Crate procrustes 

procrustes — orthogonal Procrustes, signed-permutation alignment, and Generalised Procrustes Analysis (GPA).

Convention

All four alignment functions return a transform T such that a · T ≈ reference minimizes the Frobenius norm under their respective constraints. For orthogonal and rotation_only, T = R is a K×K orthogonal matrix (with rotation_only further restricted to det(R) = +1). For signed_permutation, T = P · diag(signs) where P is the permutation encoded by assigned; equivalently, column k of a · T equals signs[k] · a[:, assigned[k]]. For sign_align, T = diag(signs) (the degenerate identity-permutation case). Matches SciPy’s (A @ R) - B minimization convention in scipy.linalg.orthogonal_procrustes. For multi-matrix consensus alignment, see generalized.

Structs

GpaAlignment

Result of generalized.

GpaOptions

Options for generalized. Construct via GpaOptions::default() and override fields with struct-update syntax.

OrthogonalAlignment

Result of orthogonal.

SignAlignment

Result of sign_align.

SignedPermutationAlignment

Result of signed_permutation.

Enums

GpaInit

Initial consensus seed for generalized.

InnerAligner

Inner per-iteration aligner used by generalized.

ProcrustesError

Error variants returned by the alignment functions (orthogonal, rotation_only, signed_permutation, sign_align, generalized).

Functions

generalized

Generalised Procrustes Analysis: iterative consensus alignment of N matrices.

orthogonal

Solve min_R ‖a · R − reference‖_F over orthogonal K×K R.

rotation_only

Orthogonal Procrustes restricted to proper rotations (det(R) = +1, R ∈ SO(K)).

sign_align

Sign-only alignment: for each column k, choose s[k] ∈ {−1, +1} to maximise ⟨s[k] · a[:, k], reference[:, k]⟩. Closed-form, O(M·K).

signed_permutation

Solve min_{P ∈ S_K, s ∈ {±1}^K} ‖a · P · diag(s) − reference‖_F exactly.

Type Aliases

Mat

heap allocated resizable matrix, similar to a 2d alloc::vec::Vec

MatRef

immutable view over a matrix, similar to an immutable reference to a 2d strided slice