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warp.tile_cholesky#

warp.tile_cholesky(
A: Tile[Float, tuple[int, int]],
fill_mode: str,
) → Tile[Float, tuple[int, int]]#

  • Kernel

  • Differentiable

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

When fill_mode="lower" (default), returns lower-triangular L such that LL^T = A. When fill_mode="upper", returns upper-triangular U such that U^T U = A.

The fill_mode parameter must be a compile-time constant.

Backward propagation computes gradients with respect to the corresponding triangular parameterization of A (lower triangle when fill_mode="lower", upper triangle when fill_mode="upper").

Supported datatypes are:

  • float32

  • float64

Parameters:

  • A – A square, symmetric positive-definite matrix.

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

Returns:

A triangular matrix L or U.