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_custom_funcs():
# Checking the standard 1-norm and standard inner product, just to
# see that the functions are handled correctly.
r2 = odl.Rn(2)
r2x = r2.element([1, -1])
r2y = r2.element([-2, 3])
# inner = -5, dist = 5, norms = (sqrt(2), sqrt(13))
r3 = odl.Rn(3)
r3x = r3.element([3, 4, 4])
r3y = r3.element([1, -2, 1])
# inner = -1, dist = 7, norms = (sqrt(41), sqrt(6))
pspace_2 = odl.ProductSpace(r2, r3, exponent=2.0)
x = pspace_2.element((r2x, r3x))
y = pspace_2.element((r2y, r3y))
pspace_custom = odl.ProductSpace(r2, r3, inner=custom_inner)
xc = pspace_custom.element((r2x, r3x))
yc = pspace_custom.element((r2y, r3y))
assert almost_equal(x.inner(y), xc.inner(yc))
pspace_1 = odl.ProductSpace(r2, r3, exponent=1.0)
x = pspace_1.element((r2x, r3x))
y = pspace_1.element((r2y, r3y))
pspace_custom = odl.ProductSpace(r2, r3, norm=custom_norm)
xc = pspace_custom.element((r2x, r3x))
assert almost_equal(x.norm(), xc.norm())
pspace_custom = odl.ProductSpace(r2, r3, dist=custom_dist)
xc = pspace_custom.element((r2x, r3x))
yc = pspace_custom.element((r2y, r3y))
assert almost_equal(x.dist(y), xc.dist(yc))
with pytest.raises(TypeError):
odl.ProductSpace(r2, r3, a=1) # extra keyword argument
with pytest.raises(ValueError):
odl.ProductSpace(r2, r3, norm=custom_norm, inner=custom_inner)
with pytest.raises(ValueError):
odl.ProductSpace(r2, r3, dist=custom_dist, inner=custom_inner)
with pytest.raises(ValueError):
odl.ProductSpace(r2, r3, norm=custom_norm, dist=custom_dist)
with pytest.raises(ValueError):
odl.ProductSpace(r2, r3, norm=custom_norm, exponent=1.0)
with pytest.raises(ValueError):
odl.ProductSpace(r2, r3, norm=custom_norm, weight=2.0)
with pytest.raises(ValueError):
odl.ProductSpace(r2, r3, dist=custom_dist, weight=2.0)
with pytest.raises(ValueError):
odl.ProductSpace(r2, r3, inner=custom_inner, weight=2.0)
def test_getitem_fancy():
r1 = odl.Rn(1)
r2 = odl.Rn(2)
r3 = odl.Rn(3)
H = odl.ProductSpace(r1, r2, r3)
assert H[[0, 2]] == odl.ProductSpace(r1, r3)
assert H[[0, 2]][0] is r1
assert H[[0, 2]][1] is r3
def test_vector_getitem_fancy():
H = odl.ProductSpace(odl.Rn(1), odl.Rn(2), odl.Rn(3))
x1 = H[0].element([0])
x2 = H[1].element([1, 2])
x3 = H[2].element([3, 4, 5])
x = H.element([x1, x2, x3])
assert x[[0, 2]].space == H[[0, 2]]
assert x[[0, 2]][0] is x1
assert x[[0, 2]][1] is x3
def test_getitem_slice():
r1 = odl.Rn(1)
r2 = odl.Rn(2)
r3 = odl.Rn(3)
H = odl.ProductSpace(r1, r2, r3)
assert H[:2] == odl.ProductSpace(r1, r2)
assert H[:2][0] is r1
assert H[:2][1] is r2
assert H[3:] == odl.ProductSpace(field=r1.field)
def test_getitem_single():
r1 = odl.Rn(1)
r2 = odl.Rn(2)
H = odl.ProductSpace(r1, r2)
assert H[-2] is r1
assert H[-1] is r2
assert H[0] is r1
assert H[1] is r2
with pytest.raises(IndexError):
H[-3]
H[2]
def test_vector_getitem_single():
H = odl.ProductSpace(odl.Rn(1), odl.Rn(2))
x1 = H[0].element([0])
x2 = H[1].element([1, 2])
x = H.element([x1, x2])
assert x[-2] is x1
assert x[-1] is x2
assert x[0] is x1
assert x[1] is x2
with pytest.raises(IndexError):
x[-3]
x[2]
def test_vector_equals():
H = odl.ProductSpace(odl.Rn(1), odl.Rn(2))
x = H.element([[0], [1, 2]])
assert x != 0 # test == not always true
assert x == x
x_2 = H.element([[0], [1, 2]])
assert x == x_2
x_3 = H.element([[3], [1, 2]])
assert x != x_3
x_4 = H.element([[0], [1, 3]])
assert x != x_4
def test_metric():
H = odl.Rn(2)
v11 = H.element([1, 2])
v12 = H.element([5, 3])
v21 = H.element([1, 2])
v22 = H.element([8, 9])
# 1-norm
HxH = odl.ProductSpace(H, H, exponent=1.0)
w1 = HxH.element([v11, v12])
w2 = HxH.element([v21, v22])
assert almost_equal(HxH.dist(w1, w2), H.dist(v11, v21) + H.dist(v12, v22))
# 2-norm
HxH = odl.ProductSpace(H, H, exponent=2.0)
w1 = HxH.element([v11, v12])
w2 = HxH.element([v21, v22])
assert almost_equal(HxH.dist(w1, w2),
(H.dist(v11, v21)**2 + H.dist(v12, v22)**2)**(1 / 2.0))
# inf norm
HxH = odl.ProductSpace(H, H, exponent=float('inf'))
w1 = HxH.element([v11, v12])
w2 = HxH.element([v21, v22])
assert almost_equal(HxH.dist(w1, w2),
max(H.dist(v11, v21), H.dist(v12, v22)))
def test_pspace_op_weighted_init():
r3 = odl.Rn(3)
ran = odl.ProductSpace(r3, 2, weight=[1, 2])
I = odl.IdentityOperator(r3)
with pytest.raises(NotImplementedError):
odl.ProductSpaceOperator([[I], [0]], range=ran)
def test_comp_proj_indices():
r3 = odl.Rn(3)
r33 = odl.ProductSpace(r3, 3)
x = r33.element([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
proj = odl.ComponentProjection(r33, [0, 2])
assert x[[0, 2]] == proj(x)
assert x[[0, 2]] == proj(x, out=proj.range.element())
