Tidied up code.
Some of the code was nasty. I cleaned it up a bit. I also started moving tests into a tests/ directory. You can run python -m unittest to run them. I still need to add more tests to make sure things are working as expected.
This commit is contained in:
Michael Whittaker
parent
63b88c38d5
commit
a42bccaf0c
6 changed files with 521 additions and 354 deletions
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@ -1,5 +1,5 @@
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from .expr import Node, choose, majority
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from .quorum_system import QuorumSystem
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from .quorum_system import QuorumSystem, Strategy
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from .viz import (
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plot_node_load,
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plot_node_load_on,
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@ -1,6 +1,5 @@
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from typing import Any, Callable, List, NamedTuple, Optional, Tuple
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import math
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import unittest
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class Point(NamedTuple):
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@ -90,165 +89,3 @@ def max_of_segments(segments: List[Segment]) -> List[Tuple[float, float]]:
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xs.append(p.x)
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xs.sort()
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return [(x, max(segments, key=lambda s: s(x))(x)) for x in xs]
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class TestGeometry(unittest.TestCase):
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def test_eq(self):
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l = Point(0, 1)
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r = Point(1, 1)
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m = Point(0.5, 0.5)
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self.assertEqual(Segment(l, r), Segment(l, r))
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self.assertNotEqual(Segment(l, r), Segment(l, m))
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def test_compatible(self):
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s1 = Segment(Point(0, 1), Point(1, 2))
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s2 = Segment(Point(0, 2), Point(1, 1))
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s3 = Segment(Point(0.5, 2), Point(1, 1))
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self.assertTrue(s1.compatible(s2))
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self.assertTrue(s2.compatible(s1))
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self.assertFalse(s1.compatible(s3))
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self.assertFalse(s3.compatible(s1))
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self.assertFalse(s2.compatible(s3))
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self.assertFalse(s3.compatible(s2))
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def test_call(self):
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segment = Segment(Point(0, 0), Point(1, 1))
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for x in [0.0, 0.25, 0.5, 0.75, 1.0]:
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self.assertEqual(segment(x), x)
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segment = Segment(Point(0, 0), Point(1, 2))
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for x in [0.0, 0.25, 0.5, 0.75, 1.0]:
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self.assertEqual(segment(x), 2*x)
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segment = Segment(Point(1, 2), Point(3, 6))
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for x in [1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0]:
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self.assertEqual(segment(x), 2*x)
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segment = Segment(Point(0, 1), Point(1, 0))
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for x in [0.0, 0.25, 0.5, 0.75, 1.0]:
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self.assertEqual(segment(x), 1 - x)
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def test_slope(self):
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self.assertEqual(Segment(Point(0, 0), Point(1, 1)).slope(), 1.0)
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self.assertEqual(Segment(Point(0, 1), Point(1, 2)).slope(), 1.0)
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self.assertEqual(Segment(Point(1, 1), Point(2, 2)).slope(), 1.0)
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self.assertEqual(Segment(Point(1, 1), Point(2, 3)).slope(), 2.0)
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self.assertEqual(Segment(Point(1, 1), Point(2, 0)).slope(), -1.0)
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def test_above(self):
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s1 = Segment(Point(0, 0), Point(1, 0.5))
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s2 = Segment(Point(0, 0.5), Point(1, 2))
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s3 = Segment(Point(0, 1.5), Point(1, 0.5))
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self.assertFalse(s1.above(s1))
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self.assertFalse(s1.above(s2))
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self.assertFalse(s1.above(s3))
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self.assertTrue(s2.above(s1))
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self.assertFalse(s2.above(s2))
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self.assertFalse(s2.above(s3))
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self.assertTrue(s3.above(s1))
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self.assertFalse(s3.above(s2))
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self.assertFalse(s3.above(s3))
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def test_above_eq(self):
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s1 = Segment(Point(0, 0), Point(1, 0.5))
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s2 = Segment(Point(0, 0.5), Point(1, 2))
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s3 = Segment(Point(0, 1.5), Point(1, 0.5))
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self.assertTrue(s1.above_eq(s1))
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self.assertFalse(s1.above_eq(s2))
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self.assertFalse(s1.above_eq(s3))
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self.assertTrue(s2.above_eq(s1))
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self.assertTrue(s2.above_eq(s2))
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self.assertFalse(s2.above_eq(s3))
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self.assertTrue(s3.above_eq(s1))
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self.assertFalse(s3.above_eq(s2))
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self.assertTrue(s3.above_eq(s3))
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def test_intersects(self):
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s1 = Segment(Point(0, 0), Point(1, 0.5))
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s2 = Segment(Point(0, 0.5), Point(1, 2))
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s3 = Segment(Point(0, 1.5), Point(1, 0.5))
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self.assertTrue(s1.intersects(s1))
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self.assertFalse(s1.intersects(s2))
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self.assertTrue(s1.intersects(s3))
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self.assertFalse(s2.intersects(s1))
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self.assertTrue(s2.intersects(s2))
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self.assertTrue(s2.intersects(s3))
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self.assertTrue(s3.intersects(s1))
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self.assertTrue(s3.intersects(s2))
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self.assertTrue(s3.intersects(s3))
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def test_intersection(self):
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s1 = Segment(Point(0, 0), Point(1, 1))
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s2 = Segment(Point(0, 1), Point(1, 0))
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s3 = Segment(Point(0, 1), Point(1, 1))
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s4 = Segment(Point(0, 0.25), Point(1, 0.25))
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self.assertEqual(s1.intersection(s1), None)
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self.assertEqual(s1.intersection(s2), Point(0.5, 0.5))
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self.assertEqual(s1.intersection(s3), Point(1, 1))
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self.assertEqual(s1.intersection(s4), Point(0.25, 0.25))
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self.assertEqual(s2.intersection(s1), Point(0.5, 0.5))
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self.assertEqual(s2.intersection(s2), None)
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self.assertEqual(s2.intersection(s3), Point(0, 1))
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self.assertEqual(s2.intersection(s4), Point(0.75, 0.25))
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self.assertEqual(s3.intersection(s1), Point(1, 1))
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self.assertEqual(s3.intersection(s2), Point(0, 1))
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self.assertEqual(s3.intersection(s3), None)
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self.assertEqual(s3.intersection(s4), None)
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self.assertEqual(s4.intersection(s1), Point(0.25, 0.25))
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self.assertEqual(s4.intersection(s2), Point(0.75, 0.25))
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self.assertEqual(s4.intersection(s3), None)
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self.assertEqual(s4.intersection(s4), None)
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def test_max_one_segment(self):
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s1 = Segment(Point(0, 0), Point(1, 1))
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s2 = Segment(Point(0, 1), Point(1, 0))
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s3 = Segment(Point(0, 1), Point(1, 1))
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s4 = Segment(Point(0, 0.25), Point(1, 0.25))
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s5 = Segment(Point(0, 0.75), Point(1, 0.75))
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def is_subset(xs: List[Any], ys: List[Any]) -> bool:
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return all(x in ys for x in xs)
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for s in [s1, s2, s3, s4, s5]:
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self.assertEqual(max_of_segments([s]), [s.l, s.r])
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expected = [
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([s1, s1], [(0, 0), (1, 1)]),
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([s1, s2], [(0, 1), (0.5, 0.5), (1, 1)]),
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([s1, s3], [(0, 1), (1, 1)]),
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([s1, s4], [(0, 0.25), (0.25, 0.25), (1, 1)]),
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([s1, s5], [(0, 0.75), (0.75, 0.75), (1, 1)]),
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([s2, s2], [(0, 1), (1, 0)]),
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([s2, s3], [(0, 1), (1, 1)]),
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([s2, s4], [(0, 1), (0.75, 0.25), (1, 0.25)]),
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([s2, s5], [(0, 1), (0.25, 0.75), (1, 0.75)]),
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([s3, s3], [(0, 1), (1, 1)]),
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([s3, s4], [(0, 1), (1, 1)]),
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([s3, s5], [(0, 1), (1, 1)]),
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([s4, s4], [(0, 0.25), (1, 0.25)]),
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([s4, s5], [(0, 0.75), (1, 0.75)]),
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([s5, s5], [(0, 0.75), (1, 0.75)]),
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([s1, s2, s4], [(0, 1), (0.5, 0.5), (1, 1)]),
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([s1, s2, s5], [(0, 1), (0.25, 0.75), (0.75, 0.75), (1, 1)]),
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]
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for segments, path in expected:
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self.assertTrue(is_subset(path, max_of_segments(segments)))
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self.assertTrue(is_subset(path, max_of_segments(segments[::-1])))
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if __name__ == '__main__':
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unittest.main()
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@ -1,6 +1,3 @@
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# TODO(mwhittaker): We can define a set of read quorums that are not minimal.
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# Does this mess things up?
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from . import distribution
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from . import geometry
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from .distribution import Distribution
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@ -16,7 +13,6 @@ import pulp
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T = TypeVar('T')
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LOAD = 'load'
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NETWORK = 'network'
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LATENCY = 'latency'
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@ -29,8 +25,7 @@ class QuorumSystem(Generic[T]):
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writes: Optional[Expr[T]] = None) -> None:
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if reads is not None and writes is not None:
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optimal_writes = reads.dual()
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if not all(optimal_writes.is_quorum(write_quorum)
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for write_quorum in writes.quorums()):
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if not all(optimal_writes.is_quorum(wq) for wq in writes.quorums()):
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raise ValueError(
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'Not all read quorums intersect all write quorums')
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@ -63,9 +58,15 @@ class QuorumSystem(Generic[T]):
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def is_write_quorum(self, xs: Set[T]) -> bool:
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return self.writes.is_quorum(xs)
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def node(self, x: T) -> Node[T]:
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return self.x_to_node[x]
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def nodes(self) -> Set[Node[T]]:
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return self.reads.nodes() | self.writes.nodes()
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def elements(self) -> Set[T]:
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return {node.x for node in self.nodes()}
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def resilience(self) -> int:
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return min(self.read_resilience(), self.write_resilience())
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@ -75,6 +76,107 @@ class QuorumSystem(Generic[T]):
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def write_resilience(self) -> int:
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return self.writes.resilience()
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def dup_free(self) -> bool:
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return self.reads.dup_free() and self.writes.dup_free()
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def load(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) -> float:
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return self.strategy(
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optimize,
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load_limit,
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network_limit,
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latency_limit,
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read_fraction,
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write_fraction,
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f
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).load(read_fraction, write_fraction)
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def capacity(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) -> float:
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return self.strategy(
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optimize,
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load_limit,
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network_limit,
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latency_limit,
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read_fraction,
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write_fraction,
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f
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).capacity(read_fraction, write_fraction)
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def network_load(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) -> float:
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return self.strategy(
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optimize,
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load_limit,
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network_limit,
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latency_limit,
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read_fraction,
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write_fraction,
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f
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).network_load(read_fraction, write_fraction)
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def latency(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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network_limit: Optional[float] = None,
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) -> float:
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return self.strategy(
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optimize,
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load_limit,
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network_limit,
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latency_limit,
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read_fraction,
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write_fraction,
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f
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).latency(read_fraction, write_fraction)
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def uniform_strategy(self, f: int = 0) -> 'Strategy[T]':
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"""
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uniform_strategy(f) returns a uniform strategy over the minimal
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f-resilient quorums. That is, every minimal f-resilient quorum is
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equally likely to be chosen.
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"""
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if f < 0:
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raise ValueError('f must be >= 0')
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elif f == 0:
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read_quorums = list(self.read_quorums())
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write_quorums = list(self.write_quorums())
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else:
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xs = list(self.elements())
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read_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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write_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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if len(read_quorums) == 0:
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raise ValueError(f'There are no {f}-resilient read quorums')
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if len(write_quorums) == 0:
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raise ValueError(f'There are no {f}-resilient write quorums')
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read_quorums = self._minimize(read_quorums)
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write_quorums = self._minimize(write_quorums)
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sigma_r = {frozenset(rq): 1 / len(rq) for rq in read_quorums}
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sigma_w = {frozenset(wq): 1 / len(wq) for wq in write_quorums}
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return Strategy(self, sigma_r, sigma_w)
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def strategy(self,
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optimize: str = LOAD,
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load_limit: Optional[float] = None,
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@ -82,10 +184,10 @@ class QuorumSystem(Generic[T]):
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latency_limit: Optional[datetime.timedelta] = None,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) \
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-> 'Strategy[T]':
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if f < 0:
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raise ValueError('f must be >= 0')
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f: int = 0) -> 'Strategy[T]':
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if optimize not in {LOAD, NETWORK, LATENCY}:
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raise ValueError(
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f'optimize must be one of {LOAD}, {NETWORK}, or {LATENCY}')
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if optimize == LOAD and load_limit is not None:
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raise ValueError(
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@ -99,6 +201,9 @@ class QuorumSystem(Generic[T]):
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raise ValueError(
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'a latency limit cannot be set when optimizing for latency')
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if f < 0:
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raise ValueError('f must be >= 0')
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d = distribution.canonicalize_rw(read_fraction, write_fraction)
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if f == 0:
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return self._load_optimal_strategy(
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@ -110,7 +215,7 @@ class QuorumSystem(Generic[T]):
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network_limit=network_limit,
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latency_limit=latency_limit)
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else:
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xs = [node.x for node in self.nodes()]
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xs = list(self.elements())
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read_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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write_quorums = list(self._f_resilient_quorums(f, xs, self.reads))
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if len(read_quorums) == 0:
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@ -126,13 +231,23 @@ class QuorumSystem(Generic[T]):
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network_limit=network_limit,
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latency_limit=latency_limit)
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def dup_free(self) -> bool:
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return self.reads.dup_free() and self.writes.dup_free()
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def _minimize(self, sets: List[Set[T]]) -> List[Set[T]]:
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sets = sorted(sets, key=lambda s: len(s))
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minimal_elements: List[Set[T]] = []
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for x in sets:
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if not any(x >= y for y in minimal_elements):
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minimal_elements.append(x)
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return minimal_elements
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def _f_resilient_quorums(self,
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f: int,
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xs: List[T],
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e: Expr) -> Iterator[Set[T]]:
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"""
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Consider a set X of elements in xs. We say X is f-resilient if, despite
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removing an arbitrary set of f elements from X, X is a quorum in e.
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_f_resilient_quorums returns the set of all f-resilient quorums.
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"""
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assert f >= 1
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def helper(s: Set[T], i: int) -> Iterator[Set[T]]:
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@ -148,25 +263,6 @@ class QuorumSystem(Generic[T]):
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return helper(set(), 0)
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def load(self,
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read_fraction: Optional[Distribution] = None,
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write_fraction: Optional[Distribution] = None,
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f: int = 0) \
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-> float:
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return 0
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# TODO(mwhittaker): Remove.
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# sigma = self.strategy(read_fraction, write_fraction, f)
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# return sigma.load(read_fraction, write_fraction)
|
||||
|
||||
def capacity(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None,
|
||||
f: int = 0) \
|
||||
-> float:
|
||||
return 0
|
||||
# TODO(mwhittaker): Remove.
|
||||
# return 1 / self.load(read_fraction, write_fraction, f)
|
||||
|
||||
def _read_quorum_latency(self, quorum: Set[Node[T]]) -> datetime.timedelta:
|
||||
return self._quorum_latency(quorum, self.is_read_quorum)
|
||||
|
||||
|
|
@ -205,54 +301,132 @@ class QuorumSystem(Generic[T]):
|
|||
read_quorums = [{a, b}, {c, d}]
|
||||
write_quorums = [{a, c}, {a, d}, {b, c}, {b, d}]
|
||||
|
||||
We can form a linear program to compute the optimal load of this quorum
|
||||
system for some fixed read fraction fr as follows. First, we create a
|
||||
variable ri for every read quorum i and a variable wi for every write
|
||||
quorum i. ri represents the probabilty of selecting the ith read
|
||||
quorum, and wi represents the probabilty of selecting the ith write
|
||||
quorum. We introduce an additional variable l that represents the load
|
||||
and solve the following linear program.
|
||||
We want to find the strategy that is optimal with respect to load,
|
||||
network load, or latency that satisfies the provided load, network
|
||||
load, or latency constraints.
|
||||
|
||||
min L subject to
|
||||
r0 + r1 + r2 = 1
|
||||
w0 + w1 = 1
|
||||
fr (r0) + (1 - fr) (w0 + w1) <= L # a's load
|
||||
fr (r0) + (1 - fr) (w2 + w3) <= L # b's load
|
||||
fr (r1) + (1 - fr) (w0 + w2) <= L # c's load
|
||||
fr (r1) + (1 - fr) (w1 + w3) <= L # d's load
|
||||
We can find the optimal strategy using linear programming. First, we
|
||||
create a variable ri for every read quorum i and a variable wi for
|
||||
every write quorum i. ri represents the probabilty of selecting the ith
|
||||
read quorum, and wi represents the probabilty of selecting the ith
|
||||
write quorum.
|
||||
|
||||
If we assume every element x has read capacity rcap_x and write
|
||||
capacity wcap_x, then we adjust the linear program like this.
|
||||
We now explain how to represent load, network load, and latency as
|
||||
linear expressions.
|
||||
|
||||
min L subject to
|
||||
r0 + r1 + r2 = 1
|
||||
w0 + w1 = 1
|
||||
fr/rcap_a (r0) + (1 - fr)/wcap_a (w0 + w1) <= L # a's load
|
||||
fr/rcap_b (r0) + (1 - fr)/wcap_b (w2 + w3) <= L # b's load
|
||||
fr/rcap_c (r1) + (1 - fr)/wcap_c (w0 + w2) <= L # c's load
|
||||
fr/rcap_d (r1) + (1 - fr)/wcap_d (w1 + w3) <= L # d's load
|
||||
Load
|
||||
====
|
||||
Assume a read fraction fr and write fraction fw. The load of a node a is
|
||||
|
||||
Assume we have fr = 0.9 with 80% probabilty and fr = 0.5 with 20%. Then
|
||||
we adjust the linear program as follows to find the strategy that
|
||||
minimzes the average load.
|
||||
load(a) = (fr * rprob(a) / rcap(a)) + (fw * wprob(a) / wcap(a))
|
||||
|
||||
min 0.8 * L_0.9 + 0.2 * L_0.5 subject to
|
||||
r0 + r1 + r2 = 1
|
||||
w0 + w1 = 1
|
||||
0.9/rcap_a (r0) + 0.1/wcap_a (w0 + w1) <= L_0.9 # a's load
|
||||
0.9/rcap_b (r0) + 0.1/wcap_b (w2 + w3) <= L_0.9 # b's load
|
||||
0.9/rcap_c (r1) + 0.1/wcap_c (w0 + w2) <= L_0.9 # c's load
|
||||
0.9/rcap_d (r1) + 0.1/wcap_d (w1 + w3) <= L_0.9 # d's load
|
||||
0.5/rcap_a (r0) + 0.5/wcap_a (w0 + w1) <= L_0.5 # a's load
|
||||
0.5/rcap_b (r0) + 0.5/wcap_b (w2 + w3) <= L_0.5 # b's load
|
||||
0.5/rcap_c (r1) + 0.5/wcap_c (w0 + w2) <= L_0.5 # c's load
|
||||
0.5/rcap_d (r1) + 0.5/wcap_d (w1 + w3) <= L_0.5 # d's load
|
||||
where prob_r(a) and prob_w(a) are the probabilities that a is selected
|
||||
as part of a read or write quorum respectively; and rcap(a) and wcap(a)
|
||||
are the read and write capacities of a. We can express prob_r(a) and
|
||||
prob_w(a) as follows:
|
||||
|
||||
rprob(a) = sum({ri | a is in read quorum i})
|
||||
wprob(a) = sum({wi | a is in write quorum i})
|
||||
|
||||
Using the example grid quorum above, we have:
|
||||
|
||||
rprob(a) = r0 wprob(a) = w0 + w1
|
||||
rprob(b) = r0 wprob(b) = w2 + w3
|
||||
rprob(c) = r1 wprob(c) = w0 + w2
|
||||
rprob(d) = r1 wprob(d) = w1 + w3
|
||||
|
||||
The load of a strategy is the maximum load on any node. We can compute
|
||||
this by minimizing a new variable l and constraining the load of every
|
||||
node to be less than l. Using the example above, we have
|
||||
|
||||
min l subject to
|
||||
fr * r0 * rcap(a) + fw * (w0 + w1) * wcap(a) <= l
|
||||
fr * r0 * rcap(b) + fw * (w2 + w3) * wcap(b) <= l
|
||||
fr * r1 * rcap(c) + fw * (w0 + w2) * wcap(c) <= l
|
||||
fr * r1 * rcap(d) + fw * (w1 + w3) * wcap(d) <= l
|
||||
|
||||
To compute the load of a strategy with respect to a distribution of
|
||||
read_fractions, we compute the load for every value of fr and weight
|
||||
according to the distribution. For example, imagine fr is 0.9 80% of
|
||||
the time and 0.5 20% of the time. We have:
|
||||
|
||||
min 0.8 * l0.9 + 0.2 * l0.5
|
||||
0.9 * r0 * rcap(a) + 0.1 * (w0 + w1) * wcap(a) <= l0.9
|
||||
0.9 * r0 * rcap(b) + 0.1 * (w2 + w3) * wcap(b) <= l0.9
|
||||
0.9 * r1 * rcap(c) + 0.1 * (w0 + w2) * wcap(c) <= l0.9
|
||||
0.9 * r1 * rcap(d) + 0.1 * (w1 + w3) * wcap(d) <= l0.9
|
||||
0.5 * r0 * rcap(a) + 0.5 * (w0 + w1) * wcap(a) <= l0.5
|
||||
0.5 * r0 * rcap(b) + 0.5 * (w2 + w3) * wcap(b) <= l0.5
|
||||
0.5 * r1 * rcap(c) + 0.5 * (w0 + w2) * wcap(c) <= l0.5
|
||||
0.5 * r1 * rcap(d) + 0.5 * (w1 + w3) * wcap(d) <= l0.5
|
||||
|
||||
Let the expression for load be LOAD.
|
||||
|
||||
Network
|
||||
=======
|
||||
The network load of a strategy is the expected size of a quorum. For a
|
||||
fixed fr, We can compute the network load as:
|
||||
|
||||
fr * sum_i(size(read quorum i) * ri) +
|
||||
fw * sum_i(size(write quorum i) * ri)
|
||||
|
||||
Using the example above:
|
||||
|
||||
fr * (2*r0 + 2*r1) + fw * (2*w0 + 2*w1 + 2*w2 + 2*w3)
|
||||
|
||||
For a distribution of read fractions, we compute the weighted average.
|
||||
Let the expression for network load be NETWORK.
|
||||
|
||||
Latency
|
||||
=======
|
||||
The latency of a strategy is the expected latency of a quorum. We can
|
||||
compute the latency as:
|
||||
|
||||
fr * sum_i(latency(read quorum i) * ri) +
|
||||
fw * sum_i(latency(write quorum i) * ri)
|
||||
|
||||
Using the example above (assuming every node has a latency of 1):
|
||||
|
||||
fr * (1*r0 + 1*r1) + fw * (1*w0 + 1*w1 + 1*w2 + 1*w3)
|
||||
|
||||
For a distribution of read fractions, we compute the weighted average.
|
||||
Let the expression for latency be LATENCY.
|
||||
|
||||
Linear Program
|
||||
==============
|
||||
To find an optimal strategy, we use a linear program. The objective
|
||||
specified by the user is minimized, and any provided constraints are
|
||||
added as constraints to the program. For example, imagine the user
|
||||
wants a load optimal strategy with network load <= 2 and latency <= 3.
|
||||
We form the program:
|
||||
|
||||
min LOAD subject to
|
||||
sum_i(ri) = 1 # ensure we have a valid distribution on read quorums
|
||||
sum_i(wi) = 1 # ensure we have a valid distribution on write quorums
|
||||
NETWORK <= 2
|
||||
LATENCY <= 3
|
||||
|
||||
Using the example above assuming a fixed fr, we have:
|
||||
|
||||
min l subject to
|
||||
fr * r0 * rcap(a) + fw * (w0 + w1) * wcap(a) <= l
|
||||
fr * r0 * rcap(b) + fw * (w2 + w3) * wcap(b) <= l
|
||||
fr * r1 * rcap(c) + fw * (w0 + w2) * wcap(c) <= l
|
||||
fr * r1 * rcap(d) + fw * (w1 + w3) * wcap(d) <= l
|
||||
fr * (2*r0 + 2*r1) + fw * (2*w0 + 2*w1 + 2*w2 + 2*w3) <= 2
|
||||
fr * (1*r0 + 1*r1) + fw * (1*w0 + 1*w1 + 1*w2 + 1*w3) <= 3
|
||||
|
||||
If we instead wanted to minimize network load with load <= 4 and
|
||||
latency <= 5, we would have the following program:
|
||||
|
||||
min fr * (2*r0 + 2*r1) +
|
||||
fw * (2*w0 + 2*w1 + 2*w2 + 2*w3) subject to
|
||||
fr * r0 * rcap(a) + fw * (w0 + w1) * wcap(a) <= 4
|
||||
fr * r0 * rcap(b) + fw * (w2 + w3) * wcap(b) <= 4
|
||||
fr * r1 * rcap(c) + fw * (w0 + w2) * wcap(c) <= 4
|
||||
fr * r1 * rcap(d) + fw * (w1 + w3) * wcap(d) <= 4
|
||||
fr * (1*r0 + 1*r1) + fw * (1*w0 + 1*w1 + 1*w2 + 1*w3) <= 5
|
||||
"""
|
||||
nodes = self.nodes()
|
||||
x_to_node = {node.x: node for node in nodes}
|
||||
read_capacity = {node.x: node.read_capacity for node in nodes}
|
||||
write_capacity = {node.x: node.write_capacity for node in nodes}
|
||||
|
||||
# Create a variable for every read quorum and every write quorum. While
|
||||
# we do this, map each element x to the read and write quorums that
|
||||
# it's in. For example, image we have the following read and write
|
||||
|
|
@ -285,46 +459,46 @@ class QuorumSystem(Generic[T]):
|
|||
for x in write_quorum:
|
||||
x_to_write_quorum_vars[x].append(v)
|
||||
|
||||
fr = sum(weight * f for (f, weight) in read_fraction.items())
|
||||
fr = sum(p * fr for (fr, p) in read_fraction.items())
|
||||
|
||||
def network() -> pulp.LpAffineExpression:
|
||||
read_network = fr * sum(
|
||||
reads = fr * sum(
|
||||
v * len(rq)
|
||||
for (rq, v) in zip(read_quorums, read_quorum_vars)
|
||||
)
|
||||
write_network = (1 - fr) * sum(
|
||||
writes = (1 - fr) * sum(
|
||||
v * len(wq)
|
||||
for (wq, v) in zip(write_quorums, write_quorum_vars)
|
||||
)
|
||||
return read_network + write_network
|
||||
return reads + writes
|
||||
|
||||
def latency() -> pulp.LpAffineExpression:
|
||||
read_latency = fr * sum(
|
||||
reads = fr * sum(
|
||||
v * self._read_quorum_latency(quorum).total_seconds()
|
||||
for (rq, v) in zip(read_quorums, read_quorum_vars)
|
||||
for quorum in [{x_to_node[x] for x in rq}]
|
||||
for quorum in [{self.node(x) for x in rq}]
|
||||
)
|
||||
write_latency = (1. - fr) * sum(
|
||||
writes = (1 - fr) * sum(
|
||||
v * self._write_quorum_latency(quorum).total_seconds()
|
||||
for (wq, v) in zip(write_quorums, write_quorum_vars)
|
||||
for quorum in [{x_to_node[x] for x in wq}]
|
||||
for quorum in [{self.node(x) for x in wq}]
|
||||
)
|
||||
return read_latency + write_latency
|
||||
return reads + writes
|
||||
|
||||
def fr_load(problem: pulp.LpProblem, fr: float) -> pulp.LpAffineExpression:
|
||||
l = pulp.LpVariable(f'l_{fr}', 0, 1)
|
||||
|
||||
for node in nodes:
|
||||
for node in self.nodes():
|
||||
x = node.x
|
||||
x_load: pulp.LpAffineExpression = 0
|
||||
|
||||
if x in x_to_read_quorum_vars:
|
||||
vs = x_to_read_quorum_vars[x]
|
||||
x_load += fr * sum(vs) / read_capacity[x]
|
||||
x_load += fr * sum(vs) / self.node(x).read_capacity
|
||||
|
||||
if x in x_to_write_quorum_vars:
|
||||
vs = x_to_write_quorum_vars[x]
|
||||
x_load += (1 - fr) * sum(vs) / write_capacity[x]
|
||||
x_load += (1 - fr) * sum(vs) / self.node(x).write_capacity
|
||||
|
||||
problem += (x_load <= l, f'{x}{fr}')
|
||||
|
||||
|
|
@ -332,11 +506,11 @@ class QuorumSystem(Generic[T]):
|
|||
|
||||
def load(problem: pulp.LpProblem,
|
||||
read_fraction: Dict[float, float]) -> pulp.LpAffineExpression:
|
||||
return sum(weight * fr_load(problem, fr)
|
||||
for (fr, weight) in read_fraction.items())
|
||||
return sum(p * fr_load(problem, fr)
|
||||
for (fr, p) in read_fraction.items())
|
||||
|
||||
# Form the linear program to find the load.
|
||||
problem = pulp.LpProblem("load", pulp.LpMinimize)
|
||||
# Form the linear program.
|
||||
problem = pulp.LpProblem("optimal_strategy", pulp.LpMinimize)
|
||||
|
||||
# We add these constraints to make sure that the probabilities we
|
||||
# select form valid probabilty distributions.
|
||||
|
|
@ -365,152 +539,147 @@ class QuorumSystem(Generic[T]):
|
|||
'latency limit')
|
||||
|
||||
# Solve the linear program.
|
||||
print(problem)
|
||||
problem.solve(pulp.apis.PULP_CBC_CMD(msg=False))
|
||||
if problem.status != pulp.LpStatusOptimal:
|
||||
raise ValueError('no strategy satisfies the given constraints')
|
||||
|
||||
# Prune out any quorums with 0 probability.
|
||||
non_zero_read_quorums = [
|
||||
(rq, v.varValue)
|
||||
sigma_r = {
|
||||
frozenset(rq): v.varValue
|
||||
for (rq, v) in zip(read_quorums, read_quorum_vars)
|
||||
if v.varValue != 0]
|
||||
non_zero_write_quorums = [
|
||||
(wq, v.varValue)
|
||||
if v.varValue != 0
|
||||
}
|
||||
sigma_w = {
|
||||
frozenset(wq): v.varValue
|
||||
for (wq, v) in zip(write_quorums, write_quorum_vars)
|
||||
if v.varValue != 0]
|
||||
return Strategy(self,
|
||||
[rq for (rq, _) in non_zero_read_quorums],
|
||||
[weight for (_, weight) in non_zero_read_quorums],
|
||||
[wq for (wq, _) in non_zero_write_quorums],
|
||||
[weight for (_, weight) in non_zero_write_quorums])
|
||||
if v.varValue != 0
|
||||
}
|
||||
|
||||
return Strategy(self, sigma_r, sigma_w)
|
||||
|
||||
|
||||
class Strategy(Generic[T]):
|
||||
def __init__(self,
|
||||
qs: QuorumSystem[T],
|
||||
reads: List[Set[T]],
|
||||
read_weights: List[float],
|
||||
writes: List[Set[T]],
|
||||
write_weights: List[float]) -> None:
|
||||
sigma_r: Dict[FrozenSet[T], float],
|
||||
sigma_w: Dict[FrozenSet[T], float]) -> None:
|
||||
self.qs = qs
|
||||
self.reads = reads
|
||||
self.read_weights = read_weights
|
||||
self.writes = writes
|
||||
self.write_weights = write_weights
|
||||
self.sigma_r = sigma_r
|
||||
self.sigma_w = sigma_w
|
||||
|
||||
self.unweighted_read_load: Dict[T, float] = \
|
||||
collections.defaultdict(float)
|
||||
for (read_quorum, weight) in zip(self.reads, self.read_weights):
|
||||
# The probability that x is chosen as part of a read quorum.
|
||||
self.x_read_probability: Dict[T, float] = collections.defaultdict(float)
|
||||
for (read_quorum, p) in self.sigma_r.items():
|
||||
for x in read_quorum:
|
||||
self.unweighted_read_load[x] += weight
|
||||
self.x_read_probability[x] += p
|
||||
|
||||
self.unweighted_write_load: Dict[T, float] = \
|
||||
collections.defaultdict(float)
|
||||
for (write_quorum, weight) in zip(self.writes, self.write_weights):
|
||||
# The probability that x is chosen as part of a write quorum.
|
||||
self.x_write_probability: Dict[T, float] = collections.defaultdict(float)
|
||||
for (write_quorum, weight) in self.sigma_w.items():
|
||||
for x in write_quorum:
|
||||
self.unweighted_write_load[x] += weight
|
||||
self.x_write_probability[x] += weight
|
||||
|
||||
@no_type_check
|
||||
def __str__(self) -> str:
|
||||
non_zero_reads = {tuple(r): p
|
||||
for (r, p) in zip(self.reads, self.read_weights)
|
||||
if p > 0}
|
||||
non_zero_writes = {tuple(w): p
|
||||
for (w, p) in zip(self.writes, self.write_weights)
|
||||
if p > 0}
|
||||
return f'Strategy(reads={non_zero_reads}, writes={non_zero_writes})'
|
||||
# T may not comparable, so mypy complains about this sort.
|
||||
reads = {tuple(sorted(rq)): p for (rq, p) in self.sigma_r.items()}
|
||||
writes = {tuple(sorted(wq)): p for (wq, p) in self.sigma_w.items()}
|
||||
return f'Strategy(reads={reads}, writes={writes})'
|
||||
|
||||
def quorum_system(self) -> QuorumSystem[T]:
|
||||
return self.qs
|
||||
|
||||
def node(self, x: T) -> Node[T]:
|
||||
return self.qs.node(x)
|
||||
|
||||
def nodes(self) -> Set[Node[T]]:
|
||||
return self.qs.nodes()
|
||||
|
||||
def get_read_quorum(self) -> Set[T]:
|
||||
return np.random.choice(self.reads, p=self.read_weights)
|
||||
return set(np.random.choice(list(self.sigma_r.keys()),
|
||||
p=list(self.sigma_r.values())))
|
||||
|
||||
def get_write_quorum(self) -> Set[T]:
|
||||
return np.random.choice(self.writes, p=self.write_weights)
|
||||
return set(np.random.choice(list(self.sigma_w.keys()),
|
||||
p=list(self.sigma_w.values())))
|
||||
|
||||
def load(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> float:
|
||||
write_fraction: Optional[Distribution] = None) -> float:
|
||||
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
||||
return sum(weight * self._load(fr)
|
||||
for (fr, weight) in d.items())
|
||||
return sum(p * self._load(fr) for (fr, p) in d.items())
|
||||
|
||||
# TODO(mwhittaker): Rename throughput.
|
||||
def capacity(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> float:
|
||||
write_fraction: Optional[Distribution] = None) -> float:
|
||||
return 1 / self.load(read_fraction, write_fraction)
|
||||
|
||||
def network_load(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) -> float:
|
||||
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
||||
fr = sum(weight * f for (f, weight) in d.items())
|
||||
read_network_load = fr * sum(
|
||||
len(rq) * p
|
||||
for (rq, p) in zip(self.reads, self.read_weights)
|
||||
)
|
||||
write_network_load = (1 - fr) * sum(
|
||||
len(wq) * p
|
||||
for (wq, p) in zip(self.writes, self.write_weights)
|
||||
)
|
||||
return read_network_load + write_network_load
|
||||
fr = sum(p * fr for (fr, p) in d.items())
|
||||
reads = fr * sum(p * len(rq) for (rq, p) in self.sigma_r.items())
|
||||
writes = (1 - fr) * sum(p * len(wq) for (wq, p) in self.sigma_w.items())
|
||||
return reads + writes
|
||||
|
||||
# mypy doesn't like calling sum with timedeltas.
|
||||
@no_type_check
|
||||
def latency(self,
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> datetime.timedelta:
|
||||
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
||||
fr = sum(weight * f for (f, weight) in d.items())
|
||||
fr = sum(p * fr for (fr, p) in d.items())
|
||||
|
||||
read_latency = fr * sum((
|
||||
self.qs._read_quorum_latency(quorum) * p # type: ignore
|
||||
for (rq, p) in zip(self.reads, self.read_weights)
|
||||
for quorum in [{self.qs.x_to_node[x] for x in rq}]
|
||||
), datetime.timedelta(seconds=0)) # type: ignore
|
||||
write_latency = (1 - fr) * sum((
|
||||
self.qs._write_quorum_latency(quorum) * p # type: ignore
|
||||
for (wq, p) in zip(self.writes, self.write_weights)
|
||||
for quorum in [{self.qs.x_to_node[x] for x in wq}]
|
||||
), datetime.timedelta(seconds=0)) # type:ignore
|
||||
return read_latency + write_latency # type: ignore
|
||||
reads = fr * sum((
|
||||
p * self.qs._read_quorum_latency({self.node(x) for x in rq})
|
||||
for (rq, p) in self.sigma_r.items()
|
||||
), datetime.timedelta(seconds=0))
|
||||
|
||||
writes = (1 - fr) * sum((
|
||||
p * self.qs._write_quorum_latency({self.node(x) for x in wq})
|
||||
for (wq, p) in self.sigma_w.items()
|
||||
), datetime.timedelta(seconds=0))
|
||||
|
||||
return reads + writes
|
||||
|
||||
def node_load(self,
|
||||
node: Node[T],
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> float:
|
||||
write_fraction: Optional[Distribution] = None) -> float:
|
||||
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
||||
return sum(weight * self._node_load(node.x, fr)
|
||||
for (fr, weight) in d.items())
|
||||
return sum(p * self._node_load(node, fr) for (fr, p) in d.items())
|
||||
|
||||
def node_utilization(self,
|
||||
node: Node[T],
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> float:
|
||||
# TODO(mwhittaker): Implement.
|
||||
return 0.0
|
||||
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
||||
return sum(p * self._node_utilization(node, fr)
|
||||
for (fr, p) in d.items())
|
||||
|
||||
def node_throghput(self,
|
||||
def node_throughput(self,
|
||||
node: Node[T],
|
||||
read_fraction: Optional[Distribution] = None,
|
||||
write_fraction: Optional[Distribution] = None) \
|
||||
-> float:
|
||||
# TODO(mwhittaker): Implement.
|
||||
return 0.0
|
||||
|
||||
def _node_load(self, x: T, fr: float) -> float:
|
||||
"""
|
||||
_node_load returns the load on x given a fixed read fraction fr.
|
||||
"""
|
||||
fw = 1 - fr
|
||||
node = self.qs.x_to_node[x]
|
||||
return (fr * self.unweighted_read_load[x] / node.read_capacity +
|
||||
fw * self.unweighted_write_load[x] / node.write_capacity)
|
||||
write_fraction: Optional[Distribution] = None) -> float:
|
||||
d = distribution.canonicalize_rw(read_fraction, write_fraction)
|
||||
return sum(p * self._node_throughput(node, fr) for (fr, p) in d.items())
|
||||
|
||||
def _load(self, fr: float) -> float:
|
||||
"""
|
||||
_load returns the load given a fixed read fraction fr.
|
||||
"""
|
||||
return max(self._node_load(node.x, fr) for node in self.qs.nodes())
|
||||
return max(self._node_load(node, fr) for node in self.nodes())
|
||||
|
||||
def _node_load(self, node: Node[T], fr: float) -> float:
|
||||
fw = 1 - fr
|
||||
return (fr * self.x_read_probability[node.x] / node.read_capacity +
|
||||
fw * self.x_write_probability[node.x] / node.write_capacity)
|
||||
|
||||
def _node_utilization(self, node: Node[T], fr: float) -> float:
|
||||
return self._node_load(node, fr) / self._load(fr)
|
||||
|
||||
def _node_throughput(self, node: Node[T], fr: float) -> float:
|
||||
cap = 1 / self._load(fr)
|
||||
fw = 1 - fr
|
||||
return cap * (fr * self.x_read_probability[node.x] +
|
||||
fw * self.x_write_probability[node.x])
|
||||
|
|
|
|||
|
|
@ -4,7 +4,7 @@ from .distribution import Distribution
|
|||
from .expr import Node
|
||||
from .geometry import Point, Segment
|
||||
from .quorum_system import Strategy
|
||||
from typing import Dict, List, Optional, Set, Tuple, TypeVar
|
||||
from typing import Dict, FrozenSet, List, Optional, Set, Tuple, TypeVar
|
||||
import collections
|
||||
import matplotlib
|
||||
import matplotlib.pyplot as plt
|
||||
|
|
@ -107,19 +107,18 @@ def _plot_node_load_on(ax: plt.Axes,
|
|||
x_index = {x: i for (i, x) in enumerate(x_list)}
|
||||
x_ticks = list(range(len(x_list)))
|
||||
|
||||
def one_hot(quorum: Set[T]) -> np.array:
|
||||
def one_hot(quorum: FrozenSet[T]) -> np.array:
|
||||
bar_heights = np.zeros(len(x_list))
|
||||
for x in quorum:
|
||||
bar_heights[x_index[x]] = 1
|
||||
return bar_heights
|
||||
|
||||
def plot_quorums(quorums: List[Set[T]],
|
||||
weights: List[float],
|
||||
def plot_quorums(sigma: Dict[FrozenSet[T], float],
|
||||
fraction: float,
|
||||
bottoms: np.array,
|
||||
capacities: np.array,
|
||||
cmap: matplotlib.colors.Colormap):
|
||||
for (i, (quorum, weight)) in enumerate(zip(quorums, weights)):
|
||||
for (i, (quorum, weight)) in enumerate(sigma.items()):
|
||||
bar_heights = scale * fraction * weight * one_hot(quorum)
|
||||
if scale_by_node_capacity:
|
||||
bar_heights /= capacities
|
||||
|
|
@ -127,7 +126,7 @@ def _plot_node_load_on(ax: plt.Axes,
|
|||
ax.bar(x_ticks,
|
||||
bar_heights,
|
||||
bottom=bottoms,
|
||||
color=cmap(0.75 - i * 0.5 / len(quorums)),
|
||||
color=cmap(0.75 - i * 0.5 / len(sigma)),
|
||||
edgecolor='white', width=0.8)
|
||||
|
||||
for j, (bar_height, bottom) in enumerate(zip(bar_heights, bottoms)):
|
||||
|
|
@ -142,9 +141,9 @@ def _plot_node_load_on(ax: plt.Axes,
|
|||
read_capacities = np.array([node.read_capacity for node in nodes])
|
||||
write_capacities = np.array([node.write_capacity for node in nodes])
|
||||
bottoms = np.zeros(len(x_list))
|
||||
plot_quorums(sigma.reads, sigma.read_weights, fr, bottoms, read_capacities,
|
||||
plot_quorums(sigma.sigma_r, fr, bottoms, read_capacities,
|
||||
matplotlib.cm.get_cmap('Reds'))
|
||||
plot_quorums(sigma.writes, sigma.write_weights, fw, bottoms,
|
||||
plot_quorums(sigma.sigma_w, fw, bottoms,
|
||||
write_capacities, matplotlib.cm.get_cmap('Blues'))
|
||||
ax.set_xticks(x_ticks)
|
||||
ax.set_xticklabels(str(x) for x in x_list)
|
||||
|
|
|
|||
0
tests/__init__.py
Normal file
0
tests/__init__.py
Normal file
162
tests/test_geometry.py
Normal file
162
tests/test_geometry.py
Normal file
|
|
@ -0,0 +1,162 @@
|
|||
from quorums import *
|
||||
from quorums.geometry import *
|
||||
from typing import Any, Callable, List, NamedTuple, Optional, Tuple
|
||||
import unittest
|
||||
|
||||
|
||||
class TestGeometry(unittest.TestCase):
|
||||
def test_eq(self):
|
||||
l = Point(0, 1)
|
||||
r = Point(1, 1)
|
||||
m = Point(0.5, 0.5)
|
||||
self.assertEqual(Segment(l, r), Segment(l, r))
|
||||
self.assertNotEqual(Segment(l, r), Segment(l, m))
|
||||
|
||||
def test_compatible(self):
|
||||
s1 = Segment(Point(0, 1), Point(1, 2))
|
||||
s2 = Segment(Point(0, 2), Point(1, 1))
|
||||
s3 = Segment(Point(0.5, 2), Point(1, 1))
|
||||
self.assertTrue(s1.compatible(s2))
|
||||
self.assertTrue(s2.compatible(s1))
|
||||
self.assertFalse(s1.compatible(s3))
|
||||
self.assertFalse(s3.compatible(s1))
|
||||
self.assertFalse(s2.compatible(s3))
|
||||
self.assertFalse(s3.compatible(s2))
|
||||
|
||||
def test_call(self):
|
||||
segment = Segment(Point(0, 0), Point(1, 1))
|
||||
for x in [0.0, 0.25, 0.5, 0.75, 1.0]:
|
||||
self.assertEqual(segment(x), x)
|
||||
|
||||
segment = Segment(Point(0, 0), Point(1, 2))
|
||||
for x in [0.0, 0.25, 0.5, 0.75, 1.0]:
|
||||
self.assertEqual(segment(x), 2*x)
|
||||
|
||||
segment = Segment(Point(1, 2), Point(3, 6))
|
||||
for x in [1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0]:
|
||||
self.assertEqual(segment(x), 2*x)
|
||||
|
||||
segment = Segment(Point(0, 1), Point(1, 0))
|
||||
for x in [0.0, 0.25, 0.5, 0.75, 1.0]:
|
||||
self.assertEqual(segment(x), 1 - x)
|
||||
|
||||
def test_slope(self):
|
||||
self.assertEqual(Segment(Point(0, 0), Point(1, 1)).slope(), 1.0)
|
||||
self.assertEqual(Segment(Point(0, 1), Point(1, 2)).slope(), 1.0)
|
||||
self.assertEqual(Segment(Point(1, 1), Point(2, 2)).slope(), 1.0)
|
||||
self.assertEqual(Segment(Point(1, 1), Point(2, 3)).slope(), 2.0)
|
||||
self.assertEqual(Segment(Point(1, 1), Point(2, 0)).slope(), -1.0)
|
||||
|
||||
def test_above(self):
|
||||
s1 = Segment(Point(0, 0), Point(1, 0.5))
|
||||
s2 = Segment(Point(0, 0.5), Point(1, 2))
|
||||
s3 = Segment(Point(0, 1.5), Point(1, 0.5))
|
||||
|
||||
self.assertFalse(s1.above(s1))
|
||||
self.assertFalse(s1.above(s2))
|
||||
self.assertFalse(s1.above(s3))
|
||||
|
||||
self.assertTrue(s2.above(s1))
|
||||
self.assertFalse(s2.above(s2))
|
||||
self.assertFalse(s2.above(s3))
|
||||
|
||||
self.assertTrue(s3.above(s1))
|
||||
self.assertFalse(s3.above(s2))
|
||||
self.assertFalse(s3.above(s3))
|
||||
|
||||
def test_above_eq(self):
|
||||
s1 = Segment(Point(0, 0), Point(1, 0.5))
|
||||
s2 = Segment(Point(0, 0.5), Point(1, 2))
|
||||
s3 = Segment(Point(0, 1.5), Point(1, 0.5))
|
||||
|
||||
self.assertTrue(s1.above_eq(s1))
|
||||
self.assertFalse(s1.above_eq(s2))
|
||||
self.assertFalse(s1.above_eq(s3))
|
||||
|
||||
self.assertTrue(s2.above_eq(s1))
|
||||
self.assertTrue(s2.above_eq(s2))
|
||||
self.assertFalse(s2.above_eq(s3))
|
||||
|
||||
self.assertTrue(s3.above_eq(s1))
|
||||
self.assertFalse(s3.above_eq(s2))
|
||||
self.assertTrue(s3.above_eq(s3))
|
||||
|
||||
def test_intersects(self):
|
||||
s1 = Segment(Point(0, 0), Point(1, 0.5))
|
||||
s2 = Segment(Point(0, 0.5), Point(1, 2))
|
||||
s3 = Segment(Point(0, 1.5), Point(1, 0.5))
|
||||
|
||||
self.assertTrue(s1.intersects(s1))
|
||||
self.assertFalse(s1.intersects(s2))
|
||||
self.assertTrue(s1.intersects(s3))
|
||||
|
||||
self.assertFalse(s2.intersects(s1))
|
||||
self.assertTrue(s2.intersects(s2))
|
||||
self.assertTrue(s2.intersects(s3))
|
||||
|
||||
self.assertTrue(s3.intersects(s1))
|
||||
self.assertTrue(s3.intersects(s2))
|
||||
self.assertTrue(s3.intersects(s3))
|
||||
|
||||
def test_intersection(self):
|
||||
s1 = Segment(Point(0, 0), Point(1, 1))
|
||||
s2 = Segment(Point(0, 1), Point(1, 0))
|
||||
s3 = Segment(Point(0, 1), Point(1, 1))
|
||||
s4 = Segment(Point(0, 0.25), Point(1, 0.25))
|
||||
|
||||
self.assertEqual(s1.intersection(s1), None)
|
||||
self.assertEqual(s1.intersection(s2), Point(0.5, 0.5))
|
||||
self.assertEqual(s1.intersection(s3), Point(1, 1))
|
||||
self.assertEqual(s1.intersection(s4), Point(0.25, 0.25))
|
||||
|
||||
self.assertEqual(s2.intersection(s1), Point(0.5, 0.5))
|
||||
self.assertEqual(s2.intersection(s2), None)
|
||||
self.assertEqual(s2.intersection(s3), Point(0, 1))
|
||||
self.assertEqual(s2.intersection(s4), Point(0.75, 0.25))
|
||||
|
||||
self.assertEqual(s3.intersection(s1), Point(1, 1))
|
||||
self.assertEqual(s3.intersection(s2), Point(0, 1))
|
||||
self.assertEqual(s3.intersection(s3), None)
|
||||
self.assertEqual(s3.intersection(s4), None)
|
||||
|
||||
self.assertEqual(s4.intersection(s1), Point(0.25, 0.25))
|
||||
self.assertEqual(s4.intersection(s2), Point(0.75, 0.25))
|
||||
self.assertEqual(s4.intersection(s3), None)
|
||||
self.assertEqual(s4.intersection(s4), None)
|
||||
|
||||
def test_max_one_segment(self):
|
||||
s1 = Segment(Point(0, 0), Point(1, 1))
|
||||
s2 = Segment(Point(0, 1), Point(1, 0))
|
||||
s3 = Segment(Point(0, 1), Point(1, 1))
|
||||
s4 = Segment(Point(0, 0.25), Point(1, 0.25))
|
||||
s5 = Segment(Point(0, 0.75), Point(1, 0.75))
|
||||
|
||||
def is_subset(xs: List[Any], ys: List[Any]) -> bool:
|
||||
return all(x in ys for x in xs)
|
||||
|
||||
for s in [s1, s2, s3, s4, s5]:
|
||||
self.assertEqual(max_of_segments([s]), [s.l, s.r])
|
||||
|
||||
expected = [
|
||||
([s1, s1], [(0, 0), (1, 1)]),
|
||||
([s1, s2], [(0, 1), (0.5, 0.5), (1, 1)]),
|
||||
([s1, s3], [(0, 1), (1, 1)]),
|
||||
([s1, s4], [(0, 0.25), (0.25, 0.25), (1, 1)]),
|
||||
([s1, s5], [(0, 0.75), (0.75, 0.75), (1, 1)]),
|
||||
([s2, s2], [(0, 1), (1, 0)]),
|
||||
([s2, s3], [(0, 1), (1, 1)]),
|
||||
([s2, s4], [(0, 1), (0.75, 0.25), (1, 0.25)]),
|
||||
([s2, s5], [(0, 1), (0.25, 0.75), (1, 0.75)]),
|
||||
([s3, s3], [(0, 1), (1, 1)]),
|
||||
([s3, s4], [(0, 1), (1, 1)]),
|
||||
([s3, s5], [(0, 1), (1, 1)]),
|
||||
([s4, s4], [(0, 0.25), (1, 0.25)]),
|
||||
([s4, s5], [(0, 0.75), (1, 0.75)]),
|
||||
([s5, s5], [(0, 0.75), (1, 0.75)]),
|
||||
|
||||
([s1, s2, s4], [(0, 1), (0.5, 0.5), (1, 1)]),
|
||||
([s1, s2, s5], [(0, 1), (0.25, 0.75), (0.75, 0.75), (1, 1)]),
|
||||
]
|
||||
for segments, path in expected:
|
||||
self.assertTrue(is_subset(path, max_of_segments(segments)))
|
||||
self.assertTrue(is_subset(path, max_of_segments(segments[::-1])))
|
||||
Loading…
Reference in a new issue