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Diff for /OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd between version 1.5 and 1.13

version 1.5, 2014/03/16 03:11:07 version 1.13, 2016/02/15 07:42:07
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 % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.4 2013/03/26 05:53:57 takayama Exp $  % $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}  \name{hgm.pwishart}
 \alias{hgm.pwishart}  \alias{hgm.pwishart}
 %- Also NEED an '\alias' for EACH other topic documented here.  %- Also NEED an '\alias' for EACH other topic documented here.
 \title{  \title{
     The function hgm.pwishart evaluates the cumulative distribution function      The function hgm.pwishart evaluates the cumulative distribution function
   of random wishart matrix.    of random wishart matrices.
 }  }
 \description{  \description{
     The function hgm.pwishart evaluates the cumulative distribution function      The function hgm.pwishart evaluates the cumulative distribution function
   of random wishart matrix of size m times m.    of random wishart matrices of size m times m.
 }  }
 \usage{  \usage{
 hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,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.  %- maybe also 'usage' for other objects documented here.
 \arguments{  \arguments{
Line 32  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
Line 33  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
   }    }
   \item{dp}{    \item{dp}{
     Sampling interval of solutions by the Runge-Kutta method.      Sampling interval of solutions by the Runge-Kutta method.
       When autoplot=1, it is automatically set.
   }    }
   \item{q}{    \item{q}{
     The second value y[0] of this function is the Prob(L1 < q)      The second value y[0] of this function is the Prob(L1 < q)
Line 39  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
Line 41  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
   }    }
   \item{mode}{    \item{mode}{
     When mode=c(1,0,0), it returns the evaluation      When mode=c(1,0,0), it returns the evaluation
     of the matrix hypergeometric series and its derivatives at x0.      of the matrix hypergeometric series and its derivatives at q0.
     When mode=c(1,1,(m^2+1)*p), intermediate values of P(L1 < x) with respect to      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.      p-steps of x are also returned.  Sampling interval is controled by dp.
       When autoplot=1, it is automatically set.
   }    }
   \item{method}{    \item{method}{
     a-rk4 is the default value.      a-rk4 is the default value.
Line 50  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
Line 53  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
   }    }
   \item{err}{    \item{err}{
     When err=c(e1,e2), e1 is the absolute error and e2 is the relative error.      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      This parameter controls the adative Runge-Kutta method.
     err=c(0.0, 1e-10), because initial values are usually very small.      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}{    \item{automatic}{
     automatic=1 is the default value.      automatic=1 is the default value.
Line 59  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
Line 63  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
     |(F(i)-F(i-1))/F(i-1)| < assigned_series_error where      |(F(i)-F(i-1))/F(i-1)| < assigned_series_error where
     F(i) is the degree i approximation of the hypergeometric series      F(i) is the degree i approximation of the hypergeometric series
     with matrix argument.      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}{    \item{assigned_series_error}{
     assigned_series_error=0.00001 is the default value.      assigned_series_error=0.00001 is the default value.
Line 68  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
Line 74  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
     If it is 1, then steps of automatic degree updates and several parameters      If it is 1, then steps of automatic degree updates and several parameters
     are output to stdout and stderr.      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{  \details{
   It is evaluated by the Koev-Edelman algorithm when x is near the origin and    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.    by the HGM when x is far from the origin.
   We can obtain more accurate result when the variables h is smaller,    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.    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.    is to make x larger and to check if the y[0] approaches to 1.
 %  \code{\link[RCurl]{postForm}}.  %  \code{\link[RCurl]{postForm}}.
 }  }
Line 87  See the reference below.
Line 98  See the reference below.
 }  }
 \references{  \references{
 H.Hashiguchi, Y.Numata, N.Takayama, A.Takemura,  H.Hashiguchi, Y.Numata, N.Takayama, A.Takemura,
 Holonomic gradient method for the distribution function of the largest root of a Wishart matrix  Holonomic gradient method for the distribution function of the largest root of a Wishart matrix,
 \url{http://arxiv.org/abs/1201.0472},  Journal of Multivariate Analysis, 117, (2013) 296-312,
   \url{http://dx.doi.org/10.1016/j.jmva.2013.03.011},
 }  }
 \author{  \author{
 Nobuki Takayama  Nobuki Takayama
 }  }
 \note{  \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 }{....} ~  %% ~Make other sections like Warning with \section{Warning }{....} ~
   
 \seealso{  %\seealso{
 %%\code{\link{oxm.matrix_r2tfb}}  %%%\code{\link{oxm.matrix_r2tfb}}
 }  %}
 \examples{  \examples{
 ## =====================================================  ## =====================================================
 ## Example 1.  ## Example 1.
Line 112  hgm.pwishart(m=3,n=5,beta=c(1,2,3),q=10)
Line 130  hgm.pwishart(m=3,n=5,beta=c(1,2,3),q=10)
 ## =====================================================  ## =====================================================
 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));  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);  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)  #plot(c)
 }  }
 % Add one or more standard keywords, see file 'KEYWORDS' in the  % Add one or more standard keywords, see file 'KEYWORDS' in the
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