#
# first simulated data set in R
#

library(mva)

# generate the data: normal distributions

data <- cbind(rnorm(1000),rnorm(1000))

# set the covariance and mean
sigma <- cbind(c(2,1),c(1,2))
m <- c(-5,5)
ones <- matrix( c(rep(1,1000), rep(1,1000)), ncol=2)

# rotate the data
r <- chol(sigma)
data.r <- data %*% r

# shift the data
data.r.s <- data.r + (ones %*% diag(m))

par( mfrow = c(2,2), pty = "s")

plot(data, pch=".", xlim=c(-10,10), ylim=c(-10,10))
plot(data.r, pch=".", xlim=c(-10,10), ylim=c(-10,10))
plot(data.r.s, pch=".", xlim=c(-10,10), ylim=c(-10,10))

data.r.s.pca <- prcomp(data.r.s)

plot(data.r.s.pca$x, pch=".", xlim=c(-10,10), ylim=c(-10,10))