Sweep operator
Sweeps a covariance matrix with respect to a subset of indices.
swp(V, b)
V |
a symmetric positive definite matrix, the covariance matrix. |
b |
a subset of indices of the columns of |
The sweep operator has been introduced by Beaton (1964) as a tool for inverting symmetric matrices (see Dempster, 1969).
a square matrix U of the same order as V. If a is
the complement of b, then U[a,b] is the matrix of
regression coefficients of a given b and U[a,a]
is the corresponding covariance matrix of the residuals.
If b is empty the function returns V.
If b is the vector 1:nrow(V) (or its permutation) then
the function returns the opposite of the inverse of V.
Giovanni M. Marchetti
Beaton, A.E. (1964). The use of special matrix operators in statistical calculus. Ed.D. thesis, Harvard University. Reprinted as Educational Testing Service Research Bulletin 64-51. Princeton.
Dempster, A.P. (1969). Elements of continuous multivariate analysis. Reading: Addison-Wesley.
## A very simple example V <- matrix(c(10, 1, 1, 2), 2, 2) swp(V, 2)
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