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warp.tile_lower_solve#

warp.tile_lower_solve(
L: Tile[Float, tuple[int, int]],
y: Tile[Float, tuple[int]],
) → Tile[Float, tuple[int]]#

  • Kernel

  • Differentiable

Solve for z in Lz = y, where L is a lower triangular matrix.

This performs general forward substitution for a lower triangular system.

Backward propagation computes gradients with respect to y and the lower-triangular parameterization of L. The strictly upper triangle of L does not affect the solve and receives zero gradient.

Supported datatypes are:

  • float32

  • float64

Parameters:

  • L – A square, non-singular, lower triangular matrix

  • y – A 1D or 2D tile with compatible shape

Returns:

A tile of the same shape as y such that Lz = y.