Procrustes Rotation

Orthogonal Procrustes rotation, provided by the ROTATE directive, operates on two sets of coordinates for n points in r dimensions contained in the n×r matrices X and Y. The aim is to shift, rotate and (optionally) stretch or dilate the Y-configuration so that it best matches the X-set. (Best here means minimizing the sum of the squared distances between the points in the X-set and the matching shifted and rotated points in the Y-set.)