version 1.1, 2016/02/13 06:47:50 |
version 1.8, 2016/10/28 02:27:39 |
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% $OpenXM$ |
% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.c2wishart.Rd,v 1.7 2016/03/01 07:29:18 takayama Exp $ |
\name{hgm.p2wishart} |
\name{hgm.p2wishart} |
\alias{hgm.p2wishart} |
\alias{hgm.p2wishart} |
%- 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.p2wishart evaluates the cumulative distribution function |
The function hgm.p2wishart evaluates the cumulative distribution function |
of the largest eigenvalues of inverse(S2)*S1. |
of the largest eigenvalues of W1*inverse(W2). |
} |
} |
\description{ |
\description{ |
The function hgm.p2wishart evaluates the cumulative distribution function |
The function hgm.p2wishart evaluates the cumulative distribution function |
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} |
} |
\usage{ |
\usage{ |
hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,method, |
hgm.p2wishart(m,n1,n2,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 34 hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,me |
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Line 34 hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,me |
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} |
} |
\item{dp}{ |
\item{dp}{ |
Sampling interval of solutions by the Runge-Kutta method. |
Sampling interval of solutions by the Runge-Kutta method. |
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When autoplot=1 or dp is negative, it is automatically set. |
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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 41 hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,me |
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Line 43 hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,me |
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} |
} |
\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. |
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When autoplot=1, mode is automatically set. |
} |
} |
\item{method}{ |
\item{method}{ |
a-rk4 is the default value. |
a-rk4 is the default value. |
Line 52 hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,me |
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Line 55 hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,me |
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} |
} |
\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., |
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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 72 hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,me |
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Line 76 hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,me |
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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. |
} |
} |
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\item{autoplot}{ |
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autoplot=0 is the default value. |
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If it is 1, then this function outputs an input for plot |
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(which is equivalent to setting the 3rd argument of the mode parameter properly). |
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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,...), ... |
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When the adaptive Runge-Kutta method is used, the step size h may change |
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automatically, |
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which makes the sampling period change, in other words, the sampling points |
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q0+q/100, q0+2*q/100, q0+3*q/100, ... may change. |
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In this case, the output matrix may contain zero rows in the tail or overfull. |
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In case of the overful, use the mode option to get the all result. |
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} |
} |
} |
\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 91 See the reference below. |
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Line 107 See the reference below. |
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} |
} |
\references{ |
\references{ |
H.Hashiguchi, N.Takayama, A.Takemura, |
H.Hashiguchi, N.Takayama, A.Takemura, |
in preparation. |
Distribution of ratio of two Wishart matrices and evaluation of cumulative probability by holonomic gradient method. |
} |
} |
\author{ |
\author{ |
Nobuki Takayama |
Nobuki Takayama |
Line 119 hgm.p2wishart(m=3,n1=5,n2=10,beta=c(1,2,4),q=4) |
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Line 135 hgm.p2wishart(m=3,n1=5,n2=10,beta=c(1,2,4),q=4) |
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## ===================================================== |
## ===================================================== |
## Example 2. |
## Example 2. |
## ===================================================== |
## ===================================================== |
b<-hgm.p2wishart(m=3,n1=5,n2=10,beta=c(1,2,4),q0=0.1,q=20,approxdeg=20,mode=c(1,1,(8+1)*100)); |
b<-hgm.p2wishart(m=3,n1=5,n2=10,beta=c(1,2,4),q0=0.3,q=20,approxdeg=20,mode=c(1,1,(8+1)*1000)); |
c<-matrix(b,ncol=16+1,byrow=1); |
c<-matrix(b,ncol=8+1,byrow=1); |
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#plot(c) |
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## ===================================================== |
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## Example 3. |
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## ===================================================== |
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c<-hgm.p2wishart(m=3,n1=5,n2=10,beta=c(1,2,4),q0=0.3,q=20,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 |