def test_pointwise_norm_real(exponent):
# 1d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 1)
pwnorm = PointwiseNorm(vfspace, exponent)
testarr = np.array([[[1, 2], [3, 4]]])
true_norm = np.linalg.norm(testarr, ord=exponent, axis=0)
func = vfspace.element(testarr)
func_pwnorm = pwnorm(func)
assert all_almost_equal(func_pwnorm, true_norm.reshape(-1))
out = fspace.element()
pwnorm(func, out=out)
assert all_almost_equal(out, true_norm.reshape(-1))
# 3d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 3)
pwnorm = PointwiseNorm(vfspace, exponent)
testarr = np.array([[[1, 2], [3, 4]], [[0, -1], [0, 1]], [[1, 1], [1, 1]]])
true_norm = np.linalg.norm(testarr, ord=exponent, axis=0)
func = vfspace.element(testarr)
func_pwnorm = pwnorm(func)
assert all_almost_equal(func_pwnorm, true_norm.reshape(-1))
out = fspace.element()
pwnorm(func, out=out)
assert all_almost_equal(out, true_norm.reshape(-1))
def test_pointwise_norm_init_properties():
# 1d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 1, exponent=1)
# Make sure the code runs and test the properties
pwnorm = PointwiseNorm(vfspace)
assert pwnorm.base_space == fspace
assert all_equal(pwnorm.weights, [1])
assert not pwnorm.is_weighted
assert pwnorm.exponent == 1.0
repr(pwnorm)
pwnorm = PointwiseNorm(vfspace, exponent=2)
assert pwnorm.exponent == 2
pwnorm = PointwiseNorm(vfspace, weighting=2)
assert all_equal(pwnorm.weights, [2])
assert pwnorm.is_weighted
# 3d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 3, exponent=1)
# Make sure the code runs and test the properties
pwnorm = PointwiseNorm(vfspace)
assert pwnorm.base_space == fspace
assert all_equal(pwnorm.weights, [1, 1, 1])
assert not pwnorm.is_weighted
assert pwnorm.exponent == 1.0
repr(pwnorm)
pwnorm = PointwiseNorm(vfspace, exponent=2)
assert pwnorm.exponent == 2
pwnorm = PointwiseNorm(vfspace, weighting=[1, 2, 3])
assert all_equal(pwnorm.weights, [1, 2, 3])
assert pwnorm.is_weighted
# Bad input
with pytest.raises(TypeError):
PointwiseNorm(odl.rn(3)) # No power space
with pytest.raises(ValueError):
PointwiseNorm(vfspace, exponent=0.5) # < 1 not allowed
with pytest.raises(ValueError):
PointwiseNorm(vfspace, weighting=-1) # < 0 not allowed
with pytest.raises(ValueError):
PointwiseNorm(vfspace, weighting=[1, 0, 1]) # 0 invalid
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_weighted(exponent):
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 3)
weight = np.array([1.0, 2.0, 3.0])
pwnorm = PointwiseNorm(vfspace, exponent, weighting=weight)
testarr = np.array([[[1, 2], [3, 4]], [[0, -1], [0, 1]], [[1, 1], [1, 1]]])
if exponent in (1.0, float('inf')):
true_norm = np.linalg.norm(weight[:, None, None] * testarr,
ord=exponent,
axis=0)
else:
true_norm = np.linalg.norm(weight[:, None, None]**(1 / exponent) *
testarr,
ord=exponent,
axis=0)
func = vfspace.element(testarr)
func_pwnorm = pwnorm(func)
assert all_almost_equal(func_pwnorm, true_norm.reshape(-1))
out = fspace.element()
pwnorm(func, out=out)
assert all_almost_equal(out, true_norm.reshape(-1))
def test_pointwise_norm_complex(exponent):
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2), dtype=complex)
vfspace = ProductSpace(fspace, 3)
pwnorm = PointwiseNorm(vfspace, exponent)
testarr = np.array([[[1 + 1j, 2], [3, 4 - 2j]], [[0, -1], [0, 1]],
[[1j, 1j], [1j, 1j]]])
true_norm = np.linalg.norm(testarr, ord=exponent, axis=0)
func = vfspace.element(testarr)
func_pwnorm = pwnorm(func)
assert all_almost_equal(func_pwnorm, true_norm)
out = fspace.element()
pwnorm(func, out=out)
assert all_almost_equal(out, true_norm)
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)))
