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Calcite | Level 5

I am replicating Rick's Covariance / Correlation Cholesky transformation within Proc IML as follows:

proc iml;

  D = { 1 2 3,

  2 4 3,

  3 3 9};

  X = root(D)`*root(D);

  print D;

  print X;


Interestingly, X does not equal D.  I am wondering if this is due to D not being Positive Definite or, in other words, Det(D) <0.  The code runs without any indication of a problem.....had I not printed X, I would have never known that that Root(D)`*Root(D) would not equal D.

Any thoughts on why this is the case?


Interesting. I've never seen this behavior before. The correct behavior would be for the ROOT function to report an error in the log:

ERROR: (execution) Matrix should be positive definite

If I were to guess, I'd say that the exact integer values are causing a numerical problem in the ROOT function such that the ROOT function does not report the error. In the following code I perturb an element by a tiny amount and the ROOT function correctly reports that the matrix is not PD:

D[1] = D[1] + 1e-8;

G = root(D);

I will enter a bug report at SAS so that someone can look into this situation further.

Calcite | Level 5

Thanks Dr. Wicklin.



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