def test_usp_4(method):
# table1 from https://doi.org/10.1098/rspa.2021.0549
w = [[18, 36, 21, 9, 6], [12, 36, 45, 36, 21], [6, 9, 9, 3, 3],
[3, 9, 9, 6, 3]]
r1 = perm.usp(w, method=method, size=9999, random_state=1)
r2 = perm.usp(np.transpose(w), method=method, size=1, random_state=1)
assert_allclose(r1.statistic, r2.statistic)
expected = 0.004106 # checked against USP R package
assert_allclose(r1.statistic, expected, atol=1e-6)
# according to paper, pvalue is 0.001, but USP R package gives correct value
expected = 0.0024 # computed from USP R package with b=99999
assert_allclose(r1.pvalue, expected, atol=0.001)
def test_usp_5(method, rng):
w = np.empty((100, 100))
for i in range(100):
for j in range(100):
w[i, j] = (i + j) % 2
r = perm.usp(w, method=method, size=99, random_state=1)
assert r.pvalue > 0.1
def test_usp_2(method, rng):
x = rng.normal(0, 2, size=100).astype(int)
w = np.histogram2d(x, x, range=((-5, 5), (-5, 5)))[0]
r = perm.usp(w, method=method, size=99, random_state=1)
assert r.pvalue == 0.01
def test_usp_1(method, rng):
x = rng.normal(0, 2, size=100)
y = rng.normal(1, 3, size=100)
w = np.histogram2d(x, y, bins=(5, 10))[0]
r = perm.usp(w, size=100, random_state=1)
assert r.pvalue > 0.05
def test_usp_bias(rng):
# We compute the p-value as an upper limit to the type I error rate.
# Therefore, the p-value is not unbiased. For size=1, we expect
# an average p-value = (1 + 0.5) / (1 + 1) = 0.75
got = [
perm.usp(rng.poisson(1000, size=(2, 2)), size=1, random_state=i).pvalue
for i in range(1000)
]
assert_allclose(np.mean(got), 0.75, atol=0.05)
def test_usp_bad_input():
with pytest.raises(ValueError):
perm.usp([[1, 2], [3, 4]], size=0)
with pytest.raises(ValueError):
perm.usp([[1, 2], [3, 4]], size=-1)
with pytest.raises(ValueError):
perm.usp([1, 2])
with pytest.raises(ValueError):
perm.usp([[1, 2], [3, 4]], method="foo")
def test_usp(k, n, method, benchmark):
w = np.zeros((k, k))
rng = np.random.default_rng(1)
for _ in range(n):
i = rng.integers(k)
j = rng.integers(k)
w[i, j] += 1
assert np.sum(w) == n
benchmark(lambda: usp(
w, method=method, precision=0, max_size=100, random_state=1))
def test_usp_3(method, rng):
cov = np.empty((2, 2))
cov[0, 0] = 2**2
cov[1, 1] = 3**2
rho = 0.5
cov[0, 1] = rho * np.sqrt(cov[0, 0] * cov[1, 1])
cov[1, 0] = cov[0, 1]
xy = rng.multivariate_normal([0, 1], cov, size=500).astype(int)
w = np.histogram2d(*xy.T)[0]
r = perm.usp(w, method=method, random_state=1)
assert r.pvalue < 0.0012