Solve: Generalised inverse solution of Ax = B
In limSolve: Solving Linear Inverse Models

Description Usage Arguments Value Note Author(s) References See Also Examples

Generalised inverse solution of

Ax=B

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

`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.

a vector with the generalised inverse solution.

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.

Karline Soetaert <karline.soetaert@nioz.nl>

package MASS:

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

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

solve the R default

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

              [,1]
[1,]  4.440892e-16
[2,] -2.220446e-16
[3,] -8.881784e-16
[4,] -1.332268e-15
      [,1]        [,2]        [,3]   [,4]
[1,] -0.45 -0.19166667  0.06666667  0.325
[2,]  0.35  0.15833333 -0.03333333 -0.225
[3,] -0.10 -0.03333333  0.03333333  0.100