def test_3D__gradient_id():
img = np.array([[1, 3], [4, 2], [1, 0]])
for l1_ratio in [0., .1, .3, .5, .7, .9, 1.]:
gid = _gradient_id(img, l1_ratio)
np.testing.assert_array_equal(
gid.shape, [img.ndim + 1] + list(img.shape))
def test_3D__gradient_id():
img = np.array([[1, 3], [4, 2], [1, 0]])
for l1_ratio in [0., .1, .3, .5, .7, .9, 1.]:
gid = _gradient_id(img, l1_ratio)
np.testing.assert_array_equal(
gid.shape, [img.ndim + 1] + list(img.shape))
def test_2D__gradient_id():
img = np.array([[1, 3], [4, 2]])
for l1_ratio in [0.0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0]:
gid = _gradient_id(img, l1_ratio)
np.testing.assert_array_equal(gid.shape, [img.ndim + 1] + list(img.shape))
np.testing.assert_array_equal(l1_ratio * img, gid[-1])
def test_1D__gradient_id():
for size in [1, 2, 10]:
img = np.arange(size)
for l1_ratio in [0.0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0]:
gid = _gradient_id(img, l1_ratio=l1_ratio)
np.testing.assert_array_equal(gid.shape, [img.ndim + 1] + list(img.shape))
np.testing.assert_array_equal(l1_ratio * img, gid[-1])
def test_1D__gradient_id():
for size in [1, 2, 10]:
img = np.arange(size)
for l1_ratio in [0., .1, .3, .5, .7, .9, 1.]:
gid = _gradient_id(img, l1_ratio=l1_ratio)
np.testing.assert_array_equal(
gid.shape, [img.ndim + 1] + list(img.shape))
np.testing.assert_array_equal(l1_ratio * img, gid[-1])
def test_grad_div_adjoint_arbitrary_ndim(size=5, max_ndim=5):
# We need to check that <D x, y> = <x, DT y> for x and y random vectors
rng = check_random_state(42)
for ndim in range(1, max_ndim):
shape = tuple([size] * ndim)
x = rng.normal(size=shape)
y = rng.normal(size=[ndim + 1] + list(shape))
for l1_ratio in [0., .1, .3, .5, .7, .9, 1.]:
np.testing.assert_almost_equal(
np.sum(_gradient_id(x, l1_ratio=l1_ratio) * y),
-np.sum(x * _div_id(y, l1_ratio=l1_ratio)))
def test_grad_div_adjoint_arbitrary_ndim(size=5, max_ndim=5):
# We need to check that <D x, y> = <x, DT y> for x and y random vectors
rng = check_random_state(42)
for ndim in range(1, max_ndim):
shape = tuple([size] * ndim)
x = rng.normal(size=shape)
y = rng.normal(size=[ndim + 1] + list(shape))
for l1_ratio in [0.0, 0.1, 0.3, 0.5, 0.7, 0.9, 1.0]:
np.testing.assert_almost_equal(
np.sum(_gradient_id(x, l1_ratio=l1_ratio) * y), -np.sum(x * _div_id(y, l1_ratio=l1_ratio))
)
def test_tvl1_from_gradient(size=5, n_samples=10, random_state=42):
rng = np.random.RandomState(random_state)
shape = [size] * 3
n_voxels = np.prod(shape)
X = rng.randn(n_samples, n_voxels)
y = rng.randn(n_samples)
w = rng.randn(*shape)
mask = np.ones_like(w).astype(np.bool)
for alpha in [0., 1e-1, 1e-3]:
for l1_ratio in [0., .5, 1.]:
gradid = _gradient_id(w, l1_ratio=l1_ratio)
assert_equal(
_tvl1_objective(X, y,
w.copy().ravel(), alpha, l1_ratio, mask),
_squared_loss(X, y, w.copy().ravel(), compute_grad=False) +
alpha * _tvl1_objective_from_gradient(gradid))
def test_tvl1_from_gradient(size=5, n_samples=10, random_state=42):
rng = np.random.RandomState(random_state)
shape = [size] * 3
n_voxels = np.prod(shape)
X = rng.randn(n_samples, n_voxels)
y = rng.randn(n_samples)
w = rng.randn(*shape)
mask = np.ones_like(w).astype(np.bool)
for alpha in [0., 1e-1, 1e-3]:
for l1_ratio in [0., .5, 1.]:
gradid = _gradient_id(w, l1_ratio=l1_ratio)
assert_equal(_tvl1_objective(
X, y, w.copy().ravel(), alpha, l1_ratio, mask),
_squared_loss(X, y, w.copy().ravel(),
compute_grad=False
) + alpha * _tvl1_objective_from_gradient(
gradid))
