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

Author

Listed:
  • Sam Schulhofer-Wohl

    (Federal Reserve Bank of Minneapolis)

Programming Language

Stata

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.

Suggested Citation

  • Sam Schulhofer-Wohl, 2011. "SMWOODBURY: Stata module to compute Sherman-Morrison-Woodbury rank-k update to matrix inverse," Statistical Software Components S457377, Boston College Department of Economics.
    • Handle: RePEc:boc:bocode:s457377
    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.
    as

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    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury.mata
    File Function: program code
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_lu_solve.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_lu.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_qr_solve.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_qr.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_lu_solve.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_lu.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_posdef_solve.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_posdef.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_qr_solve.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym1_qr.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_lu_solve.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_lu.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_posdef_solve.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_posdef.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_qr_solve.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/s/smwoodbury_sym2_qr.sthlp
    File Function: help file
    Download Restriction: no
    File URL: http://fmwww.bc.edu/repec/bocode/l/lsmwoodbury.mlib
    File Function: Mata object library
    Download Restriction: no
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