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From |
Venable <venablito@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Fri, 25 Sep 2009 10:24:30 -0400 |

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. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Efficient, foolproof calculation of matrix quadratic form with block-diagonal middle matrix? (Mata)***From:*Austin Nichols <austinnichols@gmail.com>

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