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test_parfun.py
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test_parfun.py
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import itertools
import pytest
from barvikron import *
def sturmfels_expected(b):
"""
Closed formula from Sturmfels (1995).
"""
u, v, w = sorted(b, reverse=True)
if (u + v + w) % 2 == 1:
return 0
if u >= v + w:
psi = v * w / 2 + v * w**2 / 8 - w**3 / 24
if u % 2 == 0 and v % 2 == 0:
psi += 1 + v / 2 + 2 * w / 3
elif u % 2 == 1 and v % 2 == 1:
psi += 1 / 2 + v / 2 + 5 * w / 12
else:
psi += 1 / 2 + 3 * v / 8 + 13 * w / 24
else:
psi = (
-(u**2) / 8
- v**2 / 8
- w**2 / 8
+ u * v / 4
+ u * w / 4
+ v * w / 4
+ u**3 / 48
- u**2 * v / 16
- u**2 * w / 16
+ u * v**2 / 16
+ u * v * w / 8
+ u * w**2 / 16
- v**3 / 48
- v**2 * w / 16
+ v * w**2 / 16
- w**3 / 16
)
if u % 2 == 0 and v % 2 == 0:
psi += 1 + u / 6 + v / 3 + w / 2
elif u % 2 == 1 and v % 2 == 1:
psi += 1 / 2 + u / 6 + v / 3 + w / 4
else:
psi += 1 / 2 + u / 6 + 5 * v / 24 + 3 * w / 8
return int(round(psi))
def test_construction():
vpn = VectorPartitionFunction([[1, 0], [0, 1], [1, 1]])
assert vpn.A.shape == (3, 2)
@pytest.mark.parametrize("b", itertools.product(range(1, 5), repeat=3))
def test_sturmfels_evaluation(b, evaluator):
sturmfels_vpn = VectorPartitionFunction(
[[2, 1, 1, 0, 0, 0], [0, 1, 0, 2, 1, 0], [0, 0, 1, 0, 1, 2]]
)
# compare evaluation for all b in {1,...,4}^3
got = sturmfels_vpn.eval(b, evaluator)
expected = sturmfels_expected(b)
assert got == expected