Dear all,

I made a simple test of the Cholesky decomposition in the package 'Matrix',
by considering 2 variables 100% correlated.
http://blogs.sas.com/content/iml/2012/02/08/use-the-cholesky-transformation-to-correlate-and-uncorrelate-variables/

The full code is below and can be simply copy&paste in the R prompt.

After uncorrelation I still have a correlation of +-100%...

###########################################
# 4 observations of 2 variables, 100% correlated
obs=matrix(nrow=2,ncol=4)
obs[1,]=seq(from=1, to=4, by=1)
obs[2,]=obs[1,]

# Plot
plot( obs[1,], obs[2,],pch=16)

# Correlation matrix
corr=matrix(nrow=2,ncol=2)
corr[1,2]=0.95
corr[2,1]=0.95
corr[1,1]=1
corr[2,2]=1

# Cholesky decomposition
choM=chol(corr)

# Decorrelated observation
decObs=matrix(nrow=2,ncol=4)
for( i in 1:4 ) decObs[,i]=choM%*%obs[,i]

# Other possibility
#decObs=solve(choM,obs)

# Plot
plot(decObs[1,], decObs[2,],pch=16)
###########################################

Does anyone have an idea?

Thanks,
regards,
Xavier



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Xavier Prudent
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Computational biology and evolutionary genomics
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