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st: Problem with Cholesky matrix function?


From   Kaleb Michaud <kaleb@stanford.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Problem with Cholesky matrix function?
Date   Sun, 23 Nov 2003 17:14:42 -0800

(It's been 5 hours so I'm sending this one again - strange list behavior?)

I'm trying to produce for a Monte Carlo task 100K random vectors in 10-D space with N(0,S) distribution where the covariance matrix S is defined by:

symmetric S[10,10]
r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
c1 1
c2 2 2
c3 3 3 3
c4 4 4 4 4
c5 5 5 5 5 5
c6 6 6 6 6 6 6
c7 7 7 7 7 7 7 7
c8 8 8 8 8 8 8 8 8
c9 9 9 9 9 9 9 9 9 9
c10 10 10 10 10 10 10 10 10 10 10

The problem is this:

. matrix C = cholesky(S)
matrix not positive definite
r(506);

Now, I've searched the list archives, the web and am pretty sure S is positive definite. I discovered this problem using the -drawnorm- program (it passed of the internal tests as a covariance matrix until it reached the cholesky function).

Any ideas as to what I can do (assuming either my matrix isn't positive definite or this function isn't working right)?

Thanks!
Kaleb Michaud
Arthritis Research Center

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