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import numpy as np
from cogent.util.unit_test import TestCase, main
from cogent.maths.stats.jackknife import JackknifeStats
__author__ = "Anuj Pahwa, Gavin Huttley"
__copyright__ = "Copyright 2007-2012, The Cogent Project"
__credits__ = ["Anuj Pahwa", "Gavin Huttley"]
__license__ = "GPL"
__version__ = "1.5.3"
__maintainer__ = "Gavin Huttley"
__email__ = "Gavin.Huttley@anu.edu.au"
__status__ = "Production"
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 is 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)
self.assertAlmostEquals(test_knife.JackknifedStat, 1.2905845)
self.assertAlmostEquals(test_knife.StandardError, 0.2884490)
self.assertTrue(test_knife._jackknifed_stat is not 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.JackknifedStat
expected_standard_err = [30.69509346, 1.87179671]
got_standard_err = test_knife.StandardError
for index in [0,1]:
self.assertAlmostEqual(got_jk_stat[index], expected_jk_stat[index])
self.assertAlmostEqual(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]):
self.assertAlmostEqual(got_subsample_stats[index],
expected_subsample_stats[index], places=4)
self.assertAlmostEqual(got_pseudovalues[index],
expected_pseudovalues[index], places=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]):
self.assertAlmostEqual(got_subsample_stats[index1][index2],
expected_subsample_stats[index1][index2],
places=4)
self.assertAlmostEqual(got_pseudovalues[index1][index2],
expected_pseudovalues[index1][index2],
places=4)
if __name__ == "__main__":
main()
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