Commit 64fafb5d by Matthew Tam

### 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) Inputs: ------------ 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. scaling if False, the scaling component of the transformation is forced to 1 reflection 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. Outputs ------------ d the residual sum of squared errors, normalized according to a measure of the scale of X, ((X - X.mean(0))**2).sum() Z the matrix of transformed Y-values tform 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 = np.dot(X0.T, Y0) U,s,Vt = np.linalg.svd(A,full_matrices=False) V = Vt.T T = np.dot(V, 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 = np.dot(V, 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*np.dot(Y0, T) + muX else: b = 1 d = 1 + ssY/ssX - 2 * traceTA * normY / normX Z = normY*np.dot(Y0, T) + muX # transformation matrix if my < m: T = T[:my,:] c = muX - b*np.dot(muY, 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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