Commit 64fafb5d authored by Matthew Tam's avatar Matthew Tam
Browse files

added the 1PTQ datafile and a Procrustes analysis utility function.

parent f3a2e11f
import numpy as np
def procrustes(X, Y, scaling=True, reflection='best'):
A port of MATLAB's `procrustes` function to Numpy.
Procrustes analysis determines a linear transformation (translation,
reflection, orthogonal rotation and scaling) of the points in Y to best
conform them to the points in matrix X, using the sum of squared errors
as the goodness of fit criterion.
d, Z, [tform] = procrustes(X, Y)
X, Y
matrices of target and input coordinates. they must have equal
numbers of points (rows), but Y may have fewer dimensions
(columns) than X.
if False, the scaling component of the transformation is forced
to 1
if 'best' (default), the transformation solution may or may not
include a reflection component, depending on which fits the data
best. setting reflection to True or False forces a solution with
reflection or no reflection respectively.
the residual sum of squared errors, normalized according to a
measure of the scale of X, ((X - X.mean(0))**2).sum()
the matrix of transformed Y-values
a dict specifying the rotation, translation and scaling that
maps X --> Y
n,m = X.shape
ny,my = Y.shape
muX = X.mean(0)
muY = Y.mean(0)
X0 = X - muX
Y0 = Y - muY
ssX = np.linalg.norm(X0, 'fro')**2 #(X0**2.).sum()
ssY = np.linalg.norm(Y0, 'fro')**2 #(Y0**2.).sum()
# centred Frobenius norm
normX = np.sqrt(ssX)
normY = np.sqrt(ssY)
# scale to equal (unit) norm
X0 /= normX
Y0 /= normY
if my < m:
Y0 = np.concatenate((Y0, np.zeros(n, m-my)),0)
# optimum rotation matrix of Y
A =, Y0)
U,s,Vt = np.linalg.svd(A,full_matrices=False)
V = Vt.T
T =, U.T)
if reflection is not 'best':
# does the current solution use a reflection?
have_reflection = np.linalg.det(T) < 0
# if that's not what was specified, force another reflection
if reflection != have_reflection:
V[:,-1] *= -1
s[-1] *= -1
T =, U.T)
traceTA = s.sum()
if scaling:
# optimum scaling of Y
b = traceTA * normX / normY
# standarised distance between X and b*Y*T + c
d = 1 - traceTA**2
# transformed coords
Z = normX*traceTA*, T) + muX
b = 1
d = 1 + ssY/ssX - 2 * traceTA * normY / normX
Z = normY*, T) + muX
# transformation matrix
if my < m:
T = T[:my,:]
c = muX - b*, T)
tform = {'rotation':T, 'scale':b, 'translation':c}
return d, Z, tform
......@@ -8,5 +8,6 @@ The "Utilities"-module contains various ...
from .Laplace_matrix import *
from .Procrustes import *
__all__ = ["Laplace_matrix"]
__all__ = ["Laplace_matrix","procrustes"]
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