Annotation of OpenXM/src/R/r-packages/hgm/man/hgm.c2wishart.Rd, Revision 1.2
1.2 ! takayama 1: % $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.c2wishart.Rd,v 1.1 2016/02/13 06:47:50 takayama Exp $
1.1 takayama 2: \name{hgm.p2wishart}
3: \alias{hgm.p2wishart}
4: %- Also NEED an '\alias' for EACH other topic documented here.
5: \title{
6: The function hgm.p2wishart evaluates the cumulative distribution function
7: of the largest eigenvalues of inverse(S2)*S1.
8: }
9: \description{
10: The function hgm.p2wishart evaluates the cumulative distribution function
11: of the largest eigenvalues of W1*inverse(W2) where W1 and W2 are Wishart
12: matrices of size m*m of the freedom n1 and n2 respectively.
13: }
14: \usage{
15: hgm.p2wishart(m,n1,n2,beta,q0,approxdeg,h,dp,q,mode,method,
1.2 ! takayama 16: err,automatic,assigned_series_error,verbose,autoplot)
1.1 takayama 17: }
18: %- maybe also 'usage' for other objects documented here.
19: \arguments{
20: \item{m}{The dimension of the Wishart matrix.}
21: \item{n1}{The degree of freedome of the Wishart distribution S1}
22: \item{n2}{The degree of freedome of the Wishart distribution S2}
23: \item{beta}{The eigenvalues of inverse(S2)*S1 where S1 and S2 are
24: covariant matrices of W1 and W2 respectively.
25: }
26: \item{q0}{The point to evaluate the matrix hypergeometric series. q0>0}
27: \item{approxdeg}{
28: Zonal polynomials upto the approxdeg are calculated to evaluate
29: values near the origin. A zonal polynomial is determined by a given
30: partition (k1,...,km). We call the sum k1+...+km the degree.
31: }
32: \item{h}{
33: A (small) step size for the Runge-Kutta method. h>0.
34: }
35: \item{dp}{
36: Sampling interval of solutions by the Runge-Kutta method.
37: }
38: \item{q}{
39: The second value y[0] of this function is the Prob(L1 < q)
40: where L1 is the first eigenvalue of the Wishart matrix.
41: }
42: \item{mode}{
43: When mode=c(1,0,0), it returns the evaluation
44: of the matrix hypergeometric series and its derivatives at x0.
45: When mode=c(1,1,(m^2+1)*p), intermediate values of P(L1 < x) with respect to
46: p-steps of x are also returned. Sampling interval is controled by dp.
47: }
48: \item{method}{
49: a-rk4 is the default value.
50: When method="a-rk4", the adaptive Runge-Kutta method is used.
51: Steps are automatically adjusted by err.
52: }
53: \item{err}{
54: When err=c(e1,e2), e1 is the absolute error and e2 is the relative error.
55: As long as NaN is not returned, it is recommended to set to
56: err=c(0.0, 1e-10), because initial values are usually very small.
57: }
58: \item{automatic}{
59: automatic=1 is the default value.
60: If it is 1, the degree of the series approximation will be increased until
61: |(F(i)-F(i-1))/F(i-1)| < assigned_series_error where
62: F(i) is the degree i approximation of the hypergeometric series
63: with matrix argument.
64: Step sizes for the Runge-Kutta method are also set automatically from
65: the assigned_series_error if it is 1.
66: }
67: \item{assigned_series_error}{
68: assigned_series_error=0.00001 is the default value.
69: }
70: \item{verbose}{
71: verbose=0 is the default value.
72: If it is 1, then steps of automatic degree updates and several parameters
73: are output to stdout and stderr.
74: }
1.2 ! takayama 75: \item{autoplot}{
! 76: autoplot=0 is the default value.
! 77: If it is 1, then it outputs an input for plot.
! 78: }
1.1 takayama 79: }
80: \details{
81: It is evaluated by the Koev-Edelman algorithm when x is near the origin and
82: by the HGM when x is far from the origin.
83: We can obtain more accurate result when the variables h is smaller,
84: x0 is relevant value (not very big, not very small),
85: and the approxdeg is more larger.
86: A heuristic method to set parameters x0, h, approxdeg properly
87: is to make x larger and to check if the y[0] approaches to 1.
88: % \code{\link[RCurl]{postForm}}.
89: }
90: \value{
91: The output is x, y[0], ..., y[2^m] in the default mode,
92: y[0] is the value of the cumulative distribution
93: function P(L1 < x) at x. y[1],...,y[2^m] are some derivatives.
94: See the reference below.
95: }
96: \references{
97: H.Hashiguchi, N.Takayama, A.Takemura,
98: in preparation.
99: }
100: \author{
101: Nobuki Takayama
102: }
103: \note{
104: This function does not work well under the following cases:
105: 1. The beta (the set of eigenvalues)
106: is degenerated or is almost degenerated.
107: 2. The beta is very skew, in other words, there is a big eigenvalue
108: and there is also a small eigenvalue.
109: The error control is done by a heuristic method.
110: The obtained value is not validated automatically.
111: }
112:
113: %% ~Make other sections like Warning with \section{Warning }{....} ~
114:
115: %\seealso{
116: %%%\code{\link{oxm.matrix_r2tfb}}
117: %}
118: \examples{
119: ## =====================================================
120: ## Example 1.
121: ## =====================================================
122: hgm.p2wishart(m=3,n1=5,n2=10,beta=c(1,2,4),q=4)
123: ## =====================================================
124: ## Example 2.
125: ## =====================================================
1.2 ! takayama 126: 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));
! 127: c<-matrix(b,ncol=8+1,byrow=1);
! 128: #plot(c)
! 129: ## =====================================================
! 130: ## Example 3.
! 131: ## =====================================================
! 132: c<-hgm.p2wishart(m=3,n1=5,n2=10,beta=c(1,2,4),q0=0.3,q=20,approxdeg=20,autoplot=1);
1.1 takayama 133: #plot(c)
134: }
135: % Add one or more standard keywords, see file 'KEYWORDS' in the
136: % R documentation directory.
137: \keyword{ Cumulative distribution function of random two wishart matrices }
138: \keyword{ Holonomic gradient method }
139: \keyword{ HGM }
140:
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