Module stability_toolkit 

Extended numeric stability toolkit (gradients, error helpers, array-based activations)

Numeric Stability Toolkit

Extended numeric stability utilities that complement the core stability module.

This module provides:

• Error helpers: relative_error, absolute_error
• Compensated summation: convenience wrapper around Kahan accumulation
• Stable activations: softmax_array, sigmoid_array (ndarray-based)
• Condition estimation: condition_number_1d for 1-D ratio analysis
• Numerical differentiation: numerical_gradient with forward/backward/central modes
• Gradient checking: check_gradient to compare analytical vs numerical gradients

Structs

GradientCheckResult

Result of a gradient check.

Enums

DifferenceMode

Mode of finite difference approximation.

Functions

absolute_error

Absolute error between two values: |a - b|.

check_gradient

Check an analytical gradient against a numerical gradient.

compensated_sum

Compute a compensated (Kahan) sum of a slice.

compensated_sum_array

Compute a compensated (Neumaier) sum of an ndarray view.

condition_number_1d

Estimate a “condition number” for a 1-D array as max(|x|) / min_nonzero(|x|).

log_sum_exp_array

Numerically stable log-sum-exp for an ndarray 1-D array.

max_relative_error

Maximum relative error across all elements.

numerical_gradient

Compute the numerical gradient of a scalar function at point x.

pairwise_sum_array

Pairwise summation for an ndarray view.

relative_error

Relative error between computed and reference: |computed - reference| / |reference|.

relative_errors

Element-wise relative errors between two arrays. Returns Err if the arrays have different lengths.

sigmoid_array

Numerically stable sigmoid for an ndarray 1-D array.

softmax_array

Numerically stable softmax for an ndarray 1-D array.