def test_pointwise_norm_gradient_real(exponent):
# The operator is not differentiable for exponent 'inf'
if exponent == float('inf'):
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 1)
pwnorm = PointwiseNorm(vfspace, exponent)
point = vfspace.one()
with pytest.raises(NotImplementedError):
pwnorm.derivative(point)
return
# 1d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 1)
pwnorm = PointwiseNorm(vfspace, exponent)
point = noise_element(vfspace)
direction = noise_element(vfspace)
# Computing expected result
tmp = pwnorm(point).ufuncs.power(1 - exponent)
v_field = vfspace.element()
for i in range(len(v_field)):
v_field[i] = tmp * point[i] * np.abs(point[i])**(exponent - 2)
pwinner = odl.PointwiseInner(vfspace, v_field)
expected_result = pwinner(direction)
func_pwnorm = pwnorm.derivative(point)
assert all_almost_equal(func_pwnorm(direction), expected_result)
# 3d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 3)
pwnorm = PointwiseNorm(vfspace, exponent)
point = noise_element(vfspace)
direction = noise_element(vfspace)
# Computing expected result
tmp = pwnorm(point).ufuncs.power(1 - exponent)
v_field = vfspace.element()
for i in range(len(v_field)):
v_field[i] = tmp * point[i] * np.abs(point[i])**(exponent - 2)
pwinner = odl.PointwiseInner(vfspace, v_field)
expected_result = pwinner(direction)
func_pwnorm = pwnorm.derivative(point)
assert all_almost_equal(func_pwnorm(direction), expected_result)
def test_pointwise_norm_gradient_real_with_zeros(exponent):
# The gradient is only well-defined in points with zeros if the exponent is
# >= 2 and < inf
if exponent < 2 or exponent == float('inf'):
pytest.skip('differential of operator has singularity for this '
'exponent')
# 1d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 1)
pwnorm = PointwiseNorm(vfspace, exponent)
test_point = np.array([[[0, 0], # This makes the point singular for p < 2
[1, 2]]])
test_direction = np.array([[[1, 2],
[4, 5]]])
point = vfspace.element(test_point)
direction = vfspace.element(test_direction)
func_pwnorm = pwnorm.derivative(point)
assert not np.any(np.isnan(func_pwnorm(direction)))
# 3d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 3)
pwnorm = PointwiseNorm(vfspace, exponent)
test_point = np.array([[[0, 0], # This makes the point singular for p < 2
[1, 2]],
[[3, 4],
[0, 0]], # This makes the point singular for p < 2
[[5, 6],
[7, 8]]])
test_direction = np.array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]],
[[8, 9],
[0, 1]]])
point = vfspace.element(test_point)
direction = vfspace.element(test_direction)
func_pwnorm = pwnorm.derivative(point)
assert not np.any(np.isnan(func_pwnorm(direction)))