Module helpers 

Helper functions for numerical integration and common operations.

Constants

DEFAULT_CONVERGENCE_TOL

Default convergence tolerance for iterative algorithms.

NUMERICAL_EPS

Small epsilon for numerical comparisons (e.g., avoiding division by zero).

Functions

cumulative_trapz

Cumulative integration using Simpson’s rule where possible.

extract_curves

Extract curves from column-major data matrix.

gradient

Numerical gradient that auto-detects uniform vs non-uniform grids.

gradient_nonuniform

Numerical gradient for non-uniform grids using 3-point Lagrange derivative.

gradient_uniform

Numerical gradient with uniform spacing using 5-point stencil (O(h⁴)).

l2_distance

Compute L2 distance between two curves using integration weights.

linear_interp

Linear interpolation at point t using binary search.

simpsons_weights

Compute Simpson’s 1/3 rule integration weights for a grid.

simpsons_weights_2d

Compute 2D integration weights using tensor product of 1D weights.

trapz

Trapezoidal integration of y over x.