multiway (version 1.0-2)

mpinv: Moore-Penrose Pseudoinverse

Description

Calculates the Moore-Penrose pseudoinverse of the input matrix using a truncated singular value decomposition.

Usage

mpinv(X, tol=.Machine$double.eps)

Arguments

X

Real-valued matrix.

tol

Stability tolerance for singular values.

Value

Returns pseudoinverse of X.

References

Moore, E.H. (1920). On the reciprocal of the general algebraic matrix. Bulletin of the American Mathematical Society 26, 394-395.

Penrose, R. (1950). A generalized inverse for matrices. Mathematical Proceedings of the Cambridge Philosophical Society 51, 406-413.

Examples

##########   EXAMPLE   ##########

set.seed(1)
X <- matrix(rnorm(2000),100,20)
Xi <- mpinv(X)
sum( ( X - X %*% Xi %*% X )^2 )
sum( ( Xi - Xi %*% X %*% Xi )^2 )
isSymmetric(X %*% Xi)
isSymmetric(Xi %*% X)