def test_proximal_composition(pos_scalar, sigma):
"""Test for proximal of composition with semi-orthogonal linear operator.
This test is for ``prox[f * L](x)``, where ``L`` is a linear operator such
that ``L * L.adjoint = mu * IdentityOperator``. Specifically, ``L`` is
taken to be ``scal * IdentityOperator``, since this is equivalent to
scaling of the argument.
"""
sigma = float(sigma)
space = odl.uniform_discr(0, 1, 10)
prox_factory = proximal_l2_squared(space)
# The semi-orthogonal linear operator
scal = pos_scalar
L = odl.ScalingOperator(space, scal)
mu = scal ** 2 # L = scal * I => L * L.adjoint = scal ** 2 * I
prox_factory_composition = proximal_composition(prox_factory, L, mu)
prox = prox_factory_composition(sigma)
assert isinstance(prox, odl.Operator)
x = space.element(np.arange(-5, 5))
prox_x = prox(x)
equiv_prox = proximal_arg_scaling(prox_factory, scal)(sigma)
expected_result = equiv_prox(x)
assert all_almost_equal(prox_x, expected_result, places=PLACES)
def test_proximal_quadratic_perturbation(nonneg_scalar, sigma):
"""Test for the proximal of quadratic perturbation."""
sigma = float(sigma)
space = odl.uniform_discr(0, 1, 10)
lam = 1.2
prox_factory = proximal_l2_squared(space, lam=lam)
# parameter for the quadratic perturbation, needs to be non-negative
a = nonneg_scalar
# Test without linear term
if a != 0:
with pytest.raises(ValueError):
# negative values not allowed
proximal_quadratic_perturbation(prox_factory, -a)
prox = proximal_quadratic_perturbation(prox_factory, a)(sigma)
x = noise_element(space)
expected_result = x / (2 * sigma * (lam + a) + 1)
assert all_almost_equal(prox(x), expected_result, places=PLACES)
# Test with linear term
u = noise_element(space)
prox = proximal_quadratic_perturbation(prox_factory, a, u)(sigma)
expected_result = (x - sigma * u) / (2 * sigma * (lam + a) + 1)
assert all_almost_equal(prox(x), expected_result, places=PLACES)
def test_proximal_composition(pos_scalar, sigma):
"""Test for proximal of composition with semi-orthogonal linear operator.
This test is for ``prox[f * L](x)``, where ``L`` is a linear operator such
that ``L * L.adjoint = mu * IdentityOperator``. Specifically, ``L`` is
taken to be ``scal * IdentityOperator``, since this is equivalent to
scaling of the argument.
"""
sigma = float(sigma)
space = odl.uniform_discr(0, 1, 10)
prox_factory = proximal_l2_squared(space)
# The semi-orthogonal linear operator
scal = pos_scalar
L = odl.ScalingOperator(space, scal)
mu = scal ** 2 # L = scal * I => L * L.adjoint = scal ** 2 * I
prox_factory_composition = proximal_composition(prox_factory, L, mu)
prox = prox_factory_composition(sigma)
assert isinstance(prox, odl.Operator)
x = space.element(np.arange(-5, 5))
prox_x = prox(x)
equiv_prox = proximal_arg_scaling(prox_factory, scal)(sigma)
expected_result = equiv_prox(x)
assert all_almost_equal(prox_x, expected_result, places=PLACES)
def test_proximal_quadratic_perturbation(nonneg_scalar, sigma):
"""Test for the proximal of quadratic perturbation."""
sigma = float(sigma)
space = odl.uniform_discr(0, 1, 10)
lam = 1.2
prox_factory = proximal_l2_squared(space, lam=lam)
# parameter for the quadratic perturbation, needs to be non-negative
a = nonneg_scalar
# Test without linear term
if a != 0:
with pytest.raises(ValueError):
# negative values not allowed
proximal_quadratic_perturbation(prox_factory, -a)
prox = proximal_quadratic_perturbation(prox_factory, a)(sigma)
x = noise_element(space)
expected_result = x / (2 * sigma * (lam + a) + 1)
assert all_almost_equal(prox(x), expected_result, places=PLACES)
# Test with linear term
u = noise_element(space)
prox = proximal_quadratic_perturbation(prox_factory, a, u)(sigma)
expected_result = (x - sigma * u) / (2 * sigma * (lam + a) + 1)
assert all_almost_equal(prox(x), expected_result, places=PLACES)
def test_proximal_translation(sigma):
"""Test for the proximal of a translation: ``prox[F(. - g)]``."""
sigma = float(sigma)
space = odl.uniform_discr(0, 1, 10)
lam = 1.2
prox_factory = proximal_l2_squared(space, lam=lam)
translation = noise_element(space)
prox = proximal_translation(prox_factory, translation)(sigma)
x = noise_element(space)
expected_result = ((x + 2 * sigma * lam * translation) /
(1 + 2 * sigma * lam))
assert all_almost_equal(prox(x), expected_result, places=PLACES)
def test_proximal_arg_scaling(scalar, sigma):
"""Test for the proximal of scaling: ``prox[F(. * a)]``."""
sigma = float(sigma)
space = odl.uniform_discr(0, 1, 10)
lam = 1.2
prox_factory = proximal_l2_squared(space, lam=lam)
scaling_param = scalar
prox = proximal_arg_scaling(prox_factory, scaling_param)(sigma)
x = noise_element(space)
# works for scaling_param == 0, too
expected_result = x / (2 * sigma * lam * scaling_param ** 2 + 1)
assert all_almost_equal(prox(x), expected_result, places=PLACES)
def test_proximal_arg_scaling(scalar, sigma):
"""Test for the proximal of scaling: ``prox[F(. * a)]``."""
sigma = float(sigma)
space = odl.uniform_discr(0, 1, 10)
lam = 1.2
prox_factory = proximal_l2_squared(space, lam=lam)
scaling_param = scalar
prox = proximal_arg_scaling(prox_factory, scaling_param)(sigma)
x = noise_element(space)
# works for scaling_param == 0, too
expected_result = x / (2 * sigma * lam * scaling_param ** 2 + 1)
assert all_almost_equal(prox(x), expected_result, places=PLACES)
def test_proximal_translation(sigma):
"""Test for the proximal of a translation: ``prox[F(. - g)]``."""
sigma = float(sigma)
space = odl.uniform_discr(0, 1, 10)
lam = 1.2
prox_factory = proximal_l2_squared(space, lam=lam)
translation = noise_element(space)
prox = proximal_translation(prox_factory, translation)(sigma)
x = noise_element(space)
expected_result = ((x + 2 * sigma * lam * translation) /
(1 + 2 * sigma * lam))
assert all_almost_equal(prox(x), expected_result, places=PLACES)