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, device = NULL)

Arguments

x: An mlx array.
upper: Logical; if TRUE, x is upper triangular, otherwise lower triangular.
device: Execution target for APIs that expose a one-off device or stream override. Supply "gpu", "cpu", or an mlx_stream created via mlx_new_stream(). Ordinary array operations use the current mlx_device() instead.

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), device = "cpu")
#> mlx array [3 x 3]
#>   dtype: float32
#>   values:
#>           [,1]     [,2]     [,3]
#> [1,] 0.1525249 0.000000 0.000000
#> [2,] 0.0000000 1.428797 0.000000
#> [3,] 0.0000000 0.000000 2.136137