st: new package smwoodbury

[Sam Schulhofer-Wohl <sschulh1.work@gmail.com>]

Thanks to Kit Baum, a new package -smwoodbury- is available for
download from SSC.

-smwoodbury- provides Mata functions that implement the
Sherman-Morrison-Woodbury formula for a rank-k update to a matrix
inverse and that use the formula to efficiently solve matrix
equations.

The formula is: inv(A+U*C*V) = inv(A) -
inv(A)*U*inv(inv(C)+V*inv(A)*U)*V*inv(A), where A is NxN, U is NxK, C
is KxK, and V is KxN.

Use of this formula can save computation time when N is much larger
than K and either inv(A) is easy to calculate or inv(A+U*C*V) must be
calculated many times for different values of U, C and V. Such
situations arise, for example, in Markov chain Monte Carlo estimation
of mixed models.

The package provides functions that are optimized for a variety of
special cases, such as U=V' or A=I. In addition, functions are
provided that efficiently solve the equation (A+U*C*V)*X = Y for X
without directly inverting A+U*C*V.

-- 
Sam Schulhofer-Wohl
Senior Economist
Research Department
Federal Reserve Bank of Minneapolis
90 Hennepin Ave.
Minneapolis MN 55480-0291
(612) 204-5484
wohls@minneapolisfed.org

Views expressed herein are those of the author and not necessarily
those of the Federal Reserve Bank of Minneapolis or the Federal
Reserve System.
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