Converting Covariance Matrix to Correlation Matrix

I know of MATLAB function to convert a covariance matrix to a correlation matrix but I'm a teacher and want to demonstrate matrix manipulation. I can do the conversion using for loops as below but can't figure out how to do this more elegantly (using matrix operations).

d=diag(cov).^.5;
for i=1:length(cov)
for j=1:length(cov)
corr(i,j)=cov(i,j)./(d(i)*d(j));
end
end

Thanks in advance for any help.

Answer 1

[Peter Perkins]

Jim, if you mean, "matrix operations" as in "something out of a math book", then you can right and left multiply by diag(d), where d is 1./sqrt(diag(C)). If you mean "MATLAB matrix operations", then you can use ./ with d*d'.

You might find it interesting to look at the guts of corrcoef, where the code takes a bit more care.

Hope this helps.

[Jim Moser]

Peter, yes I saw that suggested elsewhere and it puzzled me. If the covariance matrix is 3x3, then left multiplying it by the transpose of the diagonal gives a 1x3 and multiplying the diagonal by that gives a 1x1. The code I listed gives a 3x3 correlation matrix.

And yes by "matrix operations" I was hoping for something that would match a standard text treatment.

[Peter Perkins]

Sorry, I think I meant diag(1./sqrt(diag(C))). If C is a 3x3 cov matrix, then diag(C) is a vector, and diag(1./sqrt(diag(C))) is a 3x3 diagonal matrix.

Answer 2

[James Tursa]

A method using outer product and element-wise divide:

d = sqrt(diag(cov));
corr = cov./(d*d');

[Jim Moser]

Thank you, exactly what I was sure was there but couldn't see.

Answer 3

[Matt J]

corr=bsxfun(@rdivide,cov, d(:));
corr=bsxfun(@rdivide, corr,d(:).');