MPinv | R Documentation |
Computes the Moore-Penrose generalized inverse.
MPinv(mat, tolerance = 100*.Machine$double.eps, rank = NULL, method = "svd")
mat |
a real matrix. |
tolerance |
A positive scalar which determines the tolerance for detecting zeroes among the singular values. |
rank |
Either |
method |
Character, one of |
Real-valuedness is not checked, neither is symmetry when method
= "chol"
.
A matrix, with an additional attribute named "rank"
containing
the numerically determined rank of the matrix.
David Firth and Heather Turner
Harville, D. A. (1997). Matrix Algebra from a Statistician's Perspective. New York: Springer.
Courrieu, P. (2005). Fast computation of Moore-Penrose inverse matrices. Neural Information Processing 8, 25–29
ginv
A <- matrix(c(1, 1, 0, 1, 1, 0, 2, 3, 4), 3, 3) B <- MPinv(A) A %*% B %*% A - A # essentially zero B %*% A %*% B - B # essentially zero attr(B, "rank") # here 2 ## demonstration that "svd" and "chol" deliver essentially the same ## results for symmetric matrices: A <- crossprod(A) MPinv(A) - MPinv(A, method = "chol") ## (essentially zero)
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