def test_theta_set_operations(self):
k = 12 # 2^k = 4096 rows in the table
n = 1 << 18 # ~256k unique values
# we'll have 1/4 of the values overlap
offset = int(3 * n / 4) # it's a float w/o cast
# create a couple sketches and inject some values
sk1 = self.generate_theta_sketch(n, k)
sk2 = self.generate_theta_sketch(n, k, offset)
# UNIONS
# create a union object
union = theta_union(k)
union.update(sk1)
union.update(sk2)
# getting result from union returns a compact_theta_sketch
# compact theta sketches can be used in additional unions
# or set operations but cannot accept further item updates
result = union.get_result()
self.assertTrue(isinstance(result, compact_theta_sketch))
# since our process here is deterministic, we have
# checked and know the exact answer is within one
# standard deviation of the estimate
self.assertLessEqual(result.get_lower_bound(1), 7 * n / 4)
self.assertGreaterEqual(result.get_upper_bound(1), 7 * n / 4)
# INTERSECTIONS
# create an intersection object
intersect = theta_intersection() # no lg_k
intersect.update(sk1)
intersect.update(sk2)
# has_result() indicates the intersection has been used,
# although the result may be the empty set
self.assertTrue(intersect.has_result())
# as with unions, the result is a compact sketch
result = intersect.get_result()
self.assertTrue(isinstance(result, compact_theta_sketch))
# we know the sets overlap by 1/4
self.assertLessEqual(result.get_lower_bound(1), n / 4)
self.assertGreaterEqual(result.get_upper_bound(1), n / 4)
# A NOT B
# create an a_not_b object
anb = theta_a_not_b() # no lg_k
result = anb.compute(sk1, sk2)
# as with unions, the result is a compact sketch
self.assertTrue(isinstance(result, compact_theta_sketch))
# we know the sets overlap by 1/4, so the remainder is 3/4
self.assertLessEqual(result.get_lower_bound(1), 3 * n / 4)
self.assertGreaterEqual(result.get_upper_bound(1), 3 * n / 4)
def __init__(self, theta_sketch=None, union=None, compact_theta=None):
if theta_sketch is None:
theta_sketch = datasketches.update_theta_sketch()
if union is None:
union = datasketches.theta_union()
else:
union = _copy_union(union)
if compact_theta is not None:
union.update(compact_theta)
self.theta_sketch = theta_sketch
self.union = union
def get_result(self):
"""
Generate a theta sketch
Returns
-------
compact_sketch : datasketches.compact_theta_sketch
Read-only compact theta sketch with full statistics.
"""
new_union = datasketches.theta_union()
new_union.update(self.union.get_result())
new_union.update(self.theta_sketch)
return new_union.get_result()
def merge(self, other):
"""
Merge another `ThetaSketch` with this one, returning a new object
Parameters
----------
other : ThetaSketch
Other theta sketch
Returns
-------
new : ThetaSketch
New theta sketch with merged statistics
"""
new_union = datasketches.theta_union()
new_union.update(self.get_result())
new_union.update(other.get_result())
return ThetaSketch(union=new_union)
def _copy_union(union):
new_union = datasketches.theta_union()
new_union.update(union.get_result())
return new_union
def test_theta_set_operations(self):
k = 12 # 2^k = 4096 rows in the table
n = 1 << 18 # ~256k unique values
# we'll have 1/4 of the values overlap
offset = int(3 * n / 4) # it's a float w/o cast
# create a couple sketches and inject some values
sk1 = self.generate_theta_sketch(n, k)
sk2 = self.generate_theta_sketch(n, k, offset)
# UNIONS
# create a union object
union = theta_union(k)
union.update(sk1)
union.update(sk2)
# getting result from union returns a compact_theta_sketch
# compact theta sketches can be used in additional unions
# or set operations but cannot accept further item updates
result = union.get_result()
self.assertTrue(isinstance(result, compact_theta_sketch))
# since our process here is deterministic, we have
# checked and know the exact answer is within one
# standard deviation of the estimate
self.assertLessEqual(result.get_lower_bound(1), 7 * n / 4)
self.assertGreaterEqual(result.get_upper_bound(1), 7 * n / 4)
# INTERSECTIONS
# create an intersection object
intersect = theta_intersection() # no lg_k
intersect.update(sk1)
intersect.update(sk2)
# has_result() indicates the intersection has been used,
# although the result may be the empty set
self.assertTrue(intersect.has_result())
# as with unions, the result is a compact sketch
result = intersect.get_result()
self.assertTrue(isinstance(result, compact_theta_sketch))
# we know the sets overlap by 1/4
self.assertLessEqual(result.get_lower_bound(1), n / 4)
self.assertGreaterEqual(result.get_upper_bound(1), n / 4)
# A NOT B
# create an a_not_b object
anb = theta_a_not_b() # no lg_k
result = anb.compute(sk1, sk2)
# as with unions, the result is a compact sketch
self.assertTrue(isinstance(result, compact_theta_sketch))
# we know the sets overlap by 1/4, so the remainder is 3/4
self.assertLessEqual(result.get_lower_bound(1), 3 * n / 4)
self.assertGreaterEqual(result.get_upper_bound(1), 3 * n / 4)
# JACCARD SIMILARITY
# Jaccard Similarity measure returns (lower_bound, estimate, upper_bound)
jac = theta_jaccard_similarity.jaccard(sk1, sk2)
# we can check that results are in the expected order
self.assertLess(jac[0], jac[1])
self.assertLess(jac[1], jac[2])
# checks for sketch equivalency
self.assertTrue(theta_jaccard_similarity.exactly_equal(sk1, sk1))
self.assertFalse(theta_jaccard_similarity.exactly_equal(sk1, sk2))
# we can apply a check for similarity or dissimilarity at a
# given threshhold, at 97.7% confidence.
# check that the Jaccard Index is at most (upper bound) 0.2.
# exact result would be 1/7
self.assertTrue(
theta_jaccard_similarity.dissimilarity_test(sk1, sk2, 0.2))
# check that the Jaccard Index is at least (lower bound) 0.7
# exact result would be 3/4, using result from A NOT B test
self.assertTrue(
theta_jaccard_similarity.similarity_test(sk1, result, 0.7))
