def test_proximal_convconj_l1_simple_space_with_data():
"""Proximal factory for the convex conjugate of the L1-norm."""
# Image space
space = odl.uniform_discr(0, 1, 10)
x_arr = np.arange(-5, 5)
x = space.element(x_arr)
# RHS data
g_arr = np.arange(10, 0, -1)
g = space.element(g_arr)
# Factory function returning the proximal operator
lam = 2
prox_factory = proximal_convex_conj_l1(space, lam=lam, g=g)
# Initialize the proximal operator of F^*
sigma = 0.25
prox = prox_factory(sigma)
assert isinstance(prox, odl.Operator)
# Apply the proximal operator returning its optimal point
x_opt = space.element()
prox(x, x_opt)
# Explicit computation: (x - sigma * g) / max(lam, |x - sigma * g|)
denom = np.maximum(lam, np.abs(x_arr - sigma * g_arr))
x0_verify = lam * (x_arr - sigma * g_arr) / denom
assert all_almost_equal(x_opt, x0_verify, HIGH_ACC)
def test_proximal_convconj_l1_product_space():
"""Proximal factory for the convex conjugate of the L1-norm using
product spaces."""
# Product space for matrix of operators
op_domain = odl.ProductSpace(odl.uniform_discr(0, 1, 10), 2)
# Element in the product space where the proximal operator is evaluated
x0_arr = np.arange(-5, 5)
x1_arr = np.arange(10, 0, -1)
x = op_domain.element([x0_arr, x1_arr])
# Create a data element in the product space
g0_arr = x1_arr.copy()
g1_arr = x0_arr.copy()
g = op_domain.element([g0_arr, g1_arr])
# Factory function returning the proximal operator
lam = 2
prox_factory = proximal_convex_conj_l1(op_domain,
lam=lam,
g=g,
isotropic=True)
# Initialize the proximal operator
sigma = 0.25
prox = prox_factory(sigma)
assert isinstance(prox, odl.Operator)
# Apply the proximal operator returning its optimal point
x_opt = prox(x)
# Explicit computation: (x - sigma * g) / max(lam, |x - sigma * g|)
denom = np.maximum(
lam,
np.sqrt((x0_arr - sigma * g0_arr)**2 + (x1_arr - sigma * g1_arr)**2))
x_verify = lam * (x - sigma * g) / denom
# Compare components
assert all_almost_equal(x_verify, x_opt)
def test_proximal_convconj_l1_simple_space_without_data():
"""Proximal factory for the convex conjugate of the L1-norm."""
# Image space
space = odl.uniform_discr(0, 1, 10)
# Image element
x_arr = np.arange(-5, 5)
x = space.element(x_arr)
# Factory function returning the proximal operator
lam = 2
prox_factory = proximal_convex_conj_l1(space, lam=lam)
# Initialize the proximal operator of F^*
sigma = 0.25
prox = prox_factory(sigma)
assert isinstance(prox, odl.Operator)
# Apply the proximal operator returning its optimal point
# Explicit computation: x / max(lam, |x|)
denom = np.maximum(lam, np.sqrt(x_arr**2))
x_exact = lam * x_arr / denom
# Using out
x_opt = space.element()
x_result = prox(x, x_opt)
assert x_result is x_opt
assert all_almost_equal(x_opt, x_exact, HIGH_ACC)
# Without out
x_result = prox(x)
assert all_almost_equal(x_result, x_exact, HIGH_ACC)
# With aliased out
x_result = prox(x, x)
assert all_almost_equal(x_result, x_exact, HIGH_ACC)
