def test_pointwise_inner_init_properties():
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 3, exponent=2)
# Make sure the code runs and test the properties
pwinner = PointwiseInner(vfspace, vfspace.one())
assert pwinner.base_space == fspace
assert all_equal(pwinner.weights, [1, 1, 1])
assert not pwinner.is_weighted
repr(pwinner)
pwinner = PointwiseInner(vfspace, vfspace.one(), weight=[1, 2, 3])
assert all_equal(pwinner.weights, [1, 2, 3])
assert pwinner.is_weighted
# Bad input
with pytest.raises(TypeError):
PointwiseInner(odl.Rn(3), odl.Rn(3).one()) # No power space
# TODO: Does not raise currently, although bad_vecfield not in vfspace!
"""
bad_vecfield = ProductSpace(fspace, 3, exponent=1).one()
with pytest.raises(TypeError):
PointwiseInner(vfspace, bad_vecfield)
"""
with pytest.raises(ValueError):
PointwiseInner(vfspace, vfspace.one(), weight=-1) # < 0 not allowed
with pytest.raises(ValueError):
PointwiseInner(vfspace, vfspace.one(), weight=[1, 0, 1]) # 0 invalid
def test_pointwise_inner_adjoint():
# 1d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2), dtype=complex)
vfspace = ProductSpace(fspace, 1)
array = np.array([[[-1, -3], [2, 0]]])
pwinner = PointwiseInner(vfspace, vecfield=array)
testarr = np.array([[1 + 1j, 2], [3, 4 - 2j]])
true_inner_adj = testarr[None, :, :] * array
testfunc = fspace.element(testarr)
testfunc_pwinner_adj = pwinner.adjoint(testfunc)
assert all_almost_equal(testfunc_pwinner_adj,
true_inner_adj.reshape([1, -1]))
out = vfspace.element()
pwinner.adjoint(testfunc, out=out)
assert all_almost_equal(out, true_inner_adj.reshape([1, -1]))
# 3d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2), dtype=complex)
vfspace = ProductSpace(fspace, 3)
array = np.array([[[-1 - 1j, -3], [2, 2j]], [[-1j, 0], [0, 1]],
[[-1, 1 + 2j], [1, 1]]])
pwinner = PointwiseInner(vfspace, vecfield=array)
testarr = np.array([[1 + 1j, 2], [3, 4 - 2j]])
true_inner_adj = testarr[None, :, :] * array
testfunc = fspace.element(testarr)
testfunc_pwinner_adj = pwinner.adjoint(testfunc)
assert all_almost_equal(testfunc_pwinner_adj,
true_inner_adj.reshape([3, -1]))
out = vfspace.element()
pwinner.adjoint(testfunc, out=out)
assert all_almost_equal(out, true_inner_adj.reshape([3, -1]))
def test_pointwise_inner_adjoint():
# 1d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2), dtype=complex)
vfspace = ProductSpace(fspace, 1)
array = np.array([[[-1, -3],
[2, 0]]])
pwinner = PointwiseInner(vfspace, vecfield=array)
testarr = np.array([[1 + 1j, 2],
[3, 4 - 2j]])
true_inner_adj = testarr[None, :, :] * array
testfunc = fspace.element(testarr)
testfunc_pwinner_adj = pwinner.adjoint(testfunc)
assert all_almost_equal(testfunc_pwinner_adj,
true_inner_adj.reshape([1, -1]))
out = vfspace.element()
pwinner.adjoint(testfunc, out=out)
assert all_almost_equal(out, true_inner_adj.reshape([1, -1]))
# 3d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2), dtype=complex)
vfspace = ProductSpace(fspace, 3)
array = np.array([[[-1 - 1j, -3],
[2, 2j]],
[[-1j, 0],
[0, 1]],
[[-1, 1 + 2j],
[1, 1]]])
pwinner = PointwiseInner(vfspace, vecfield=array)
testarr = np.array([[1 + 1j, 2],
[3, 4 - 2j]])
true_inner_adj = testarr[None, :, :] * array
testfunc = fspace.element(testarr)
testfunc_pwinner_adj = pwinner.adjoint(testfunc)
assert all_almost_equal(testfunc_pwinner_adj,
true_inner_adj.reshape([3, -1]))
out = vfspace.element()
pwinner.adjoint(testfunc, out=out)
assert all_almost_equal(out, true_inner_adj.reshape([3, -1]))
def test_pointwise_inner_adjoint_weighted():
# Weighted product space only
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2), dtype=complex)
vfspace = ProductSpace(fspace, 3, weight=[2, 4, 6])
array = np.array([[[-1 - 1j, -3], [2, 2j]], [[-1j, 0], [0, 1]],
[[-1, 1 + 2j], [1, 1]]])
pwinner = PointwiseInner(vfspace, vecfield=array)
testarr = np.array([[1 + 1j, 2], [3, 4 - 2j]])
true_inner_adj = testarr[None, :, :] * array # same as unweighted case
testfunc = fspace.element(testarr)
testfunc_pwinner_adj = pwinner.adjoint(testfunc)
assert all_almost_equal(testfunc_pwinner_adj,
true_inner_adj.reshape([3, -1]))
out = vfspace.element()
pwinner.adjoint(testfunc, out=out)
assert all_almost_equal(out, true_inner_adj.reshape([3, -1]))
# Using different weighting in the inner product
pwinner = PointwiseInner(vfspace, vecfield=array, weight=[4, 8, 12])
testarr = np.array([[1 + 1j, 2], [3, 4 - 2j]])
true_inner_adj = 2 * testarr[None, :, :] * array # w / v = (2, 2, 2)
testfunc = fspace.element(testarr)
testfunc_pwinner_adj = pwinner.adjoint(testfunc)
assert all_almost_equal(testfunc_pwinner_adj,
true_inner_adj.reshape([3, -1]))
out = vfspace.element()
pwinner.adjoint(testfunc, out=out)
assert all_almost_equal(out, true_inner_adj.reshape([3, -1]))
def test_pointwise_inner_real():
# 1d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 1)
array = np.array([[[-1, -3], [2, 0]]])
pwinner = PointwiseInner(vfspace, vecfield=array)
testarr = np.array([[[1, 2], [3, 4]]])
true_inner = np.sum(testarr * array, axis=0)
func = vfspace.element(testarr)
func_pwinner = pwinner(func)
assert all_almost_equal(func_pwinner, true_inner.reshape(-1))
out = fspace.element()
pwinner(func, out=out)
assert all_almost_equal(out, true_inner.reshape(-1))
# 3d
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 3)
array = np.array([[[-1, -3], [2, 0]], [[0, 0], [0, 1]], [[-1, 1], [1, 1]]])
pwinner = PointwiseInner(vfspace, vecfield=array)
testarr = np.array([[[1, 2], [3, 4]], [[0, -1], [0, 1]], [[1, 1], [1, 1]]])
true_inner = np.sum(testarr * array, axis=0)
func = vfspace.element(testarr)
func_pwinner = pwinner(func)
assert all_almost_equal(func_pwinner, true_inner.reshape(-1))
out = fspace.element()
pwinner(func, out=out)
assert all_almost_equal(out, true_inner.reshape(-1))
def test_pointwise_inner_adjoint_weighted():
# Weighted product space only
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2), dtype=complex)
vfspace = ProductSpace(fspace, 3, weight=[2, 4, 6])
array = np.array([[[-1 - 1j, -3],
[2, 2j]],
[[-1j, 0],
[0, 1]],
[[-1, 1 + 2j],
[1, 1]]])
pwinner = PointwiseInner(vfspace, vecfield=array)
testarr = np.array([[1 + 1j, 2],
[3, 4 - 2j]])
true_inner_adj = testarr[None, :, :] * array # same as unweighted case
testfunc = fspace.element(testarr)
testfunc_pwinner_adj = pwinner.adjoint(testfunc)
assert all_almost_equal(testfunc_pwinner_adj,
true_inner_adj.reshape([3, -1]))
out = vfspace.element()
pwinner.adjoint(testfunc, out=out)
assert all_almost_equal(out, true_inner_adj.reshape([3, -1]))
# Using different weighting in the inner product
pwinner = PointwiseInner(vfspace, vecfield=array, weight=[4, 8, 12])
testarr = np.array([[1 + 1j, 2],
[3, 4 - 2j]])
true_inner_adj = 2 * testarr[None, :, :] * array # w / v = (2, 2, 2)
testfunc = fspace.element(testarr)
testfunc_pwinner_adj = pwinner.adjoint(testfunc)
assert all_almost_equal(testfunc_pwinner_adj,
true_inner_adj.reshape([3, -1]))
out = vfspace.element()
pwinner.adjoint(testfunc, out=out)
assert all_almost_equal(out, true_inner_adj.reshape([3, -1]))
def test_pointwise_inner_weighted():
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2))
vfspace = ProductSpace(fspace, 3)
array = np.array([[[-1, -3], [2, 0]], [[0, 0], [0, 1]], [[-1, 1], [1, 1]]])
weight = np.array([1.0, 2.0, 3.0])
pwinner = PointwiseInner(vfspace, vecfield=array, weight=weight)
testarr = np.array([[[1, 2], [3, 4]], [[0, -1], [0, 1]], [[1, 1], [1, 1]]])
true_inner = np.sum(weight[:, None, None] * testarr * array, axis=0)
func = vfspace.element(testarr)
func_pwinner = pwinner(func)
assert all_almost_equal(func_pwinner, true_inner.reshape(-1))
out = fspace.element()
pwinner(func, out=out)
assert all_almost_equal(out, true_inner.reshape(-1))
def test_pointwise_inner_complex():
fspace = odl.uniform_discr([0, 0], [1, 1], (2, 2), dtype=complex)
vfspace = ProductSpace(fspace, 3)
array = np.array([[[-1 - 1j, -3], [2, 2j]], [[-1j, 0], [0, 1]],
[[-1, 1 + 2j], [1, 1]]])
pwinner = PointwiseInner(vfspace, vecfield=array)
testarr = np.array([[[1 + 1j, 2], [3, 4 - 2j]], [[0, -1], [0, 1]],
[[1j, 1j], [1j, 1j]]])
true_inner = np.sum(testarr * array.conj(), axis=0)
func = vfspace.element(testarr)
func_pwinner = pwinner(func)
assert all_almost_equal(func_pwinner, true_inner.reshape(-1))
out = fspace.element()
pwinner(func, out=out)
assert all_almost_equal(out, true_inner.reshape(-1))
