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Diff for /OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd between version 1.10 and 1.16

version 1.10, 2015/03/27 02:36:30 version 1.16, 2022/04/07 00:56:44
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 % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.9 2015/03/26 11:54:13 takayama Exp $  % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.15 2016/03/01 07:29:18 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.
Line 12 
Line 12 
 }  }
 \usage{  \usage{
 hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
             err,automatic,assigned_series_error,verbose)              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 33  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 or dp is negative, it is automatically set.
       if it is 0, no sample is stored.
   }    }
   \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 40  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
Line 42  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 51  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
Line 54  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) or by increasing q0 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 71  hgm.pwishart(m,n,beta,q0,approxdeg,h,dp,q,mode,method,
Line 75  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 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 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 92  See the reference below.
Line 108  See the reference below.
 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,
 Journal of Multivariate Analysis, 117, (2013) 296-312,  Journal of Multivariate Analysis, 117, (2013) 296-312,
 \url{http://dx.doi.org/10.1016/j.jmva.2013.03.011},  \doi{10.1016/j.jmva.2013.03.011},
 }  }
 \author{  \author{
 Nobuki Takayama  Nobuki Takayama
Line 122  hgm.pwishart(m=3,n=5,beta=c(1,2,3),q=10)
Line 138  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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