Module alignment 

Elastic alignment and SRSF (Square-Root Slope Function) transforms.

This module provides phase-amplitude separation for functional data via the elastic framework. Key capabilities:

• srsf_transform / srsf_inverse — SRSF representation and reconstruction
• elastic_align_pair — Pairwise curve alignment via dynamic programming
• elastic_distance — Elastic (Fisher-Rao) distance between curves
• align_to_target — Align a set of curves to a common target
• karcher_mean — Karcher (Fréchet) mean in the elastic metric
• elastic_self_distance_matrix / elastic_cross_distance_matrix — Distance matrices
• reparameterize_curve / compose_warps — Warping utilities

Structs

AlignmentResult

Result of aligning one curve to another.

AlignmentSetResult

Result of aligning a set of curves to a common target.

KarcherMeanResult

Result of the Karcher mean computation.

Functions

align_to_target

Align all curves in data to a single target curve.

compose_warps

Compose two warping functions: (γ₁ ∘ γ₂)(t) = γ₁(γ₂(t)).

elastic_align_pair

Align curve f2 to curve f1 using the elastic framework.

elastic_cross_distance_matrix

Compute the elastic distance matrix between two sets of curves.

elastic_distance

Compute the elastic distance between two curves.

elastic_self_distance_matrix

Compute the symmetric elastic distance matrix for a set of curves.

karcher_mean

reparameterize_curve

Reparameterize a curve by a warping function.

srsf_inverse

Reconstruct a curve from its SRSF representation.

srsf_transform

Compute the Square-Root Slope Function (SRSF) transform.