def test_pre_fastica():
N, T = 3, 1000
rng = np.random.RandomState(42)
names = ['tanh', 'cube']
for j, fun in enumerate([Tanh(params=dict(alpha=0.5)), 'cube']):
if j == 0:
S = rng.laplace(size=(N, T))
else:
S = rng.uniform(low=-1, high=1, size=(N, T))
A = rng.randn(N, N)
X = np.dot(A, S)
K, W, Y = picard(X.copy(),
fun=fun,
ortho=False,
random_state=0,
fastica_it=10)
if fun == 'tanh':
fun = Tanh()
elif fun == 'exp':
fun = Exp()
elif fun == 'cube':
fun = Cube()
# Get the final gradient norm
psiY = fun.score_and_der(Y)[0]
G = np.inner(psiY, Y) / float(T) - np.eye(N)
err_msg = 'fun %s, gradient norm greater than tol' % names[j]
assert_allclose(G, np.zeros((N, N)), atol=1e-7, err_msg=err_msg)
assert_equal(Y.shape, X.shape)
assert_equal(W.shape, A.shape)
assert_equal(K.shape, A.shape)
WA = W.dot(K).dot(A)
WA = permute(WA) # Permute and scale
err_msg = 'fun %s, wrong unmixing matrix' % names[j]
assert_allclose(WA, np.eye(N), rtol=0, atol=1e-1, err_msg=err_msg)
def test_picardo():
N, T = 3, 2000
rng = np.random.RandomState(4)
S = rng.laplace(size=(N, T))
A = rng.randn(N, N)
X = np.dot(A, S)
names = ['tanh', 'exp', 'cube']
for fastica_it in [None, 2]:
for fun in names:
print(fun)
K, W, Y = picard(X.copy(),
fun=fun,
ortho=True,
random_state=rng,
fastica_it=fastica_it,
verbose=True)
if fun == 'tanh':
fun = Tanh()
elif fun == 'exp':
fun = Exp()
elif fun == 'cube':
fun = Cube()
# Get the final gradient norm
psiY = fun.score_and_der(Y)[0]
G = np.inner(psiY, Y) / float(T) - np.eye(N)
G = (G - G.T) / 2. # take skew-symmetric part
err_msg = 'fun %s, gradient norm greater than tol' % fun
assert_allclose(G, np.zeros((N, N)), atol=1e-7, err_msg=err_msg)
assert_equal(Y.shape, X.shape)
assert_equal(W.shape, A.shape)
assert_equal(K.shape, A.shape)
WA = W.dot(K).dot(A)
WA = permute(WA) # Permute and scale
err_msg = 'fun %s, wrong unmixing matrix' % fun
assert_allclose(WA, np.eye(N), rtol=0, atol=0.1, err_msg=err_msg)
def test_shift():
N, T = 5, 1000
rng = np.random.RandomState(42)
S = rng.laplace(size=(N, T))
A = rng.randn(N, N)
offset = rng.randn(N)
X = np.dot(A, S) + offset[:, None]
_, W, Y, X_mean = picard(X.copy(),
ortho=False,
whiten=False,
return_X_mean=True,
random_state=rng)
assert_allclose(offset, X_mean, rtol=0, atol=0.2)
WA = W.dot(A)
WA = permute(WA)
assert_allclose(WA, np.eye(N), rtol=0, atol=0.2)
def test_extended():
N, T = 4, 2000
n = N // 2
rng = np.random.RandomState(42)
S = np.concatenate(
(rng.laplace(size=(n, T)), rng.uniform(low=-1, high=1, size=(n, T))),
axis=0)
print(S.shape)
A = rng.randn(N, N)
X = np.dot(A, S)
K, W, Y = picard(X, ortho=False, random_state=0, extended=True)
assert Y.shape == X.shape
assert W.shape == A.shape
assert K.shape == A.shape
WA = W.dot(K).dot(A)
WA = permute(WA) # Permute and scale
err_msg = 'wrong unmixing matrix'
assert_allclose(WA, np.eye(N), rtol=0, atol=1e-1, err_msg=err_msg)
###############################################################################
# Plot the corresponding functions
x = np.linspace(-2, 2, 100)
log_likelihood = custom_density.log_lik(x)
psi, psi_der = custom_density.score_and_der(x)
names = ['log-likelihood', 'score', 'score derivative']
plt.figure()
for values, name in zip([log_likelihood, psi, psi_der], names):
plt.plot(x, values, label=name)
plt.legend()
plt.title("Custom density")
plt.show()
###############################################################################
# Run Picard on toy dataset using this density
rng = np.random.RandomState(0)
N, T = 5, 1000
S = rng.laplace(size=(N, T))
A = rng.randn(N, N)
X = np.dot(A, S)
K, W, Y = picard(X, fun=custom_density, random_state=0)
plt.figure()
plt.imshow(permute(W.dot(K).dot(A)), interpolation='nearest')
plt.title('Product between the estimated unmixing matrix and the mixing'
'matrix')
plt.show()