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From |
May Boggess <mboggess@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Problem with Cholesky matrix function? |

Date |
24 Nov 2003 08:59:02 -0600 |

On Sun, 2003-11-23 at 19:14, Kaleb Michaud wrote: > 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); > For a matrix to be positive definite it needs to have all positive eigenvalues. So, Kaleb can check his matrix by using -symeigen- to compute the eigenvalues of S. I have pasted some code below that does this. Out of curiosity I also looked at the matrices that had the same pattern in the entries as S, but smaller sizes, and found that they had similar structure to the eigenvalues, that is, they all have one large positive eigenvalue and the rest negative. The code below will run these cases as well. yours, --May mboggess@stata.com matrix S=[1,2,3,4,5,6,7,8,9,10\2,2,3,4,5,6,7,8,9,10\3,3,3,4,5,6,7,8,9,10\ /* */4,4,4,4,5,6,7,8,9,10\5,5,5,5,5,6,7,8,9,10\6,6,6,6,6,6,7,8,9,10\ /* */ 7,7,7,7,7,7,7,8,9,10\8,8,8,8,8,8,8,8,9,10\9,9,9,9,9,9,9,9,9,10\ /* */10,10,10,10,10,10,10,10,10,10] mat list S mat symeigen X v = S mat list v matrix S=[1,2,3,4,5,6,7,8,9\2,2,3,4,5,6,7,8,9\3,3,3,4,5,6,7,8,9\ /* */4,4,4,4,5,6,7,8,9\5,5,5,5,5,6,7,8,9\6,6,6,6,6,6,7,8,9\ /* */7,7,7,7,7,7,7,8,9\8,8,8,8,8,8,8,8,9\9,9,9,9,9,9,9,9,9] mat list S mat symeigen X v = S mat list v matrix S=[1,2,3,4,5,6,7,8\2,2,3,4,5,6,7,8\3,3,3,4,5,6,7,8\ /* */4,4,4,4,5,6,7,8\5,5,5,5,5,6,7,8\6,6,6,6,6,6,7,8\ /* */7,7,7,7,7,7,7,8\8,8,8,8,8,8,8,8] mat list S mat symeigen X v = S mat list v matrix S=[1,2,3,4,5,6,7\2,2,3,4,5,6,7\3,3,3,4,5,6,7\ /* */4,4,4,4,5,6,7\5,5,5,5,5,6,7\6,6,6,6,6,6,7\ /* */7,7,7,7,7,7,7] mat list S mat symeigen X v = S mat list v matrix S=[1,2,3,4,5,6\2,2,3,4,5,6\3,3,3,4,5,6\ /* */4,4,4,4,5,6\5,5,5,5,5,6\6,6,6,6,6,6] mat list S mat symeigen X v = S mat list v matrix S=[1,2,3,4,5\2,2,3,4,5\3,3,3,4,5\ /* */4,4,4,4,5\5,5,5,5,5] mat list S mat symeigen X v = S mat list v matrix S=[1,2,3,4\2,2,3,4\3,3,3,4\4,4,4,4] mat list S mat symeigen X v = S mat list v matrix S=[1,2,3\2,2,3\3,3,3] mat list S mat symeigen X v = S mat list v matrix S=[1,2\2,2] mat list S mat symeigen X v = S mat list v * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Problem with Cholesky matrix function?***From:*Kaleb Michaud <kaleb@stanford.edu>

**References**:**st: Problem with Cholesky matrix function?***From:*Kaleb Michaud <kaleb@stanford.edu>

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