def test_env_unique_fraction(self):
"""should report unique fraction of bl in each env """
# testing old unique fraction
cur_count_array = self.count_array.copy()
bound_indices = bind_to_array(self.nodes, cur_count_array)
total_bl = sum(self.branch_lengths)
bool_descendants(bound_indices)
env_bl_sums, env_bl_ufracs = env_unique_fraction(
self.branch_lengths, cur_count_array)
# env A has 0 unique bl, B has 4, C has 1
self.assertEqual(env_bl_sums, [0, 4, 1])
self.assertEqual(env_bl_ufracs, [0, 4 / 17.0, 1 / 17.0])
cur_count_array = self.old_count_array.copy()
bound_indices = bind_to_array(self.old_nodes, cur_count_array)
total_bl = sum(self.old_branch_lengths)
bool_descendants(bound_indices)
env_bl_sums, env_bl_ufracs = env_unique_fraction(
self.old_branch_lengths, cur_count_array)
# env A has 0 unique bl, B has 4, C has 1
self.assertEqual(env_bl_sums, env_bl_sums)
self.assertEqual(env_bl_sums, [1.29, 0.33999999999999997, 0.63])
self.assertEqual(env_bl_ufracs,
[1.29 / 2.9, 0.33999999999999997 / 2.9, 0.63 / 2.9])
def test_fitch_descendants_missing_data(self):
"""fitch_descendants should work with missing data"""
#tree and envs for testing missing values
t_str = '(((a:1,b:2):4,(c:3,d:1):2):1,(e:2,f:1):3);'
env_str = """a A
b B
c D
d C
e C
f D"""
t = DndParser(t_str, UniFracTreeNode)
node_index, nodes = index_tree(t)
env_counts = count_envs(env_str.split('\n'))
count_array, unique_envs, env_to_index, node_to_index = \
index_envs(env_counts, node_index)
branch_lengths = get_branch_lengths(node_index)
#test just the AB pair
ab_counts = count_array[:, 0:2]
bindings = bind_to_array(nodes, ab_counts)
changes = fitch_descendants(bindings, counter=FitchCounter)
self.assertEqual(changes, 1)
orig_result = ab_counts.copy()
#check that the original Fitch counter gives the expected
#incorrect parsimony result
changes = fitch_descendants(bindings, counter=FitchCounterDense)
self.assertEqual(changes, 5)
new_result = ab_counts.copy()
#check that the two versions fill the array with the same values
self.assertEqual(orig_result, new_result)
def test_weighted_one_sample(self):
"""weighted one sample should match weighted matrix"""
#should match web site calculations
envs = self.count_array
bound_indices = bind_to_array(self.nodes, envs)
sum_descendants(bound_indices)
bl = self.branch_lengths
tip_indices = [n._leaf_index for n in self.t.tips()]
result = weighted_unifrac_matrix(bl, envs, tip_indices)
for i in range(len(result)):
one_sam_res = weighted_one_sample(i, bl, envs, tip_indices)
self.assertEqual(result[i], one_sam_res)
self.assertEqual(result[:, i], one_sam_res)
#should work with branch length corrections
td = bl.copy()[:, newaxis]
tip_bindings = bind_to_parent_array(self.t, td)
tips = [n._leaf_index for n in self.t.tips()]
tip_distances(td, tip_bindings, tips)
result = weighted_unifrac_matrix(bl,
envs,
tip_indices,
bl_correct=True,
tip_distances=td)
for i in range(len(result)):
one_sam_res = weighted_one_sample(i,
bl,
envs,
tip_indices,
bl_correct=True,
tip_distances=td)
self.assertEqual(result[i], one_sam_res)
self.assertEqual(result[:, i], one_sam_res)
def test_weighted_unifrac_matrix(self):
"""weighted unifrac matrix should ret correct results for model tree"""
# should match web site calculations
envs = self.count_array
bound_indices = bind_to_array(self.nodes, envs)
sum_descendants(bound_indices)
bl = self.branch_lengths
tip_indices = [n._leaf_index for n in self.t.tips()]
result = weighted_unifrac_matrix(bl, envs, tip_indices)
exp = array([[0, 9.1, 4.5], [9.1, 0, 6.4], [4.5, 6.4, 0]])
assert (abs(result - exp)).max() < 0.001
# should work with branch length corrections
td = bl.copy()[:, newaxis]
tip_bindings = bind_to_parent_array(self.t, td)
tips = [n._leaf_index for n in self.t.tips()]
tip_distances(td, tip_bindings, tips)
result = weighted_unifrac_matrix(bl, envs, tip_indices, bl_correct=True, tip_distances=td)
exp = array(
[
[0, 9.1 / 11.5, 4.5 / (10.5 + 1.0 / 3)],
[9.1 / 11.5, 0, 6.4 / (11 + 1.0 / 3)],
[4.5 / (10.5 + 1.0 / 3), 6.4 / (11 + 1.0 / 3), 0],
]
)
assert (abs(result - exp)).max() < 0.001
def test_fitch_descendants(self):
"""fitch_descendants should assign states by fitch parsimony, ret. #"""
id_, child = index_tree(self.t3)
a = zeros((11, 3)) + 99 # fill with junk
bindings = bind_to_array(child, a)
# load in leaf envs
a[0] = a[1] = a[2] = a[7] = [0, 1, 0]
a[3] = [1, 0, 0]
a[6] = [0, 0, 1]
changes = fitch_descendants(bindings)
self.assertEqual(changes, 2)
self.assertEqual(
a,
array(
[
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[1, 0, 0],
[0, 1, 0],
[1, 0, 0],
[0, 0, 1],
[0, 1, 0],
[1, 1, 0],
[0, 1, 1],
[0, 1, 0],
]
),
)
def test_bool_descendants(self):
"""bool_descendants should be true if any descendant true"""
# self.t3 = DndParser('(((a,b,c),(d)),(e,f))', UniFracTreeNode)
id_, child = index_tree(self.t3)
a = zeros((11, 3)) + 99 # fill with junk
bindings = bind_to_array(child, a)
# load in leaf envs
a[0] = a[1] = a[2] = a[7] = [0, 1, 0]
a[3] = [1, 0, 0]
a[6] = [0, 0, 1]
bool_descendants(bindings)
self.assertEqual(
a,
array(
[
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[1, 0, 0],
[0, 1, 0],
[1, 0, 0],
[0, 0, 1],
[0, 1, 0],
[1, 1, 0],
[0, 1, 1],
[1, 1, 1],
]
),
)
def test_sum_descendants(self):
"""sum_descendants should sum total descendants w/ each state"""
id_, child = index_tree(self.t3)
a = zeros((11, 3)) + 99 # fill with junk
bindings = bind_to_array(child, a)
# load in leaf envs
a[0] = a[1] = a[2] = a[7] = [0, 1, 0]
a[3] = [1, 0, 0]
a[6] = [0, 0, 1]
sum_descendants(bindings)
self.assertEqual(
a,
array(
[
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[1, 0, 0],
[0, 3, 0],
[1, 0, 0],
[0, 0, 1],
[0, 1, 0],
[1, 3, 0],
[0, 1, 1],
[1, 4, 1],
]
),
)
def test_weighted_one_sample(self):
"""weighted one sample should match weighted matrix"""
#should match web site calculations
envs = self.count_array
bound_indices = bind_to_array(self.nodes, envs)
sum_descendants(bound_indices)
bl = self.branch_lengths
tip_indices = [n._leaf_index for n in self.t.tips()]
result = weighted_unifrac_matrix(bl, envs, tip_indices)
for i in range(len(result)):
one_sam_res = weighted_one_sample(i, bl, envs, tip_indices)
self.assertEqual(result[i], one_sam_res)
self.assertEqual(result[:,i], one_sam_res)
#should work with branch length corrections
td = bl.copy()[:,newaxis]
tip_bindings = bind_to_parent_array(self.t, td)
tips = [n._leaf_index for n in self.t.tips()]
tip_distances(td, tip_bindings, tips)
result = weighted_unifrac_matrix(bl, envs, tip_indices, bl_correct=True,
tip_distances=td)
for i in range(len(result)):
one_sam_res = weighted_one_sample(i, bl, envs, tip_indices,
bl_correct=True, tip_distances=td)
self.assertEqual(result[i], one_sam_res)
self.assertEqual(result[:,i], one_sam_res)
def test_unifrac_matrix(self):
"""unifrac_matrix should return correct results for model tree"""
m = array([[1,0,1],[1,1,0],[0,1,0],[0,0,1],[0,1,0],[0,1,1],[1,1,1],\
[0,1,1],[1,1,1]])
bl = self.branch_lengths
result = unifrac_matrix(bl, m)
self.assertEqual(result, array([[0, 10/16.,8/13.],[10/16.,0,8/17.],\
[8/13.,8/17.,0]]))
#should work if we tell it the measure is asymmetric
result = unifrac_matrix(bl, m, is_symmetric=False)
self.assertEqual(result, array([[0, 10/16.,8/13.],[10/16.,0,8/17.],\
[8/13.,8/17.,0]]))
#should work if the measure really is asymmetric
result = unifrac_matrix(bl,
m,
metric=unnormalized_G,
is_symmetric=False)
self.assertEqual(result, array([[0, 1/17.,2/17.],[9/17.,0,6/17.],\
[6/17.,2/17.,0]]))
#should also match web site calculations
envs = self.count_array
bound_indices = bind_to_array(self.nodes, envs)
bool_descendants(bound_indices)
result = unifrac_matrix(bl, envs)
exp = array([[0, 0.6250, 0.6154], [0.6250, 0, \
0.4706], [0.6154, 0.4707, 0]])
assert (abs(result - exp)).max() < 0.001
def test_weighted_unifrac_matrix(self):
"""weighted unifrac matrix should return correct results for model tree"""
#should match web site calculations
envs = self.count_array
bound_indices = bind_to_array(self.nodes, envs)
sum_descendants(bound_indices)
bl = self.branch_lengths
tip_indices = [n._leaf_index for n in self.t.tips()]
result = weighted_unifrac_matrix(bl, envs, tip_indices)
exp = array([[0, 9.1, 4.5], [9.1, 0, \
6.4], [4.5, 6.4, 0]])
assert (abs(result - exp)).max() < 0.001
#should work with branch length corrections
td = bl.copy()[:, newaxis]
tip_bindings = bind_to_parent_array(self.t, td)
tips = [n._leaf_index for n in self.t.tips()]
tip_distances(td, tip_bindings, tips)
result = weighted_unifrac_matrix(bl,
envs,
tip_indices,
bl_correct=True,
tip_distances=td)
exp = array([[0, 9.1/11.5, 4.5/(10.5+1./3)], [9.1/11.5, 0, \
6.4/(11+1./3)], [4.5/(10.5+1./3), 6.4/(11+1./3), 0]])
assert (abs(result - exp)).max() < 0.001
def test_fitch_descendants_missing_data(self):
"""fitch_descendants should work with missing data"""
#tree and envs for testing missing values
t_str = '(((a:1,b:2):4,(c:3,d:1):2):1,(e:2,f:1):3);'
env_str = """a A
b B
c D
d C
e C
f D"""
t = DndParser(t_str, UniFracTreeNode)
node_index, nodes = index_tree(t)
env_counts = count_envs(env_str.split('\n'))
count_array, unique_envs, env_to_index, node_to_index = \
index_envs(env_counts, node_index)
branch_lengths = get_branch_lengths(node_index)
#test just the AB pair
ab_counts = count_array[:, 0:2]
bindings = bind_to_array(nodes, ab_counts)
changes = fitch_descendants(bindings, counter=FitchCounter)
self.assertEqual(changes, 1)
orig_result = ab_counts.copy()
#check that the original Fitch counter gives the expected
#incorrect parsimony result
changes = fitch_descendants(bindings, counter=FitchCounterDense)
self.assertEqual(changes, 5)
new_result = ab_counts.copy()
#check that the two versions fill the array with the same values
self.assertEqual(orig_result, new_result)
def test_delete_empty_parents(self):
"""delete_empty_parents should remove empty parents from bound indices"""
id_to_node, node_first_last = index_tree(self.t)
bound_indices = bind_to_array(node_first_last, self.count_array[:,0:1])
bool_descendants(bound_indices)
self.assertEqual(len(bound_indices), 4)
deleted = delete_empty_parents(bound_indices)
self.assertEqual(len(deleted), 2)
for d in deleted:
self.assertEqual(d[0][0], 1)
def test_weighted_unifrac_vector(self):
"""weighted_unifrac_vector should ret correct results for model tree"""
envs = self.count_array
bound_indices = bind_to_array(self.nodes, envs)
sum_descendants(bound_indices)
bl = self.branch_lengths
tip_indices = [n._leaf_index for n in self.t.tips()]
result = weighted_unifrac_vector(bl, envs, tip_indices)
self.assertFloatEqual(
result[0],
sum(
[
abs(1.0 / 2 - 2.0 / 8) * 1,
abs(1.0 / 2 - 1.0 / 8) * 2,
abs(0 - 1.0 / 8) * 3,
abs(0 - 3.0 / 8) * 1,
abs(0 - 1.0 / 8) * 1,
abs(0 - 4.0 / 8) * 2,
abs(2.0 / 2 - 3.0 / 8) * 4,
abs(0.0 - 5.0 / 8) * 3.0,
]
),
)
self.assertFloatEqual(
result[1],
sum(
[
abs(0 - 0.6) * 1,
abs(0.2 - 0.2) * 2,
abs(0.2 - 0) * 3,
abs(0.6 - 0) * 1,
abs(0 - 0.2) * 1,
abs(0.6 - 0.2) * 2,
abs(0.2 - 0.8) * 4,
abs(0.8 - 0.2) * 3,
]
),
)
self.assertFloatEqual(
result[2],
sum(
[
abs(2.0 / 3 - 1.0 / 7) * 1,
abs(0 - 2.0 / 7) * 2,
abs(0 - 1.0 / 7) * 3,
abs(0 - 3.0 / 7) * 1,
abs(1.0 / 3 - 0) * 1,
abs(1.0 / 3 - 3.0 / 7) * 2,
abs(2.0 / 3 - 3.0 / 7) * 4,
abs(1.0 / 3 - 4.0 / 7) * 3,
]
),
)
def test_delete_empty_parents(self):
"""delete_empty_parents should remove empty parents from bound indices"""
id_to_node, node_first_last = index_tree(self.t)
bound_indices = bind_to_array(node_first_last, self.count_array[:,
0:1])
bool_descendants(bound_indices)
self.assertEqual(len(bound_indices), 4)
deleted = delete_empty_parents(bound_indices)
self.assertEqual(len(deleted), 2)
for d in deleted:
self.assertEqual(d[0][0], 1)
def test_env_unique_fraction(self):
"""should report unique fraction of bl in each env """
# testing old unique fraction
cur_count_array = self.count_array.copy()
bound_indices = bind_to_array(self.nodes, cur_count_array)
total_bl = sum(self.branch_lengths)
bool_descendants(bound_indices)
env_bl_sums, env_bl_ufracs = env_unique_fraction(self.branch_lengths, cur_count_array)
# env A has 0 unique bl, B has 4, C has 1
self.assertEqual(env_bl_sums, [0,4,1])
self.assertEqual(env_bl_ufracs, [0,4/17.0,1/17.0])
cur_count_array = self.old_count_array.copy()
bound_indices = bind_to_array(self.old_nodes, cur_count_array)
total_bl = sum(self.old_branch_lengths)
bool_descendants(bound_indices)
env_bl_sums, env_bl_ufracs = env_unique_fraction(self.old_branch_lengths, cur_count_array)
# env A has 0 unique bl, B has 4, C has 1
self.assertEqual(env_bl_sums, env_bl_sums)
self.assertEqual(env_bl_sums, [1.29, 0.33999999999999997, 0.63])
self.assertEqual(env_bl_ufracs, [1.29/2.9,0.33999999999999997/2.9, 0.63/2.9])
def test_sum_descendants(self):
"""sum_descendants should sum total descendants w/ each state"""
id_, child = index_tree(self.t3)
a = zeros((11, 3)) + 99 #fill with junk
bindings = bind_to_array(child, a)
#load in leaf envs
a[0] = a[1] = a[2] = a[7] = [0, 1, 0]
a[3] = [1, 0, 0]
a[6] = [0, 0, 1]
sum_descendants(bindings)
self.assertEqual(a, \
array([[0,1,0],[0,1,0],[0,1,0],[1,0,0],[0,3,0],[1,0,0],\
[0,0,1],[0,1,0],[1,3,0],[0,1,1],[1,4,1]])
)
def test_traverse_reduce(self):
"""traverse_reduce should reduce array in traversal order."""
id_, child = index_tree(self.t3)
a = zeros((11, 3)) + 99 # fill with junk
bindings = bind_to_array(child, a)
# load in leaf envs
a[0] = a[1] = a[2] = a[7] = [0, 1, 0]
a[3] = [1, 0, 0]
a[6] = [0, 0, 1]
f = logical_or.reduce
traverse_reduce(bindings, f)
self.assertEqual(
a,
array(
[
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[1, 0, 0],
[0, 1, 0],
[1, 0, 0],
[0, 0, 1],
[0, 1, 0],
[1, 1, 0],
[0, 1, 1],
[1, 1, 1],
]
),
)
f = sum
traverse_reduce(bindings, f)
self.assertEqual(
a,
array(
[
[0, 1, 0],
[0, 1, 0],
[0, 1, 0],
[1, 0, 0],
[0, 3, 0],
[1, 0, 0],
[0, 0, 1],
[0, 1, 0],
[1, 3, 0],
[0, 1, 1],
[1, 4, 1],
]
),
)
def test_fitch_descendants(self):
"""fitch_descendants should assign states by fitch parsimony, ret. #"""
id_, child = index_tree(self.t3)
a = zeros((11, 3)) + 99 #fill with junk
bindings = bind_to_array(child, a)
#load in leaf envs
a[0] = a[1] = a[2] = a[7] = [0, 1, 0]
a[3] = [1, 0, 0]
a[6] = [0, 0, 1]
changes = fitch_descendants(bindings)
self.assertEqual(changes, 2)
self.assertEqual(a, \
array([[0,1,0],[0,1,0],[0,1,0],[1,0,0],[0,1,0],[1,0,0],\
[0,0,1],[0,1,0],[1,1,0],[0,1,1],[0,1,0]])
)
def test_bool_descendants(self):
"""bool_descendants should be true if any descendant true"""
#self.t3 = DndParser('(((a,b,c),(d)),(e,f))', UniFracTreeNode)
id_, child = index_tree(self.t3)
a = zeros((11, 3)) + 99 #fill with junk
bindings = bind_to_array(child, a)
#load in leaf envs
a[0] = a[1] = a[2] = a[7] = [0, 1, 0]
a[3] = [1, 0, 0]
a[6] = [0, 0, 1]
bool_descendants(bindings)
self.assertEqual(a, \
array([[0,1,0],[0,1,0],[0,1,0],[1,0,0],[0,1,0],[1,0,0],\
[0,0,1],[0,1,0],[1,1,0],[0,1,1],[1,1,1]])
)
def test_weighted_unifrac_vector(self):
"""weighted_unifrac_vector should return correct results for model tree"""
envs = self.count_array
bound_indices = bind_to_array(self.nodes, envs)
sum_descendants(bound_indices)
bl = self.branch_lengths
tip_indices = [n._leaf_index for n in self.t.tips()]
result = weighted_unifrac_vector(bl, envs, tip_indices)
self.assertFloatEqual(
result[0],
sum([
abs(1. / 2 - 2. / 8) * 1,
abs(1. / 2 - 1. / 8) * 2,
abs(0 - 1. / 8) * 3,
abs(0 - 3. / 8) * 1,
abs(0 - 1. / 8) * 1,
abs(0 - 4. / 8) * 2,
abs(2. / 2 - 3. / 8) * 4,
abs(0. - 5. / 8) * 3.
]))
self.assertFloatEqual(
result[1],
sum([
abs(0 - .6) * 1,
abs(.2 - .2) * 2,
abs(.2 - 0) * 3,
abs(.6 - 0) * 1,
abs(0 - .2) * 1,
abs(.6 - .2) * 2,
abs(.2 - .8) * 4,
abs(.8 - .2) * 3
]))
self.assertFloatEqual(
result[2],
sum([
abs(2. / 3 - 1. / 7) * 1,
abs(0 - 2. / 7) * 2,
abs(0 - 1. / 7) * 3,
abs(0 - 3. / 7) * 1,
abs(1. / 3 - 0) * 1,
abs(1. / 3 - 3. / 7) * 2,
abs(2. / 3 - 3. / 7) * 4,
abs(1. / 3 - 4. / 7) * 3
]))
def test_unifrac_matrix(self):
"""unifrac_matrix should return correct results for model tree"""
m = array([[1, 0, 1], [1, 1, 0], [0, 1, 0], [0, 0, 1], [0, 1, 0], [0, 1, 1], [1, 1, 1], [0, 1, 1], [1, 1, 1]])
bl = self.branch_lengths
result = unifrac_matrix(bl, m)
self.assertEqual(result, array([[0, 10 / 16.0, 8 / 13.0], [10 / 16.0, 0, 8 / 17.0], [8 / 13.0, 8 / 17.0, 0]]))
# should work if we tell it the measure is asymmetric
result = unifrac_matrix(bl, m, is_symmetric=False)
self.assertEqual(result, array([[0, 10 / 16.0, 8 / 13.0], [10 / 16.0, 0, 8 / 17.0], [8 / 13.0, 8 / 17.0, 0]]))
# should work if the measure really is asymmetric
result = unifrac_matrix(bl, m, metric=unnormalized_G, is_symmetric=False)
self.assertEqual(result, array([[0, 1 / 17.0, 2 / 17.0], [9 / 17.0, 0, 6 / 17.0], [6 / 17.0, 2 / 17.0, 0]]))
# should also match web site calculations
envs = self.count_array
bound_indices = bind_to_array(self.nodes, envs)
bool_descendants(bound_indices)
result = unifrac_matrix(bl, envs)
exp = array([[0, 0.6250, 0.6154], [0.6250, 0, 0.4706], [0.6154, 0.4707, 0]])
assert (abs(result - exp)).max() < 0.001
def test_bind_to_array(self):
"""bind_to_array should return correct array ranges"""
a = reshape(arange(33), (11, 3))
id_, child = index_tree(self.t3)
bindings = bind_to_array(child, a)
self.assertEqual(len(bindings), 5)
self.assertEqual(bindings[0][0], a[4])
self.assertEqual(bindings[0][1], a[0:3])
self.assertEqual(bindings[0][1].shape, (3, 3))
self.assertEqual(bindings[1][0], a[5])
self.assertEqual(bindings[1][1], a[3:4])
self.assertEqual(bindings[1][1].shape, (1, 3))
self.assertEqual(bindings[2][0], a[8])
self.assertEqual(bindings[2][1], a[4:6])
self.assertEqual(bindings[2][1].shape, (2, 3))
self.assertEqual(bindings[3][0], a[9])
self.assertEqual(bindings[3][1], a[6:8])
self.assertEqual(bindings[3][1].shape, (2, 3))
self.assertEqual(bindings[4][0], a[10])
self.assertEqual(bindings[4][1], a[8:10])
self.assertEqual(bindings[4][1].shape, (2, 3))
def test_traverse_reduce(self):
"""traverse_reduce should reduce array in traversal order."""
id_, child = index_tree(self.t3)
a = zeros((11, 3)) + 99 #fill with junk
bindings = bind_to_array(child, a)
#load in leaf envs
a[0] = a[1] = a[2] = a[7] = [0, 1, 0]
a[3] = [1, 0, 0]
a[6] = [0, 0, 1]
f = logical_or.reduce
traverse_reduce(bindings, f)
self.assertEqual(a,\
array([[0,1,0],[0,1,0],[0,1,0],[1,0,0],[0,1,0],[1,0,0],\
[0,0,1],[0,1,0],[1,1,0],[0,1,1],[1,1,1]])
)
f = sum
traverse_reduce(bindings, f)
self.assertEqual( a, \
array([[0,1,0],[0,1,0],[0,1,0],[1,0,0],[0,3,0],[1,0,0],\
[0,0,1],[0,1,0],[1,3,0],[0,1,1],[1,4,1]])
)
def test_bind_to_array(self):
"""bind_to_array should return correct array ranges"""
a = reshape(arange(33), (11,3))
id_, child = index_tree(self.t3)
bindings = bind_to_array(child, a)
self.assertEqual(len(bindings), 5)
self.assertEqual(bindings[0][0], a[4])
self.assertEqual(bindings[0][1], a[0:3])
self.assertEqual(bindings[0][1].shape, (3,3))
self.assertEqual(bindings[1][0], a[5])
self.assertEqual(bindings[1][1], a[3:4])
self.assertEqual(bindings[1][1].shape, (1,3))
self.assertEqual(bindings[2][0], a[8])
self.assertEqual(bindings[2][1], a[4:6])
self.assertEqual(bindings[2][1].shape, (2,3))
self.assertEqual(bindings[3][0], a[9])
self.assertEqual(bindings[3][1], a[6:8])
self.assertEqual(bindings[3][1].shape, (2,3))
self.assertEqual(bindings[4][0], a[10])
self.assertEqual(bindings[4][1], a[8:10])
self.assertEqual(bindings[4][1].shape, (2,3))
