gnm: MPinv – R documentation

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gnm

MPinv

Moore-Penrose Pseudoinverse of a Real-valued Matrix

Description

Computes the Moore-Penrose generalized inverse.

Usage

MPinv(mat, tolerance = 100*.Machine$double.eps,
      rank = NULL, method = "svd")

Arguments

`mat`	a real matrix.
`tolerance`	A positive scalar which determines the tolerance for detecting zeroes among the singular values.
`rank`	Either `NULL`, in which case the rank of `mat` is determined numerically; or an integer specifying the rank of `mat` if it is known. No check is made on the validity of any non-`NULL` value.
`method`	Character, one of `"svd", "chol"`. The specification `method = "chol"` is valid only for symmetric matrices.

Details

Real-valuedness is not checked, neither is symmetry when method = "chol".

Value

A matrix, with an additional attribute named "rank" containing the numerically determined rank of the matrix.

Author(s)

David Firth and Heather Turner

References

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

Examples

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)

gnm

Generalized Nonlinear Models

v1.1-1

GPL-2 | GPL-3

Authors

Heather Turner [aut, cre] (<https://orcid.org/0000-0002-1256-3375>), David Firth [aut] (<https://orcid.org/0000-0003-0302-2312>), Brian Ripley [ctb], Bill Venables [ctb], Douglas M. Bates [ctb], Martin Maechler [ctb] (<https://orcid.org/0000-0002-8685-9910>)

Initial release