109 lines
2.8 KiB
Python
109 lines
2.8 KiB
Python
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import numpy as np
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from numpy.testing import assert_allclose
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import pytest
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from logistic import f, iterate_f
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# set the random seed for once here
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SEED = np.random.randint(0, 2**31)
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@pytest.fixture
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def random_state():
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print(f'Using seed {SEED}')
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random_state = np.random.RandomState(SEED)
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return random_state
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@pytest.mark.parametrize('a', [1, 2, 3])
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@pytest.mark.parametrize('b', [5, 6, 7])
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def test_addition_increases(a, b):
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print(a, b)
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assert b + a > a
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@pytest.mark.parametrize(
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'x, r, expected',
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[
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(0.1, 2.2, 0.198),
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(0.2, 3.4, 0.544),
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(0.75, 1.7, 0.31875),
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]
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)
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def test_f(x, r, expected):
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result = f(x, r)
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assert_allclose(result, expected)
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@pytest.mark.parametrize(
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'x, r, it, expected',
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[
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(0.1, 2.2, 1, [0.198]),
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(0.2, 3.4, 4, [0.544, 0.843418, 0.449019, 0.841163]),
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(0.75, 1.7, 2, [0.31875, 0.369152]),
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]
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)
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def test_iterate_f(x, r, it, expected):
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result = iterate_f(it, x, r)
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assert_allclose(result, expected, rtol=1e-5)
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def test_attractor_converges():
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SEED = 42
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random_state = np.random.RandomState(SEED)
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for _ in range(100):
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x = random_state.uniform(0, 1)
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result = iterate_f(100, x, 1.5)
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assert_allclose(result[-1], 1 / 3)
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####################################################################
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# These only work after adding the fixture
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####################################################################
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@pytest.mark.xfail
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def test_attractor_converges2(random_state):
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for _ in range(100):
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x = random_state.uniform(0, 1)
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result = iterate_f(100, x, 1.5)
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assert_allclose(result[-1], 1 / 3)
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@pytest.mark.xfail
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def test_chaotic_behavior(random_state):
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r = 3.8
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for _ in range(10):
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x = random_state.uniform(0, 1)
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result = iterate_f(100000, x, r)
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assert np.all(result >= 0.0)
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assert np.all(result <= 1.0)
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assert min(np.abs(np.diff(result[-1000:]))) > 1e-6
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@pytest.mark.xfail
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def test_sensitivity_to_initial_conditions(random_state):
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"""
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`f` is a function and `x0` and `y0` are two possible seeds.
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If `f` has SDIC then:
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there is a number `delta` such that for any `x0` there is a `y0` that is
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not more than `init_error` away from `x0`, where the initial condition `y0`
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has the property that there is some integer n such that after n iterations,
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the orbit is more than `delta` away from the orbit of `x0`. That is
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|xn-yn| > delta
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"""
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delta = 0.1
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n = 10000
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x0 = random_state.rand()
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x0_diffs = random_state.rand(100) * 0.001 - 0.0005
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result_list = []
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for x0_diff in x0_diffs:
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x1 = x0 + x0_diff
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l_x = iterate_f(n, x0, 3.8)
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l_y = iterate_f(n, x1, 3.8)
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result_list.append(any(abs(l_x - l_y) > delta))
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assert any(result_list)
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