Visualize QR algorithm for covariance matrix

qrviz.R

library(mvtnorm)
library(reshape2)
library(ggplot2)
library(gganimate)
library(dplyr)

Sig = matrix(c(1,0.8,0.8,1),2,2)
scatters = vector("list", 5)
heats = vector("list", 5)
X = rmvnorm(5000, sigma=Sig)
df_sig = melt(Sig, varnames = c("row","column"))
scatters[[1]] = data.frame(X, it=1)
heats[[1]] = mutate(df_sig, it=1)
for(i in 2:5){
  res_qr = qr(Sig)
  Q = qr.Q(res_qr)
  Sig = t(Q)%*%Sig%*%Q
  X = rmvnorm(1000, sigma=Sig)
  df_sig = melt(Sig, varnames = c("row","column"))
  scatters[[i]] = data.frame(X, it=i)
  heats[[i]] = mutate(df_sig, it=i)
}

scatters = bind_rows(scatters)
heats = bind_rows(heats)

p1 = ggplot(scatters,aes(X1,X2))+
  geom_point(alpha=0.25)+
  facet_wrap(~it)+
  theme_bw(18)
print(p1)

p1 = ggplot(scatters,aes(X1,X2))+
  geom_point(alpha=0.25)+
  transition_manual(it)+
  theme_bw(18)
print(p1)

p2 = ggplot(heats, aes(x=column, y=row, fill=value))+
  geom_tile(colour="grey") +
  facet_wrap(~it)+
  scale_fill_gradient2()+
  scale_x_continuous(breaks=1:2)+
  scale_y_reverse(breaks=1:2)+
  theme_bw(18)
print(p2)

p2 = ggplot(heats, aes(x=column, y=row, fill=value))+
  geom_tile(colour="grey") +
  transition_manual(it)+
  scale_fill_gradient2()+
  scale_x_continuous(breaks=1:2)+
  scale_y_reverse(breaks=1:2)+
  theme_bw(18)
print(p2)

anim_save(filename = "qr_rnorm.gif", animation = p1)
anim_save(filename = "qr_cov.gif", animation = p2)