def test_ztz(use_whitening):
n_atoms = 7
n_trials = 3
n_channels = 5
n_times_valid = 500
n_times_atom = 10
n_times = n_times_valid + n_times_atom - 1
random_state = None
rng = check_random_state(random_state)
X = rng.randn(n_trials, n_channels, n_times)
z = rng.randn(n_trials, n_atoms, n_times_valid)
D = rng.randn(n_atoms, n_channels, n_times_atom)
if use_whitening:
ar_model, X = whitening(X)
zw = apply_whitening(ar_model, z, mode="full")
ztz = compute_ztz(zw, n_times_atom)
grad = np.zeros(D.shape)
for t in range(n_times_atom):
grad[:, :, t] = np.tensordot(ztz[:, :, t:t + n_times_atom],
D[:, :, ::-1],
axes=([1, 2], [0, 2]))
else:
ztz = compute_ztz(z, n_times_atom)
grad = tensordot_convolve(ztz, D)
cost = np.dot(D.ravel(), grad.ravel())
X_hat = construct_X_multi(z, D)
if use_whitening:
X_hat = apply_whitening(ar_model, X_hat, mode="full")
assert np.isclose(cost, np.dot(X_hat.ravel(), X_hat.ravel()))
def test_update_z_multi_decrease_cost_function(loss, solver):
n_trials, n_channels, n_times = 2, 3, 100
n_times_atom, n_atoms = 10, 4
n_times_valid = n_times - n_times_atom + 1
reg = 0
loss_params = dict(gamma=1, sakoe_chiba_band=n_times_atom // 2)
rng = np.random.RandomState(0)
X = rng.randn(n_trials, n_channels, n_times)
uv = rng.randn(n_atoms, n_channels + n_times_atom)
z = rng.randn(n_trials, n_atoms, n_times_valid)
if loss == 'whitening':
loss_params['ar_model'], X = whitening(X, ordar=10)
loss_0 = compute_X_and_objective_multi(X=X, z_hat=z, D_hat=uv, reg=reg,
feasible_evaluation=False,
loss=loss, loss_params=loss_params)
z_hat, ztz, ztX = update_z_multi(X, uv, reg, z0=z, solver=solver,
loss=loss, loss_params=loss_params,
return_ztz=True)
loss_1 = compute_X_and_objective_multi(X=X, z_hat=z_hat, D_hat=uv,
reg=reg, feasible_evaluation=False,
loss=loss, loss_params=loss_params)
assert loss_1 < loss_0
if loss == 'l2':
assert np.allclose(ztz, compute_ztz(z_hat, n_times_atom))
assert np.allclose(ztX, compute_ztX(z_hat, X))
def test_gradient_uv(loss):
# Generate synchronous D
n_times_atom, n_times = 10, 100
n_channels = 5
n_atoms = 2
n_trials = 3
loss_params = dict(gamma=1, sakoe_chiba_band=n_times_atom // 2)
rng = np.random.RandomState()
X = rng.normal(size=(n_trials, n_channels, n_times))
z = rng.normal(size=(n_trials, n_atoms, n_times - n_times_atom + 1))
uv = rng.normal(size=(n_atoms, n_channels + n_times_atom)).ravel()
if loss == 'whitening':
loss_params['ar_model'], X = whitening(X, ordar=10)
def func(uv0):
uv0 = uv0.reshape(n_atoms, n_channels + n_times_atom)
X_hat = construct_X_multi(z, D=uv0, n_channels=n_channels)
return compute_objective(X, X_hat, loss=loss, loss_params=loss_params)
def grad(uv0):
return gradient_uv(uv=uv0,
X=X,
z=z,
flatten=True,
loss=loss,
loss_params=loss_params)
error = optimize.check_grad(func, grad, uv.ravel(), epsilon=2e-8)
grad_uv = grad(uv)
n_grad = np.sqrt(np.dot(grad_uv, grad_uv))
try:
assert error < 1e-5 * n_grad, "Gradient is false: {:.4e}".format(error)
except AssertionError:
if DEBUG:
grad_approx = optimize.approx_fprime(uv, func, 2e-8)
import matplotlib.pyplot as plt
plt.semilogy(abs(grad_approx - grad_uv))
plt.figure()
plt.plot(grad_approx, label="approx")
plt.plot(grad_uv, '--', label="grad")
plt.legend()
plt.show()
raise
if loss == 'l2':
constants = _get_d_update_constants(X, z)
msg = "Wrong value for zt*X"
assert np.allclose(
gradient_uv(0 * uv, X=X, z=z, flatten=True),
gradient_uv(0 * uv, constants=constants, flatten=True)), msg
msg = "Wrong value for zt*z"
assert np.allclose(gradient_uv(uv, X=X, z=z, flatten=True),
gradient_uv(uv, constants=constants,
flatten=True)), msg
def test_gradients(loss):
"""Check that the gradients have the correct shape.
"""
n_trials, n_channels, n_times = 5, 3, 100
n_atoms, n_times_atom = 10, 15
n_checks = 5
if loss == "dtw":
n_checks = 1
loss_params = dict(gamma=.01)
n_times_valid = n_times - n_times_atom + 1
X = np.random.randn(n_trials, n_channels, n_times)
z = np.random.randn(n_trials, n_atoms, n_times_valid)
uv = np.random.randn(n_atoms, n_channels + n_times_atom)
D = get_D(uv, n_channels)
if loss == "whitening":
loss_params['ar_model'], X = whitening(X)
# Test gradient D
assert D.shape == _gradient_d(X, z, D, loss, loss_params=loss_params).shape
def pobj(ds):
return _objective(X, z, ds.reshape(n_atoms, n_channels, -1), loss,
loss_params=loss_params)
def grad(ds):
return _gradient_d(X, z, ds, loss=loss, flatten=True,
loss_params=loss_params)
gradient_checker(pobj, grad, np.prod(D.shape), n_checks=n_checks,
grad_name="gradient D for loss '{}'".format(loss),
rtol=1e-4)
# Test gradient z
assert z[0].shape == _gradient_zi(
X, z, D, loss, loss_params=loss_params).shape
def pobj(zs):
return _objective(X[:1], zs.reshape(1, n_atoms, -1), D, loss,
loss_params=loss_params)
def grad(zs):
return gradient_zi(X[0], zs, D, loss=loss, flatten=True,
loss_params=loss_params)
gradient_checker(pobj, grad, n_atoms * n_times_valid, n_checks=n_checks,
debug=True, grad_name="gradient z for loss '{}'"
.format(loss), rtol=1e-4)
def test_gradient_d(loss):
# Generate synchronous D
n_times_atom, n_times = 10, 100
n_channels = 5
n_atoms = 2
n_trials = 3
# Constant for the DTW loss
loss_params = dict(gamma=1, sakoe_chiba_band=n_times_atom // 2)
rng = np.random.RandomState()
X = rng.normal(size=(n_trials, n_channels, n_times))
z = rng.normal(size=(n_trials, n_atoms, n_times - n_times_atom + 1))
d = rng.normal(size=(n_atoms, n_channels, n_times_atom)).ravel()
if loss == 'whitening':
loss_params['ar_model'], X = whitening(X, ordar=10)
def func(d0):
D0 = d0.reshape(n_atoms, n_channels, n_times_atom)
X_hat = construct_X_multi(z, D=D0)
return compute_objective(X, X_hat, loss=loss, loss_params=loss_params)
def grad(d0):
return gradient_d(D=d0,
X=X,
z=z,
loss=loss,
loss_params=loss_params,
flatten=True)
error = optimize.check_grad(func, grad, d, epsilon=2e-8)
grad_d = grad(d)
n_grad = np.sqrt(np.dot(grad_d, grad_d))
try:
assert error < 1e-5 * n_grad, "Gradient is false: {:.4e}".format(error)
except AssertionError:
if DEBUG:
grad_approx = optimize.approx_fprime(d, func, 2e-8)
import matplotlib.pyplot as plt
plt.semilogy(abs(grad_approx - grad_d))
plt.figure()
plt.plot(grad_approx, label="approx")
plt.plot(grad_d, '--', label="grad")
plt.legend()
plt.show()
raise
def test_consistency(loss, func):
"""Check that the result are the same for the full rank D and rank 1 uv.
"""
n_trials, n_channels, n_times = 5, 3, 30
n_atoms, n_times_atom = 4, 7
loss_params = dict(gamma=.01)
n_times_valid = n_times - n_times_atom + 1
X = np.random.randn(n_trials, n_channels, n_times)
z = np.random.randn(n_trials, n_atoms, n_times_valid)
uv = np.random.randn(n_atoms, n_channels + n_times_atom)
D = get_D(uv, n_channels)
if loss == "whitening":
loss_params['ar_model'], X = whitening(X)
val_D = func(X, z, D, loss, loss_params=loss_params)
val_uv = func(X, z, uv, loss, loss_params=loss_params)
assert np.allclose(val_D, val_uv)