def test_combine_proximal():
"""Function to combine proximal factory functions.
The combine function makes use of the separable sum property of proximal
operators.
"""
# Image space
space = odl.uniform_discr(0, 1, 10)
# Factory function returning the proximal operator
prox_factory = proximal_const_func(space)
# Combine factory function of proximal operators
combined_prox_factory = combine_proximals(prox_factory, prox_factory)
# Initialize combine proximal operator
prox = combined_prox_factory(1)
assert isinstance(prox, odl.Operator)
# Explicit construction of the combine proximal operator
prox_verify = odl.ProductSpaceOperator(
[[odl.IdentityOperator(space), None],
[None, odl.IdentityOperator(space)]])
# Create an element in the domain of the operator
x = prox_verify.domain.element([np.arange(-5, 5), np.arange(-5, 5)])
# Allocate output element
out = prox_verify.range.element()
# Apply explicitly constructed and factory-function-combined proximal
# operators
assert prox(x) == prox_verify(x)
# Test output argument
assert prox(x, out) == prox_verify(x)
# Identity mapping
assert out == x
def test_proximal_const_func():
"""Proximal factory for the constnat mapping G(x) = c."""
# Image space
space = odl.uniform_discr(0, 1, 10)
# Element in the image space where the proximal operator is evaluated
x = space.element(np.arange(-5, 5))
# Factory function returning the proximal operator
prox_factory = proximal_const_func(space)
# Initialize proximal operator of G (with an unused parameter)
prox = prox_factory(None)
# prox_tau[G](x) = x = identity operator
assert isinstance(prox, odl.IdentityOperator)
# Optimal point of the auxiliary minimization problem prox_tau[G]
x_opt = prox(x)
# Identity map
assert x == x_opt
