def test_laplacian(space, padding):
"""Discretized spatial laplacian operator."""
# Invalid space
with pytest.raises(TypeError):
Laplacian(range=odl.rn(1))
if isinstance(padding, tuple):
pad_mode, pad_const = padding
else:
pad_mode, pad_const = padding, 0
if pad_mode in ('order1', 'order2'):
return # these pad modes not supported for laplacian
# Operator instance
lap = Laplacian(space, pad_mode=pad_mode, pad_const=pad_const)
# Apply operator
dom_vec = noise_element(space)
div_dom_vec = lap(dom_vec)
# computation of divergence with helper function
expected_result = np.zeros(space.shape)
for axis, dx in enumerate(space.cell_sides):
diff_f = finite_diff(dom_vec.asarray(),
axis=axis,
dx=dx**2,
method='forward',
pad_mode=pad_mode,
pad_const=pad_const)
diff_b = finite_diff(dom_vec.asarray(),
axis=axis,
dx=dx**2,
method='backward',
pad_mode=pad_mode,
pad_const=pad_const)
expected_result += diff_f - diff_b
assert all_almost_equal(expected_result, div_dom_vec.asarray())
# Adjoint operator
derivative = lap.derivative()
deriv_lap_dom_vec = derivative(dom_vec)
ran_vec = noise_element(lap.range)
adj_lap_ran_vec = derivative.adjoint(ran_vec)
# Adjoint condition
lhs = ran_vec.inner(deriv_lap_dom_vec)
rhs = dom_vec.inner(adj_lap_ran_vec)
# Check not to use trivial data
assert lhs != 0
assert rhs != 0
assert almost_equal(lhs, rhs, places=4)
def test_laplacian(impl, padding):
"""Discretized spatial laplacian operator."""
# Invalid space
with pytest.raises(TypeError):
Divergence(range=odl.Rn(1))
if isinstance(padding, tuple):
padding_method, padding_value = padding
else:
padding_method, padding_value = padding, None
# DiscreteLp
space = odl.uniform_discr([0, 0], [1, 1], DATA_2D.shape, impl=impl)
# Operator instance
lap = Laplacian(space,
padding_method=padding_method,
padding_value=padding_value)
# Apply operator
dom_vec = lap.domain.element(DATA_2D)
div_dom_vec = lap(dom_vec)
# computation of divergence with helper function
dx0, dx1 = space.cell_sides
expected_result = np.zeros(space.shape)
for axis, dx in enumerate(space.cell_sides):
diff_f = finite_diff(dom_vec.asarray(), axis=axis, dx=dx ** 2,
method='forward',
padding_method=padding_method,
padding_value=padding_value)
diff_b = finite_diff(dom_vec.asarray(), axis=axis, dx=dx ** 2,
method='backward',
padding_method=padding_method,
padding_value=padding_value)
expected_result += diff_f - diff_b
assert all_almost_equal(expected_result, div_dom_vec.asarray())
# Adjoint operator
derivative = lap.derivative()
deriv_lap_dom_vec = derivative(dom_vec)
ran_vec = lap.range.element(DATA_2D ** 2)
adj_lap_ran_vec = derivative.adjoint(ran_vec)
# Adjoint condition
lhs = ran_vec.inner(deriv_lap_dom_vec)
rhs = dom_vec.inner(adj_lap_ran_vec)
# Check not to use trivial data
assert lhs != 0
assert rhs != 0
assert almost_equal(lhs, rhs)
def test_laplacian(space, padding):
"""Discretized spatial laplacian operator."""
# Invalid space
with pytest.raises(TypeError):
Laplacian(range=odl.rn(1))
if isinstance(padding, tuple):
pad_mode, pad_const = padding
else:
pad_mode, pad_const = padding, 0
if pad_mode in ('order1', 'order2'):
return # these pad modes not supported for laplacian
# Operator instance
lap = Laplacian(space, pad_mode=pad_mode, pad_const=pad_const)
# Apply operator
dom_vec = noise_element(space)
div_dom_vec = lap(dom_vec)
# computation of divergence with helper function
expected_result = np.zeros(space.shape)
for axis, dx in enumerate(space.cell_sides):
diff_f = finite_diff(dom_vec.asarray(), axis=axis, dx=dx ** 2,
method='forward', pad_mode=pad_mode,
pad_const=pad_const)
diff_b = finite_diff(dom_vec.asarray(), axis=axis, dx=dx ** 2,
method='backward', pad_mode=pad_mode,
pad_const=pad_const)
expected_result += diff_f - diff_b
assert all_almost_equal(expected_result, div_dom_vec.asarray())
# Adjoint operator
derivative = lap.derivative()
deriv_lap_dom_vec = derivative(dom_vec)
ran_vec = noise_element(lap.range)
adj_lap_ran_vec = derivative.adjoint(ran_vec)
# Adjoint condition
lhs = ran_vec.inner(deriv_lap_dom_vec)
rhs = dom_vec.inner(adj_lap_ran_vec)
# Check not to use trivial data
assert lhs != 0
assert rhs != 0
assert almost_equal(lhs, rhs, places=4)
def test_laplacian_init():
"""Check initialization of ``Laplacian``."""
space = odl.uniform_discr([0, 0], [1, 1], (4, 5))
op = Laplacian(space)
assert repr(op) != ''
op = Laplacian(space, range=space.astype('float32'))
assert repr(op) != ''
op = Laplacian(space, pad_const=1)
assert repr(op) != ''
op = Laplacian(space, pad_mode='order0')
assert repr(op) != ''
with pytest.raises(TypeError):
Laplacian(odl.rn(1))