1327 lines
50 KiB
Python
1327 lines
50 KiB
Python
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import os
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from collections import Counter
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from itertools import combinations, product
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import pytest
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import numpy as np
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from numpy.testing import assert_allclose, assert_equal, assert_array_equal
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from scipy.spatial import distance
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from scipy.stats import shapiro
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from scipy.stats._sobol import _test_find_index
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from scipy.stats import qmc
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from scipy.stats._qmc import (
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van_der_corput, n_primes, primes_from_2_to,
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update_discrepancy, QMCEngine, _l1_norm,
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_perturb_discrepancy, _lloyd_centroidal_voronoi_tessellation
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) # noqa
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class TestUtils:
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def test_scale(self):
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# 1d scalar
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space = [[0], [1], [0.5]]
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out = [[-2], [6], [2]]
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scaled_space = qmc.scale(space, l_bounds=-2, u_bounds=6)
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assert_allclose(scaled_space, out)
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# 2d space
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space = [[0, 0], [1, 1], [0.5, 0.5]]
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bounds = np.array([[-2, 0], [6, 5]])
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out = [[-2, 0], [6, 5], [2, 2.5]]
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scaled_space = qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
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assert_allclose(scaled_space, out)
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scaled_back_space = qmc.scale(scaled_space, l_bounds=bounds[0],
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u_bounds=bounds[1], reverse=True)
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assert_allclose(scaled_back_space, space)
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# broadcast
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space = [[0, 0, 0], [1, 1, 1], [0.5, 0.5, 0.5]]
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l_bounds, u_bounds = 0, [6, 5, 3]
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out = [[0, 0, 0], [6, 5, 3], [3, 2.5, 1.5]]
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scaled_space = qmc.scale(space, l_bounds=l_bounds, u_bounds=u_bounds)
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assert_allclose(scaled_space, out)
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def test_scale_random(self):
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rng = np.random.default_rng(317589836511269190194010915937762468165)
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sample = rng.random((30, 10))
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a = -rng.random(10) * 10
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b = rng.random(10) * 10
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scaled = qmc.scale(sample, a, b, reverse=False)
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unscaled = qmc.scale(scaled, a, b, reverse=True)
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assert_allclose(unscaled, sample)
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def test_scale_errors(self):
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with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
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space = [0, 1, 0.5]
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qmc.scale(space, l_bounds=-2, u_bounds=6)
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with pytest.raises(ValueError, match=r"Bounds are not consistent"):
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space = [[0, 0], [1, 1], [0.5, 0.5]]
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bounds = np.array([[-2, 6], [6, 5]])
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qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
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with pytest.raises(ValueError, match=r"'l_bounds' and 'u_bounds'"
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r" must be broadcastable"):
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space = [[0, 0], [1, 1], [0.5, 0.5]]
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l_bounds, u_bounds = [-2, 0, 2], [6, 5]
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qmc.scale(space, l_bounds=l_bounds, u_bounds=u_bounds)
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with pytest.raises(ValueError, match=r"'l_bounds' and 'u_bounds'"
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r" must be broadcastable"):
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space = [[0, 0], [1, 1], [0.5, 0.5]]
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bounds = np.array([[-2, 0, 2], [6, 5, 5]])
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qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
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with pytest.raises(ValueError, match=r"Sample is not in unit "
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r"hypercube"):
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space = [[0, 0], [1, 1.5], [0.5, 0.5]]
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bounds = np.array([[-2, 0], [6, 5]])
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qmc.scale(space, l_bounds=bounds[0], u_bounds=bounds[1])
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with pytest.raises(ValueError, match=r"Sample is out of bounds"):
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out = [[-2, 0], [6, 5], [8, 2.5]]
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bounds = np.array([[-2, 0], [6, 5]])
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qmc.scale(out, l_bounds=bounds[0], u_bounds=bounds[1],
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reverse=True)
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def test_discrepancy(self):
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space_1 = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
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space_1 = (2.0 * space_1 - 1.0) / (2.0 * 6.0)
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space_2 = np.array([[1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [6, 6]])
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space_2 = (2.0 * space_2 - 1.0) / (2.0 * 6.0)
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# From Fang et al. Design and modeling for computer experiments, 2006
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assert_allclose(qmc.discrepancy(space_1), 0.0081, atol=1e-4)
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assert_allclose(qmc.discrepancy(space_2), 0.0105, atol=1e-4)
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# From Zhou Y.-D. et al. Mixture discrepancy for quasi-random point
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# sets. Journal of Complexity, 29 (3-4), pp. 283-301, 2013.
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# Example 4 on Page 298
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sample = np.array([[2, 1, 1, 2, 2, 2],
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[1, 2, 2, 2, 2, 2],
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[2, 1, 1, 1, 1, 1],
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[1, 1, 1, 1, 2, 2],
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[1, 2, 2, 2, 1, 1],
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[2, 2, 2, 2, 1, 1],
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[2, 2, 2, 1, 2, 2]])
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sample = (2.0 * sample - 1.0) / (2.0 * 2.0)
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assert_allclose(qmc.discrepancy(sample, method='MD'), 2.5000,
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atol=1e-4)
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assert_allclose(qmc.discrepancy(sample, method='WD'), 1.3680,
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atol=1e-4)
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assert_allclose(qmc.discrepancy(sample, method='CD'), 0.3172,
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atol=1e-4)
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# From Tim P. et al. Minimizing the L2 and Linf star discrepancies
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# of a single point in the unit hypercube. JCAM, 2005
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# Table 1 on Page 283
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for dim in [2, 4, 8, 16, 32, 64]:
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ref = np.sqrt(3**(-dim))
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assert_allclose(qmc.discrepancy(np.array([[1]*dim]),
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method='L2-star'), ref)
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def test_discrepancy_errors(self):
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sample = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
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with pytest.raises(
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ValueError, match=r"Sample is not in unit hypercube"
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):
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qmc.discrepancy(sample)
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with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
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qmc.discrepancy([1, 3])
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sample = [[0, 0], [1, 1], [0.5, 0.5]]
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with pytest.raises(ValueError, match=r"'toto' is not a valid ..."):
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qmc.discrepancy(sample, method="toto")
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def test_discrepancy_parallel(self, monkeypatch):
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sample = np.array([[2, 1, 1, 2, 2, 2],
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[1, 2, 2, 2, 2, 2],
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[2, 1, 1, 1, 1, 1],
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[1, 1, 1, 1, 2, 2],
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[1, 2, 2, 2, 1, 1],
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[2, 2, 2, 2, 1, 1],
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[2, 2, 2, 1, 2, 2]])
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sample = (2.0 * sample - 1.0) / (2.0 * 2.0)
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assert_allclose(qmc.discrepancy(sample, method='MD', workers=8),
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2.5000,
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atol=1e-4)
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assert_allclose(qmc.discrepancy(sample, method='WD', workers=8),
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1.3680,
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atol=1e-4)
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assert_allclose(qmc.discrepancy(sample, method='CD', workers=8),
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0.3172,
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atol=1e-4)
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# From Tim P. et al. Minimizing the L2 and Linf star discrepancies
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# of a single point in the unit hypercube. JCAM, 2005
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# Table 1 on Page 283
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for dim in [2, 4, 8, 16, 32, 64]:
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ref = np.sqrt(3 ** (-dim))
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assert_allclose(qmc.discrepancy(np.array([[1] * dim]),
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method='L2-star', workers=-1), ref)
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monkeypatch.setattr(os, 'cpu_count', lambda: None)
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with pytest.raises(NotImplementedError, match="Cannot determine the"):
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qmc.discrepancy(sample, workers=-1)
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with pytest.raises(ValueError, match="Invalid number of workers..."):
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qmc.discrepancy(sample, workers=-2)
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def test_update_discrepancy(self):
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# From Fang et al. Design and modeling for computer experiments, 2006
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space_1 = np.array([[1, 3], [2, 6], [3, 2], [4, 5], [5, 1], [6, 4]])
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space_1 = (2.0 * space_1 - 1.0) / (2.0 * 6.0)
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disc_init = qmc.discrepancy(space_1[:-1], iterative=True)
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disc_iter = update_discrepancy(space_1[-1], space_1[:-1], disc_init)
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assert_allclose(disc_iter, 0.0081, atol=1e-4)
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# n<d
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rng = np.random.default_rng(241557431858162136881731220526394276199)
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space_1 = rng.random((4, 10))
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disc_ref = qmc.discrepancy(space_1)
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disc_init = qmc.discrepancy(space_1[:-1], iterative=True)
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disc_iter = update_discrepancy(space_1[-1], space_1[:-1], disc_init)
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assert_allclose(disc_iter, disc_ref, atol=1e-4)
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# errors
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with pytest.raises(ValueError, match=r"Sample is not in unit "
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r"hypercube"):
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update_discrepancy(space_1[-1], space_1[:-1] + 1, disc_init)
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with pytest.raises(ValueError, match=r"Sample is not a 2D array"):
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update_discrepancy(space_1[-1], space_1[0], disc_init)
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x_new = [1, 3]
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with pytest.raises(ValueError, match=r"x_new is not in unit "
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r"hypercube"):
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update_discrepancy(x_new, space_1[:-1], disc_init)
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x_new = [[0.5, 0.5]]
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with pytest.raises(ValueError, match=r"x_new is not a 1D array"):
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update_discrepancy(x_new, space_1[:-1], disc_init)
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x_new = [0.3, 0.1, 0]
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with pytest.raises(ValueError, match=r"x_new and sample must be "
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r"broadcastable"):
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update_discrepancy(x_new, space_1[:-1], disc_init)
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def test_perm_discrepancy(self):
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rng = np.random.default_rng(46449423132557934943847369749645759997)
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qmc_gen = qmc.LatinHypercube(5, seed=rng)
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sample = qmc_gen.random(10)
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disc = qmc.discrepancy(sample)
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for i in range(100):
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row_1 = rng.integers(10)
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row_2 = rng.integers(10)
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col = rng.integers(5)
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disc = _perturb_discrepancy(sample, row_1, row_2, col, disc)
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sample[row_1, col], sample[row_2, col] = (
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sample[row_2, col], sample[row_1, col])
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disc_reference = qmc.discrepancy(sample)
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assert_allclose(disc, disc_reference)
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def test_discrepancy_alternative_implementation(self):
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"""Alternative definitions from Matt Haberland."""
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def disc_c2(x):
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n, s = x.shape
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xij = x
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disc1 = np.sum(np.prod((1
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+ 1/2*np.abs(xij-0.5)
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- 1/2*np.abs(xij-0.5)**2), axis=1))
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xij = x[None, :, :]
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xkj = x[:, None, :]
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disc2 = np.sum(np.sum(np.prod(1
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+ 1/2*np.abs(xij - 0.5)
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+ 1/2*np.abs(xkj - 0.5)
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- 1/2*np.abs(xij - xkj), axis=2),
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axis=0))
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return (13/12)**s - 2/n * disc1 + 1/n**2*disc2
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def disc_wd(x):
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n, s = x.shape
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xij = x[None, :, :]
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xkj = x[:, None, :]
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disc = np.sum(np.sum(np.prod(3/2
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- np.abs(xij - xkj)
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+ np.abs(xij - xkj)**2, axis=2),
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axis=0))
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return -(4/3)**s + 1/n**2 * disc
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def disc_md(x):
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n, s = x.shape
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xij = x
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disc1 = np.sum(np.prod((5/3
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- 1/4*np.abs(xij-0.5)
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- 1/4*np.abs(xij-0.5)**2), axis=1))
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xij = x[None, :, :]
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xkj = x[:, None, :]
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disc2 = np.sum(np.sum(np.prod(15/8
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- 1/4*np.abs(xij - 0.5)
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- 1/4*np.abs(xkj - 0.5)
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- 3/4*np.abs(xij - xkj)
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+ 1/2*np.abs(xij - xkj)**2,
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axis=2), axis=0))
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return (19/12)**s - 2/n * disc1 + 1/n**2*disc2
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def disc_star_l2(x):
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n, s = x.shape
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return np.sqrt(
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3 ** (-s) - 2 ** (1 - s) / n
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* np.sum(np.prod(1 - x ** 2, axis=1))
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+ np.sum([
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np.prod(1 - np.maximum(x[k, :], x[j, :]))
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for k in range(n) for j in range(n)
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]) / n ** 2
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)
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rng = np.random.default_rng(117065081482921065782761407107747179201)
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sample = rng.random((30, 10))
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disc_curr = qmc.discrepancy(sample, method='CD')
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disc_alt = disc_c2(sample)
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assert_allclose(disc_curr, disc_alt)
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disc_curr = qmc.discrepancy(sample, method='WD')
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disc_alt = disc_wd(sample)
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assert_allclose(disc_curr, disc_alt)
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disc_curr = qmc.discrepancy(sample, method='MD')
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disc_alt = disc_md(sample)
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assert_allclose(disc_curr, disc_alt)
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disc_curr = qmc.discrepancy(sample, method='L2-star')
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disc_alt = disc_star_l2(sample)
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|
|
assert_allclose(disc_curr, disc_alt)
|
||
|
|
|
||
|
|
def test_n_primes(self):
|
||
|
|
primes = n_primes(10)
|
||
|
|
assert primes[-1] == 29
|
||
|
|
|
||
|
|
primes = n_primes(168)
|
||
|
|
assert primes[-1] == 997
|
||
|
|
|
||
|
|
primes = n_primes(350)
|
||
|
|
assert primes[-1] == 2357
|
||
|
|
|
||
|
|
def test_primes(self):
|
||
|
|
primes = primes_from_2_to(50)
|
||
|
|
out = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
|
||
|
|
assert_allclose(primes, out)
|
||
|
|
|
||
|
|
|
||
|
|
class TestVDC:
|
||
|
|
def test_van_der_corput(self):
|
||
|
|
sample = van_der_corput(10)
|
||
|
|
out = [0.0, 0.5, 0.25, 0.75, 0.125, 0.625,
|
||
|
|
0.375, 0.875, 0.0625, 0.5625]
|
||
|
|
assert_allclose(sample, out)
|
||
|
|
|
||
|
|
sample = van_der_corput(10, workers=4)
|
||
|
|
assert_allclose(sample, out)
|
||
|
|
|
||
|
|
sample = van_der_corput(10, workers=8)
|
||
|
|
assert_allclose(sample, out)
|
||
|
|
|
||
|
|
sample = van_der_corput(7, start_index=3)
|
||
|
|
assert_allclose(sample, out[3:])
|
||
|
|
|
||
|
|
def test_van_der_corput_scramble(self):
|
||
|
|
seed = 338213789010180879520345496831675783177
|
||
|
|
out = van_der_corput(10, scramble=True, seed=seed)
|
||
|
|
|
||
|
|
sample = van_der_corput(7, start_index=3, scramble=True, seed=seed)
|
||
|
|
assert_allclose(sample, out[3:])
|
||
|
|
|
||
|
|
sample = van_der_corput(
|
||
|
|
7, start_index=3, scramble=True, seed=seed, workers=4
|
||
|
|
)
|
||
|
|
assert_allclose(sample, out[3:])
|
||
|
|
|
||
|
|
sample = van_der_corput(
|
||
|
|
7, start_index=3, scramble=True, seed=seed, workers=8
|
||
|
|
)
|
||
|
|
assert_allclose(sample, out[3:])
|
||
|
|
|
||
|
|
def test_invalid_base_error(self):
|
||
|
|
with pytest.raises(ValueError, match=r"'base' must be at least 2"):
|
||
|
|
van_der_corput(10, base=1)
|
||
|
|
|
||
|
|
|
||
|
|
class RandomEngine(qmc.QMCEngine):
|
||
|
|
def __init__(self, d, optimization=None, seed=None):
|
||
|
|
super().__init__(d=d, optimization=optimization, seed=seed)
|
||
|
|
|
||
|
|
def _random(self, n=1, *, workers=1):
|
||
|
|
sample = self.rng.random((n, self.d))
|
||
|
|
return sample
|
||
|
|
|
||
|
|
|
||
|
|
def test_subclassing_QMCEngine():
|
||
|
|
engine = RandomEngine(2, seed=175180605424926556207367152557812293274)
|
||
|
|
|
||
|
|
sample_1 = engine.random(n=5)
|
||
|
|
sample_2 = engine.random(n=7)
|
||
|
|
assert engine.num_generated == 12
|
||
|
|
|
||
|
|
# reset and re-sample
|
||
|
|
engine.reset()
|
||
|
|
assert engine.num_generated == 0
|
||
|
|
|
||
|
|
sample_1_test = engine.random(n=5)
|
||
|
|
assert_equal(sample_1, sample_1_test)
|
||
|
|
|
||
|
|
# repeat reset and fast forward
|
||
|
|
engine.reset()
|
||
|
|
engine.fast_forward(n=5)
|
||
|
|
sample_2_test = engine.random(n=7)
|
||
|
|
|
||
|
|
assert_equal(sample_2, sample_2_test)
|
||
|
|
assert engine.num_generated == 12
|
||
|
|
|
||
|
|
|
||
|
|
def test_raises():
|
||
|
|
# input validation
|
||
|
|
with pytest.raises(ValueError, match=r"d must be a non-negative integer"):
|
||
|
|
RandomEngine((2,)) # noqa
|
||
|
|
|
||
|
|
with pytest.raises(ValueError, match=r"d must be a non-negative integer"):
|
||
|
|
RandomEngine(-1) # noqa
|
||
|
|
|
||
|
|
msg = r"'u_bounds' and 'l_bounds' must be integers"
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
engine = RandomEngine(1)
|
||
|
|
engine.integers(l_bounds=1, u_bounds=1.1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_integers():
|
||
|
|
engine = RandomEngine(1, seed=231195739755290648063853336582377368684)
|
||
|
|
|
||
|
|
# basic tests
|
||
|
|
sample = engine.integers(1, n=10)
|
||
|
|
assert_equal(np.unique(sample), [0])
|
||
|
|
|
||
|
|
assert sample.dtype == np.dtype('int64')
|
||
|
|
|
||
|
|
sample = engine.integers(1, n=10, endpoint=True)
|
||
|
|
assert_equal(np.unique(sample), [0, 1])
|
||
|
|
|
||
|
|
low = -5
|
||
|
|
high = 7
|
||
|
|
|
||
|
|
# scaling logic
|
||
|
|
engine.reset()
|
||
|
|
ref_sample = engine.random(20)
|
||
|
|
ref_sample = ref_sample * (high - low) + low
|
||
|
|
ref_sample = np.floor(ref_sample).astype(np.int64)
|
||
|
|
|
||
|
|
engine.reset()
|
||
|
|
sample = engine.integers(low, u_bounds=high, n=20, endpoint=False)
|
||
|
|
|
||
|
|
assert_equal(sample, ref_sample)
|
||
|
|
|
||
|
|
# up to bounds, no less, no more
|
||
|
|
sample = engine.integers(low, u_bounds=high, n=100, endpoint=False)
|
||
|
|
assert_equal((sample.min(), sample.max()), (low, high-1))
|
||
|
|
|
||
|
|
sample = engine.integers(low, u_bounds=high, n=100, endpoint=True)
|
||
|
|
assert_equal((sample.min(), sample.max()), (low, high))
|
||
|
|
|
||
|
|
|
||
|
|
def test_integers_nd():
|
||
|
|
d = 10
|
||
|
|
rng = np.random.default_rng(3716505122102428560615700415287450951)
|
||
|
|
low = rng.integers(low=-5, high=-1, size=d)
|
||
|
|
high = rng.integers(low=1, high=5, size=d, endpoint=True)
|
||
|
|
engine = RandomEngine(d, seed=rng)
|
||
|
|
|
||
|
|
sample = engine.integers(low, u_bounds=high, n=100, endpoint=False)
|
||
|
|
assert_equal(sample.min(axis=0), low)
|
||
|
|
assert_equal(sample.max(axis=0), high-1)
|
||
|
|
|
||
|
|
sample = engine.integers(low, u_bounds=high, n=100, endpoint=True)
|
||
|
|
assert_equal(sample.min(axis=0), low)
|
||
|
|
assert_equal(sample.max(axis=0), high)
|
||
|
|
|
||
|
|
|
||
|
|
class QMCEngineTests:
|
||
|
|
"""Generic tests for QMC engines."""
|
||
|
|
qmce = NotImplemented
|
||
|
|
can_scramble = NotImplemented
|
||
|
|
unscramble_nd = NotImplemented
|
||
|
|
scramble_nd = NotImplemented
|
||
|
|
|
||
|
|
scramble = [True, False]
|
||
|
|
ids = ["Scrambled", "Unscrambled"]
|
||
|
|
|
||
|
|
def engine(self, scramble: bool, **kwargs) -> QMCEngine:
|
||
|
|
seed = np.random.default_rng(170382760648021597650530316304495310428)
|
||
|
|
if self.can_scramble:
|
||
|
|
return self.qmce(scramble=scramble, seed=seed, **kwargs)
|
||
|
|
else:
|
||
|
|
if scramble:
|
||
|
|
pytest.skip()
|
||
|
|
else:
|
||
|
|
return self.qmce(seed=seed, **kwargs)
|
||
|
|
|
||
|
|
def reference(self, scramble: bool) -> np.ndarray:
|
||
|
|
return self.scramble_nd if scramble else self.unscramble_nd
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("scramble", scramble, ids=ids)
|
||
|
|
def test_0dim(self, scramble):
|
||
|
|
engine = self.engine(d=0, scramble=scramble)
|
||
|
|
sample = engine.random(4)
|
||
|
|
assert_array_equal(np.empty((4, 0)), sample)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("scramble", scramble, ids=ids)
|
||
|
|
def test_0sample(self, scramble):
|
||
|
|
engine = self.engine(d=2, scramble=scramble)
|
||
|
|
sample = engine.random(0)
|
||
|
|
assert_array_equal(np.empty((0, 2)), sample)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("scramble", scramble, ids=ids)
|
||
|
|
def test_1sample(self, scramble):
|
||
|
|
engine = self.engine(d=2, scramble=scramble)
|
||
|
|
sample = engine.random(1)
|
||
|
|
assert (1, 2) == sample.shape
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("scramble", scramble, ids=ids)
|
||
|
|
def test_bounds(self, scramble):
|
||
|
|
engine = self.engine(d=100, scramble=scramble)
|
||
|
|
sample = engine.random(512)
|
||
|
|
assert np.all(sample >= 0)
|
||
|
|
assert np.all(sample <= 1)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("scramble", scramble, ids=ids)
|
||
|
|
def test_sample(self, scramble):
|
||
|
|
ref_sample = self.reference(scramble=scramble)
|
||
|
|
engine = self.engine(d=2, scramble=scramble)
|
||
|
|
sample = engine.random(n=len(ref_sample))
|
||
|
|
|
||
|
|
assert_allclose(sample, ref_sample, atol=1e-1)
|
||
|
|
assert engine.num_generated == len(ref_sample)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("scramble", scramble, ids=ids)
|
||
|
|
def test_continuing(self, scramble):
|
||
|
|
engine = self.engine(d=2, scramble=scramble)
|
||
|
|
ref_sample = engine.random(n=8)
|
||
|
|
|
||
|
|
engine = self.engine(d=2, scramble=scramble)
|
||
|
|
|
||
|
|
n_half = len(ref_sample) // 2
|
||
|
|
|
||
|
|
_ = engine.random(n=n_half)
|
||
|
|
sample = engine.random(n=n_half)
|
||
|
|
assert_allclose(sample, ref_sample[n_half:], atol=1e-1)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("scramble", scramble, ids=ids)
|
||
|
|
def test_reset(self, scramble):
|
||
|
|
engine = self.engine(d=2, scramble=scramble)
|
||
|
|
ref_sample = engine.random(n=8)
|
||
|
|
|
||
|
|
engine.reset()
|
||
|
|
assert engine.num_generated == 0
|
||
|
|
|
||
|
|
sample = engine.random(n=8)
|
||
|
|
assert_allclose(sample, ref_sample)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("scramble", scramble, ids=ids)
|
||
|
|
def test_fast_forward(self, scramble):
|
||
|
|
engine = self.engine(d=2, scramble=scramble)
|
||
|
|
ref_sample = engine.random(n=8)
|
||
|
|
|
||
|
|
engine = self.engine(d=2, scramble=scramble)
|
||
|
|
|
||
|
|
engine.fast_forward(4)
|
||
|
|
sample = engine.random(n=4)
|
||
|
|
|
||
|
|
assert_allclose(sample, ref_sample[4:], atol=1e-1)
|
||
|
|
|
||
|
|
# alternate fast forwarding with sampling
|
||
|
|
engine.reset()
|
||
|
|
even_draws = []
|
||
|
|
for i in range(8):
|
||
|
|
if i % 2 == 0:
|
||
|
|
even_draws.append(engine.random())
|
||
|
|
else:
|
||
|
|
engine.fast_forward(1)
|
||
|
|
assert_allclose(
|
||
|
|
ref_sample[[i for i in range(8) if i % 2 == 0]],
|
||
|
|
np.concatenate(even_draws),
|
||
|
|
atol=1e-5
|
||
|
|
)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("scramble", [True])
|
||
|
|
def test_distribution(self, scramble):
|
||
|
|
d = 50
|
||
|
|
engine = self.engine(d=d, scramble=scramble)
|
||
|
|
sample = engine.random(1024)
|
||
|
|
assert_allclose(
|
||
|
|
np.mean(sample, axis=0), np.repeat(0.5, d), atol=1e-2
|
||
|
|
)
|
||
|
|
assert_allclose(
|
||
|
|
np.percentile(sample, 25, axis=0), np.repeat(0.25, d), atol=1e-2
|
||
|
|
)
|
||
|
|
assert_allclose(
|
||
|
|
np.percentile(sample, 75, axis=0), np.repeat(0.75, d), atol=1e-2
|
||
|
|
)
|
||
|
|
|
||
|
|
def test_raises_optimizer(self):
|
||
|
|
message = r"'toto' is not a valid optimization method"
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
self.engine(d=1, scramble=False, optimization="toto")
|
||
|
|
|
||
|
|
@pytest.mark.parametrize(
|
||
|
|
"optimization,metric",
|
||
|
|
[
|
||
|
|
("random-CD", qmc.discrepancy),
|
||
|
|
("lloyd", lambda sample: -_l1_norm(sample))]
|
||
|
|
)
|
||
|
|
def test_optimizers(self, optimization, metric):
|
||
|
|
engine = self.engine(d=2, scramble=False)
|
||
|
|
sample_ref = engine.random(n=64)
|
||
|
|
metric_ref = metric(sample_ref)
|
||
|
|
|
||
|
|
optimal_ = self.engine(d=2, scramble=False, optimization=optimization)
|
||
|
|
sample_ = optimal_.random(n=64)
|
||
|
|
metric_ = metric(sample_)
|
||
|
|
|
||
|
|
assert metric_ < metric_ref
|
||
|
|
|
||
|
|
|
||
|
|
class TestHalton(QMCEngineTests):
|
||
|
|
qmce = qmc.Halton
|
||
|
|
can_scramble = True
|
||
|
|
# theoretical values known from Van der Corput
|
||
|
|
unscramble_nd = np.array([[0, 0], [1 / 2, 1 / 3],
|
||
|
|
[1 / 4, 2 / 3], [3 / 4, 1 / 9],
|
||
|
|
[1 / 8, 4 / 9], [5 / 8, 7 / 9],
|
||
|
|
[3 / 8, 2 / 9], [7 / 8, 5 / 9]])
|
||
|
|
# theoretical values unknown: convergence properties checked
|
||
|
|
scramble_nd = np.array([[0.50246036, 0.09937553],
|
||
|
|
[0.00246036, 0.43270887],
|
||
|
|
[0.75246036, 0.7660422],
|
||
|
|
[0.25246036, 0.32159776],
|
||
|
|
[0.62746036, 0.65493109],
|
||
|
|
[0.12746036, 0.98826442],
|
||
|
|
[0.87746036, 0.21048664],
|
||
|
|
[0.37746036, 0.54381998]])
|
||
|
|
|
||
|
|
def test_workers(self):
|
||
|
|
ref_sample = self.reference(scramble=True)
|
||
|
|
engine = self.engine(d=2, scramble=True)
|
||
|
|
sample = engine.random(n=len(ref_sample), workers=8)
|
||
|
|
|
||
|
|
assert_allclose(sample, ref_sample, atol=1e-3)
|
||
|
|
|
||
|
|
# worker + integers
|
||
|
|
engine.reset()
|
||
|
|
ref_sample = engine.integers(10)
|
||
|
|
engine.reset()
|
||
|
|
sample = engine.integers(10, workers=8)
|
||
|
|
assert_equal(sample, ref_sample)
|
||
|
|
|
||
|
|
|
||
|
|
class TestLHS(QMCEngineTests):
|
||
|
|
qmce = qmc.LatinHypercube
|
||
|
|
can_scramble = False
|
||
|
|
|
||
|
|
def test_continuing(self, *args):
|
||
|
|
pytest.skip("Not applicable: not a sequence.")
|
||
|
|
|
||
|
|
def test_fast_forward(self, *args):
|
||
|
|
pytest.skip("Not applicable: not a sequence.")
|
||
|
|
|
||
|
|
def test_sample(self, *args):
|
||
|
|
pytest.skip("Not applicable: the value of reference sample is"
|
||
|
|
" implementation dependent.")
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("strength", [1, 2])
|
||
|
|
@pytest.mark.parametrize("scramble", [False, True])
|
||
|
|
@pytest.mark.parametrize("optimization", [None, "random-CD"])
|
||
|
|
def test_sample_stratified(self, optimization, scramble, strength):
|
||
|
|
seed = np.random.default_rng(37511836202578819870665127532742111260)
|
||
|
|
p = 5
|
||
|
|
n = p**2
|
||
|
|
d = 6
|
||
|
|
|
||
|
|
engine = qmc.LatinHypercube(d=d, scramble=scramble,
|
||
|
|
strength=strength,
|
||
|
|
optimization=optimization,
|
||
|
|
seed=seed)
|
||
|
|
sample = engine.random(n=n)
|
||
|
|
assert sample.shape == (n, d)
|
||
|
|
assert engine.num_generated == n
|
||
|
|
|
||
|
|
# centering stratifies samples in the middle of equal segments:
|
||
|
|
# * inter-sample distance is constant in 1D sub-projections
|
||
|
|
# * after ordering, columns are equal
|
||
|
|
expected1d = (np.arange(n) + 0.5) / n
|
||
|
|
expected = np.broadcast_to(expected1d, (d, n)).T
|
||
|
|
assert np.any(sample != expected)
|
||
|
|
|
||
|
|
sorted_sample = np.sort(sample, axis=0)
|
||
|
|
tol = 0.5 / n if scramble else 0
|
||
|
|
|
||
|
|
assert_allclose(sorted_sample, expected, atol=tol)
|
||
|
|
assert np.any(sample - expected > tol)
|
||
|
|
|
||
|
|
if strength == 2 and optimization is None:
|
||
|
|
unique_elements = np.arange(p)
|
||
|
|
desired = set(product(unique_elements, unique_elements))
|
||
|
|
|
||
|
|
for i, j in combinations(range(engine.d), 2):
|
||
|
|
samples_2d = sample[:, [i, j]]
|
||
|
|
res = (samples_2d * p).astype(int)
|
||
|
|
res_set = set((tuple(row) for row in res))
|
||
|
|
assert_equal(res_set, desired)
|
||
|
|
|
||
|
|
def test_raises(self):
|
||
|
|
message = r"not a valid strength"
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.LatinHypercube(1, strength=3)
|
||
|
|
|
||
|
|
message = r"n is not the square of a prime number"
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
engine = qmc.LatinHypercube(d=2, strength=2)
|
||
|
|
engine.random(16)
|
||
|
|
|
||
|
|
message = r"n is not the square of a prime number"
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
engine = qmc.LatinHypercube(d=2, strength=2)
|
||
|
|
engine.random(5) # because int(sqrt(5)) would result in 2
|
||
|
|
|
||
|
|
message = r"n is too small for d"
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
engine = qmc.LatinHypercube(d=5, strength=2)
|
||
|
|
engine.random(9)
|
||
|
|
|
||
|
|
message = r"'centered' is deprecated"
|
||
|
|
with pytest.warns(UserWarning, match=message):
|
||
|
|
qmc.LatinHypercube(1, centered=True)
|
||
|
|
|
||
|
|
|
||
|
|
class TestSobol(QMCEngineTests):
|
||
|
|
qmce = qmc.Sobol
|
||
|
|
can_scramble = True
|
||
|
|
# theoretical values from Joe Kuo2010
|
||
|
|
unscramble_nd = np.array([[0., 0.],
|
||
|
|
[0.5, 0.5],
|
||
|
|
[0.75, 0.25],
|
||
|
|
[0.25, 0.75],
|
||
|
|
[0.375, 0.375],
|
||
|
|
[0.875, 0.875],
|
||
|
|
[0.625, 0.125],
|
||
|
|
[0.125, 0.625]])
|
||
|
|
|
||
|
|
# theoretical values unknown: convergence properties checked
|
||
|
|
scramble_nd = np.array([[0.25331921, 0.41371179],
|
||
|
|
[0.8654213, 0.9821167],
|
||
|
|
[0.70097554, 0.03664616],
|
||
|
|
[0.18027647, 0.60895735],
|
||
|
|
[0.10521339, 0.21897069],
|
||
|
|
[0.53019685, 0.66619033],
|
||
|
|
[0.91122276, 0.34580743],
|
||
|
|
[0.45337471, 0.78912079]])
|
||
|
|
|
||
|
|
def test_warning(self):
|
||
|
|
with pytest.warns(UserWarning, match=r"The balance properties of "
|
||
|
|
r"Sobol' points"):
|
||
|
|
engine = qmc.Sobol(1)
|
||
|
|
engine.random(10)
|
||
|
|
|
||
|
|
def test_random_base2(self):
|
||
|
|
engine = qmc.Sobol(2, scramble=False)
|
||
|
|
sample = engine.random_base2(2)
|
||
|
|
assert_array_equal(self.unscramble_nd[:4], sample)
|
||
|
|
|
||
|
|
# resampling still having N=2**n
|
||
|
|
sample = engine.random_base2(2)
|
||
|
|
assert_array_equal(self.unscramble_nd[4:8], sample)
|
||
|
|
|
||
|
|
# resampling again but leading to N!=2**n
|
||
|
|
with pytest.raises(ValueError, match=r"The balance properties of "
|
||
|
|
r"Sobol' points"):
|
||
|
|
engine.random_base2(2)
|
||
|
|
|
||
|
|
def test_raise(self):
|
||
|
|
with pytest.raises(ValueError, match=r"Maximum supported "
|
||
|
|
r"dimensionality"):
|
||
|
|
qmc.Sobol(qmc.Sobol.MAXDIM + 1)
|
||
|
|
|
||
|
|
with pytest.raises(ValueError, match=r"Maximum supported "
|
||
|
|
r"'bits' is 64"):
|
||
|
|
qmc.Sobol(1, bits=65)
|
||
|
|
|
||
|
|
def test_high_dim(self):
|
||
|
|
engine = qmc.Sobol(1111, scramble=False)
|
||
|
|
count1 = Counter(engine.random().flatten().tolist())
|
||
|
|
count2 = Counter(engine.random().flatten().tolist())
|
||
|
|
assert_equal(count1, Counter({0.0: 1111}))
|
||
|
|
assert_equal(count2, Counter({0.5: 1111}))
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("bits", [2, 3])
|
||
|
|
def test_bits(self, bits):
|
||
|
|
engine = qmc.Sobol(2, scramble=False, bits=bits)
|
||
|
|
ns = 2**bits
|
||
|
|
sample = engine.random(ns)
|
||
|
|
assert_array_equal(self.unscramble_nd[:ns], sample)
|
||
|
|
|
||
|
|
with pytest.raises(ValueError, match="increasing `bits`"):
|
||
|
|
engine.random()
|
||
|
|
|
||
|
|
def test_64bits(self):
|
||
|
|
engine = qmc.Sobol(2, scramble=False, bits=64)
|
||
|
|
sample = engine.random(8)
|
||
|
|
assert_array_equal(self.unscramble_nd, sample)
|
||
|
|
|
||
|
|
|
||
|
|
class TestPoisson(QMCEngineTests):
|
||
|
|
qmce = qmc.PoissonDisk
|
||
|
|
can_scramble = False
|
||
|
|
|
||
|
|
def test_bounds(self, *args):
|
||
|
|
pytest.skip("Too costly in memory.")
|
||
|
|
|
||
|
|
def test_fast_forward(self, *args):
|
||
|
|
pytest.skip("Not applicable: recursive process.")
|
||
|
|
|
||
|
|
def test_sample(self, *args):
|
||
|
|
pytest.skip("Not applicable: the value of reference sample is"
|
||
|
|
" implementation dependent.")
|
||
|
|
|
||
|
|
def test_continuing(self, *args):
|
||
|
|
# can continue a sampling, but will not preserve the same order
|
||
|
|
# because candidates are lost, so we will not select the same center
|
||
|
|
radius = 0.05
|
||
|
|
ns = 6
|
||
|
|
engine = self.engine(d=2, radius=radius, scramble=False)
|
||
|
|
|
||
|
|
sample_init = engine.random(n=ns)
|
||
|
|
assert len(sample_init) <= ns
|
||
|
|
assert l2_norm(sample_init) >= radius
|
||
|
|
|
||
|
|
sample_continued = engine.random(n=ns)
|
||
|
|
assert len(sample_continued) <= ns
|
||
|
|
assert l2_norm(sample_continued) >= radius
|
||
|
|
|
||
|
|
sample = np.concatenate([sample_init, sample_continued], axis=0)
|
||
|
|
assert len(sample) <= ns * 2
|
||
|
|
assert l2_norm(sample) >= radius
|
||
|
|
|
||
|
|
def test_mindist(self):
|
||
|
|
rng = np.random.default_rng(132074951149370773672162394161442690287)
|
||
|
|
ns = 50
|
||
|
|
|
||
|
|
low, high = 0.08, 0.2
|
||
|
|
radii = (high - low) * rng.random(5) + low
|
||
|
|
|
||
|
|
dimensions = [1, 3, 4]
|
||
|
|
hypersphere_methods = ["volume", "surface"]
|
||
|
|
|
||
|
|
gen = product(dimensions, radii, hypersphere_methods)
|
||
|
|
|
||
|
|
for d, radius, hypersphere in gen:
|
||
|
|
engine = self.qmce(
|
||
|
|
d=d, radius=radius, hypersphere=hypersphere, seed=rng
|
||
|
|
)
|
||
|
|
sample = engine.random(ns)
|
||
|
|
|
||
|
|
assert len(sample) <= ns
|
||
|
|
assert l2_norm(sample) >= radius
|
||
|
|
|
||
|
|
def test_fill_space(self):
|
||
|
|
radius = 0.2
|
||
|
|
engine = self.qmce(d=2, radius=radius)
|
||
|
|
|
||
|
|
sample = engine.fill_space()
|
||
|
|
# circle packing problem is np complex
|
||
|
|
assert l2_norm(sample) >= radius
|
||
|
|
|
||
|
|
def test_raises(self):
|
||
|
|
message = r"'toto' is not a valid hypersphere sampling"
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.PoissonDisk(1, hypersphere="toto")
|
||
|
|
|
||
|
|
|
||
|
|
class TestMultinomialQMC:
|
||
|
|
def test_validations(self):
|
||
|
|
# negative Ps
|
||
|
|
p = np.array([0.12, 0.26, -0.05, 0.35, 0.22])
|
||
|
|
with pytest.raises(ValueError, match=r"Elements of pvals must "
|
||
|
|
r"be non-negative."):
|
||
|
|
qmc.MultinomialQMC(p, n_trials=10)
|
||
|
|
|
||
|
|
# sum of P too large
|
||
|
|
p = np.array([0.12, 0.26, 0.1, 0.35, 0.22])
|
||
|
|
message = r"Elements of pvals must sum to 1."
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.MultinomialQMC(p, n_trials=10)
|
||
|
|
|
||
|
|
p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
|
||
|
|
|
||
|
|
message = r"Dimension of `engine` must be 1."
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.MultinomialQMC(p, n_trials=10, engine=qmc.Sobol(d=2))
|
||
|
|
|
||
|
|
message = r"`engine` must be an instance of..."
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.MultinomialQMC(p, n_trials=10, engine=np.random.default_rng())
|
||
|
|
|
||
|
|
@pytest.mark.filterwarnings('ignore::UserWarning')
|
||
|
|
def test_MultinomialBasicDraw(self):
|
||
|
|
seed = np.random.default_rng(6955663962957011631562466584467607969)
|
||
|
|
p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
|
||
|
|
expected = np.array([[13, 24, 6, 35, 22]])
|
||
|
|
engine = qmc.MultinomialQMC(p, n_trials=100, seed=seed)
|
||
|
|
assert_array_equal(engine.random(1), expected)
|
||
|
|
|
||
|
|
def test_MultinomialDistribution(self):
|
||
|
|
seed = np.random.default_rng(77797854505813727292048130876699859000)
|
||
|
|
p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
|
||
|
|
engine = qmc.MultinomialQMC(p, n_trials=8192, seed=seed)
|
||
|
|
draws = engine.random(1)
|
||
|
|
assert_allclose(draws / np.sum(draws), np.atleast_2d(p), atol=1e-4)
|
||
|
|
|
||
|
|
def test_FindIndex(self):
|
||
|
|
p_cumulative = np.array([0.1, 0.4, 0.45, 0.6, 0.75, 0.9, 0.99, 1.0])
|
||
|
|
size = len(p_cumulative)
|
||
|
|
assert_equal(_test_find_index(p_cumulative, size, 0.0), 0)
|
||
|
|
assert_equal(_test_find_index(p_cumulative, size, 0.4), 2)
|
||
|
|
assert_equal(_test_find_index(p_cumulative, size, 0.44999), 2)
|
||
|
|
assert_equal(_test_find_index(p_cumulative, size, 0.45001), 3)
|
||
|
|
assert_equal(_test_find_index(p_cumulative, size, 1.0), size - 1)
|
||
|
|
|
||
|
|
@pytest.mark.filterwarnings('ignore::UserWarning')
|
||
|
|
def test_other_engine(self):
|
||
|
|
# same as test_MultinomialBasicDraw with different engine
|
||
|
|
seed = np.random.default_rng(283753519042773243071753037669078065412)
|
||
|
|
p = np.array([0.12, 0.26, 0.05, 0.35, 0.22])
|
||
|
|
expected = np.array([[12, 25, 5, 36, 22]])
|
||
|
|
base_engine = qmc.Sobol(1, scramble=True, seed=seed)
|
||
|
|
engine = qmc.MultinomialQMC(p, n_trials=100, engine=base_engine,
|
||
|
|
seed=seed)
|
||
|
|
assert_array_equal(engine.random(1), expected)
|
||
|
|
|
||
|
|
|
||
|
|
class TestNormalQMC:
|
||
|
|
def test_NormalQMC(self):
|
||
|
|
# d = 1
|
||
|
|
engine = qmc.MultivariateNormalQMC(mean=np.zeros(1))
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 1))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 1))
|
||
|
|
# d = 2
|
||
|
|
engine = qmc.MultivariateNormalQMC(mean=np.zeros(2))
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 2))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 2))
|
||
|
|
|
||
|
|
def test_NormalQMCInvTransform(self):
|
||
|
|
# d = 1
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=np.zeros(1), inv_transform=True)
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 1))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 1))
|
||
|
|
# d = 2
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=np.zeros(2), inv_transform=True)
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 2))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 2))
|
||
|
|
|
||
|
|
def test_NormalQMCSeeded(self):
|
||
|
|
# test even dimension
|
||
|
|
seed = np.random.default_rng(274600237797326520096085022671371676017)
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=np.zeros(2), inv_transform=False, seed=seed)
|
||
|
|
samples = engine.random(n=2)
|
||
|
|
samples_expected = np.array([[0.446961, -1.243236],
|
||
|
|
[-0.230754, 0.21354]])
|
||
|
|
assert_allclose(samples, samples_expected, atol=1e-4)
|
||
|
|
|
||
|
|
# test odd dimension
|
||
|
|
seed = np.random.default_rng(274600237797326520096085022671371676017)
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=np.zeros(3), inv_transform=False, seed=seed)
|
||
|
|
samples = engine.random(n=2)
|
||
|
|
samples_expected = np.array([[0.446961, -1.243236, 0.324827],
|
||
|
|
[-0.997875, 0.399134, 1.032234]])
|
||
|
|
assert_allclose(samples, samples_expected, atol=1e-4)
|
||
|
|
|
||
|
|
# same test with another engine
|
||
|
|
seed = np.random.default_rng(274600237797326520096085022671371676017)
|
||
|
|
base_engine = qmc.Sobol(4, scramble=True, seed=seed)
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=np.zeros(3), inv_transform=False,
|
||
|
|
engine=base_engine, seed=seed
|
||
|
|
)
|
||
|
|
samples = engine.random(n=2)
|
||
|
|
samples_expected = np.array([[0.446961, -1.243236, 0.324827],
|
||
|
|
[-0.997875, 0.399134, 1.032234]])
|
||
|
|
assert_allclose(samples, samples_expected, atol=1e-4)
|
||
|
|
|
||
|
|
def test_NormalQMCSeededInvTransform(self):
|
||
|
|
# test even dimension
|
||
|
|
seed = np.random.default_rng(288527772707286126646493545351112463929)
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=np.zeros(2), seed=seed, inv_transform=True)
|
||
|
|
samples = engine.random(n=2)
|
||
|
|
samples_expected = np.array([[-0.804472, 0.384649],
|
||
|
|
[0.396424, -0.117676]])
|
||
|
|
assert_allclose(samples, samples_expected, atol=1e-4)
|
||
|
|
|
||
|
|
# test odd dimension
|
||
|
|
seed = np.random.default_rng(288527772707286126646493545351112463929)
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=np.zeros(3), seed=seed, inv_transform=True)
|
||
|
|
samples = engine.random(n=2)
|
||
|
|
samples_expected = np.array([[-0.804472, 0.384649, 1.583568],
|
||
|
|
[0.165333, -2.266828, -1.655572]])
|
||
|
|
assert_allclose(samples, samples_expected, atol=1e-4)
|
||
|
|
|
||
|
|
def test_other_engine(self):
|
||
|
|
for d in (0, 1, 2):
|
||
|
|
base_engine = qmc.Sobol(d=d, scramble=False)
|
||
|
|
engine = qmc.MultivariateNormalQMC(mean=np.zeros(d),
|
||
|
|
engine=base_engine,
|
||
|
|
inv_transform=True)
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, d))
|
||
|
|
|
||
|
|
def test_NormalQMCShapiro(self):
|
||
|
|
rng = np.random.default_rng(13242)
|
||
|
|
engine = qmc.MultivariateNormalQMC(mean=np.zeros(2), seed=rng)
|
||
|
|
samples = engine.random(n=256)
|
||
|
|
assert all(np.abs(samples.mean(axis=0)) < 1e-2)
|
||
|
|
assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
|
||
|
|
# perform Shapiro-Wilk test for normality
|
||
|
|
for i in (0, 1):
|
||
|
|
_, pval = shapiro(samples[:, i])
|
||
|
|
assert pval > 0.9
|
||
|
|
# make sure samples are uncorrelated
|
||
|
|
cov = np.cov(samples.transpose())
|
||
|
|
assert np.abs(cov[0, 1]) < 1e-2
|
||
|
|
|
||
|
|
def test_NormalQMCShapiroInvTransform(self):
|
||
|
|
rng = np.random.default_rng(3234455)
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=np.zeros(2), inv_transform=True, seed=rng)
|
||
|
|
samples = engine.random(n=256)
|
||
|
|
assert all(np.abs(samples.mean(axis=0)) < 1e-2)
|
||
|
|
assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
|
||
|
|
# perform Shapiro-Wilk test for normality
|
||
|
|
for i in (0, 1):
|
||
|
|
_, pval = shapiro(samples[:, i])
|
||
|
|
assert pval > 0.9
|
||
|
|
# make sure samples are uncorrelated
|
||
|
|
cov = np.cov(samples.transpose())
|
||
|
|
assert np.abs(cov[0, 1]) < 1e-2
|
||
|
|
|
||
|
|
|
||
|
|
class TestMultivariateNormalQMC:
|
||
|
|
|
||
|
|
def test_validations(self):
|
||
|
|
|
||
|
|
message = r"Dimension of `engine` must be consistent"
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.MultivariateNormalQMC([0], engine=qmc.Sobol(d=2))
|
||
|
|
|
||
|
|
message = r"Dimension of `engine` must be consistent"
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.MultivariateNormalQMC([0, 0, 0], engine=qmc.Sobol(d=4))
|
||
|
|
|
||
|
|
message = r"`engine` must be an instance of..."
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.MultivariateNormalQMC([0, 0], engine=np.random.default_rng())
|
||
|
|
|
||
|
|
message = r"Covariance matrix not PSD."
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.MultivariateNormalQMC([0, 0], [[1, 2], [2, 1]])
|
||
|
|
|
||
|
|
message = r"Covariance matrix is not symmetric."
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.MultivariateNormalQMC([0, 0], [[1, 0], [2, 1]])
|
||
|
|
|
||
|
|
message = r"Dimension mismatch between mean and covariance."
|
||
|
|
with pytest.raises(ValueError, match=message):
|
||
|
|
qmc.MultivariateNormalQMC([0], [[1, 0], [0, 1]])
|
||
|
|
|
||
|
|
def test_MultivariateNormalQMCNonPD(self):
|
||
|
|
# try with non-pd but psd cov; should work
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
[0, 0, 0], [[1, 0, 1], [0, 1, 1], [1, 1, 2]],
|
||
|
|
)
|
||
|
|
assert engine._corr_matrix is not None
|
||
|
|
|
||
|
|
def test_MultivariateNormalQMC(self):
|
||
|
|
# d = 1 scalar
|
||
|
|
engine = qmc.MultivariateNormalQMC(mean=0, cov=5)
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 1))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 1))
|
||
|
|
|
||
|
|
# d = 2 list
|
||
|
|
engine = qmc.MultivariateNormalQMC(mean=[0, 1], cov=[[1, 0], [0, 1]])
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 2))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 2))
|
||
|
|
|
||
|
|
# d = 3 np.array
|
||
|
|
mean = np.array([0, 1, 2])
|
||
|
|
cov = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
|
||
|
|
engine = qmc.MultivariateNormalQMC(mean, cov)
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 3))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 3))
|
||
|
|
|
||
|
|
def test_MultivariateNormalQMCInvTransform(self):
|
||
|
|
# d = 1 scalar
|
||
|
|
engine = qmc.MultivariateNormalQMC(mean=0, cov=5, inv_transform=True)
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 1))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 1))
|
||
|
|
|
||
|
|
# d = 2 list
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=[0, 1], cov=[[1, 0], [0, 1]], inv_transform=True,
|
||
|
|
)
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 2))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 2))
|
||
|
|
|
||
|
|
# d = 3 np.array
|
||
|
|
mean = np.array([0, 1, 2])
|
||
|
|
cov = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
|
||
|
|
engine = qmc.MultivariateNormalQMC(mean, cov, inv_transform=True)
|
||
|
|
samples = engine.random()
|
||
|
|
assert_equal(samples.shape, (1, 3))
|
||
|
|
samples = engine.random(n=5)
|
||
|
|
assert_equal(samples.shape, (5, 3))
|
||
|
|
|
||
|
|
def test_MultivariateNormalQMCSeeded(self):
|
||
|
|
# test even dimension
|
||
|
|
rng = np.random.default_rng(180182791534511062935571481899241825000)
|
||
|
|
a = rng.standard_normal((2, 2))
|
||
|
|
A = a @ a.transpose() + np.diag(rng.random(2))
|
||
|
|
engine = qmc.MultivariateNormalQMC(np.array([0, 0]), A,
|
||
|
|
inv_transform=False, seed=rng)
|
||
|
|
samples = engine.random(n=2)
|
||
|
|
samples_expected = np.array([[0.479575, 0.934723],
|
||
|
|
[1.712571, 0.172699]])
|
||
|
|
assert_allclose(samples, samples_expected, atol=1e-4)
|
||
|
|
|
||
|
|
# test odd dimension
|
||
|
|
rng = np.random.default_rng(180182791534511062935571481899241825000)
|
||
|
|
a = rng.standard_normal((3, 3))
|
||
|
|
A = a @ a.transpose() + np.diag(rng.random(3))
|
||
|
|
engine = qmc.MultivariateNormalQMC(np.array([0, 0, 0]), A,
|
||
|
|
inv_transform=False, seed=rng)
|
||
|
|
samples = engine.random(n=2)
|
||
|
|
samples_expected = np.array([[2.463393, 2.252826, -0.886809],
|
||
|
|
[1.252468, 0.029449, -1.126328]])
|
||
|
|
assert_allclose(samples, samples_expected, atol=1e-4)
|
||
|
|
|
||
|
|
def test_MultivariateNormalQMCSeededInvTransform(self):
|
||
|
|
# test even dimension
|
||
|
|
rng = np.random.default_rng(224125808928297329711992996940871155974)
|
||
|
|
a = rng.standard_normal((2, 2))
|
||
|
|
A = a @ a.transpose() + np.diag(rng.random(2))
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
np.array([0, 0]), A, seed=rng, inv_transform=True
|
||
|
|
)
|
||
|
|
samples = engine.random(n=2)
|
||
|
|
samples_expected = np.array([[-3.095968, -0.566545],
|
||
|
|
[0.603154, 0.222434]])
|
||
|
|
assert_allclose(samples, samples_expected, atol=1e-4)
|
||
|
|
|
||
|
|
# test odd dimension
|
||
|
|
rng = np.random.default_rng(224125808928297329711992996940871155974)
|
||
|
|
a = rng.standard_normal((3, 3))
|
||
|
|
A = a @ a.transpose() + np.diag(rng.random(3))
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
np.array([0, 0, 0]), A, seed=rng, inv_transform=True
|
||
|
|
)
|
||
|
|
samples = engine.random(n=2)
|
||
|
|
samples_expected = np.array([[1.427248, -0.338187, -1.560687],
|
||
|
|
[-0.357026, 1.662937, -0.29769]])
|
||
|
|
assert_allclose(samples, samples_expected, atol=1e-4)
|
||
|
|
|
||
|
|
def test_MultivariateNormalQMCShapiro(self):
|
||
|
|
# test the standard case
|
||
|
|
seed = np.random.default_rng(188960007281846377164494575845971645056)
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=[0, 0], cov=[[1, 0], [0, 1]], seed=seed
|
||
|
|
)
|
||
|
|
samples = engine.random(n=256)
|
||
|
|
assert all(np.abs(samples.mean(axis=0)) < 1e-2)
|
||
|
|
assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
|
||
|
|
# perform Shapiro-Wilk test for normality
|
||
|
|
for i in (0, 1):
|
||
|
|
_, pval = shapiro(samples[:, i])
|
||
|
|
assert pval > 0.9
|
||
|
|
# make sure samples are uncorrelated
|
||
|
|
cov = np.cov(samples.transpose())
|
||
|
|
assert np.abs(cov[0, 1]) < 1e-2
|
||
|
|
|
||
|
|
# test the correlated, non-zero mean case
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=[1.0, 2.0], cov=[[1.5, 0.5], [0.5, 1.5]], seed=seed
|
||
|
|
)
|
||
|
|
samples = engine.random(n=256)
|
||
|
|
assert all(np.abs(samples.mean(axis=0) - [1, 2]) < 1e-2)
|
||
|
|
assert all(np.abs(samples.std(axis=0) - np.sqrt(1.5)) < 1e-2)
|
||
|
|
# perform Shapiro-Wilk test for normality
|
||
|
|
for i in (0, 1):
|
||
|
|
_, pval = shapiro(samples[:, i])
|
||
|
|
assert pval > 0.9
|
||
|
|
# check covariance
|
||
|
|
cov = np.cov(samples.transpose())
|
||
|
|
assert np.abs(cov[0, 1] - 0.5) < 1e-2
|
||
|
|
|
||
|
|
def test_MultivariateNormalQMCShapiroInvTransform(self):
|
||
|
|
# test the standard case
|
||
|
|
seed = np.random.default_rng(200089821034563288698994840831440331329)
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=[0, 0], cov=[[1, 0], [0, 1]], seed=seed, inv_transform=True
|
||
|
|
)
|
||
|
|
samples = engine.random(n=256)
|
||
|
|
assert all(np.abs(samples.mean(axis=0)) < 1e-2)
|
||
|
|
assert all(np.abs(samples.std(axis=0) - 1) < 1e-2)
|
||
|
|
# perform Shapiro-Wilk test for normality
|
||
|
|
for i in (0, 1):
|
||
|
|
_, pval = shapiro(samples[:, i])
|
||
|
|
assert pval > 0.9
|
||
|
|
# make sure samples are uncorrelated
|
||
|
|
cov = np.cov(samples.transpose())
|
||
|
|
assert np.abs(cov[0, 1]) < 1e-2
|
||
|
|
|
||
|
|
# test the correlated, non-zero mean case
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=[1.0, 2.0],
|
||
|
|
cov=[[1.5, 0.5], [0.5, 1.5]],
|
||
|
|
seed=seed,
|
||
|
|
inv_transform=True,
|
||
|
|
)
|
||
|
|
samples = engine.random(n=256)
|
||
|
|
assert all(np.abs(samples.mean(axis=0) - [1, 2]) < 1e-2)
|
||
|
|
assert all(np.abs(samples.std(axis=0) - np.sqrt(1.5)) < 1e-2)
|
||
|
|
# perform Shapiro-Wilk test for normality
|
||
|
|
for i in (0, 1):
|
||
|
|
_, pval = shapiro(samples[:, i])
|
||
|
|
assert pval > 0.9
|
||
|
|
# check covariance
|
||
|
|
cov = np.cov(samples.transpose())
|
||
|
|
assert np.abs(cov[0, 1] - 0.5) < 1e-2
|
||
|
|
|
||
|
|
def test_MultivariateNormalQMCDegenerate(self):
|
||
|
|
# X, Y iid standard Normal and Z = X + Y, random vector (X, Y, Z)
|
||
|
|
seed = np.random.default_rng(163206374175814483578698216542904486209)
|
||
|
|
engine = qmc.MultivariateNormalQMC(
|
||
|
|
mean=[0.0, 0.0, 0.0],
|
||
|
|
cov=[[1.0, 0.0, 1.0], [0.0, 1.0, 1.0], [1.0, 1.0, 2.0]],
|
||
|
|
seed=seed,
|
||
|
|
)
|
||
|
|
samples = engine.random(n=512)
|
||
|
|
assert all(np.abs(samples.mean(axis=0)) < 1e-2)
|
||
|
|
assert np.abs(np.std(samples[:, 0]) - 1) < 1e-2
|
||
|
|
assert np.abs(np.std(samples[:, 1]) - 1) < 1e-2
|
||
|
|
assert np.abs(np.std(samples[:, 2]) - np.sqrt(2)) < 1e-2
|
||
|
|
for i in (0, 1, 2):
|
||
|
|
_, pval = shapiro(samples[:, i])
|
||
|
|
assert pval > 0.8
|
||
|
|
cov = np.cov(samples.transpose())
|
||
|
|
assert np.abs(cov[0, 1]) < 1e-2
|
||
|
|
assert np.abs(cov[0, 2] - 1) < 1e-2
|
||
|
|
# check to see if X + Y = Z almost exactly
|
||
|
|
assert all(np.abs(samples[:, 0] + samples[:, 1] - samples[:, 2])
|
||
|
|
< 1e-5)
|
||
|
|
|
||
|
|
|
||
|
|
class TestLloyd:
|
||
|
|
def test_lloyd(self):
|
||
|
|
# quite sensible seed as it can go up before going further down
|
||
|
|
rng = np.random.RandomState(1809831)
|
||
|
|
sample = rng.uniform(0, 1, size=(128, 2))
|
||
|
|
base_l1 = _l1_norm(sample)
|
||
|
|
base_l2 = l2_norm(sample)
|
||
|
|
|
||
|
|
for _ in range(4):
|
||
|
|
sample_lloyd = _lloyd_centroidal_voronoi_tessellation(
|
||
|
|
sample, maxiter=1,
|
||
|
|
)
|
||
|
|
curr_l1 = _l1_norm(sample_lloyd)
|
||
|
|
curr_l2 = l2_norm(sample_lloyd)
|
||
|
|
|
||
|
|
# higher is better for the distance measures
|
||
|
|
assert base_l1 < curr_l1
|
||
|
|
assert base_l2 < curr_l2
|
||
|
|
|
||
|
|
base_l1 = curr_l1
|
||
|
|
base_l2 = curr_l2
|
||
|
|
|
||
|
|
sample = sample_lloyd
|
||
|
|
|
||
|
|
def test_lloyd_non_mutating(self):
|
||
|
|
"""
|
||
|
|
Verify that the input samples are not mutated in place and that they do
|
||
|
|
not share memory with the output.
|
||
|
|
"""
|
||
|
|
sample_orig = np.array([[0.1, 0.1],
|
||
|
|
[0.1, 0.2],
|
||
|
|
[0.2, 0.1],
|
||
|
|
[0.2, 0.2]])
|
||
|
|
sample_copy = sample_orig.copy()
|
||
|
|
new_sample = _lloyd_centroidal_voronoi_tessellation(
|
||
|
|
sample=sample_orig
|
||
|
|
)
|
||
|
|
assert_allclose(sample_orig, sample_copy)
|
||
|
|
assert not np.may_share_memory(sample_orig, new_sample)
|
||
|
|
|
||
|
|
def test_lloyd_errors(self):
|
||
|
|
with pytest.raises(ValueError, match=r"`sample` is not a 2D array"):
|
||
|
|
sample = [0, 1, 0.5]
|
||
|
|
_lloyd_centroidal_voronoi_tessellation(sample)
|
||
|
|
|
||
|
|
msg = r"`sample` dimension is not >= 2"
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
sample = [[0], [0.4], [1]]
|
||
|
|
_lloyd_centroidal_voronoi_tessellation(sample)
|
||
|
|
|
||
|
|
msg = r"`sample` is not in unit hypercube"
|
||
|
|
with pytest.raises(ValueError, match=msg):
|
||
|
|
sample = [[-1.1, 0], [0.1, 0.4], [1, 2]]
|
||
|
|
_lloyd_centroidal_voronoi_tessellation(sample)
|
||
|
|
|
||
|
|
|
||
|
|
# mindist
|
||
|
|
def l2_norm(sample):
|
||
|
|
return distance.pdist(sample).min()
|