Solve {limSolve}

Generalised inverse solution of Ax = B

Description

Generalised inverse solution of

Ax=B

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.

Note

Solve uses the Moore-Penrose generalized inverse of matrix A (function ginv from package MASS).

solve, the R default requires a square, positive definite A. Solve does not have this restriction.

Author(s)

Karline Soetaert <[e-mail]>

References

package MASS:

Venables, W. N. & Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer, New York. ISBN 0-387-95457-0

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