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from unittest import TestCase
import numpy as np
from numpy.testing import assert_allclose
from cogent3.maths.stats.jackknife import JackknifeStats
def pmcc(data, axis=1):
"""Compute the Product-moment correlation coefficient.
Expression 15.3 from Biometry by Sokal/Rohlf
This code implementation is on the proviso that the data that is provided
is two dimensional: [[Y1], [Y2]] (trying to determine the correlation
coefficient between data sets Y1 and Y2"""
if axis == 0:
data = data.transpose()
axis = 1
other_axis = 0
mean = data.mean(axis=axis)
data_less_mean = np.array([data[0] - mean[0], data[1] - mean[1]])
sum_squares = np.sum(np.square(data_less_mean), axis=axis)
sum_products = np.sum(np.prod(data_less_mean, axis=other_axis))
pmcc = np.divide(sum_products, np.sqrt(np.prod(sum_squares)))
z_trans = np.arctanh(pmcc)
return z_trans
# test data from Box 15.2; Biometry by Sokal/Rohlf
data = np.array(
[
[159, 179, 100, 45, 384, 230, 100, 320, 80, 220, 320, 210],
[
14.40,
15.20,
11.30,
2.50,
22.70,
14.90,
1.41,
15.81,
4.19,
15.39,
17.25,
9.52,
],
]
)
# factory function generator for the statistical function of interest
def stat_maker(func, data, axis):
def calc_stat(coords):
subset_data = data.take(coords, axis)
return func(subset_data, axis)
return calc_stat
# function to compute mean of a np array
def mean(data, axis):
return data.mean(axis=axis)
class JackknifeTests(TestCase):
def test_proper_initialise(self):
"""jackknife should initialise correctly"""
# Scalar
pmcc_stat = stat_maker(pmcc, data, 1)
test_knife = JackknifeStats(data.shape[1], pmcc_stat)
self.assertEqual(test_knife.n, data.shape[1])
self.assertEqual(test_knife._jackknifed_stat, None)
# Vector
mean_stat = stat_maker(mean, data, 1)
test_knife = JackknifeStats(data.shape[1], mean_stat)
self.assertEqual(test_knife.n, data.shape[1])
self.assertEqual(test_knife._jackknifed_stat, None)
def test_jackknife_stats(self):
"""jackknife results should match Sokal & Rolf example"""
# Scalar
pmcc_stat = stat_maker(pmcc, data, 1)
test_knife = JackknifeStats(data.shape[1], pmcc_stat)
assert_allclose(test_knife.jackknifed_stat, 1.2905845)
assert_allclose(test_knife.standard_error, 0.2884490)
self.assertTrue(test_knife._jackknifed_stat != None)
# Vector
mean_stat = stat_maker(mean, data, 1)
test_knife = JackknifeStats(data.shape[1], mean_stat)
expected_jk_stat = data.mean(axis=1)
got_jk_stat = test_knife.jackknifed_stat
expected_standard_err = [30.69509346, 1.87179671]
got_standard_err = test_knife.standard_error
for index in [0, 1]:
assert_allclose(got_jk_stat[index], expected_jk_stat[index])
assert_allclose(got_standard_err[index], expected_standard_err[index])
def test_tables(self):
"""jackknife should work for calculators return scalars or vectors"""
# Scalar
pmcc_stat = stat_maker(pmcc, data, 1)
test_knife = JackknifeStats(data.shape[1], pmcc_stat)
expected_subsample_stats = [
1.4151,
1.3946,
1.4314,
1.1889,
1.1323,
1.3083,
1.3561,
1.3453,
1.2412,
1.3216,
1.2871,
1.3664,
]
expected_pseudovalues = [
0.1968,
0.4224,
0.0176,
2.6852,
3.3084,
1.3718,
0.8461,
0.9650,
2.1103,
1.2253,
1.6049,
0.7333,
]
test_knife.jackknife()
got_subsample_stats = test_knife._subset_statistics
got_pseudovalues = test_knife._pseudovalues
for index in range(data.shape[1]):
np.testing.assert_almost_equal(
got_subsample_stats[index], expected_subsample_stats[index], 4
)
np.testing.assert_approx_equal(
got_pseudovalues[index], expected_pseudovalues[index], 4
)
# Vector
mean_stat = stat_maker(mean, data, 1)
test_knife = JackknifeStats(data.shape[1], mean_stat)
test_knife.jackknife()
expected_pseudovalues = data.transpose()
expected_subsample_stats = [
[198.9091, 11.8336],
[197.0909, 11.7609],
[204.2727, 12.1155],
[209.2727, 12.9155],
[178.4545, 11.0791],
[192.4545, 11.7882],
[204.2727, 13.0145],
[184.2727, 11.7055],
[206.0909, 12.7618],
[193.3636, 11.7436],
[184.2727, 11.5745],
[194.2727, 12.2773],
]
got_subsample_stats = test_knife._subset_statistics
got_pseudovalues = test_knife._pseudovalues
for index1 in range(data.shape[1]):
for index2 in range(data.shape[0]):
np.testing.assert_almost_equal(
got_subsample_stats[index1][index2],
expected_subsample_stats[index1][index2],
4,
)
np.testing.assert_almost_equal(
got_pseudovalues[index1][index2],
expected_pseudovalues[index1][index2],
4,
)
def test_tabular_properties(self):
"""constructs tabular properties"""
pmcc_stat = stat_maker(pmcc, data, 1)
test_knife = JackknifeStats(data.shape[1], pmcc_stat)
ss = test_knife.sub_sample_stats
self.assertEqual(ss.shape, (12, 2))
ss = test_knife.sample_stat
pvs = test_knife.pseudovalues
self.assertEqual(pvs.shape, (12, 2))
ss = test_knife.summary_stats
self.assertEqual(ss.shape, (1, 3))
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