Nothing
lle_spiral <-
function(){
#set dimensions/parameters
n <- 3
m <- 1
N <- 600
k <- 5
reg <- 2
ss <- FALSE
p <- 0.5
iLLE <- FALSE
v <- 0.8
#generate elementary vectors
v1 <- c(1,rep(0, each=n-1))
v2 <- c(0,1,rep(0, each=n-2))
v3 <- c(0,0,1,rep(0,each=n-3))
dt <- 0.005
#prepare rotation matrices
phix <- 0/180*pi #rotation x
phiy <- 0/180*pi #rotation y
phiz <- 0/180*pi #rotation z
Rx <- matrix( c( 1, 0, 0, 0, cos(phix), -sin(phix), 0, sin(phix), cos(phix) ), 3 )
Ry <- matrix( c( cos(phiy), 0, sin(phiy), 0, 1, 0, -sin(phiy), 0, cos(phiy) ), 3 )
Rz <- matrix( c( cos(phiz), -sin(phiz), 0, sin(phiz), cos(phiz), 0, 0, 0, 1 ), 3 )
#prepare splitscreen-plot
plotdim <- c(3,3)
split.screen(plotdim)
scr <- 1
for( T in seq(16,1.5,length=prod(plotdim)) ){
#set parameters
om <- 16*pi/T
X <- 0*matrix(rnorm(n*N),nrow=N)
#generate spiral data
for( i in (1:N)){
t=dt*i
r=t
X[i,]= r*v1*cos(om*t)+ r*v2*sin(om*t) + v3*t^3/30
}
#rotation
X <- t(Rx%*%t(X))
X <- t(Ry%*%t(X))
X <- t(Rz%*%t(X))
#perform lle
cat( "------------\nT=",T,"\n")
res <- lle(X,m,k,reg,ss=ss,p=p,id=TRUE,iLLE=iLLE)
#plot
if( (scr+2)%%3==0 ) zt=NULL else zt=""
if( scr>6 ) xt=NULL else xt=""
if( scr%%3==0 ) yt=NULL else yt=""
screen(scr)
scatterplot3d(X,cex.symbols=0.5, mar=rep(.8,4), angle=10, xlab="", ylab="", zlab="",
type="p", lwd=2, highlight.3d=TRUE, cex.axis=0.8,
main="", xlim=c(-4,4), ylim=c(-4,4),
x.ticklabs=xt, y.ticklabs=yt, z.ticklabs=zt )
if( scr < 8) text(-1.2,2,"m=1") else text(-1.2,2,"m=2")
scr <- scr + 1
}
}
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