warp.tile_cholesky_inplace

warp.tile_cholesky_inplace(

A: Tile[Float, tuple[int, int]],

fill_mode: str = 'lower',

) → None

• Kernel: true
• Python: false
• Differentiable: false

Compute the Cholesky factorization of a symmetric positive-definite matrix A in place.

With fill_mode="lower" the lower triangle of A is replaced by the factor L such that L @ L^T = A and the upper triangle is set to zero; with fill_mode="upper" the upper triangle is replaced by U such that U^T @ U = A and the lower triangle is set to zero. Only the triangle selected by fill_mode is read. fill_mode must be a compile-time constant.

Supported dtypes, the positive-definiteness requirement, and backend selection match tile_cholesky(); see it for details and a usage example.

This is a cooperative operation, so every thread in the block must call it.

This in-place variant avoids the input copy and uses half the shared memory of tile_cholesky(), but is not differentiable.

Parameters:

• A – A square, symmetric positive-definite tile with shape=(N, N), overwritten by the factor.

• fill_mode – "lower" or "upper". Must be a compile-time constant.