,prob at q/100,...), ...
+  }  
 }
 \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 is smaller,
-  x0 is relevant value (not very big, not very small),
+  q0 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
+  A heuristic method to set parameters q0, h, approxdeg properly
   is to make x larger and to check if the y[0] approaches to 1.
 %  \code{\link[RCurl]{postForm}}.
 }
@@ -72,31 +98,43 @@ 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. 
 ## =====================================================
-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.cwishart(m=4,n=10,beta=c(1,2,3,4),x0=1,x=10,approxdeg=20,mode=c(1,1,(16+1)*100));
+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)
+## =====================================================
+## Example 3. 
+## =====================================================
+c<-hgm.pwishart(m=4,n=10,beta=c(1,2,3,4),q0=1,q=10,approxdeg=20,autoplot=1);
 #plot(c)
 }
 % Add one or more standard keywords, see file 'KEYWORDS' in the