invert: Matrix Inversion with Fallback Methods

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Matrix Inversion with Fallback Methods

Description

Attempts matrix inversion using multiple methods, falling back to more robust approaches if standard inversion fails.

Usage

invert(mat, include_warnings = FALSE)

Arguments

mat	Square matrix to invert
include_warnings	Logical; default FALSE for current implementation.

Details

Tries methods in order:

1. Cholesky decomposition via chol2inv(chol(...)) for symmetric positive-definite matrices (fastest for SPD)

2. Direct inversion using armaInv() as first fallback

3. Generalized inverse using eigendecomposition with small ridge

4. Returns identity matrix if all methods fail, with optional warning

For eigendecomposition, uses a small ridge penalty (1e-16) for stability and zeroes eigenvalues below machine precision.

Value

Inverted matrix, or the identity matrix if all inversion attempts fail

Examples

## Well-conditioned matrix
A <- matrix(c(4,2,2,4), 2, 2)
invert(A) %*% A

## Singular matrix falls back to M.P. generalized inverse
B <- matrix(c(1,1,1,1), 2, 2)
invert(B) %*% B

lgspline documentation built on May 8, 2026, 5:07 p.m.