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import numpy.linalg as la | |
def tls(X,y): | |
if X.ndim is 1: | |
n = 1 # the number of variable of X | |
X = X.reshape(len(X),1) | |
else: | |
n = np.array(X).shape[1] | |
Z = np.vstack((X.T,y)).T | |
U, s, Vt = la.svd(Z, full_matrices=True) | |
V = Vt.T | |
Vxy = V[:n,n:] | |
Vyy = V[n:,n:] | |
a_tls = - Vxy / Vyy # total least squares soln | |
Xtyt = - Z.dot(V[:,n:]).dot(V[:,n:].T) | |
Xt = Xtyt[:,:n] # X error | |
y_tls = (X+Xt).dot(a_tls) | |
fro_norm = la.norm(Xtyt, 'fro') | |
return y_tls, X+Xt, a_tls, fro_norm |
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