derivkit.utils.numerics module

Numerical utilities.

derivkit.utils.numerics.central_difference_error_estimate(step_size: float, order: int = 1) → float

Computes a general heuristic size of the first omitted term in central-difference stencils.

Uses the general pattern h^2 / ((order + 1) * (order + 2)) as a rule-of-thumb O(h^2) truncation-error scale.

Parameters:

• step_size – Grid spacing.

• order – Derivative order (positive integer).

Returns:

Estimated truncation error scale.

derivkit.utils.numerics.relative_error(a: ndarray, b: ndarray) → float

Computes the relative error metric between a and b.

This metric is defined as the maximum over all components of a and b of the absolute difference divided by the maximum of 1.0 and the absolute values of a and b.

Parameters:

• a – First array-like input.

• b – Second array-like input.

Returns:

The relative error metric as a float.