MP law simulation

一个简单的例子解释随机矩阵里的MP law,

#############################
##
## A example to show the MP law in random matrix theory.
##
#############################
library(ggplot2)

## The empirical distribution
p <- 1000
n <- 2000
dat <- matrix(rnorm(p*n), nrow=p)
dat.cov <- cov(t(dat))
dat.eig <- eigen(dat.cov)
dat.val <- dat.eig$values
dat.dsty <- density(dat.val)


## plot
df.dsty <- data.frame(x=dat.dsty$x, y=dat.dsty$y)
p <- ggplot(df.dsty, aes(x = x, y = y))
p + geom_line()  + ylab('density') + ggtitle("MP law")




## The largest eigenvalue
p <- 1000
n <- 2000
K0 <- 100
lam <- list()
for (k in 1:K0){
  dat <- matrix(rnorm(p*n), nrow=p)
  dat.cov <- cov(t(dat))
  dat.eig <- eigen(dat.cov)
  dat.val <- dat.eig$values
  lam[[k]] <- dat.val 
}

lam.max <- unlist(lapply(lam,max))
lam.min <- unlist(lapply(lam,min))




######################
## plot the max and min eigenvalue
######################
plot(lam.max, ylim=c(0,3), main='extreme eigenvalues of sample covariance matrix', xlab='Id', 
     ylab='extreme eigenvalue', col='red', type='p')
lines(lam.min,type='p', col='blue')





######################
## Save the data
######################
lam.MP <- lam
save(lam.MP, file="D:/BinbinChen/Literature/Orcal Defence/Simulation.MP.Rdata")