def test_patterns_reduced_case():
""" Less sources than signals. """
# source and noise are chosen so that
# noise is uncorrelated with source
source1 = np.array([1, 3, 1, 4, 8, 1])
source2 = np.array([1, 5, 2, 4, -2, 3])
source = np.vstack((source1, source2))
noise1 = [0.4, 0.3, -0.5, -0.2, 0.2, 0.5]
noise2 = [-0.3, -0.5, +0.5, +0.4, -0.2, -0.5]
noise3 = [-0.2, -0.5, +0.5, +0.4, -0.2, -0.5]
# Mix source to signal plus some noise
signal1 = 0.2 * source1 + 0.5 * source2 + noise1
signal2 = 0.8 * source1 - 0.2 * source2 + noise2
signal3 = 0.5 * source1 - 0.3 * source2 + noise3
signal = np.vstack((signal1, signal2, signal3))
W, _, _, _ = np.linalg.lstsq(signal.T, source.T)
reconstructed = np.dot(W.T, signal)
patterns = transform_weights_to_patterns(W.T, signal, reconstructed)
# Note columns are close to given mixing 0.2/0.5, 0.8/-0.2, 0.5/-0.3
assert np.allclose([[0.18594579, 0.80136242, 0.49412571],
[0.52567645, -0.25482237, -0.36055654]], patterns)
# Also compare to solution by inversion
pattern_by_inversion = np.linalg.pinv(W)
assert not np.allclose(pattern_by_inversion, patterns), (
"In reduced case "
"inversion does not have to lead to same result as patterns and "
"in this case it shouldn't.")
def test_patterns_reduced_case():
""" Less sources than signals. """
# source and noise are chosen so that
# noise is uncorrelated with source
source1 = np.array([1,3,1,4,8,1])
source2 = np.array([1,5,2,4,-2,3])
source = np.vstack((source1, source2))
noise1 = [0.4,0.3,-0.5,-0.2,0.2,0.5]
noise2 = [-0.3,-0.5,+0.5,+0.4,-0.2,-0.5]
noise3 = [-0.2,-0.5,+0.5,+0.4,-0.2,-0.5]
# Mix source to signal plus some noise
signal1 = 0.2 * source1 + 0.5 * source2 + noise1
signal2 = 0.8 * source1 - 0.2 * source2 + noise2
signal3 = 0.5 * source1 - 0.3 * source2 + noise3
signal = np.vstack((signal1, signal2, signal3))
W, _, _, _ = np.linalg.lstsq(signal.T, source.T)
reconstructed = np.dot(W.T, signal)
patterns = transform_weights_to_patterns(W.T, signal, reconstructed)
# Note columns are close to given mixing 0.2/0.5, 0.8/-0.2, 0.5/-0.3
assert np.allclose([[ 0.18594579, 0.80136242, 0.49412571],
[ 0.52567645, -0.25482237, -0.36055654]],
patterns)
# Also compare to solution by inversion
pattern_by_inversion = np.linalg.pinv(W)
assert not np.allclose(pattern_by_inversion, patterns), ("In reduced case "
"inversion does not have to lead to same result as patterns and "
"in this case it shouldn't.")
def test_patterns_square_case():
# source and noise are chosen so that
# noise is uncorrelated with source
source1 = np.array([1, 3, 1, 4, 8, 1])
source2 = np.array([1, 5, 2, 4, -2, 3])
source = np.vstack((source1, source2))
# Mix source to signal plus some noise
noise1 = [0.4, 0.3, -0.5, -0.2, 0.2, 0.5]
noise2 = [-0.3, -0.5, +0.5, +0.4, -0.2, -0.5]
signal1 = 0.2 * source1 + 0.5 * source2 + noise1
signal2 = 0.8 * source1 - 0.2 * source2 + noise2
signal = np.vstack((signal1, signal2))
W, _, _, _ = np.linalg.lstsq(signal.T, source.T)
reconstructed = np.dot(W.T, signal)
patterns = transform_weights_to_patterns(W.T, signal, reconstructed)
# Note columns are close to given mixing 0.2/0.5, 0.8/-0.2
assert np.allclose([[0.20550224, 0.80095521], [0.54812122, -0.25528973]],
patterns)
# Also compare to solution by inversion
pattern_by_inversion = np.linalg.inv(W)
assert np.allclose(pattern_by_inversion, patterns)
def test_patterns_square_case():
# source and noise are chosen so that
# noise is uncorrelated with source
source1 = np.array([1,3,1,4,8,1])
source2 = np.array([1,5,2,4,-2,3])
source = np.vstack((source1, source2))
# Mix source to signal plus some noise
noise1 = [0.4,0.3,-0.5,-0.2,0.2,0.5]
noise2 = [-0.3,-0.5,+0.5,+0.4,-0.2,-0.5]
signal1 = 0.2 * source1 + 0.5 * source2 + noise1
signal2 = 0.8 * source1 - 0.2 * source2 + noise2
signal = np.vstack((signal1, signal2))
W, _, _, _ = np.linalg.lstsq(signal.T, source.T)
reconstructed = np.dot(W.T, signal)
patterns = transform_weights_to_patterns(W.T, signal, reconstructed)
# Note columns are close to given mixing 0.2/0.5, 0.8/-0.2
assert np.allclose([[ 0.20550224, 0.80095521],
[ 0.54812122, -0.25528973]],
patterns)
# Also compare to solution by inversion
pattern_by_inversion = np.linalg.inv(W)
assert np.allclose(pattern_by_inversion, patterns)
