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import numpy as np
import pytest
from numpy.testing import assert_almost_equal, assert_equal
from scipy.optimize import curve_fit
from resample.jackknife import (
bias,
bias_corrected,
jackknife,
resample,
variance,
cross_validation,
)
def test_resample_1d():
data = (1, 2, 3)
r = []
for x in resample(data):
r.append(x.copy())
assert_equal(r, [[2, 3], [1, 3], [1, 2]])
def test_resample_2d():
data = ((1, 2), (3, 4), (5, 6))
r = []
for x in resample(data):
r.append(x.copy())
assert_equal(r, [[(3, 4), (5, 6)], [(1, 2), (5, 6)], [(1, 2), (3, 4)]])
def test_jackknife():
data = (1, 2, 3)
r = jackknife(lambda x: x.copy(), data)
assert_equal(r, [[2, 3], [1, 3], [1, 2]])
def test_bias_on_unbiased():
data = (0, 1, 2, 3)
# bias is exactly zero for linear functions
r = bias(np.mean, data)
assert r == 0
def test_bias_on_biased_order_n_minus_one():
# this "mean" has a bias of exactly O(n^{-1})
def bad_mean(x):
return (np.sum(x) + 2) / len(x)
data = (0, 1, 2)
r = bias(bad_mean, data)
mean_jk = np.mean([bad_mean([1, 2]), bad_mean([0, 2]), bad_mean([0, 1])])
# (5/2 + 4/2 + 3/2) / 3 = 12 / 6 = 2
assert mean_jk == 2.0
# f = 5/3
# (n-1) * (mean_jk - f)
# (3 - 1) * (6/3 - 5/3) = 2/3
# note: 2/3 is exactly the bias of bad_mean for n = 3
assert r == pytest.approx(2.0 / 3.0)
def test_bias_on_array_map():
# compute mean and (biased) variance simultanously
def fn(x):
return np.mean(x), np.var(x, ddof=0)
data = (0, 1, 2)
r = bias(fn, data)
assert_almost_equal(r, (0.0, -1.0 / 3.0))
def test_bias_corrected():
# this "mean" has a bias of exactly O(n^{-1})
def bad_mean(x):
return (np.sum(x) + 2) / len(x)
# bias correction is exact up to O(n^{-1})
data = (0, 1, 2)
r = bias_corrected(bad_mean, data)
assert r == 1.0 # which is the correct unbiased mean
def test_variance():
data = (0, 1, 2)
r = variance(np.mean, data)
# formula is (n - 1) / n * sum((jf - mean(jf)) ** 2)
# fj = [3/2, 1, 1/2]
# mfj = 1
# ((3/2 - 1)^2 + (1 - 1)^2 + (1/2 - 1)^2) * 2 / 3
# (1/4 + 1/4) / 3 * 2 = 1/3
assert r == pytest.approx(1.0 / 3.0)
def test_resample_several_args():
a = [1, 2, 3]
b = [(1, 2), (2, 3), (3, 4)]
c = ["12", "3", "4"]
for ai, bi, ci in resample(a, b, c):
assert np.shape(ai) == (2,)
assert np.shape(bi) == (2, 2)
assert np.shape(ci) == (2,)
assert set(ai) <= set(a)
assert set(ci) <= set(c)
bi = list(tuple(x) for x in bi)
assert set(bi) <= set(b)
def test_resample_several_args_incompatible_keywords():
a = [1, 2, 3]
with pytest.raises(ValueError):
resample(a, [1, 2])
with pytest.raises(ValueError):
resample(a, [1, 2, 3, 4])
def test_resample_deprecation():
data = [1, 2, 3]
with pytest.warns(FutureWarning):
r = list(resample(data, False))
assert_equal(r, list(resample(data, copy=False)))
with pytest.warns(FutureWarning):
with pytest.raises(ValueError): # too many arguments
resample(data, True, 1)
@pytest.mark.filterwarnings("ignore:Covariance")
def test_cross_validation():
x = [1, 2, 3]
y = [3, 4, 5]
def predict(xi, yi, xo, npar):
def model(x, *par):
return np.polyval(par, x)
popt = curve_fit(model, xi, yi, p0=np.zeros(npar))[0]
return model(xo, *popt)
v = cross_validation(predict, x, y, 2)
assert v == pytest.approx(0)
v2 = cross_validation(predict, x, y, 1)
assert v2 == pytest.approx(1.5)
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