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Diff for /OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd between version 1.3 and 1.12

version 1.3, 2013/03/08 07:32:28 version 1.12, 2016/02/14 00:21:50
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 % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.2 2013/03/01 05:27:08 takayama Exp $  % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.11 2016/02/13 22:56:50 takayama Exp $
 \name{hgm.cwishart}  \name{hgm.pwishart}
 \alias{hgm.cwishart}  \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.cwishart 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.cwishart 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.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.  %- maybe also 'usage' for other objects documented here.
 \arguments{  \arguments{
Line 21  hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,mode,method,
Line 22  hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,mode,method,
 (a parameter of the Wishart distribution).  (a parameter of the Wishart distribution).
     The beta is equal to inverse(sigma)/2.      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}{    \item{approxdeg}{
     Zonal polynomials upto the approxdeg are calculated to evaluate      Zonal polynomials upto the approxdeg are calculated to evaluate
    values near the origin. A zonal polynomial is determined by a given     values near the origin. A zonal polynomial is determined by a given
Line 32  hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,mode,method,
Line 33  hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,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{x}{    \item{q}{
     The second value y[0] of this function is the Prob(L1 < x)      The second value y[0] of this function is the Prob(L1 < q)
     where L1 is the first eigenvalue of the Wishart matrix.      where L1 is the first eigenvalue of the Wishart matrix.
   }    }
   \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,(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.      p-steps of x are also returned.  Sampling interval is controled by dp.
       When autoplot=1, it is automatically set.
   }    }
   \item{method}{    \item{method}{
     rk4 is the default value.      a-rk4 is the default value.
     When method="a-rk4", the adaptive Runge-Kutta method is used.      When method="a-rk4", the adaptive Runge-Kutta method is used.
     Steps are automatically adjusted by err.      Steps are automatically adjusted by err.
   }    }
Line 53  hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,mode,method,
Line 56  hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,mode,method,
     As long as NaN is not returned, it is recommended to set to      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.      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.
     }
     \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 72  See the reference below.
Line 97  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.
 ## =====================================================  ## =====================================================
 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.  ## 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);  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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