Tucker's congruence and orthogonal Procrustes rotation

Linear-algebra utilities shared by MatchAlign and the recovery assessments. tucker_congruence(x, y) computes sum(x*y) / sqrt(sum(x^2) * sum(y^2)). procrustes_rotation(X, Target) finds the orthogonal R minimising ||X R - Target||_F and returns X %*% R with R attached as attribute "rotation".

Usage

tucker_congruence(x, y)

procrustes_rotation(X, Target)

Arguments

x, y

Numeric vectors (for Tucker).

X, Target

Matrices (for Procrustes).

Value

Tucker returns a scalar; Procrustes returns the rotated matrix with a "rotation" attribute.