st: Mata - generalised cross products of the form X'SX

[Gordon Hughes <G.A.Hughes@ed.ac.uk>]

I am starting a new thread, but this is really a follow-up to my post 
on performance monitoring.  Following Bill Gould's helpful suggestion 
I have identified that most of the time is consumed in loops in my 
likelihood evaluation that calculate matrices of the form Z=X'SX 
where S is symmetric but not a diagonal matrix.  Of course, I am 
doing things outside loops where I can.

This is a standard form in any GLS type calculation.  They are not 
directly amenable to use with the Mata function --cross()-- but they 
could be got into that form by forming by factorising S=QQ', then 
forming P=Q'X, and finally using P=cross(P,P).

Two questions follow:

A.  Is there any Mata function that does this more directly?  Maybe 
Stata Corp might consider extending --cross()-- to handle such 
cases.  The command --matrix glsaccum-- does this in Stata.

B.  Roughly, under what conditions might this sequence of steps 
reduce execution time and/or memory use on the assumption that the 
dimension of S is large relative to cols(X)?  In a related context I 
have to calculate X'B'BX where B is square but not symmetric and 
found that use of --cross()-- does not save much (if any) time, 
though it is probably more efficient on memory.  Hence, the overhead 
of factorisation may not pay off.  On the other hand, the initial 
factorisation would only need to be done once per function call, 
whereas the steps involving X have to be performed thousands of times 
per function call.

Gordon Hughes
g.a.hughes@ed.ac.uk

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