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Diff for /OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd between version 1.2 and 1.15

version 1.2, 2013/03/01 05:27:08 version 1.15, 2016/03/01 07:29:18
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 % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.1 2013/02/23 07:00:21 takayama Exp $  % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.14 2016/02/16 02:17:00 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)  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{
   \item{m}{The dimension of the Wishart matrix.}    \item{m}{The dimension of the Wishart matrix.}
   \item{n}{The degree of freedome (a parameter of the Wishart distribution)}    \item{n}{The degree of freedome (a parameter of the Wishart distribution)}
   \item{beta}{The eigenvalues of the inverse of the covariant matrix    \item{beta}{The eigenvalues of the inverse of the covariant matrix /2
 (a parameter of the Wishart distribution)  (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}{    \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 31  hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x)
Line 33  hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x)
   }    }
   \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 or dp is negative, it is automatically set.
       if it is 0, no sample is stored.
   }    }
   \item{x}{    \item{q}{
     The first value 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}{
       When mode=c(1,0,0), it returns the evaluation
       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}{
       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.
       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) or by increasing q0 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 this function outputs an input for plot
       (which is equivalent to setting the 3rd argument of the mode parameter properly).
       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,...), ...
       When the adaptive Runge-Kutta method is used, the step size h may change
       automatically,
       which  makes the sampling period change, in other words, the sampling points
      q0+q/100, q0+2*q/100, q0+3*q/100, ... may  change.
      In this case, the output matrix may contain zero rows in the tail or overfull.
      In case of the overful, use the mode option to get the all result.
     }
 }  }
 \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, x0 are smaller    We can obtain more accurate result when the variables h is smaller,
     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 q0, h, approxdeg properly
     is to make x larger and to check if the y[0] approaches to 1.
 %  \code{\link[RCurl]{postForm}}.  %  \code{\link[RCurl]{postForm}}.
 }  }
 \value{  \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  y[0] is the value of the cumulative distribution
 function P(L1 < x) at x.  y[1],...,y[2^m] are some derivatives.  function P(L1 < x) at x.  y[1],...,y[2^m] are some derivatives.
 See the reference below.  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. 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)
   ## =====================================================
   ## 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  % Add one or more standard keywords, see file 'KEYWORDS' in the
 % R documentation directory.  % R documentation directory.
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