R: Methods for Function solve in Package 'distr'

solve-methods {distr}

R Documentation

Methods for Function solve in Package ‘distr’

Description

solve-methods using generalized inverses for various types of matrices

Usage

solve(a,b, ...)
## S4 method for signature 'ANY,ANY'
solve(a, b, generalized = 
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S4 method for signature 'PosSemDefSymmMatrix,ANY'
solve(a, b, generalized =
getdistrOption("use.generalized.inverse.by.default"), tol = 1e-10)
## S4 method for signature 'PosDefSymmMatrix,ANY'
solve(a, b, tol = 1e-10)

Arguments

`a`	matrix to be inverted / to be solved for RHS.
`b`	a numeric or complex vector or matrix giving the right-hand side(s) of the linear system. If missing, `b` is taken to be an identity matrix and `solve` will return the inverse of `a`.
`...`	further arguments to be passed to specific methods (see `solve`).
`generalized`	logical: should generalized / Moore-Penrose inverses be used? By default uses the corresponding global option to be set by `distroptions`.
`tol`	the tolerance for detecting linear dependencies in the columns of `a`. Default is `.Machine$double.eps`.

Details

The method for the Moore-Penrose inverse for signature(a = "PosSemDefSymmMatrix", b = "ANY") uses eigen to find the eigenvalue decomposition of a and then simply "pseudo-inverts" the corresponding diagonal matrix built from eigen(a)$values, while for signature(a = "ANY", b = "ANY") it uses the svd decomposition of a and then simply "pseudo-inverts" the corresponding diagonal matrix built from svd(a)$d.

Methods

solve: signature(a = "ANY", b = "ANY"): tries to evaluate solve.default method from base in classical way; if this gives an error, this one is returned if generalized is TRUE, else it will then return a^-b where a^- is the pseudo or Moore-Penrose inverse of a.
solve: signature(a = "PosSemDefSymmMatrix", b = "ANY"): evaluates a^-b where a^- is the pseudo or Moore-Penrose inverse of a.
solve: signature(a = "PosDefSymmMatrix", b = "ANY"): evaluates solve method from base in classical way.

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de