limSolve (version 1.4)

Solve: Generalised inverse solution of Ax=B

Description

Generalised inverse solution of $$Ax=B$$ Solve uses the Moore-Penrose generalized inverse of matrix A (function ginv from package MASS). Note: solve, the Rdefault requires a square, positive definite A. Solve does not have this restriction.

Usage

Solve (A, B=diag(nrow=nrow(A)), tol=sqrt(.Machine$double.eps))

Arguments

A

numeric matrix containing the coefficients of the equations $Ax=B$.

B

numeric matrix containing the right-hand sides of the equations; the default is the unity matrix, in which case the function will return the Moore-Penrose generalized inverse of matrix A.

tol

tolerance for selecting singular values.

Value

• a vector with the generalised inverse solution.

See Also

ginv to estimate the Moore-Penrose generalized inverse of a matrix, in package MASS, solve the R default

Examples

A <- matrix(nrow=4,ncol=3,data=c(1:8,6,8,10,12)) # col3 = col1+col2
B <- 0:3
X <- Solve(A,B)            # generalised inverse solution
A %*% X - B                # should be zero (except for roundoff)
(gA <- Solve(A))           # generalised inverse of A