# jax.lax.linalg.cholesky#

jax.lax.linalg.cholesky(x, *, symmetrize_input=True)[source]#

Cholesky decomposition.

Computes the Cholesky decomposition

$A = L . L^H$

of square matrices, $$A$$, such that $$L$$ is lower triangular. The matrices of $$A$$ must be positive-definite and either Hermitian, if complex, or symmetric, if real.

Parameters
• x (Array) – A batch of square Hermitian (symmetric if real) positive-definite matrices with shape [..., n, n].

• symmetrize_input (bool) – If True, the matrix is symmetrized before Cholesky decomposition by computing $$\frac{1}{2}(x + x^H)$$. If False, only the lower triangle of x is used; the upper triangle is ignored and not accessed.

Return type

Array

Returns

The Cholesky decomposition as a matrix with the same dtype as x and shape [..., n, n]. If Cholesky decomposition fails, returns a matrix full of NaNs. The behavior on failure may change in the future.