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Re: st: Efficient, foolproof calculation of matrix quadratic form with block-diagonal middle matrix? (Mata)


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Efficient, foolproof calculation of matrix quadratic form with block-diagonal middle matrix? (Mata)
Date   Fri, 25 Sep 2009 11:21:35 -0400

Venable <venablito@gmail.com>:
See e.g.
http://www.stata.com/statalist/archive/2009-05/msg00841.html
and compare to the relevant code in
http://repec.org/bocode/o/overid.ado
--search for:
// Kronecker product with esigma	
	middle = invsym(sigma) # pw

On Fri, Sep 25, 2009 at 10:24 AM, Venable <venablito@gmail.com> wrote:
> Dear Statalisters,
>
> I am using Mata to calcuate a quadratic form, the middle matrix of
> which is block-diagonal, with all square and identical blocks. This is
> most compactly expressed in Mata as:
>
> A=X'*(I(N)#Om_Inv_Block)*X
>
> X is (NxT) x K and is made up of N cross-sectional units, each of
> which has T observations (so, a balanced panel of N with T
> observations for each unit. You can think of X as X1 \ X2 \ ... \ XN,
> with each Xn being K by T. Om_Inv_Block is TxT.
>
> This is extremely simple to code, but Mata needs to create the NTxNT
> matrix I(N)#Om_Inv_Block and with N and / or T large, this becomes a
> very, very large matrix which occasionally causes Mata to crash.
> (Interestingly, when Mata does not crash it doesn't take long at all
> to calculate.)
>
> I was wondering if there were a way for Mata to recognize the special
> structure of the block-diagonal matrix and get around the need to
> create this very large middle matrix explicitly.
>
> Alternatively, I know that I could do the sum of the N terms
> Xn'*Om_Inv_Block*Xn but I am worried that I would somehow mess this
> up. So, another solution, I suppose, would be some idiot-proof way to
> do this sum.
>
> I apologize in advance if this is obvious, has been discussed before,
> or is in the Mata manuals somewhere. I searched the Statalist using
> terms "block diagonal" and "quadatic form" (individually and together)
> and did not find a solution.
>
> Many thanks.
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