MovingFrame
ベクトルの変化を収めた行列から動標構を作る。
列数mの行列の第１〜第n列(m>n)部分のみの処理も可能。
MovingFrame(xs,n)
MovingFrame<-function(xs,n=NULL){
if(is.null(n)){
n<-length(xs[1,])
}
Es<-array(0,c(n,length(xs[,1]),length(xs[1,])))
Cs<-matrix(0,n,length(xs[,1]))
Es[1,,]<-(xs)/sqrt(apply(xs^2,1,sum))
current<-xs
for(i in 2:n){
tmp<-apply(current,2,diff)
current<-tmp
for(j in 1:length(tmp[,1])){
tmpout<-PerpendicVector(Es[i-1,j,],tmp[j,])
Es[i,j,]<-tmpout$vector
Cs[i-1,j]<-tmpout$cos
}
}
list(Es=Es,Cs=Cs)
}
\name{MovingFrame}
\alias{MovingFrame}
%- Also NEED an '\alias' for EACH other topic documented here.
\title{
MovingFrame
}
\description{
ベクトルの変化を収めた行列から動標構を作る。
列数mの行列の第１〜第n列(m>n)部分のみの処理も可能。
}
\usage{
MovingFrame(xs,n)
}
%- maybe also 'usage' for other objects documented here.
\details{
%% ~~ If necessary, more details than the description above ~~
}
\value{
\item{Es}{動標構Moving frameの単位ベクトルを束ねた行列}
\item{Cs}{入力データのMoving frameベクトル成分の、直前のMoving frameベクトル方向に対する余弦。0なら変化分は「直交」であり、1なら、変化分がない}
}
\references{
%% ~put references to the literature/web site here ~
}
\author{
%% ~~who you are~~
}
\note{
%% ~~further notes~~
}
%% ~Make other sections like Warning with \section{Warning }{....} ~
\seealso{
}
\examples{
# トーラスのRot
n<-4
Rot<-matrix(
c(0.003640657,0.02308859,0.05751062,-0.99807124,
0.542523942,-0.63809206,-0.54456963,-0.04416122,
-0.062159929,0.61777600,-0.78327751,-0.03106943,
0.837729468,0.45897523,0.29430051,0.03063146),4,4,byrow=TRUE)
# シミュレーション
E.out<-eigen(Rot)
V<-E.out[[2]]
V2<-solve(V)
S<-diag(E.out[[1]])
Niter<-10000
xs<-matrix(0,Niter,n)
xs[1,]<-runif(n)
dt<-0.005
T<-runif(Niter-1)
T<-sort(T)
dhk<-NormalBase(n)
v<-dhk[1,]
for(i in 2:Niter){
#xs[i,]<-xs[i-1,]+v*dt*T[i-1]
xs[i,]<-xs[i-1,]+v*dt
#dhk<-(V%*%S^(dt)%*%V2) %*% dhk
dhk<-(V%*%diag(E.out[[1]]^(dt))%*%V2) %*% dhk
# 単位ベクトル補正
#ll<-apply(dhk^2,1,sum)
#dhk<-((dhk)/sqrt(ll))
v<-dhk[1,]
}
library(rgl)
plot3d(xs[,1],xs[,2],xs[,3],col=rainbow(Niter))
library(gtools)
co<-combinations(n,3)
for(i in 1:length(co[,1])){
open3d()
plot3d(xs[,co[i,1]],xs[,co[i,2]],xs[,co[i,3]],col=rainbow(Niter))
}
matplot(xs,type="l")
xs<-Re(xs)
vs<-apply(xs,2,diff)
Es<-MovingFrame(vs)
matplot(t(Es[[2]]),type="l")
plot(as.data.frame(t(Es[[2]])))
}
% Add one or more standard keywords, see file 'KEYWORDS' in the
% R documentation directory.
\keyword{ ~kwd1 }
\keyword{ ~kwd2 }% __ONLY ONE__ keyword per line
