scikit_learn_flip_algorithm.py

import numpy as np
from numpy.linalg import inv
from scipy import linalg
from sklearn.decomposition import PCA
from sklearn import utils

X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])

mean_ = np.mean(X, axis=0)
X = X - mean_
U, S, V = linalg.svd(X, full_matrices=False)
print('U=', U)
print('V=', V)

# Reverse engineering the algorithm:

max_abs_cols = np.argmax(np.abs(U), axis=0)
print('max_abs_cols')
print(max_abs_cols)
submatrix = U[max_abs_cols, range(U.shape[1])]
print('submatrix = ', submatrix)
signs = np.sign(submatrix)
print('signs =', signs)
print('U flipped = ', U * signs)
print('V flipped = ', V * signs[:, np.newaxis])