cholesky
cholesky(
aIn):Var
Defined in: linalg.js:69
Cholesky factorization: returns lower-triangular L with A = L Lᵀ.
The adjoint is Murray (2016), Differentiation of the Cholesky decomposition: with Φ(X) = tril(X) halved on the diagonal,
Ā = L⁻ᵀ Φ(Lᵀ L̄) L⁻¹, symmetrized.A is assumed symmetric — only its lower triangle affects the factor — so
the returned gradient is symmetrized: it is the derivative with respect to a
SYMMETRIC perturbation of A. That is what you want when A is a covariance
built by a kernel, which is every use here. Feeding a matrix whose two
triangles disagree is a modelling error, and lina’s forward rejects it.
Parameters
aIn
Var | number[][]
symmetric positive-definite matrix
Returns
lower-triangular factor (n × n)