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Re: st: RE: RE: RE: Matrix inversion "bug"


From   celdjt@umich.edu
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: RE: RE: Matrix inversion "bug"
Date   Tue, 10 Jun 2003 12:27:46 -0400

I will have to drop by on this. There was one trip charged against my account that is to be reimbursed from another. I will be back to you.

--On Tuesday, June 10, 2003 1:05 PM -0300 Ines Butler <ibutler@ieral.org> wrote:


Al,
Thank you for your help.
I do have more observations than variables (38 observatiosn, 10
variables). Do you have any idea why this might be happening or if there
is something to do about it ?
Thanks again.
Regards

Inés Butler
IERAL Fundación Mediterránea

ibutler@ieral.org <mailto:ibutler@ieral.org>
www.ieral.org
(54 11)  4312 4114



-----Mensaje original-----
De: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]En nombre de FEIVESON, ALAN
H. (AL) (JSC-SK) (NASA)
Enviado el: Tuesday, June 10, 2003 12:49 PM
Para: 'statalist@hsphsun2.harvard.edu'
Asunto: st: RE: RE: Matrix inversion "bug"


Inés - Do you have at least as many observations as variables? If not, the
matrix will not be positive definite - only semidefinite. If you have n
variables, you must have at least n linearly independent observations row
vectors for the accumulated matrix to be positive definite. Your problem
is not the same as Mark's. If your matrix were not symmetric because of a
precision error, choloesky would return the message "matrix not symmetric"
instead of "matrix not positive definite".

Al Feiveson

-----Original Message-----
From: Ines Butler [mailto:ibutler@ieral.org]
Sent: Tuesday, June 10, 2003 9:45 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: Matrix inversion "bug"


Mark
I think I am encountering with a similar problem to the one you mention
about symentric matrices.

I am usingmat function 'mat accum' with the options noconstant and
deviations to construct a matrix from data which should return a positive
definite matrix (because divided by N-1 is the covariance matrix).
However, when I try to use cholesky factorization, an error message
appears saying that the matrix is not positive definite.
Do you have any idea on how to cope with this problem?
Thank you very much!

Inés Butler
IERAL Fundación Mediterránea



-----Mensaje original-----
De: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]En nombre de Mark Schaffer
Enviado el: Monday, June 09, 2003 8:19 PM
Para: Statalist
CC: Mark Schaffer
Asunto: st: Matrix inversion "bug"


Dear Statalisters:

Every now and then I encounter a matrix inversion "bug" in Stata.  It
cropped up yet again last week when an ivreg2 user wrote to me, and I
finally decided to see what my fellow Statalisters think of it.

Say we have a matrix M which is calculated as X*S*X'.  S is symmetric and
so is M.  We want to invert M and so the best thing to do is to use
-syminv-.  The Stata programming manual tells us to use -syminv- instead
of -inv- wherever possible.

The problem is this.  Although M is guaranteed to be symmetric in
principle, it is not guaranteed to be symmetric in practice.  Tiny
rounding errors can arise when Stata multiplies matrices.  Once in a
while, M will be very slightly non-symmetric, but when it is, -syminv-
will exit with an error.

When I first encountered this, I wrote to Stata Technical Support, and I
received a very helpful and simple fix: prior to the call to syminv,
simply do the following:

mat M = (M+M')/2

This makes the matrix symmetric.  Works, no problem.  But...

Arguably, this is just a fix for what is really a Stata bug.  Ought it be
possible for Stata's code to recognise when the result of a matrix
multiplication is supposed to be a symmetric matrix?

Whether or not this should be called a "bug", it may still be the case
that it's not possible for our friends at Stata Corp to fix it.  If so,
then there are several possibilities:

(1) Prior to using -syminv-, we should always (?) symmetrize the matrix we
want to invert using the code fragment above.

(2) Any (?) time we call -syminv-, we should use -capture-.  If the
inversion using -syminv- fails, we should call -inv-.

(3) Neither of the above is very pretty.  An alternative is to ask our
Stata Corp friends to, say, add a variant of the -syminv- function, say
-syminv2-.  This function would automatically symmetrize a square matrix
before inverting it.

What do you think?

--Mark

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