PLOTS/EIGEN at master · mlamias/PLOTS · GitHub

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## Function for arranging ggplots. use png(); arrange(p1, p2, ncol=1); dev.off() to save.
require(grid)
vp.layout <- function(x, y) viewport(layout.pos.row=x, layout.pos.col=y)
arrange_ggplot2 <- function(..., nrow=NULL, ncol=NULL, as.table=FALSE) {
  dots <- list(...)
  n <- length(dots)
  if(is.null(nrow) & is.null(ncol)) { nrow = floor(n/2) ; ncol = ceiling(n/nrow)}
  if(is.null(nrow)) { nrow = ceiling(n/ncol)}
  if(is.null(ncol)) { ncol = ceiling(n/nrow)}
  ## NOTE see n2mfrow in grDevices for possible alternative
  grid.newpage()
  pushViewport(viewport(layout=grid.layout(nrow,ncol) ) )
  ii.p <- 1
  for(ii.row in seq(1, nrow)){
    ii.table.row <- ii.row
    if(as.table) {ii.table.row <- nrow - ii.table.row + 1}
    for(ii.col in seq(1, ncol)){
      ii.table <- ii.p
      if(ii.p > n) break
      print(dots[[ii.table]], vp=vp.layout(ii.table.row, ii.col))
      ii.p <- ii.p + 1
    }
  }
}

# Generating Random Vectors from a bivariate standard
# normal, and a made-up covariance matrix:

require(ggplot2)
v1 <- rnorm(1e5)
v2 <- rnorm(1e5)
X <- rbind(v1,v2)

p1 <- qplot(v1,v2) +
  geom_point(col='firebrick') +
  geom_point(alpha = 0.01) +
  xlim(c(-20,20)) + ylim(c(-20,20))+
  geom_hline(yintercept=0, col='orange') +
  geom_vline(xintercept=0, col='orange')

C <- matrix(c(20,8,8,20), nrow=2)
eival <- eigen(C)$values
Lambda <- matrix(c(sqrt(eival[1]),0,0,sqrt(eival[2])), nrow=2)
Lambda
Stretch <- Lambda%*%X

p2 <- qplot(Stretch[1,],Stretch[2,]) +
  geom_point(col='firebrick') +
  geom_point(alpha = 0.01) +
  xlim(c(-20,20)) + ylim(c(-20,20))+
  geom_hline(yintercept=0, col='orange') +
  geom_vline(xintercept=0, col='orange')

eivec <- eigen(C)$vectors
Rot <- eivec%*%Stretch

p3 <- qplot(Rot[1,],Rot[2,]) +
  geom_point(col='firebrick') +
  geom_point(alpha = 0.01) +
  xlim(c(-20,20)) + ylim(c(-20,20))+
  geom_hline(yintercept=0, col= 'orange') +
  geom_vline(xintercept=0, col='orange')

mu <- c(3,-5)
Rand <- Rot + mu

p4 <- qplot(Rand[1,],Rand[2,]) +
  geom_point(col='firebrick') +
  geom_point(alpha = 0.01) +
  xlim(c(-20,20)) + ylim(c(-23,20)) +
  geom_hline(yintercept=0, col='orange') +
  geom_vline(xintercept=0, col='orange')

arrange_ggplot2(p1,p2,p3,p4, ncol=1)

# And the final Random Vector is:
V1 <- Rand[1,]
V2 <- Rand[2,]
V <- rbind(V1,V2)


# ALTERNATIVE PLOTTING:


# Generating Random Vectors from a bivariate standard
# normal, and a made-up covariance matrix:

v1 <- rnorm(1e5)
v2 <- rnorm(1e5)
X <- rbind(v1,v2)


C <- matrix(c(20,8,8,20), nrow=2)
eival <- eigen(C)$values
Lambda <- matrix(c(sqrt(eival[1]),0,0,sqrt(eival[2])), nrow=2)
Lambda
Stretch <- Lambda%*%X


eivec <- eigen(C)$vectors
Rot <- eivec%*%Stretch


mu <- c(3,-7)
Rand <- Rot + mu

library(RColorBrewer)

par(mfrow=c(4,1))

smoothScatter(v1,v2,
      colramp =
  colorRampPalette(c("white","red","purple4")),
  xlim=c(-20,20),ylim=c(-20,20))

abline(h=0); abline(v=0)

smoothScatter(Stretch[1,],Stretch[2,],
      colramp =
   colorRampPalette(c("white","red","purple4")))

abline(h=0); abline(v=0)

smoothScatter(Rot[1,],Rot[2,],
      colramp =
      colorRampPalette(c("white","red","purple4")))
abline(h=0); abline(v=0)


smoothScatter(Rand[1,],Rand[2,],
      colramp =
    colorRampPalette(c("white","red","purple4")))
abline(h=0); abline(v=0)


# And the final Random Vector is:
V1 <- Rand[1,]
V2 <- Rand[2,]
V <- rbind(V1,V2)