Log-determinant via the Woodbury matrix determinant lemma

Computes \(\log|A + UCV|\) using the matrix determinant lemma in \(O(nk^2 + k^3)\) time, reusing an existing Cholesky factor of \(A\).

Usage

woodbury_logdet(A_factor, U, V = NULL, C_inv = NULL)

Arguments

A_factor

An amChol object from chol_factor(), or a square numeric matrix that is automatically Cholesky-factored.

U

Numeric matrix of shape [n, k]; low-rank left factor.

V

Numeric matrix of shape [k, n]; low-rank right factor. Defaults to t(U) (symmetric update).

C_inv

Numeric matrix of shape [k, k]; inverse of the central factor \(C\). Defaults to diag(k).

Value

A length-1 numeric: \(\log|A + UCV|\).

See also

woodbury_solve, chol_factor

Examples

A <- crossprod(matrix(rnorm(25), 5)) + diag(5)
U <- matrix(rnorm(10), 5, 2)
ld <- woodbury_logdet(A, U)
is.finite(ld)
#> [1] TRUE