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
) – IfTrue
, the matrix is symmetrized before Cholesky decomposition by computing \(\frac{1}{2}(x + x^H)\). IfFalse
, only the lower triangle ofx
is used; the upper triangle is ignored and not accessed.
- Return type:
- 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.