Simulated correlation matrices

Kushal K Dey

2/23/2018

In this script, we plot the correlation and precision matrices corresponding to which, we have run the simulations.

library(ggplot2)
library(corrplot)

## corrplot 0.84 loaded

library(Matrix)
library(gridExtra)
library(corpcor)

col2 <- c("blue", "white", "red")
block <- 10
mat <- 0.3*diag(1,block) + 0.7*rep(1,block) %*% t(rep(1, block))
Sigma <-   bdiag(mat, mat, mat, mat, mat, mat, mat, mat, mat, mat)
corSigma <- cov2cor(Sigma)
icorSigma <- cov2cor(solve(corSigma))

corrplot((as.matrix(corSigma)), diag = FALSE,
         col = colorRampPalette(col2)(200),
         tl.pos = "td", tl.cex = 0.2, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "upper")

corrplot((as.matrix(icorSigma)), diag = FALSE,
         col = colorRampPalette(col2)(200),
         tl.pos = "td", tl.cex = 0.2, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "upper")

DM_toeplitz = function(n,P){
  library("MASS")
  index1=sort(sample(seq(1:n),(n/2)))
  index2=seq(1:n)[-index1]
  Sigmatp=function(P){
    a=array(0,dim=c(P,P))
    for(i in 1:P){
      for(j in 1:P){
        a[i,j]=max(1-0.1*(abs(i-j)),0)
      }
    }
    return(a)
  }
  Sigma = Sigmatp(P)
  data = mvrnorm(n,rep(0,P),Sigma)
  Xtest = data[index2,]
  Xtrain = data[index1,]
  Omega = solve(Sigma)
  return(list(Xtrain = Xtrain, Xtest = Xtest, Sigma = Sigma))
}

n <- 50
P <- 100
ll <- DM_toeplitz(n=n, P=P)
corSigma <- cov2cor(ll$Sigma)
icorSigma <- cov2cor(solve(corSigma))

corrplot((as.matrix(corSigma)), diag = FALSE,
         col = colorRampPalette(col2)(200),
         tl.pos = "td", tl.cex = 0.2, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "upper")

corrplot((as.matrix(icorSigma)), diag = FALSE,
         col = colorRampPalette(col2)(200),
         tl.pos = "td", tl.cex = 0.2, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "upper")

diags <- list()
diags[[1]] <- rep(1, 100)
diags[[2]] <- rep(-0.5, 100)
Kinv <- bandSparse(100, k = -(0:1), diag = diags, symm = TRUE)
K <- solve(Kinv)
corSigma <- cov2cor(K)
icorSigma <- cov2cor(solve(corSigma))

corrplot((as.matrix(corSigma)), diag = FALSE,
         col = colorRampPalette(col2)(200),
         tl.pos = "td", tl.cex = 0.2, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "upper")

corrplot((as.matrix(icorSigma)), diag = FALSE,
         col = colorRampPalette(col2)(200),
         tl.pos = "td", tl.cex = 0.2, tl.col = "black",
         rect.col = "white",na.label.col = "white",
         method = "color", type = "upper")

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