def test_gradient_cuda():
"""Discretized spatial gradient operator using CUDA."""
# DiscreteLp Vector
discr_space = odl.uniform_discr([0, 0], [6, 2.5], DATA_2D.shape,
impl='cuda')
dom_vec = discr_space.element(DATA_2D)
# computation of gradient components with helper function
dx0, dx1 = discr_space.cell_sides
diff_0 = finite_diff(DATA_2D, axis=0, dx=dx0, padding_method='constant')
diff_1 = finite_diff(DATA_2D, axis=1, dx=dx1, padding_method='constant')
# gradient
grad = Gradient(discr_space)
grad_vec = grad(dom_vec)
assert len(grad_vec) == DATA_2D.ndim
assert all_equal(grad_vec[0].asarray(), diff_0)
assert all_equal(grad_vec[1].asarray(), diff_1)
# adjoint operator
ran_vec = grad.range.element([DATA_2D, DATA_2D ** 2])
adj_vec = grad.adjoint(ran_vec)
lhs = ran_vec.inner(grad_vec)
rhs = dom_vec.inner(adj_vec)
assert lhs != 0
assert rhs != 0
assert lhs == rhs
def test_gradient(space, method, padding):
"""Discretized spatial gradient operator."""
places = 2 if space.dtype == np.float32 else 4
with pytest.raises(TypeError):
Gradient(odl.rn(1), method=method)
if isinstance(padding, tuple):
pad_mode, pad_const = padding
else:
pad_mode, pad_const = padding, 0
# DiscreteLp Vector
dom_vec = noise_element(space)
dom_vec_arr = dom_vec.asarray()
# gradient
grad = Gradient(space, method=method,
pad_mode=pad_mode,
pad_const=pad_const)
grad_vec = grad(dom_vec)
assert len(grad_vec) == space.ndim
# computation of gradient components with helper function
for axis, dx in enumerate(space.cell_sides):
diff = finite_diff(dom_vec_arr, axis=axis, dx=dx, method=method,
pad_mode=pad_mode,
pad_const=pad_const)
assert all_almost_equal(grad_vec[axis].asarray(), diff)
# Test adjoint operator
derivative = grad.derivative()
ran_vec = noise_element(derivative.range)
deriv_grad_vec = derivative(dom_vec)
adj_grad_vec = derivative.adjoint(ran_vec)
lhs = ran_vec.inner(deriv_grad_vec)
rhs = dom_vec.inner(adj_grad_vec)
# Check not to use trivial data
assert lhs != 0
assert rhs != 0
assert almost_equal(lhs, rhs, places=places)
# higher dimensional arrays
lin_size = 3
for ndim in [1, 3, 6]:
# DiscreteLpElement
space = odl.uniform_discr([0.] * ndim, [1.] * ndim, [lin_size] * ndim)
dom_vec = odl.phantom.cuboid(space, [0.2] * ndim, [0.8] * ndim)
# gradient
grad = Gradient(space, method=method,
pad_mode=pad_mode,
pad_const=pad_const)
grad(dom_vec)
def test_gradient_init():
"""Check initialization of ``Gradient``."""
space = odl.uniform_discr([0, 0], [1, 1], (4, 5))
vspace = space**2
op = Gradient(space)
assert repr(op) != ''
op = Gradient(range=vspace)
assert repr(op) != ''
op = Gradient(space, range=space.astype('float32')**2)
assert repr(op) != ''
op = Gradient(space, method='central')
assert repr(op) != ''
op = Gradient(space, pad_const=1)
assert repr(op) != ''
op = Gradient(space, pad_mode='order1')
assert repr(op) != ''
with pytest.raises(TypeError):
Gradient(odl.rn(1))
with pytest.raises(TypeError):
Gradient(space, range=space)
with pytest.raises(ValueError):
Gradient(space, range=space**3)
def _reconstruct(self, observation, out):
observation = self.observation_space.element(observation)
out[:] = self.x0
gradient = Gradient(self.op.domain)
L = [self.op, gradient]
f = ZeroFunctional(self.op.domain)
l2_norm = 0.5 * L2NormSquared(self.op.range).translated(observation)
l12_norm = self.lam * GroupL1Norm(gradient.range)
g = [l2_norm, l12_norm]
op_norm = power_method_opnorm(self.op, maxiter=20)
gradient_norm = power_method_opnorm(gradient, maxiter=20)
sigma_ray_trafo = 45.0 / op_norm**2
sigma_gradient = 45.0 / gradient_norm**2
sigma = [sigma_ray_trafo, sigma_gradient]
h = ZeroFunctional(self.op.domain)
forward_backward_pd(out,
f,
g,
L,
h,
self.tau,
sigma,
self.niter,
callback=self.callback)
return out
def _reconstruct(self, observation, out):
observation = self.observation_space.element(observation)
out_ = out
if out not in self.reco_space:
out_ = self.reco_space.zero()
out_[:] = self.x0
gradient = Gradient(self.op.domain)
L = BroadcastOperator(self.op, gradient)
f = ZeroFunctional(self.op.domain)
l2_norm = L2NormSquared(self.op.range).translated(observation)
l1_norm = self.lam * L1Norm(gradient.range)
g = SeparableSum(l2_norm, l1_norm)
op_norm = 1.1 * power_method_opnorm(L, maxiter=20)
sigma = self.tau * op_norm**2
admm.admm_linearized(out_,
f,
g,
L,
self.tau,
sigma,
self.niter,
callback=self.callback)
if out not in self.reco_space:
out[:] = out_
return out
def test_gradient_cpu():
"""Discretized spatial gradient operator."""
with pytest.raises(TypeError):
Gradient(odl.Rn(1))
# DiscreteLp Vector
discr_space = odl.uniform_discr([0, 0], [6, 2.5], DATA_2D.shape)
dom_vec = discr_space.element(DATA_2D)
# computation of gradient components with helper function
dx0, dx1 = discr_space.cell_sides
diff_0 = finite_diff(DATA_2D, axis=0, dx=dx0, method='forward',
padding_method='constant')
diff_1 = finite_diff(DATA_2D, axis=1, dx=dx1, method='forward',
padding_method='constant')
# gradient
grad = Gradient(discr_space)
grad_vec = grad(dom_vec)
assert len(grad_vec) == DATA_2D.ndim
assert all_equal(grad_vec[0].asarray(), diff_0)
assert all_equal(grad_vec[1].asarray(), diff_1)
# Test adjoint operator
ran_vec = grad.range.element([DATA_2D, DATA_2D ** 2])
adj_vec = grad.adjoint(ran_vec)
lhs = ran_vec.inner(grad_vec)
rhs = dom_vec.inner(adj_vec)
# Check not to use trivial data
assert lhs != 0
assert rhs != 0
assert lhs == rhs
# higher dimensional arrays
lin_size = 3
for ndim in range(1, 6):
# DiscreteLp Vector
discr_space = odl.uniform_discr([0.] * ndim, [lin_size] * ndim,
[lin_size] * ndim)
dom_vec = discr_space.element(ndvolume(lin_size, ndim))
# gradient
grad = Gradient(discr_space)
grad(dom_vec)
def test_gradient(space, method, padding):
"""Discretized spatial gradient operator."""
places = 2 if space.dtype == np.float32 else 4
with pytest.raises(TypeError):
Gradient(odl.rn(1), method=method)
if isinstance(padding, tuple):
pad_mode, pad_const = padding
else:
pad_mode, pad_const = padding, 0
# DiscreteLp Vector
dom_vec = noise_element(space)
dom_vec_arr = dom_vec.asarray()
# gradient
grad = Gradient(space,
method=method,
pad_mode=pad_mode,
pad_const=pad_const)
grad_vec = grad(dom_vec)
assert len(grad_vec) == space.ndim
# computation of gradient components with helper function
for axis, dx in enumerate(space.cell_sides):
diff = finite_diff(dom_vec_arr,
axis=axis,
dx=dx,
method=method,
pad_mode=pad_mode,
pad_const=pad_const)
assert all_almost_equal(grad_vec[axis].asarray(), diff)
# Test adjoint operator
derivative = grad.derivative()
ran_vec = noise_element(derivative.range)
deriv_grad_vec = derivative(dom_vec)
adj_grad_vec = derivative.adjoint(ran_vec)
lhs = ran_vec.inner(deriv_grad_vec)
rhs = dom_vec.inner(adj_grad_vec)
# Check not to use trivial data
assert lhs != 0
assert rhs != 0
assert almost_equal(lhs, rhs, places=places)
# Higher-dimensional arrays
lin_size = 3
for ndim in [1, 3, 6]:
space = odl.uniform_discr([0.] * ndim, [1.] * ndim, [lin_size] * ndim)
dom_vec = odl.phantom.cuboid(space, [0.2] * ndim, [0.8] * ndim)
grad = Gradient(space,
method=method,
pad_mode=pad_mode,
pad_const=pad_const)
grad(dom_vec)
def test_gradient(method, impl, padding):
"""Discretized spatial gradient operator."""
with pytest.raises(TypeError):
Gradient(odl.Rn(1), method=method)
if isinstance(padding, tuple):
padding_method, padding_value = padding
else:
padding_method, padding_value = padding, None
# DiscreteLp Vector
discr_space = odl.uniform_discr([0, 0], [1, 1], DATA_2D.shape, impl=impl)
dom_vec = discr_space.element(DATA_2D)
# computation of gradient components with helper function
dx0, dx1 = discr_space.cell_sides
diff_0 = finite_diff(DATA_2D, axis=0, dx=dx0, method=method,
padding_method=padding_method,
padding_value=padding_value)
diff_1 = finite_diff(DATA_2D, axis=1, dx=dx1, method=method,
padding_method=padding_method,
padding_value=padding_value)
# gradient
grad = Gradient(discr_space, method=method,
padding_method=padding_method,
padding_value=padding_value)
grad_vec = grad(dom_vec)
assert len(grad_vec) == DATA_2D.ndim
assert all_almost_equal(grad_vec[0].asarray(), diff_0)
assert all_almost_equal(grad_vec[1].asarray(), diff_1)
# Test adjoint operator
derivative = grad.derivative()
ran_vec = derivative.range.element([DATA_2D, DATA_2D ** 2])
deriv_grad_vec = derivative(dom_vec)
adj_grad_vec = derivative.adjoint(ran_vec)
lhs = ran_vec.inner(deriv_grad_vec)
rhs = dom_vec.inner(adj_grad_vec)
# Check not to use trivial data
assert lhs != 0
assert rhs != 0
assert almost_equal(lhs, rhs)
# higher dimensional arrays
lin_size = 3
for ndim in [1, 3, 6]:
# DiscreteLp Vector
space = odl.uniform_discr([0.] * ndim, [1.] * ndim, [lin_size] * ndim)
dom_vec = odl.phantom.cuboid(space, [0.2] * ndim, [0.8] * ndim)
# gradient
grad = Gradient(space, method=method,
padding_method=padding_method,
padding_value=padding_value)
grad(dom_vec)
def __init__(self, domain, diagonal_neighbour=False):
"""Initialize a new instance.
Parameters
----------
domain : `LinearSpace` or `Field`, optional
Set of elements on which the operator can be applied.
"""
self.diagonal_neighbour = diagonal_neighbour
if not isinstance(domain, DiscreteLp):
raise NotImplementedError('Onlt works for `uniform_discr`')
super().__init__(domain=domain, range=domain)
self.shape_param = domain.shape
self.elem_len = np.prod(self.shape_param)
self.forward_grad = Gradient(domain=domain,
method='forward',
pad_mode='order0')
self.backward_grad = Gradient(domain=domain,
method='backward',
pad_mode='order0')
def _reconstruct(self, observation, out):
observation = self.observation_space.element(observation)
out[:] = self.x0
l2_norm = L2NormSquared(self.op.range)
discrepancy = l2_norm * (self.op - observation)
gradient = Gradient(self.op.domain)
l1_norm = GroupL1Norm(gradient.range)
smoothed_l1 = MoreauEnvelope(l1_norm, sigma=0.03)
regularizer = smoothed_l1 * gradient
f = discrepancy + self.lam * regularizer
opnorm = power_method_opnorm(self.op)
hessinv_estimate = ScalingOperator(self.op.domain, 1 / opnorm**2)
newton.bfgs_method(f,
out,
maxiter=self.niter,
hessinv_estimate=hessinv_estimate,
callback=self.callback)
return out
def _reconstruct(self, observation, out):
observation = self.observation_space.element(observation)
out[:] = self.x0
gradient = Gradient(self.op.domain)
L = BroadcastOperator(self.op, gradient)
f = ZeroFunctional(self.op.domain)
l2_norm = L2NormSquared(self.op.range).translated(observation)
l1_norm = self.lam * L1Norm(gradient.range)
g = [l2_norm, l1_norm]
tau, sigma = douglas_rachford.douglas_rachford_pd_stepsize(L)
douglas_rachford.douglas_rachford_pd(out,
f,
g,
L,
self.niter,
tau,
sigma,
callback=self.callback)
return out
def _reconstruct(self, observation, out):
observation = self.observation_space.element(observation)
out[:] = self.x0
gradient = Gradient(self.op.domain)
L = BroadcastOperator(self.op, gradient)
f = ZeroFunctional(self.op.domain)
l2_norm = L2NormSquared(self.op.range).translated(observation)
l1_norm = self.lam * L1Norm(gradient.range)
g = SeparableSum(l2_norm, l1_norm)
tau, sigma = primal_dual_hybrid_gradient.pdhg_stepsize(L)
primal_dual_hybrid_gradient.pdhg(out,
f,
g,
L,
self.niter,
tau,
sigma,
callback=self.callback)
return out