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from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import TestCase, run_module_suite, assert_equal, \
assert_array_equal
from scipy.stats import rankdata, tiecorrect
class TestTieCorrect(TestCase):
def test_empty(self):
"""An empty array requires no correction, should return 1.0."""
ranks = np.array([], dtype=np.float64)
c = tiecorrect(ranks)
assert_equal(c, 1.0)
def test_one(self):
"""A single element requires no correction, should return 1.0."""
ranks = np.array([1.0], dtype=np.float64)
c = tiecorrect(ranks)
assert_equal(c, 1.0)
def test_no_correction(self):
"""Arrays with no ties require no correction."""
ranks = np.arange(2.0)
c = tiecorrect(ranks)
assert_equal(c, 1.0)
ranks = np.arange(3.0)
c = tiecorrect(ranks)
assert_equal(c, 1.0)
def test_basic(self):
"""Check a few basic examples of the tie correction factor."""
# One tie of two elements
ranks = np.array([1.0, 2.5, 2.5])
c = tiecorrect(ranks)
T = 2.0
N = ranks.size
expected = 1.0 - (T**3 - T) / (N**3 - N)
assert_equal(c, expected)
# One tie of two elements (same as above, but tie is not at the end)
ranks = np.array([1.5, 1.5, 3.0])
c = tiecorrect(ranks)
T = 2.0
N = ranks.size
expected = 1.0 - (T**3 - T) / (N**3 - N)
assert_equal(c, expected)
# One tie of three elements
ranks = np.array([1.0, 3.0, 3.0, 3.0])
c = tiecorrect(ranks)
T = 3.0
N = ranks.size
expected = 1.0 - (T**3 - T) / (N**3 - N)
assert_equal(c, expected)
# Two ties, lengths 2 and 3.
ranks = np.array([1.5, 1.5, 4.0, 4.0, 4.0])
c = tiecorrect(ranks)
T1 = 2.0
T2 = 3.0
N = ranks.size
expected = 1.0 - ((T1**3 - T1) + (T2**3 - T2)) / (N**3 - N)
assert_equal(c, expected)
class TestRankData(TestCase):
def test_empty(self):
"""stats.rankdata([]) should return an empty array."""
a = np.array([], dtype=np.int)
r = rankdata(a)
assert_array_equal(r, np.array([], dtype=np.float64))
r = rankdata([])
assert_array_equal(r, np.array([], dtype=np.float64))
def test_one(self):
"""Check stats.rankdata with an array of length 1."""
data = [100]
a = np.array(data, dtype=np.int)
r = rankdata(a)
assert_array_equal(r, np.array([1.0], dtype=np.float64))
r = rankdata(data)
assert_array_equal(r, np.array([1.0], dtype=np.float64))
def test_basic(self):
"""Basic tests of stats.rankdata."""
data = [100, 10, 50]
expected = np.array([3.0, 1.0, 2.0], dtype=np.float64)
a = np.array(data, dtype=np.int)
r = rankdata(a)
assert_array_equal(r, expected)
r = rankdata(data)
assert_array_equal(r, expected)
data = [40, 10, 30, 10, 50]
expected = np.array([4.0, 1.5, 3.0, 1.5, 5.0], dtype=np.float64)
a = np.array(data, dtype=np.int)
r = rankdata(a)
assert_array_equal(r, expected)
r = rankdata(data)
assert_array_equal(r, expected)
data = [20, 20, 20, 10, 10, 10]
expected = np.array([5.0, 5.0, 5.0, 2.0, 2.0, 2.0], dtype=np.float64)
a = np.array(data, dtype=np.int)
r = rankdata(a)
assert_array_equal(r, expected)
r = rankdata(data)
assert_array_equal(r, expected)
# The docstring states explicitly that the argument is flattened.
a2d = a.reshape(2, 3)
r = rankdata(a2d)
assert_array_equal(r, expected)
def test_large_int(self):
data = np.array([2**60, 2**60+1], dtype=np.uint64)
r = rankdata(data)
assert_array_equal(r, [1.0, 2.0])
data = np.array([2**60, 2**60+1], dtype=np.int64)
r = rankdata(data)
assert_array_equal(r, [1.0, 2.0])
data = np.array([2**60, -2**60+1], dtype=np.int64)
r = rankdata(data)
assert_array_equal(r, [2.0, 1.0])
def test_big_tie(self):
for n in [10000, 100000, 1000000]:
data = np.ones(n, dtype=int)
r = rankdata(data)
expected_rank = 0.5 * (n + 1)
assert_array_equal(r, expected_rank * data,
"test failed with n=%d" % n)
_cases = (
# values, method, expected
([], 'average', []),
([], 'min', []),
([], 'max', []),
([], 'dense', []),
([], 'ordinal', []),
#
([100], 'average', [1.0]),
([100], 'min', [1.0]),
([100], 'max', [1.0]),
([100], 'dense', [1.0]),
([100], 'ordinal', [1.0]),
#
([100, 100, 100], 'average', [2.0, 2.0, 2.0]),
([100, 100, 100], 'min', [1.0, 1.0, 1.0]),
([100, 100, 100], 'max', [3.0, 3.0, 3.0]),
([100, 100, 100], 'dense', [1.0, 1.0, 1.0]),
([100, 100, 100], 'ordinal', [1.0, 2.0, 3.0]),
#
([100, 300, 200], 'average', [1.0, 3.0, 2.0]),
([100, 300, 200], 'min', [1.0, 3.0, 2.0]),
([100, 300, 200], 'max', [1.0, 3.0, 2.0]),
([100, 300, 200], 'dense', [1.0, 3.0, 2.0]),
([100, 300, 200], 'ordinal', [1.0, 3.0, 2.0]),
#
([100, 200, 300, 200], 'average', [1.0, 2.5, 4.0, 2.5]),
([100, 200, 300, 200], 'min', [1.0, 2.0, 4.0, 2.0]),
([100, 200, 300, 200], 'max', [1.0, 3.0, 4.0, 3.0]),
([100, 200, 300, 200], 'dense', [1.0, 2.0, 3.0, 2.0]),
([100, 200, 300, 200], 'ordinal', [1.0, 2.0, 4.0, 3.0]),
#
([100, 200, 300, 200, 100], 'average', [1.5, 3.5, 5.0, 3.5, 1.5]),
([100, 200, 300, 200, 100], 'min', [1.0, 3.0, 5.0, 3.0, 1.0]),
([100, 200, 300, 200, 100], 'max', [2.0, 4.0, 5.0, 4.0, 2.0]),
([100, 200, 300, 200, 100], 'dense', [1.0, 2.0, 3.0, 2.0, 1.0]),
([100, 200, 300, 200, 100], 'ordinal', [1.0, 3.0, 5.0, 4.0, 2.0]),
#
([10] * 30, 'ordinal', np.arange(1.0, 31.0)),
)
def test_cases():
def check_case(values, method, expected):
r = rankdata(values, method=method)
assert_array_equal(r, expected)
for values, method, expected in _cases:
yield check_case, values, method, expected
if __name__ == "__main__":
run_module_suite()
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