def test_valid_curve_direction():
"""Test that arguments to curve and direction are valid"""
with pytest.raises(ValueError):
kl = KneeLocator(range(3), [1, 3, 5], curve="bad curve")
with pytest.raises(ValueError):
kl = KneeLocator(range(3), [1, 3, 5], direction="bad direction")
def test_plot_knee():
"""Test that plotting is functional"""
x, y = dg.figure2()
kl = KneeLocator(x, y, S=1.0, curve="concave", interp_method="interp1d")
num_figures_before = plt.gcf().number
kl.plot_knee()
num_figures_after = plt.gcf().number
assert num_figures_before < num_figures_after
def test_flat_maxima():
"""The global maxima has a sequentially equal value in the difference curve"""
x = [
0,
1.0,
2.0,
3.0,
4.0,
5.0,
6.0,
7.0,
8.0,
9.0,
10.0,
11.0,
12.0,
13.0,
14.0,
15.0,
16.0,
17.0,
]
y = [
1,
0.787701317715959,
0.7437774524158126,
0.6559297218155198,
0.5065885797950219,
0.36749633967789164,
0.2547584187408492,
0.16251830161054173,
0.10395314787701318,
0.06734992679355783,
0.043923865300146414,
0.027818448023426062,
0.01903367496339678,
0.013177159590043924,
0.010248901903367497,
0.007320644216691069,
0.005856515373352855,
0.004392386530014641,
]
# When S=0.0 the first local maximum is found.
kl = KneeLocator(x, y, curve="convex", direction="decreasing", S=0.0)
assert math.isclose(kl.knee, 1.0, rel_tol=0.05)
# When S=1.0 the global maximum is found.
kl = KneeLocator(x, y, curve="convex", direction="decreasing", S=1.0)
assert math.isclose(kl.knee, 8.0, rel_tol=0.05)
def test_concave_decreasing(interp_method):
"""test a concave decreasing function"""
x, y = dg.concave_decreasing()
kn = KneeLocator(
x, y, curve="concave", direction="decreasing", interp_method=interp_method
)
assert kn.knee == 7
def test_list_input():
"""Indirectly test that flip works on lists as input"""
x, y = dg.figure2()
kl = KneeLocator(
x.tolist(), y.tolist(), S=1.0, curve="concave", interp_method="polynomial"
)
assert math.isclose(kl.knee, 0.22, rel_tol=0.05)
def test_convex_decreasing(interp_method):
"""test a convex decreasing function"""
x, y = dg.convex_decreasing()
kl = KneeLocator(
x, y, curve="convex", direction="decreasing", interp_method=interp_method
)
assert kl.knee == 2
def test_convex_decreasing_bumpy(interp_method, expected):
"""test a bumpy convex decreasing function"""
x, y = dg.bumpy()
kl = KneeLocator(
x, y, curve="convex", direction="decreasing", interp_method=interp_method
)
assert kl.knee == expected
def test_figure2(interp_method):
"""From the kneedle manuscript"""
x, y = dg.figure2()
kl = KneeLocator(x, y, S=1.0, curve="concave", interp_method=interp_method)
assert math.isclose(kl.knee, 0.22, rel_tol=0.05)
assert math.isclose(kl.elbow, 0.22, rel_tol=0.05)
assert math.isclose(kl.norm_elbow, kl.knee, rel_tol=0.05)
def model_selector(self, model_dict, plot=False, save=True): # code for selecting optimal K-means model
# code for selecting optimal cluster model returns the model
errors = []
model_dict = OrderedDict(sorted(model_dict.items()))
cluster_list = list(model_dict.keys())
for m in model_dict.values():
error = self.get_error(m)
errors.append(error)
# Calculate elbow
kn = KneeLocator(cluster_list, errors, direction='decreasing', curve='convex')
elbow = kn.knee
print('[ClusterModel:model_selector]: recommended K = {}'.format(elbow))
# Plot Elbow
fig, ax = plt.subplots(1)
ax.plot(cluster_list, errors, color='b', marker='o')
ax.vlines(x=elbow, linestyles='--', color='black', ymin=0, ymax=max(errors)+10)
ax.set_title('Cluster Model Elbow Plot - Optimal K = {}'.format(elbow))
ax.set_xlabel('Cluster K')
ax.set_ylabel('Model Error (Inertia)')
if save:
if self.model_folder:
if not os.path.exists(self.model_folder+'/results'):
os.makedirs(self.model_folder+'/results')
print('[ClusterModel:model_selector]: saving Elbow Plot to {} dir.'.format(self.model_folder +'/results/'))
plt.savefig(self.model_folder +'/results/Elbow_Plot.png')
if plot:
plt.show()
return model_dict[elbow]
def test_convex_increasing_truncated(interp_method):
"""test a truncated convex increasing function"""
x, y = dg.convex_increasing()
kl = KneeLocator(
x[:-3] / 10, y[:-3] / 10, curve="convex", interp_method=interp_method
)
assert kl.knee == 0.4
def test_concave_increasing_truncated(interp_method):
"""test a truncated concave increasing function"""
kn = KneeLocator(x[:-3] / 10,
y_concave_inc[:-3] / 10,
curve='concave',
interp_method=interp_method)
assert kn.knee == 0.2
def test_convex_increasing(interp_method):
"""test a convex increasing function"""
kn = KneeLocator(x,
y_convex_inc,
curve='convex',
interp_method=interp_method)
assert kn.knee == 7
def test_gamma():
np.random.seed(23)
n = 1000
x = range(1, n + 1)
y = sorted(np.random.gamma(0.5, 1.0, n), reverse=True)
kl = KneeLocator(x, y, curve='convex', direction='decreasing')
assert kl.knee == 43
def test_convex_decreasing_bumpy(interp_method, expected):
"""test a bumpy convex decreasing function"""
kn = KneeLocator(x_bumpy,
y_bumpy,
curve='convex',
direction='decreasing',
interp_method=interp_method)
assert kn.knee == expected
def test_y():
"""Test the y value"""
x, y = dg.figure2()
kl = KneeLocator(x, y, S=1.0, curve="concave", interp_method="interp1d")
assert math.isclose(kl.knee_y, 1.897, rel_tol=0.03)
assert math.isclose(kl.all_knees_y[0], 1.897, rel_tol=0.03)
assert math.isclose(kl.norm_knee_y, 0.758, rel_tol=0.03)
assert math.isclose(kl.all_norm_knees_y[0], 0.758, rel_tol=0.03)
def test_convex_decreasing(interp_method):
"""test a convex decreasing function"""
kn = KneeLocator(x,
y_convex_dec,
curve='convex',
direction='decreasing',
interp_method=interp_method)
assert kn.knee == 2
def test_convex_decreasing_truncated(interp_method):
"""test a truncated convex decreasing function"""
kn = KneeLocator(x[:-3] / 10,
y_convex_dec[:-3] / 10,
curve='convex',
direction='decreasing',
interp_method=interp_method)
assert kn.knee == 0.2
def test_concave_decreasing_truncated(interp_method):
"""test a truncated concave decreasing function"""
x, y = dg.concave_decreasing()
kl = KneeLocator(x[:-3] / 10,
y[:-3] / 10,
curve='concave',
direction='decreasing',
interp_method=interp_method)
assert kl.knee == 0.4
def test_gamma_online_offline(online, expected):
"""Tests online and offline knee detection.
Notable that a large number of samples are highly sensitive to S parameter
"""
np.random.seed(23)
n = 1000
x = range(1, n + 1)
y = sorted(np.random.gamma(0.5, 1.0, n), reverse=True)
kl = KneeLocator(x, y, curve="convex", direction="decreasing", online=online)
assert kl.knee == expected
def test_all_knees():
x, y = dg.bumpy()
kl = KneeLocator(x, y, curve='convex', direction='decreasing', online=True)
kl.all_elbows == set([41, 46, 53, 26, 31])
kl.all_norm_elbows == set([
0.2921348314606742,
0.348314606741573,
0.5955056179775281,
0.4606741573033708,
0.5168539325842696,
])
def test_sensitivity():
"""Test the S parameter -- where S is the number of flat points to identify before calling a knee"""
np.random.seed(23)
sensitivity = [1, 3, 5, 10, 100, 200, 400]
detected_knees = []
expected_knees = [43, 137, 178, 258, 305, 482, 482]
n = 1000
x = range(1, n + 1)
y = sorted(np.random.gamma(0.5, 1.0, n), reverse=True)
for s, expected_knee in zip(sensitivity, expected_knees):
kl = KneeLocator(x, y, curve='convex', direction='decreasing', S=s)
detected_knees.append(kl.knee)
assert kl.knee, expected_knee
def test_NoisyGaussian():
"""From the Kneedle manuscript"""
x, y = dg.noisy_gaussian(mu=50, sigma=10, N=1000, seed=42)
kl = KneeLocator(
x,
y,
S=1.0,
curve="concave",
interp_method="polynomial",
polynomial_degree=11,
online=True,
)
assert math.isclose(kl.knee, 63.0, rel_tol=1e-02)
def test_y_no_knee():
"""Test the y value, if there is no knee found."""
kl = KneeLocator(
np.array([1, 2, 3]),
np.array([0.90483742, 0.81873075, 0.74081822]),
S=1.0,
curve="convex",
direction="decreasing",
interp_method="interp1d",
online=False,
)
assert kl.knee_y is None
assert kl.norm_knee_y is None
def test_all_knees():
x, y = dg.bumpy()
kl = KneeLocator(x, y, curve="convex", direction="decreasing", online=True)
assert np.isclose(sorted(kl.all_elbows), [26, 31, 41, 46, 53]).all()
assert np.isclose(
sorted(kl.all_norm_elbows),
[
0.2921348314606742,
0.348314606741573,
0.4606741573033708,
0.5168539325842696,
0.5955056179775281,
],
).all()
def test_sine():
x = np.arange(0, 10, 0.1)
y_sin = np.sin(x)
sine_combos = [
('decreasing', 'convex'),
('increasing', 'convex'),
('increasing', 'concave'),
('decreasing', 'concave')
]
expected_knees = [4.5, 4.9, 1.4, 7.7, 8.1, 1.8]
detected_knees = []
for direction, curve in sine_combos:
kl_sine = KneeLocator(x, y_sin, direction=direction, curve=curve, S=1)
detected_knees.extend(kl_sine.all_knees)
assert np.isclose(expected_knees, detected_knees).all()
def test_sine():
x = np.arange(0, 10, 0.1)
y_sin = np.sin(x)
sine_combos = [
("decreasing", "convex"),
("increasing", "convex"),
("increasing", "concave"),
("decreasing", "concave"),
]
expected_knees = [4.5, 4.9, 7.7, 1.8]
detected_knees = []
for direction, curve in sine_combos:
kl_sine = KneeLocator(
x, y_sin, direction=direction, curve=curve, S=1, online=True
)
detected_knees.append(kl_sine.knee)
assert np.isclose(expected_knees, detected_knees).all()
def test_convex_increasing(interp_method):
"""test a convex increasing function"""
x, y = dg.convex_increasing()
kl = KneeLocator(x, y, curve='convex', interp_method=interp_method)
assert kl.knee == 7
def test_concave_increasing(interp_method):
"""test a concave increasing function"""
x, y = dg.concave_increasing()
kn = KneeLocator(x, y, curve='concave', interp_method=interp_method)
assert kn.knee == 2
def test_NoisyGaussian(interp_method):
"""From the Kneedle manuscript"""
x, y = dg.noisy_gaussian(mu=50, sigma=10, N=10000)
kl = KneeLocator(x, y, S=1.0, curve='concave', interp_method=interp_method)
assert math.isclose(kl.knee, 60.5, rel_tol=7.0)
def test_logistic():
y = np.array(
[
2.00855493e-45,
1.10299045e-43,
4.48168384e-42,
1.22376580e-41,
5.10688883e-40,
1.18778110e-38,
5.88777891e-35,
4.25317895e-34,
4.06507035e-33,
6.88084518e-32,
2.99321831e-31,
1.13291723e-30,
1.05244482e-28,
2.67578448e-27,
1.22522190e-26,
2.36517846e-26,
8.30369408e-26,
1.24303033e-25,
2.27726918e-25,
1.06330422e-24,
5.55017673e-24,
1.92068553e-23,
3.31361011e-23,
1.13575247e-22,
1.75386416e-22,
6.52680518e-22,
2.05106011e-21,
6.37285545e-21,
4.16125535e-20,
1.12709507e-19,
5.75853420e-19,
1.73333796e-18,
2.70099890e-18,
7.53254646e-18,
1.38139433e-17,
3.60081965e-17,
8.08419977e-17,
1.86378584e-16,
5.36224556e-16,
8.89404640e-16,
2.34045104e-15,
4.72168880e-15,
6.84378992e-15,
2.26898430e-14,
3.10087652e-14,
2.78081199e-13,
1.06479577e-12,
2.81002203e-12,
4.22067092e-12,
9.27095863e-12,
1.54519738e-11,
4.53347819e-11,
1.35564441e-10,
2.35242087e-10,
4.45253545e-10,
9.78613696e-10,
1.53140922e-09,
2.81648560e-09,
6.70890436e-09,
1.49724785e-08,
5.59553565e-08,
1.39510811e-07,
7.64761811e-07,
1.40723957e-06,
4.97638863e-06,
2.12817943e-05,
3.26471410e-05,
1.02599591e-04,
3.18774179e-04,
5.67297630e-04,
9.22732716e-04,
1.17445643e-03,
3.59279384e-03,
3.61936491e-02,
6.39493416e-02,
1.29304829e-01,
1.72272215e-01,
3.46945901e-01,
5.02826602e-01,
6.24800042e-01,
7.38412957e-01,
7.59931663e-01,
7.73374421e-01,
7.91421897e-01,
8.29325597e-01,
8.57718637e-01,
8.73286061e-01,
8.77056835e-01,
8.93173768e-01,
9.05435646e-01,
9.17217910e-01,
9.19119179e-01,
9.24810910e-01,
9.26306908e-01,
9.28621233e-01,
9.33855835e-01,
9.37263027e-01,
9.41651642e-01,
]
)
x = np.array(
[
1.0,
2.0,
3.0,
4.0,
5.0,
6.0,
7.0,
8.0,
9.0,
10.0,
11.0,
12.0,
13.0,
14.0,
15.0,
16.0,
17.0,
18.0,
19.0,
20.0,
21.0,
22.0,
23.0,
24.0,
25.0,
26.0,
27.0,
28.0,
29.0,
30.0,
31.0,
32.0,
33.0,
34.0,
35.0,
36.0,
37.0,
38.0,
39.0,
40.0,
41.0,
42.0,
43.0,
44.0,
45.0,
46.0,
47.0,
48.0,
49.0,
50.0,
51.0,
52.0,
53.0,
54.0,
55.0,
56.0,
57.0,
58.0,
59.0,
60.0,
61.0,
62.0,
63.0,
64.0,
65.0,
66.0,
67.0,
68.0,
69.0,
70.0,
71.0,
72.0,
73.0,
74.0,
75.0,
76.0,
77.0,
78.0,
79.0,
80.0,
81.0,
82.0,
83.0,
84.0,
85.0,
86.0,
87.0,
88.0,
89.0,
90.0,
91.0,
92.0,
93.0,
94.0,
95.0,
96.0,
97.0,
98.0,
]
)
kl = KneeLocator(x, y, curve="convex", direction="increasing", online=True,)
assert kl.knee == 73
