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

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

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

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.