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.

  • x – 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.


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.