initial commit with 2024 materials

hands_on_solutions/logistic_fun/test_logistic.py

@@ -0,0 +1,108 @@
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+
+from logistic import f, iterate_f
+
+# set the random seed for once here
+SEED = np.random.randint(0, 2**31)
+
+
+@pytest.fixture
+def random_state():
+    print(f'Using seed {SEED}')
+    random_state = np.random.RandomState(SEED)
+    return random_state
+
+
+
+@pytest.mark.parametrize('a', [1, 2, 3])
+@pytest.mark.parametrize('b', [5, 6, 7])
+def test_addition_increases(a, b):
+    print(a, b)
+    assert b + a > a
+
+
+
+@pytest.mark.parametrize(
+    'x, r, expected',
+    [
+        (0.1, 2.2, 0.198),
+        (0.2, 3.4, 0.544),
+        (0.75, 1.7, 0.31875),
+    ]
+)
+def test_f(x, r, expected):
+    result = f(x, r)
+    assert_allclose(result, expected)
+
+
+@pytest.mark.parametrize(
+    'x, r, it, expected',
+    [
+        (0.1, 2.2, 1, [0.198]),
+        (0.2, 3.4, 4, [0.544, 0.843418, 0.449019, 0.841163]),
+        (0.75, 1.7, 2, [0.31875, 0.369152]),
+    ]
+)
+def test_iterate_f(x, r, it, expected):
+    result = iterate_f(it, x, r)
+    assert_allclose(result, expected, rtol=1e-5)
+
+
+def test_attractor_converges():
+    SEED = 42
+    random_state = np.random.RandomState(SEED)
+
+    for _ in range(100):
+        x = random_state.uniform(0, 1)
+        result = iterate_f(100, x, 1.5)
+        assert_allclose(result[-1], 1 / 3)
+
+####################################################################
+# These only work after adding the fixture
+####################################################################
+
+
+@pytest.mark.xfail
+def test_attractor_converges2(random_state):
+    for _ in range(100):
+        x = random_state.uniform(0, 1)
+        result = iterate_f(100, x, 1.5)
+        assert_allclose(result[-1], 1 / 3)
+
+
+@pytest.mark.xfail
+def test_chaotic_behavior(random_state):
+    r = 3.8
+    for _ in range(10):
+        x = random_state.uniform(0, 1)
+        result = iterate_f(100000, x, r)
+        assert np.all(result >= 0.0)
+        assert np.all(result <= 1.0)
+        assert min(np.abs(np.diff(result[-1000:]))) > 1e-6
+
+
+@pytest.mark.xfail
+def test_sensitivity_to_initial_conditions(random_state):
+    """
+    `f` is a function and `x0` and `y0` are two possible seeds.
+    If `f` has SDIC then:
+    there is a number `delta` such that for any `x0` there is a `y0` that is
+    not more than `init_error` away from `x0`, where the initial condition `y0`
+    has the property that there is some integer n such that after n iterations,
+    the orbit is more than `delta` away from the orbit of `x0`. That is
+    |xn-yn| > delta
+    """
+    delta = 0.1
+    n = 10000
+    x0 = random_state.rand()
+    x0_diffs = random_state.rand(100) * 0.001 - 0.0005
+
+    result_list = []
+    for x0_diff in x0_diffs:
+        x1 = x0 + x0_diff
+        l_x = iterate_f(n, x0, 3.8)
+        l_y = iterate_f(n, x1, 3.8)
+        result_list.append(any(abs(l_x - l_y) > delta))
+    assert any(result_list)