11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167 | def weber_fechner_law(
name="Weber-Fechner Law",
resolution=100,
constant=1.0,
maximum_stimulus_intensity=5.0,
):
"""
Weber-Fechner Law
Args:
name: name of the experiment
resolution: number of allowed values for stimulus 1 and 2
constant: constant multiplier
maximum_stimulus_intensity: maximum value for stimulus 1 and 2
Examples:
>>> experiment = weber_fechner_law()
# The runner can accept numpy arrays or pandas DataFrames, but the return value will
# always be a pandas DataFrame.
>>> experiment.run(np.array([[.1,.2]]), random_state=42)
S1 S2 difference_detected
0 0.1 0.2 0.696194
>>> experiment.run(pd.DataFrame({'S1': [0.1], 'S2': [0.2]}), random_state=42)
S1 S2 difference_detected
0 0.1 0.2 0.696194
"""
params = dict(
name=name,
resolution=resolution,
constant=constant,
maximum_stimulus_intensity=maximum_stimulus_intensity,
)
iv1 = IV(
name="S1",
allowed_values=np.linspace(
1 / resolution, maximum_stimulus_intensity, resolution
),
value_range=(1 / resolution, maximum_stimulus_intensity),
units="intensity",
variable_label="Stimulus 1 Intensity",
type=ValueType.REAL,
)
iv2 = IV(
name="S2",
allowed_values=np.linspace(
1 / resolution, maximum_stimulus_intensity, resolution
),
value_range=(1 / resolution, maximum_stimulus_intensity),
units="intensity",
variable_label="Stimulus 2 Intensity",
type=ValueType.REAL,
)
dv1 = DV(
name="difference_detected",
value_range=(0, maximum_stimulus_intensity),
units="sensation",
variable_label="Sensation",
type=ValueType.REAL,
)
variables = VariableCollection(
independent_variables=[iv1, iv2],
dependent_variables=[dv1],
)
def run(
conditions: Union[pd.DataFrame, np.ndarray, np.recarray],
added_noise=0.01,
random_state: Optional[int] = None,
):
rng = np.random.default_rng(random_state)
X = np.array(conditions)
Y = np.zeros((X.shape[0], 1))
for idx, x in enumerate(X):
y = constant * np.log(x[1] / x[0]) + rng.normal(0, added_noise)
Y[idx] = y
experiment_data = pd.DataFrame(conditions)
experiment_data.columns = [v.name for v in variables.independent_variables]
experiment_data[dv1.name] = Y
return experiment_data
ground_truth = partial(run, added_noise=0.0)
def domain():
s1_values = variables.independent_variables[0].allowed_values
s2_values = variables.independent_variables[1].allowed_values
X = np.array(np.meshgrid(s1_values, s2_values)).T.reshape(-1, 2)
# remove all combinations where s1 > s2
X = X[X[:, 0] <= X[:, 1]]
return X
def plotter(
model=None,
):
import matplotlib.colors as mcolors
import matplotlib.pyplot as plt
colors = mcolors.TABLEAU_COLORS
col_keys = list(colors.keys())
S0_list = [1, 2, 4]
delta_S = np.linspace(0, 5, 100)
for idx, S0_value in enumerate(S0_list):
S0 = S0_value + np.zeros(delta_S.shape)
S1 = S0 + delta_S
X = np.array([S0, S1]).T
y = ground_truth(X)
plt.plot(
delta_S,
y,
label=f"$S_0 = {S0_value}$ (Original)",
c=colors[col_keys[idx]],
)
if model is not None:
y = model.predict(X)
plt.plot(
delta_S,
y,
label=f"$S_0 = {S0_value}$ (Recovered)",
c=colors[col_keys[idx]],
linestyle="--",
)
x_limit = [0, variables.independent_variables[0].value_range[1]]
y_limit = [0, 2]
x_label = r"Stimulus Intensity Difference $\Delta S = S_1 - S_0$"
y_label = "Perceived Intensity of Stimulus $S_1$"
plt.xlim(x_limit)
plt.ylim(y_limit)
plt.xlabel(x_label, fontsize="large")
plt.ylabel(y_label, fontsize="large")
plt.legend(loc=2, fontsize="medium")
plt.title("Weber-Fechner Law", fontsize="x-large")
collection = SyntheticExperimentCollection(
name=name,
description=weber_fechner_law.__doc__,
variables=variables,
run=run,
ground_truth=ground_truth,
domain=domain,
plotter=plotter,
params=params,
factory_function=weber_fechner_law,
)
return collection
|