def test_dist(fn):
[xarr, yarr], [x, y] = example_vectors(fn, n=2)
correct_dist = np.linalg.norm(xarr - yarr)
assert almost_equal(fn.dist(x, y), correct_dist)
assert almost_equal(x.dist(y), correct_dist)
def test_const_norm(exponent):
rn = CudaRn(5)
xarr, x = example_vectors(rn)
constant = 1.5
weighting = CudaFnConstWeighting(constant, exponent=exponent)
factor = 1 if exponent == float('inf') else constant ** (1 / exponent)
true_norm = factor * np.linalg.norm(xarr, ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
weighting.norm(x)
else:
assert almost_equal(weighting.norm(x), true_norm)
# Same with free function
pnorm = odl.cu_weighted_norm(constant, exponent=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
pnorm(x)
else:
assert almost_equal(pnorm(x), true_norm)
def test_norm(fn):
xarr, x = example_vectors(fn)
correct_norm = np.linalg.norm(xarr)
assert almost_equal(fn.norm(x), correct_norm)
assert almost_equal(x.norm(), correct_norm)
def test_pnorm(exponent):
for fn in (Rn(3, exponent=exponent), Cn(3, exponent=exponent)):
xarr, x = _vectors(fn)
correct_norm = np.linalg.norm(xarr, ord=exponent)
assert almost_equal(fn.norm(x), correct_norm)
assert almost_equal(x.norm(), correct_norm)
def test_vector_dist(exponent):
rn = CudaRn(5)
[xarr, yarr], [x, y] = example_vectors(rn, n=2)
weight = _pos_vector(CudaRn(5))
weighting = CudaFnVectorWeighting(weight, exponent=exponent)
if exponent in (1.0, float('inf')):
true_dist = np.linalg.norm(weight.asarray() * (xarr - yarr),
ord=exponent)
else:
true_dist = np.linalg.norm(
weight.asarray() ** (1 / exponent) * (xarr - yarr), ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
weighting.dist(x, y)
else:
assert almost_equal(weighting.dist(x, y), true_dist)
# Same with free function
pdist = odl.cu_weighted_dist(weight, exponent=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
pdist(x, y)
else:
assert almost_equal(pdist(x, y), true_dist)
def test_norm(fn):
xarr, x = _vectors(fn)
correct_norm = np.linalg.norm(xarr)
assert almost_equal(fn.norm(x), correct_norm)
assert almost_equal(x.norm(), correct_norm)
def test_vector_norm(exponent):
rn = CudaRn(5)
xarr, x = example_vectors(rn)
weight = _pos_vector(CudaRn(5))
weighting = CudaFnVectorWeighting(weight, exponent=exponent)
if exponent in (1.0, float('inf')):
true_norm = np.linalg.norm(weight.asarray() * xarr, ord=exponent)
else:
true_norm = np.linalg.norm(weight.asarray() ** (1 / exponent) * xarr,
ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
weighting.norm(x)
else:
assert almost_equal(weighting.norm(x), true_norm)
# Same with free function
pnorm = odl.cu_weighted_norm(weight, exponent=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
pnorm(x)
else:
assert almost_equal(pnorm(x), true_norm)
def test_custom_dist(fn):
xarr, yarr, x, y = _vectors(fn, 2)
def dist(x, y):
return np.linalg.norm(x - y)
def other_dist(x, y):
return np.linalg.norm(x - y, ord=1)
w = FnCustomDist(dist)
w_same = FnCustomDist(dist)
w_other = FnCustomDist(other_dist)
assert w == w
assert w == w_same
assert w != w_other
with pytest.raises(NotImplementedError):
w.inner(x, y)
with pytest.raises(NotImplementedError):
w.norm(x)
true_dist = np.linalg.norm(xarr - yarr)
assert almost_equal(w.dist(x, y), true_dist)
assert almost_equal(w.dist(x, x), 0)
with pytest.raises(TypeError):
FnCustomDist(1)
def test_inner(fn):
xd = _element(fn)
yd = _element(fn)
correct_inner = np.vdot(yd, xd)
assert almost_equal(fn.inner(xd, yd), correct_inner)
assert almost_equal(xd.inner(yd), correct_inner)
def test_vector_inner():
rn = odl.CudaRn(5)
xarr, yarr, x, y = _vectors(rn, 2)
weight_vec = _pos_array(odl.Rn(5))
weight_elem = rn.element(weight_vec)
weighting_vec = CudaFnVectorWeighting(weight_vec)
weighting_elem = CudaFnVectorWeighting(weight_elem)
true_inner = np.vdot(yarr, xarr * weight_vec)
assert almost_equal(weighting_vec.inner(x, y), true_inner)
assert almost_equal(weighting_elem.inner(x, y), true_inner)
# Same with free function
inner_vec = odl.cu_weighted_inner(weight_vec)
inner_elem = odl.cu_weighted_inner(weight_elem)
assert almost_equal(inner_vec(x, y), true_inner)
assert almost_equal(inner_elem(x, y), true_inner)
# Exponent != 2 -> no inner product, should raise
with pytest.raises(NotImplementedError):
CudaFnVectorWeighting(weight_vec, exponent=1.0).inner(x, y)
def test_norm():
H = odl.Rn(2)
v1 = H.element([1, 2])
v2 = H.element([5, 3])
# 1-norm
HxH = odl.ProductSpace(H, H, ord=1.0)
w = HxH.element([v1, v2])
assert almost_equal(HxH.norm(w), H.norm(v1) + H.norm(v2))
# 2-norm
HxH = odl.ProductSpace(H, H, ord=2.0)
w = HxH.element([v1, v2])
assert almost_equal(
HxH.norm(w), (H.norm(v1) ** 2 + H.norm(v2) ** 2) ** (1 / 2.0))
# -inf norm
HxH = odl.ProductSpace(H, H, ord=-float('inf'))
w = HxH.element([v1, v2])
assert almost_equal(HxH.norm(w), min(H.norm(v1), H.norm(v2)))
# inf norm
HxH = odl.ProductSpace(H, H, ord=float('inf'))
w = HxH.element([v1, v2])
assert almost_equal(HxH.norm(w), max(H.norm(v1), H.norm(v2)))
# Custom norm
def my_norm(x):
return np.sum(x) # Same as 1-norm
HxH = odl.ProductSpace(H, H, prod_norm=my_norm)
w = HxH.element([v1, v2])
assert almost_equal(HxH.norm(w), H.norm(v1) + H.norm(v2))
def test_const_dist(exponent):
rn = odl.CudaRn(5)
xarr, yarr, x, y = _vectors(rn, n=2)
constant = 1.5
weighting = CudaFnConstWeighting(constant, exponent=exponent)
factor = 1 if exponent == float('inf') else constant ** (1 / exponent)
true_dist = factor * np.linalg.norm(xarr - yarr, ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
weighting.dist(x, y)
else:
assert almost_equal(weighting.dist(x, y), true_dist)
# Same with free function
pdist = odl.cu_weighted_dist(constant, exponent=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
pdist(x, y)
else:
assert almost_equal(pdist(x, y), true_dist)
def test_quadratic_form(space):
"""Test the quadratic form functional."""
operator = odl.IdentityOperator(space)
vector = space.one()
constant = 0.363
func = odl.solvers.QuadraticForm(operator, vector, constant)
x = noise_element(space)
# Checking that values is stored correctly
assert func.operator == operator
assert func.vector == vector
assert func.constant == constant
# Evaluation of the functional
expected_result = x.inner(operator(x)) + vector.inner(x) + constant
assert almost_equal(func(x), expected_result)
# Also test with some values as none
func_no_offset = odl.solvers.QuadraticForm(operator, constant=constant)
expected_result = x.inner(operator(x)) + constant
assert almost_equal(func_no_offset(x), expected_result)
func_no_operator = odl.solvers.QuadraticForm(vector=vector,
constant=constant)
expected_result = vector.inner(x) + constant
assert almost_equal(func_no_operator(x), expected_result)
# The gradient
expected_gradient = 2 * operator(x) + vector
assert all_almost_equal(func.gradient(x), expected_gradient)
# The convex conjugate
assert isinstance(func.convex_conj, odl.solvers.QuadraticForm)
def test_vector_norm(exponent):
rn = odl.CudaRn(5)
xarr, x = _vectors(rn)
weight = _pos_vector(odl.CudaRn(5))
weighting = CudaFnVectorWeighting(weight, exponent=exponent)
if exponent in (1.0, float('inf')):
true_norm = np.linalg.norm(weight.asarray() * xarr, ord=exponent)
else:
true_norm = np.linalg.norm(weight.asarray() ** (1 / exponent) * xarr,
ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
weighting.norm(x)
else:
assert almost_equal(weighting.norm(x), true_norm)
# Same with free function
pnorm = odl.cu_weighted_norm(weight, exponent=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
pnorm(x)
else:
assert almost_equal(pnorm(x), true_norm)
def test_vector_dist(exponent):
rn = odl.CudaRn(5)
xarr, yarr, x, y = _vectors(rn, n=2)
weight = _pos_vector(odl.CudaRn(5))
weighting = CudaFnVectorWeighting(weight, exponent=exponent)
if exponent in (1.0, float('inf')):
true_dist = np.linalg.norm(weight.asarray() * (xarr - yarr),
ord=exponent)
else:
true_dist = np.linalg.norm(
weight.asarray() ** (1 / exponent) * (xarr - yarr), ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
weighting.dist(x, y)
else:
assert almost_equal(weighting.dist(x, y), true_dist)
# Same with free function
pdist = odl.cu_weighted_dist(weight, exponent=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
pdist(x, y)
else:
assert almost_equal(pdist(x, y), true_dist)
def test_custom_norm(fn):
xarr, yarr, x, y = _vectors(fn, 2)
norm = np.linalg.norm
def other_norm(x):
return np.linalg.norm(x, ord=1)
w = CudaFnCustomNorm(norm)
w_same = CudaFnCustomNorm(norm)
w_other = CudaFnCustomNorm(other_norm)
assert w == w
assert w == w_same
assert w != w_other
with pytest.raises(NotImplementedError):
w.inner(x, y)
true_norm = np.linalg.norm(xarr)
assert almost_equal(w.norm(x), true_norm)
true_dist = np.linalg.norm(xarr - yarr)
assert almost_equal(w.dist(x, y), true_dist)
assert almost_equal(w.dist(x, x), 0)
with pytest.raises(TypeError):
CudaFnCustomNorm(1)
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_dist(fn):
xarr, yarr, x, y = _vectors(fn, n=2)
correct_dist = np.linalg.norm(xarr - yarr)
assert almost_equal(fn.dist(x, y), correct_dist)
assert almost_equal(x.dist(y), correct_dist)
def test_const_dist(exponent):
rn = CudaRn(5)
[xarr, yarr], [x, y] = example_vectors(rn, n=2)
constant = 1.5
weighting = CudaFnConstWeighting(constant, exponent=exponent)
factor = 1 if exponent == float('inf') else constant ** (1 / exponent)
true_dist = factor * np.linalg.norm(xarr - yarr, ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
weighting.dist(x, y)
else:
assert almost_equal(weighting.dist(x, y), true_dist)
# Same with free function
pdist = odl.cu_weighted_dist(constant, exponent=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
pdist(x, y)
else:
assert almost_equal(pdist(x, y), true_dist)
def test_custom_inner(fn):
[xarr, yarr], [x, y] = example_vectors(fn, 2)
def inner(x, y):
return np.vdot(y, x)
w = CudaFnCustomInnerProduct(inner)
w_same = CudaFnCustomInnerProduct(inner)
w_other = CudaFnCustomInnerProduct(np.dot)
w_d = CudaFnCustomInnerProduct(inner, dist_using_inner=False)
assert w == w
assert w == w_same
assert w != w_other
assert w != w_d
true_inner = inner(xarr, yarr)
assert almost_equal(w.inner(x, y), true_inner)
true_norm = np.linalg.norm(xarr)
assert almost_equal(w.norm(x), true_norm)
true_dist = np.linalg.norm(xarr - yarr)
# Using 3 places (single precision default) since the result is always
# double even if the underlying computation was only single precision
assert almost_equal(w.dist(x, y), true_dist, places=3)
assert almost_equal(w_d.dist(x, y), true_dist)
with pytest.raises(TypeError):
CudaFnCustomInnerProduct(1)
def test_pnorm(exponent):
for fn in (Rn(3, exponent=exponent), Cn(3, exponent=exponent)):
xarr, x = example_vectors(fn)
correct_norm = np.linalg.norm(xarr, ord=exponent)
assert almost_equal(fn.norm(x), correct_norm)
assert almost_equal(x.norm(), correct_norm)
def test_dist(fn):
[xarr, yarr], [x, y] = noise_elements(fn, n=2)
correct_dist = np.linalg.norm(xarr - yarr)
assert almost_equal(fn.dist(x, y), correct_dist)
assert almost_equal(x.dist(y), correct_dist)
def test_norm(fn):
xarr, x = noise_elements(fn)
correct_norm = np.linalg.norm(xarr)
assert almost_equal(fn.norm(x), correct_norm)
assert almost_equal(x.norm(), correct_norm)
def test_pnorm(exponent):
for fn in (odl.rn(3, exponent=exponent), odl.cn(3, exponent=exponent)):
xarr, x = noise_elements(fn)
correct_norm = np.linalg.norm(xarr, ord=exponent)
assert almost_equal(fn.norm(x), correct_norm)
assert almost_equal(x.norm(), correct_norm)
def test_inner(fn):
xd = noise_element(fn)
yd = noise_element(fn)
correct_inner = np.vdot(yd, xd)
assert almost_equal(fn.inner(xd, yd), correct_inner)
assert almost_equal(xd.inner(yd), correct_inner)
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_custom_norm(fn):
[xarr, yarr], [x, y] = example_vectors(fn, 2)
norm = np.linalg.norm
def other_norm(x):
return np.linalg.norm(x, ord=1)
w = CudaFnCustomNorm(norm)
w_same = CudaFnCustomNorm(norm)
w_other = CudaFnCustomNorm(other_norm)
assert w == w
assert w == w_same
assert w != w_other
with pytest.raises(NotImplementedError):
w.inner(x, y)
true_norm = np.linalg.norm(xarr)
assert almost_equal(w.norm(x), true_norm)
true_dist = np.linalg.norm(xarr - yarr)
assert almost_equal(w.dist(x, y), true_dist)
with pytest.raises(TypeError):
CudaFnCustomNorm(1)
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, weighting=2.0)
with pytest.raises(ValueError):
odl.ProductSpace(r2, r3, dist=custom_dist, weighting=2.0)
with pytest.raises(ValueError):
odl.ProductSpace(r2, r3, inner=custom_inner, weighting=2.0)
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_pdist(exponent):
for fn in (odl.rn(3, exponent=exponent), odl.cn(3, exponent=exponent)):
[xarr, yarr], [x, y] = noise_elements(fn, n=2)
correct_dist = np.linalg.norm(xarr - yarr, ord=exponent)
assert almost_equal(fn.dist(x, y), correct_dist)
assert almost_equal(x.dist(y), correct_dist)
def test_pdist(exponent):
for fn in (Rn(3, exponent=exponent), Cn(3, exponent=exponent)):
xarr, yarr, x, y = _vectors(fn, n=2)
correct_dist = np.linalg.norm(xarr - yarr, ord=exponent)
assert almost_equal(fn.dist(x, y), correct_dist)
assert almost_equal(x.dist(y), correct_dist)
def test_pdist(exponent):
for fn in (Rn(3, exponent=exponent), Cn(3, exponent=exponent)):
[xarr, yarr], [x, y] = example_vectors(fn, n=2)
correct_dist = np.linalg.norm(xarr - yarr, ord=exponent)
assert almost_equal(fn.dist(x, y), correct_dist)
assert almost_equal(x.dist(y), correct_dist)
def test_dist(tspace):
weighting_const = tspace.weighting.const
[xarr, yarr], [x, y] = noise_elements(tspace, 2)
correct_dist = np.linalg.norm(xarr - yarr) * np.sqrt(weighting_const)
assert almost_equal(tspace.dist(x, y), correct_dist, places=2)
assert almost_equal(x.dist(y), correct_dist, places=2)
def test_dist(fn):
weighting = np.sqrt(fn_weighting(fn))
[xarr, yarr], [x, y] = example_vectors(fn, 2)
correct_dist = np.linalg.norm(xarr - yarr) * weighting
assert almost_equal(fn.dist(x, y), correct_dist, places=2)
assert almost_equal(x.dist(y), correct_dist, places=2)
def test_norm(tspace):
weighting_const = tspace.weighting.const
xarr, x = noise_elements(tspace)
correct_norm = np.linalg.norm(xarr) * np.sqrt(weighting_const)
assert almost_equal(tspace.norm(x), correct_norm, places=2)
assert almost_equal(x.norm(), correct_norm, places=2)
def test_norm(fn):
weighting = np.sqrt(fn_weighting(fn))
xarr, x = noise_elements(fn)
correct_norm = np.linalg.norm(xarr) * weighting
assert almost_equal(fn.norm(x), correct_norm, places=2)
assert almost_equal(x.norm(), correct_norm, places=2)
def test_norm(fn):
weighting = np.sqrt(fn_weighting(fn))
xarr, x = example_vectors(fn)
correct_norm = np.linalg.norm(xarr) * weighting
assert almost_equal(fn.norm(x), correct_norm, places=2)
assert almost_equal(x.norm(), correct_norm, places=2)
def test_dist(fn):
weighting = np.sqrt(fn_weighting(fn))
[xarr, yarr], [x, y] = example_vectors(fn, 2)
correct_dist = np.linalg.norm(xarr - yarr) * weighting
assert almost_equal(fn.dist(x, y), correct_dist, places=2)
assert almost_equal(x.dist(y), correct_dist, places=2)
def test_norm(fn):
weighting = np.sqrt(fn_weighting(fn))
xarr, x = noise_elements(fn)
correct_norm = np.linalg.norm(xarr) * weighting
assert almost_equal(fn.norm(x), correct_norm, places=2)
assert almost_equal(x.norm(), correct_norm, places=2)
def test_norm(fn):
weighting = np.sqrt(fn_weighting(fn))
xarr, x = example_vectors(fn)
correct_norm = np.linalg.norm(xarr) * weighting
assert almost_equal(fn.norm(x), correct_norm, places=2)
assert almost_equal(x.norm(), correct_norm, places=2)
def test_inner(fn):
weighting = fn_weighting(fn)
[xarr, yarr], [x, y] = example_vectors(fn, 2)
correct_inner = np.vdot(yarr, xarr) * weighting
assert almost_equal(fn.inner(x, y), correct_inner, places=2)
assert almost_equal(x.inner(y), correct_inner, places=2)
def test_inner(tspace):
weighting_const = tspace.weighting.const
[xarr, yarr], [x, y] = noise_elements(tspace, 2)
correct_inner = np.vdot(yarr, xarr) * weighting_const
assert almost_equal(tspace.inner(x, y), correct_inner, places=2)
assert almost_equal(x.inner(y), correct_inner, places=2)
def test_inner(fn):
weighting = fn_weighting(fn)
[xarr, yarr], [x, y] = example_vectors(fn, 2)
correct_inner = np.vdot(yarr, xarr) * weighting
assert almost_equal(fn.inner(x, y), correct_inner, places=2)
assert almost_equal(x.inner(y), correct_inner, places=2)
def test_L2_norm(space, sigma):
"""Test the L2-norm."""
func = odl.solvers.L2Norm(space)
x = noise_element(space)
x_norm = x.norm()
# Test functional evaluation
expected_result = np.sqrt((x ** 2).inner(space.one()))
assert almost_equal(func(x), expected_result)
# Test gradient
if x_norm > 0:
expected_result = x / x.norm()
assert all_almost_equal(func.gradient(x), expected_result)
# Verify that the gradient at zero is zero
assert all_almost_equal(func.gradient(func.domain.zero()), space.zero())
# Test proximal operator - expecting
# x * (1 - sigma/||x||) if ||x|| > sigma, 0 else
norm_less_than_sigma = 0.99 * sigma * x / x_norm
assert all_almost_equal(func.proximal(sigma)(norm_less_than_sigma),
space.zero())
norm_larger_than_sigma = 1.01 * sigma * x / x_norm
expected_result = (norm_larger_than_sigma *
(1.0 - sigma / norm_larger_than_sigma.norm()))
assert all_almost_equal(func.proximal(sigma)(norm_larger_than_sigma),
expected_result)
# Test convex conjugate
func_cc = func.convex_conj
# Test evaluation of the convex conjugate - expecting
# 0 if ||x|| < 1, infty else
norm_larger_than_one = 1.01 * x / x_norm
assert func_cc(norm_larger_than_one) == np.inf
norm_less_than_one = 0.99 * x / x_norm
assert func_cc(norm_less_than_one) == 0
# Gradient of the convex conjugate (not implemeted)
with pytest.raises(NotImplementedError):
func_cc.gradient
# Test the proximal of the convex conjugate - expecting
# x if ||x||_2 < 1, x/||x|| else
if x_norm < 1:
expected_result = x
else:
expected_result = x / x_norm
assert all_almost_equal(func_cc.proximal(sigma)(x), expected_result)
# Verify that the biconjugate is the functional itself
func_cc_cc = func_cc.convex_conj
assert almost_equal(func_cc_cc(x), func(x))
def test_part_deriv_cpu():
"""Discretized partial derivative."""
with pytest.raises(TypeError):
PartialDerivative(odl.Rn(1))
# discretized space
space = odl.uniform_discr([0, 0], [2, 1], DATA_2D.shape)
# operator
partial_0 = PartialDerivative(space, axis=0, method='central',
padding_method='constant')
partial_1 = PartialDerivative(space, axis=1, method='central',
padding_method='constant')
# discretized space vector
vec = partial_0.domain.element(DATA_2D)
# partial derivative
partial_vec_0 = partial_0(vec)
partial_vec_1 = partial_1(vec)
# explicit calculation of finite difference
# axis: 0
diff_0 = np.zeros_like(DATA_2D)
# interior: second-order accurate differences
diff_0[1:-1, :] = (DATA_2D[2:, :] - DATA_2D[:-2, :]) / 2.0
# boundary: second-order accurate central differences with zero padding
diff_0[0, :] = DATA_2D[1, :] / 2.0
diff_0[-1, :] = -DATA_2D[-2, :] / 2.0
diff_0 /= space.cell_sides[0]
# axis: 1
diff_1 = np.zeros_like(DATA_2D)
# interior: second-order accurate differences
diff_1[:, 1:-1] = (DATA_2D[:, 2:] - DATA_2D[:, :-2]) / 2.0
# boundary: second-order accurate central differences with zero padding
diff_1[:, 0] = DATA_2D[:, 1] / 2.0
diff_1[:, -1] = -DATA_2D[:, -2] / 2.0
diff_1 /= space.cell_sides[1]
# assert `dfe0` and `dfe1` do differ
assert (diff_0 != diff_1).any()
assert partial_vec_0 != partial_vec_1
assert all_equal(partial_vec_0.asarray(), diff_0)
assert all_equal(partial_vec_1.asarray(), diff_1)
# adjoint operator
vec1 = space.element(DATA_2D)
vec2 = space.element(DATA_2D + np.random.rand(*DATA_2D.shape))
assert almost_equal(partial_0(vec1).inner(vec2),
vec1.inner(partial_0.adjoint(vec2)))
assert almost_equal(partial_1(vec1).inner(vec2),
vec1.inner(partial_1.adjoint(vec2)))
def test_multiplication_with_vector(space):
"""Test for multiplying a functional with a vector, both left and right."""
# Less strict checking for single precision
places = 3 if space.dtype == np.float32 else 5
x = noise_element(space)
y = noise_element(space)
func = odl.solvers.L2NormSquared(space)
wrong_space = odl.uniform_discr(1, 2, 10)
y_other_space = noise_element(wrong_space)
# Multiplication from the right. Make sure it is a
# FunctionalRightVectorMult
func_times_y = func * y
assert isinstance(func_times_y, odl.solvers.FunctionalRightVectorMult)
expected_result = func(y * x)
assert almost_equal(func_times_y(x), expected_result, places=places)
# Test for the gradient.
# Explicit calculations: 2*y*y*x
expected_result = 2.0 * y * y * x
assert all_almost_equal(func_times_y.gradient(x),
expected_result,
places=places)
# Test for convex_conj
cc_func_times_y = func_times_y.convex_conj
# Explicit calculations: 1/4 * ||x/y||_2^2
expected_result = 1.0 / 4.0 * (x / y).norm()**2
assert almost_equal(cc_func_times_y(x), expected_result, places=places)
# Make sure that right muliplication is not allowed with vector from
# another space
with pytest.raises(TypeError):
func * y_other_space
# Multiplication from the left. Make sure it is a FunctionalLeftVectorMult
y_times_func = y * func
assert isinstance(y_times_func, odl.FunctionalLeftVectorMult)
expected_result = y * func(x)
assert all_almost_equal(y_times_func(x), expected_result, places=places)
# Now, multiplication with vector from another space is ok (since it is the
# same as scaling that vector with the scalar returned by the functional).
y_other_times_func = y_other_space * func
assert isinstance(y_other_times_func, odl.FunctionalLeftVectorMult)
expected_result = y_other_space * func(x)
assert all_almost_equal(y_other_times_func(x),
expected_result,
places=places)
def test_begin():
set_ = IntervalProd(1, 2)
assert almost_equal(set_.begin, 1)
set_ = IntervalProd(-np.inf, 0)
assert almost_equal(set_.begin, -np.inf)
set_ = IntervalProd([1], [2])
assert almost_equal(set_.begin, 1)
set_ = IntervalProd([1, 2, 3], [5, 6, 7])
assert all_equal(set_.begin, [1, 2, 3])
def test_begin():
set_ = IntervalProd(1, 2)
assert almost_equal(set_.begin, 1)
set_ = IntervalProd(-np.inf, 0)
assert almost_equal(set_.begin, -np.inf)
set_ = IntervalProd([1], [2])
assert almost_equal(set_.begin, 1)
set_ = IntervalProd([1, 2, 3], [5, 6, 7])
assert all_equal(set_.begin, [1, 2, 3])
def test_end():
set_ = IntervalProd(1, 2)
assert almost_equal(set_.end, 2)
set_ = IntervalProd(0, np.inf)
assert almost_equal(set_.end, np.inf)
set_ = IntervalProd([1], [2])
assert almost_equal(set_.end, 2)
set_ = IntervalProd([1, 2, 3], [5, 6, 7])
assert all_equal(set_.end, [5, 6, 7])
def test_max_pt():
set_ = IntervalProd(1, 2)
assert almost_equal(set_.max_pt, 2)
set_ = IntervalProd(0, np.inf)
assert almost_equal(set_.max_pt, np.inf)
set_ = IntervalProd([1], [2])
assert almost_equal(set_.max_pt, 2)
set_ = IntervalProd([1, 2, 3], [5, 6, 7])
assert all_equal(set_.max_pt, [5, 6, 7])
def test_end():
set_ = IntervalProd(1, 2)
assert almost_equal(set_.end, 2)
set_ = IntervalProd(0, np.inf)
assert almost_equal(set_.end, np.inf)
set_ = IntervalProd([1], [2])
assert almost_equal(set_.end, 2)
set_ = IntervalProd([1, 2, 3], [5, 6, 7])
assert all_equal(set_.end, [5, 6, 7])
def test_max_pt():
set_ = IntervalProd(1, 2)
assert almost_equal(set_.max_pt, 2)
set_ = IntervalProd(0, np.inf)
assert almost_equal(set_.max_pt, np.inf)
set_ = IntervalProd([1], [2])
assert almost_equal(set_.max_pt, 2)
set_ = IntervalProd([1, 2, 3], [5, 6, 7])
assert all_equal(set_.max_pt, [5, 6, 7])
def test_min_pt():
set_ = IntervalProd(1, 2)
assert almost_equal(set_.min_pt, 1)
set_ = IntervalProd(-np.inf, 0)
assert almost_equal(set_.min_pt, -np.inf)
set_ = IntervalProd([1], [2])
assert almost_equal(set_.min_pt, 1)
set_ = IntervalProd([1, 2, 3], [5, 6, 7])
assert all_equal(set_.min_pt, [1, 2, 3])
def test_min_pt():
set_ = IntervalProd(1, 2)
assert almost_equal(set_.min_pt, 1)
set_ = IntervalProd(-np.inf, 0)
assert almost_equal(set_.min_pt, -np.inf)
set_ = IntervalProd([1], [2])
assert almost_equal(set_.min_pt, 1)
set_ = IntervalProd([1, 2, 3], [5, 6, 7])
assert all_equal(set_.min_pt, [1, 2, 3])
def test_multiplication_with_vector(space):
"""Test for multiplying a functional with a vector, both left and right."""
# Less strict checking for single precision
places = 3 if space.dtype == np.float32 else 5
x = noise_element(space)
y = noise_element(space)
func = odl.solvers.L2NormSquared(space)
wrong_space = odl.uniform_discr(1, 2, 10)
y_other_space = noise_element(wrong_space)
# Multiplication from the right. Make sure it is a
# FunctionalRightVectorMult
func_times_y = func * y
assert isinstance(func_times_y, odl.solvers.FunctionalRightVectorMult)
expected_result = func(y * x)
assert almost_equal(func_times_y(x), expected_result, places=places)
# Test for the gradient.
# Explicit calculations: 2*y*y*x
expected_result = 2.0 * y * y * x
assert all_almost_equal(func_times_y.gradient(x), expected_result,
places=places)
# Test for convex_conj
cc_func_times_y = func_times_y.convex_conj
# Explicit calculations: 1/4 * ||x/y||_2^2
expected_result = 1.0 / 4.0 * (x / y).norm()**2
assert almost_equal(cc_func_times_y(x), expected_result, places=places)
# Make sure that right muliplication is not allowed with vector from
# another space
with pytest.raises(TypeError):
func * y_other_space
# Multiplication from the left. Make sure it is a FunctionalLeftVectorMult
y_times_func = y * func
assert isinstance(y_times_func, odl.FunctionalLeftVectorMult)
expected_result = y * func(x)
assert all_almost_equal(y_times_func(x), expected_result, places=places)
# Now, multiplication with vector from another space is ok (since it is the
# same as scaling that vector with the scalar returned by the functional).
y_other_times_func = y_other_space * func
assert isinstance(y_other_times_func, odl.FunctionalLeftVectorMult)
expected_result = y_other_space * func(x)
assert all_almost_equal(y_other_times_func(x), expected_result,
places=places)
def test_norm(exponent):
r3 = odl.CudaRn(3, exponent=exponent)
xarr, x = _vectors(r3)
correct_norm = np.linalg.norm(xarr, ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
r3.norm(x)
x.norm()
else:
assert almost_equal(r3.norm(x), correct_norm)
assert almost_equal(x.norm(), correct_norm)
def test_norm(exponent):
r3 = CudaRn(3, exponent=exponent)
xarr, x = example_vectors(r3)
correct_norm = np.linalg.norm(xarr, ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
r3.norm(x)
x.norm()
else:
assert almost_equal(r3.norm(x), correct_norm)
assert almost_equal(x.norm(), correct_norm)
def test_dist(exponent):
r3 = odl.CudaRn(3, exponent=exponent)
xarr, yarr, x, y = _vectors(r3, n=2)
correct_dist = np.linalg.norm(xarr - yarr, ord=exponent)
if exponent == float('inf'):
# Not yet implemented, should raise
with pytest.raises(NotImplementedError):
r3.dist(x, y)
with pytest.raises(NotImplementedError):
x.dist(y)
else:
assert almost_equal(r3.dist(x, y), correct_dist)
assert almost_equal(x.dist(y), correct_dist)