| sherman.morrison {fastmatrix} | R Documentation |
The Sherman-Morrison formula gives a convenient expression for the inverse of the rank 1 update (\bold{A} + \bold{bd}^T) where \bold{A} is a n\times n matrix and \bold{b}, \bold{d} are n-dimensional vectors. Thus
(\bold{A} + \bold{bd}^T)^{-1} = \bold{A}^{-1} - \frac{\bold{A}^{-1}\bold{bd}^T \bold{A}^{-1}}{1 + \bold{d}^T\bold{A}^{-1}\bold{b}}.
sherman.morrison(a, b, d = b, inverted = FALSE)
a |
a numeric matrix. |
b |
a numeric vector. |
d |
a numeric vector. |
inverted |
logical. If |
Method of sherman.morrison calls BLAS level 2 subroutines DGEMV and
DGER for computational efficiency.
a square matrix of the same order as a.
n <- 10 ones <- rep(1, n) a <- 0.5 * diag(n) z <- sherman.morrison(a, ones, 0.5 * ones) z