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autora.experiment_runner.synthetic.psychophysics.stevens_power_law

stevens_power_law(name="Stevens' Power Law", resolution=100, proportionality_constant=1.0, modality_constant=0.8, maximum_stimulus_intensity=5.0)

Stevens' Power Law

Parameters:

Name Type Description Default
name

name of the experiment

 "Stevens' Power Law"
resolution

number of allowed values for stimulus

 100
modality_constant

power constant

 0.8
proportionality_constant

constant multiplier

 1.0
maximum_stimulus_intensity

maximum value for stimulus

 5.0

Examples: >>> s = stevens_power_law() >>> s.run(np.array([[.9]]), random_state=42) S perceived_intensity 0 0.9 0.922213

Source code in autora/experiment_runner/synthetic/psychophysics/stevens_power_law.py 
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def stevens_power_law(
    name="Stevens' Power Law",
    resolution=100,
    proportionality_constant=1.0,
    modality_constant=0.8,
    maximum_stimulus_intensity=5.0,
):
    """
    Stevens' Power Law

    Args:
        name: name of the experiment
        resolution: number of allowed values for stimulus
        modality_constant: power constant
        proportionality_constant: constant multiplier
        maximum_stimulus_intensity: maximum value for stimulus
    Examples:
        >>> s = stevens_power_law()
        >>> s.run(np.array([[.9]]), random_state=42)
             S  perceived_intensity
        0  0.9             0.922213
    """

    params = dict(
        name=name,
        resolution=resolution,
        proportionality_constant=proportionality_constant,
        modality_constant=modality_constant,
        maximum_stimulus_intensity=maximum_stimulus_intensity,
    )

    iv1 = IV(
        name="S",
        allowed_values=np.linspace(
            1 / resolution, maximum_stimulus_intensity, resolution
        ),
        value_range=(1 / resolution, maximum_stimulus_intensity),
        units="intensity",
        variable_label="Stimulus Intensity",
        type=ValueType.REAL,
    )

    dv1 = DV(
        name="perceived_intensity",
        value_range=(0, maximum_stimulus_intensity),
        units="sensation",
        variable_label="Perceived Intensity",
        type=ValueType.REAL,
    )

    variables = VariableCollection(
        independent_variables=[iv1],
        dependent_variables=[dv1],
    )

    def run(
        conditions: Union[pd.DataFrame, np.ndarray, np.recarray],
        added_noise: float = 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 = proportionality_constant * x[0] ** modality_constant + 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[variables.dependent_variables[0].name] = Y
        return experiment_data

    ground_truth = partial(run, added_noise=0.0)

    def domain():
        s_values = variables.independent_variables[0].allowed_values

        X = np.array(np.meshgrid(s_values)).T.reshape(-1, 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())
        X = domain()
        y = ground_truth(X)[dv1.name]
        plt.plot(X, y, label="Original", c=colors[col_keys[0]])
        if model is not None:
            y = model.predict(X)
            plt.plot(X, y, label="Recovered", c=colors[col_keys[0]], linestyle="--")
        x_limit = [0, variables.independent_variables[0].value_range[1]]
        y_limit = [0, 4]
        x_label = "Stimulus Intensity"
        y_label = "Perceived Stimulus Intensity"

        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("Stevens' Power Law", fontsize="x-large")
        plt.show()

    collection = SyntheticExperimentCollection(
        name=name,
        description=stevens_power_law.__doc__,
        variables=variables,
        run=run,
        ground_truth=ground_truth,
        domain=domain,
        plotter=plotter,
        params=params,
        factory_function=stevens_power_law,
    )
    return collection