219 lines
7.3 KiB
Python
219 lines
7.3 KiB
Python
|
from __future__ import division, print_function, absolute_import
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from numpy.testing import assert_equal, assert_array_equal
|
||
|
|
|
||
|
|
from scipy.stats import rankdata, tiecorrect
|
||
|
|
|
||
|
|
|
||
|
|
class TestTieCorrect(object):
|
||
|
|
|
||
|
|
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)
|
||
|
|
|
||
|
|
def test_overflow(self):
|
||
|
|
ntie, k = 2000, 5
|
||
|
|
a = np.repeat(np.arange(k), ntie)
|
||
|
|
n = a.size # ntie * k
|
||
|
|
out = tiecorrect(rankdata(a))
|
||
|
|
assert_equal(out, 1.0 - k * (ntie**3 - ntie) / float(n**3 - n))
|
||
|
|
|
||
|
|
|
||
|
|
class TestRankData(object):
|
||
|
|
|
||
|
|
def test_empty(self):
|
||
|
|
"""stats.rankdata([]) should return an empty array."""
|
||
|
|
a = np.array([], dtype=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=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=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=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=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_rankdata_object_string(self):
|
||
|
|
min_rank = lambda a: [1 + sum(i < j for i in a) for j in a]
|
||
|
|
max_rank = lambda a: [sum(i <= j for i in a) for j in a]
|
||
|
|
ordinal_rank = lambda a: min_rank([(x, i) for i, x in enumerate(a)])
|
||
|
|
|
||
|
|
def average_rank(a):
|
||
|
|
return [(i + j) / 2.0 for i, j in zip(min_rank(a), max_rank(a))]
|
||
|
|
|
||
|
|
def dense_rank(a):
|
||
|
|
b = np.unique(a)
|
||
|
|
return [1 + sum(i < j for i in b) for j in a]
|
||
|
|
|
||
|
|
rankf = dict(min=min_rank, max=max_rank, ordinal=ordinal_rank,
|
||
|
|
average=average_rank, dense=dense_rank)
|
||
|
|
|
||
|
|
def check_ranks(a):
|
||
|
|
for method in 'min', 'max', 'dense', 'ordinal', 'average':
|
||
|
|
out = rankdata(a, method=method)
|
||
|
|
assert_array_equal(out, rankf[method](a))
|
||
|
|
|
||
|
|
val = ['foo', 'bar', 'qux', 'xyz', 'abc', 'efg', 'ace', 'qwe', 'qaz']
|
||
|
|
check_ranks(np.random.choice(val, 200))
|
||
|
|
check_ranks(np.random.choice(val, 200).astype('object'))
|
||
|
|
|
||
|
|
val = np.array([0, 1, 2, 2.718, 3, 3.141], dtype='object')
|
||
|
|
check_ranks(np.random.choice(val, 200).astype('object'))
|
||
|
|
|
||
|
|
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():
|
||
|
|
for values, method, expected in _cases:
|
||
|
|
r = rankdata(values, method=method)
|
||
|
|
assert_array_equal(r, expected)
|