def test_proximal_convconj_kl_simple_space():
"""Test for proximal factory for the convex conjugate of KL divergence."""
# Image space
space = odl.uniform_discr(0, 1, 10)
# Element in image space where the proximal operator is evaluated
x = space.element(np.arange(-5, 5))
# Data
g = space.element(np.arange(10, 0, -1))
# Factory function returning the proximal operator
lam = 2
prox_factory = proximal_cconj_kl(space, lam=lam, g=g)
# Initialize the proximal operator of F^*
sigma = 0.25
prox = prox_factory(sigma)
assert isinstance(prox, odl.Operator)
# Allocate an output element
x_opt = space.element()
# Apply the proximal operator returning its optimal point
prox(x, x_opt)
# Explicit computation:
x_verify = (lam + x - np.sqrt((x - lam) ** 2 + 4 * lam * sigma * g)) / 2
assert all_almost_equal(x_opt, x_verify, HIGH_ACC)
def test_proximal_convconj_kl_product_space():
"""Test for product spaces in proximal for conjugate of KL divergence"""
# 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])
# Element in the product space with given data
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_cconj_kl(op_domain, lam=lam, g=g)
# Initialize the proximal operator
sigma = 0.25
prox = prox_factory(sigma)
assert isinstance(prox, odl.Operator)
# Allocate an output element
x_opt = op_domain.element()
# Apply the proximal operator returning its optimal point
prox(x, x_opt)
# Explicit computation:
x_verify = (lam + x - np.sqrt((x - lam) ** 2 + 4 * lam * sigma * g)) / 2
# Compare components
assert all_almost_equal(x_verify, x_opt)