Compute matrix inverse via Cholesky decomposition

Computes the inverse of a positive definite matrix from its Cholesky factor. Note: x should be the Cholesky factor (L or U), not the original matrix.

Usage

mlx_cholesky_inv(x, upper = FALSE)

Arguments

x: An mlx array.
upper: Logical; if TRUE, x is upper triangular, otherwise lower triangular.

Value

The inverse of the original matrix (A^-1 where A = LL' or A = U'U).

Details

For a more R-like interface, see chol2inv().

Examples

# Create a positive definite matrix
A <- matrix(rnorm(9), 3, 3)
A <- t(A) %*% A
# Compute Cholesky factor
L <- chol(A, pivot = FALSE, upper = FALSE)
# Get inverse from Cholesky factor
mlx_cholesky_inv(as_mlx(L))
#> mlx array [3 x 3]
#>   dtype: float32
#>   device: gpu
#>   values:
#>         [,1]     [,2]      [,3]
#> [1,] 0.52139 0.000000 0.0000000
#> [2,] 0.00000 4.931555 0.0000000
#> [3,] 0.00000 0.000000 0.3226744