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


From   Venable <venablito@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 12:06:54 -0400

Thanks very much for your quick and informative response.

Just so I can be sure: what you are doing is along the lines of the
sum of N terms approach in my post, correct?

On Fri, Sep 25, 2009 at 11:21 AM, Austin Nichols
<austinnichols@gmail.com> wrote:
> 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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