Module helpers

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Helper functions for numerical integration and common operations.

Enums§

DEFAULT_CONVERGENCE_TOL: Default convergence tolerance for iterative algorithms.
NUMERICAL_EPS: Small epsilon for numerical comparisons (e.g., avoiding division by zero).

aic: Compute AIC from residual sum of squares.
bandwidth_candidates_from_dists: Extract bandwidth candidates from a flat n×n distance matrix.
bic: Compute BIC from residual sum of squares.
cumulative_trapz: Cumulative integration using Simpson’s rule where possible.
extract_curves: Extract curves from column-major data matrix.
fdata_interpolate: Interpolate functional data to a new grid.
gaussian_kernel: Gaussian kernel: K(d, h) = exp(-d² / (2h²)).
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.
quantile_sorted: Compute a quantile from a sorted slice.
r_squared: Compute R² (coefficient of determination).
r_squared_adj: Compute adjusted R².
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.
sort_nan_safe: Sort a slice using total ordering that treats NaN as equal.
trapz: Trapezoidal integration of y over x.