def test_primal_dual_with_li():
"""Test for the forward-backward solver with infimal convolution.
The test is done by minimizing the functional ``(g @ l)(x)``, where
``(g @ l)(x) = inf_y { g(y) + l(x - y) }``,
g is the indicator function on [-3, -1], and l(x) = 1/2||x||_2^2.
The optimal solution to this problem is given by x in [-3, -1].
"""
# Parameter values for the box constraint
upper_lim = -1
lower_lim = -3
space = odl.rn(1)
lin_ops = [odl.IdentityOperator(space)]
g = [odl.solvers.IndicatorBox(space, lower=lower_lim, upper=upper_lim)]
f = odl.solvers.ZeroFunctional(space)
l = [odl.solvers.L2NormSquared(space)]
# Centering around a point further away from [-3,-1].
x = space.element(10)
douglas_rachford_pd(x, f, g, lin_ops, tau=0.5, sigma=[1.0], niter=20, l=l)
assert lower_lim - 10**-LOW_ACCURACY <= float(x)
assert float(x) <= upper_lim + 10**-LOW_ACCURACY
def test_primal_dual_l1():
"""Verify that the correct value is returned for l1 dist optimization.
Solves the optimization problem
min_x ||x - data_1||_1 + 0.5 ||x - data_2||_1
which has optimum value data_1.
"""
# Define the space
space = odl.rn(5)
# Operator
L = [odl.IdentityOperator(space)]
# Data
data_1 = odl.util.testutils.noise_element(space)
data_2 = odl.util.testutils.noise_element(space)
# Proximals
f = odl.solvers.L1Norm(space).translated(data_1)
g = [0.5 * odl.solvers.L1Norm(space).translated(data_2)]
# Solve with f term dominating
x = space.zero()
douglas_rachford_pd(x, f, g, L, tau=3.0, sigma=[1.0], niter=10)
assert all_almost_equal(x, data_1, places=2)
def test_primal_dual_l1():
"""Verify that the correct value is returned for l1 dist optimization.
Solves the optimization problem
min_x ||x - data_1||_1 + 0.5 ||x - data_2||_1
which has optimum value data_1.
"""
# Define the space
space = odl.rn(5)
# Operator
L = [odl.IdentityOperator(space)]
# Data
data_1 = odl.util.testutils.noise_element(space)
data_2 = odl.util.testutils.noise_element(space)
# Proximals
f = odl.solvers.L1Norm(space).translated(data_1)
g = [0.5 * odl.solvers.L1Norm(space).translated(data_2)]
# Solve with f term dominating
x = space.zero()
douglas_rachford_pd(x, f, g, L, tau=3.0, sigma=[1.0], niter=10)
assert all_almost_equal(x, data_1, places=2)
def test_primal_dual_with_li():
"""Test for the forward-backward solver with infimal convolution.
The test is done by minimizing the functional ``(g @ l)(x)``, where
``(g @ l)(x) = inf_y { g(y) + l(x - y) }``,
g is the indicator function on [-3, -1], and l(x) = 1/2||x||_2^2.
The optimal solution to this problem is given by x in [-3, -1].
"""
# Parameter values for the box constraint
upper_lim = -1
lower_lim = -3
space = odl.rn(1)
lin_ops = [odl.IdentityOperator(space)]
g = [odl.solvers.IndicatorBox(space, lower=lower_lim, upper=upper_lim)]
f = odl.solvers.ZeroFunctional(space)
l = [odl.solvers.L2NormSquared(space)]
# Centering around a point further away from [-3,-1].
x = space.element(10)
douglas_rachford_pd(x, f, g, lin_ops, tau=0.5, sigma=[1.0], niter=20, l=l)
assert lower_lim - 10 ** -LOW_ACCURACY <= float(x)
assert float(x) <= upper_lim + 10 ** -LOW_ACCURACY
def test_primal_dual_no_operator():
"""Verify that the correct value is returned when there is no operator.
Solves the optimization problem
min_x ||x - data_1||_1
which has optimum value data_1.
"""
# Define the space
space = odl.rn(5)
# Operator
L = []
# Data
data_1 = odl.util.testutils.noise_element(space)
# Proximals
f = odl.solvers.L1Norm(space).translated(data_1)
g = []
# Solve with f term dominating
x = space.zero()
douglas_rachford_pd(x, f, g, L, tau=3.0, sigma=[], niter=10)
assert all_almost_equal(x, data_1, ndigits=2)
def test_primal_dual_input_handling():
"""Test to see that input is handled correctly."""
space1 = odl.uniform_discr(0, 1, 10)
lin_ops = [odl.ZeroOperator(space1), odl.ZeroOperator(space1)]
g = [odl.solvers.ZeroFunctional(space1),
odl.solvers.ZeroFunctional(space1)]
f = odl.solvers.ZeroFunctional(space1)
# Check that the algorithm runs. With the above operators, the algorithm
# returns the input.
x0 = noise_element(space1)
x = x0.copy()
niter = 3
douglas_rachford_pd(x, f, g, lin_ops, tau=1.0,
sigma=[1.0, 1.0], niter=niter)
assert x == x0
# Testing that sizes needs to agree:
# Too few sigma_i:s
with pytest.raises(ValueError):
douglas_rachford_pd(x, f, g, lin_ops, tau=1.0,
sigma=[1.0], niter=niter)
# Too many operators
g_too_many = [odl.solvers.ZeroFunctional(space1),
odl.solvers.ZeroFunctional(space1),
odl.solvers.ZeroFunctional(space1)]
with pytest.raises(ValueError):
douglas_rachford_pd(x, f, g_too_many, lin_ops,
tau=1.0, sigma=[1.0, 1.0], niter=niter)
# Test for correct space
space2 = odl.uniform_discr(1, 2, 10)
x = noise_element(space2)
with pytest.raises(ValueError):
douglas_rachford_pd(x, f, g, lin_ops, tau=1.0,
sigma=[1.0, 1.0], niter=niter)
def test_primal_dual_input_handling():
"""Test to see that input is handled correctly."""
space1 = odl.uniform_discr(0, 1, 10)
lin_ops = [odl.ZeroOperator(space1), odl.ZeroOperator(space1)]
g = [
odl.solvers.ZeroFunctional(space1),
odl.solvers.ZeroFunctional(space1)
]
f = odl.solvers.ZeroFunctional(space1)
# Check that the algorithm runs. With the above operators, the algorithm
# returns the input.
x0 = noise_element(space1)
x = x0.copy()
niter = 3
douglas_rachford_pd(x,
f,
g,
lin_ops,
tau=1.0,
sigma=[1.0, 1.0],
niter=niter)
assert x == x0
# Testing that sizes needs to agree:
# Too few sigma_i:s
with pytest.raises(ValueError):
douglas_rachford_pd(x,
f,
g,
lin_ops,
tau=1.0,
sigma=[1.0],
niter=niter)
# Too many operators
g_too_many = [
odl.solvers.ZeroFunctional(space1),
odl.solvers.ZeroFunctional(space1),
odl.solvers.ZeroFunctional(space1)
]
with pytest.raises(ValueError):
douglas_rachford_pd(x,
f,
g_too_many,
lin_ops,
tau=1.0,
sigma=[1.0, 1.0],
niter=niter)
# Test for correct space
space2 = odl.uniform_discr(1, 2, 10)
x = noise_element(space2)
with pytest.raises(ValueError):
douglas_rachford_pd(x,
f,
g,
lin_ops,
tau=1.0,
sigma=[1.0, 1.0],
niter=niter)
