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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*Guest scientist at the Max-Planck-Institut für Physik komplexer Systeme*
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*Max Planck-Institute for Molecular Cell Biology and Genetics*
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Phone: +49 351 210-2621
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