test_rpca.py

import numpy as np
from sklearn.decomposition.rpca import rpca
from numpy.linalg import matrix_rank


def gen_synthetic(n, sparseness, rank):
    r = rank  # Rank
    X = np.random.normal(0, 1/float(n), size=(n, r))
    Y = np.random.normal(0, 1/float(n), size=(n, r))
    L = np.dot(X, Y.T)
    p = sparseness/2
    S = np.random.choice([0, 1, -1], size=(n, n), p=[1 - 2*p, p, p])

    return L, S


L, S = gen_synthetic(500, 0.05, 25)
X = L + S

L, S, (U, s, Vt) = rpca(X, verbose=True)
r = np.count_nonzero(s)
components = Vt[:r]

l = np.dot(X, components.T)
L_ = np.dot(l, components)

print('Components rank = %d' % matrix_rank(components))
print('L_ rank = %d' % matrix_rank(L_))

assert np.allclose(L, np.dot(np.dot(U, np.diag(s)), Vt))
assert np.allclose(L, L_)