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41 lines
1.1 KiB
Python
41 lines
1.1 KiB
Python
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import numpy as np
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from tsi_sim import theory
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F = 1 / 30
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T = 10000
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def test_expected_ratio_unbiased_at_q1():
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assert abs(float(theory.expected_ratio(F, 1.0)) - 1.0) < 1e-12
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def test_expected_ratio_monotone_in_q():
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qs = np.linspace(0.5, 1.0, 20)
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er = theory.expected_ratio(F, qs)
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assert np.all(np.diff(er) > 0) # accuracy improves as q -> 1
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assert np.all(er <= 1.0 + 1e-12) # always an underestimate
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def test_variance_bound_matches_at_q1():
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v = float(theory.variance_ratio(F, 1.0, T))
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assert abs(v - theory.variance_bound(F, T)) < 1e-15
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def test_optimal_beta_is_half_stability_bound():
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for q in (0.7, 0.85, 0.95):
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opt = float(theory.optimal_beta(F, q))
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bound = float(theory.beta_stability_bound(F, q))
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assert abs(opt - bound / 2) < 1e-12
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def test_block_count_ceiling_above_one():
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c = theory.block_count_ceiling(F)
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assert 1.015 < c < 1.02 # -ln(1-1/30)/(1/30) ~ 1.01705
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def test_fixed_point_bias_about_one_percent():
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b = theory.fixed_point_bias(F)
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assert abs(b - (F / (33 / 1000))) < 1e-12
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assert 1.005 < b < 1.02
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