SMWOODBURY: Stata module to compute Sherman-Morrison-Woodbury rank-k update to matrix inverse

Sam Schulhofer-Wohl

Statistical Software Components from Boston College Department of Economics

Abstract: This package provides a set of 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.

Language: Stata
Requires: Stata version 12
Keywords: matrix inverse; Sherman-Morrison-Woodbury (search for similar items in EconPapers)
Date: 2011-12-22
Note: This module should be installed from within Stata by typing "ssc install smwoodbury". The module is made available under terms of the GPL v3 (https://www.gnu.org/licenses/gpl-3.0.txt). Windows users should not attempt to download these files with a web browser.
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Downloads: (external link)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury.mata program code (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_lu_solve.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_lu.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_qr_solve.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_qr.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_lu_solve.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_lu.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_posdef_solve.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_posdef.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_qr_solve.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_qr.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_lu_solve.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_lu.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_posdef_solve.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_posdef.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_qr_solve.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_qr.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/l/lsmwoodbury.mlib Mata object library (application/x-stata)

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