Update file permission using git

For example, add execute

git update-index --chmod=+x script.sh

Reference:
https://stackoverflow.com/questions/10516201/updating-and-committing-only-a-files-permissions-using-git-version-control

Variance explained by PCs

    #Simulate a dataset with 4 hightly correlated variables
    x=rnorm(20)
    x=cbind(v1=x, v2=x+rnorm(20,sd=0.02), v3=x+rnorm(20,sd=0.01), v4=x+rnorm(20,sd=0.03))
    #check correlation matrix
    cor(x)
    #Compute variances of the original variables
    apply(x,2,var)
    #Total variance
    (total=sum(apply(x,2,var)))

   #Compute PCA. Note here we don't center or scale the data just to keep the original variance
    pca=prcomp(x,center = FALSE, scale. = FALSE)
    pca
    #Check variance explained by the PCs
    pca$sdev^2
    #Variance can also be computed from rotated data or PCA scores
    apply(pca$x,2,var)
    #Compare the sum of total variances by the PCs, which should equal to the total variance of the original variables
    sum(pca$sdev^2)
    #Proportion of variance explained by PCs
    pca$sdev^2/total
    #Check correlation between the original variables and PC1
    apply(x,2,cor,y=prcomp(x)$x[,'PC1'])
    #Check correlation between the original variables and PC2
    apply(x,2,cor,y=prcomp(x)$x[,'PC2'])
    #Check correlation between the original variables and PC3
    apply(x,2,cor,y=prcomp(x)$x[,'PC3'])
    #Check correlation between the original variables and PC4
    apply(x,2,cor,y=prcomp(x)$x[,'PC4'])

    #Now let us compare PCs with a new "naive" coordinate: the mean across variables
    average=rowMeans(x)
    #variance of average values
    var(average)
    #Proportion of variance explained by average
    var(average)/total
    #Check correlation between the original variables and average
    apply(x,2,cor,y=average)