I have a program which will generate a SciPy lambdify expression (symbolic function) with a variable number of unknown variables. I am trying to fit to this function using the curve_fit utility without explicitly passing the exact number of variables to the function.

import numpy as np
import matplotlib as mpl
mpl.use('TkAgg')
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy import integrate
import sympy as sy


def step_function(t, start, end):
    return 1 * ((t >= start) & (t < end))


def gen_data(x_data, model, gradients, offset=0, noise=0.1):  # generate some fake data
    y = [model(x, offset, gradients[0], gradients[1], gradients[2]) for x in x_data]
    y = np.asarray(y, dtype=np.float32)
    if noise:
        y += np.random.normal(0, 1, 100)
    return y


t, a = sy.symbols('t, a')
grad_symbols = sy.symbols('b, c, d')
x = np.arange(0, 100)
gradient_changes = [0, 30, 60, 100]
gradients = [1, 2, -4]
grad = []

for t1, t2, LFD in zip(iter(gradient_changes[::1]), iter(gradient_changes[1::1]), iter(grad_symbols)):
    grad.append(((t - t1) * LFD) * sy.SingularityFunction(t, t1, gradient_changes[-1]))

data_model = sy.lambdify((t, a) + grad_symbols,
                          a + sum(grad), ({'SingularityFunction': step_function}, 'numpy'))

y = gen_data(x, data_model, gradients, noise=0.1)

fig, ax = plt.subplots()  # Create a figure containing a single axes.
ax.plot(x, y, label='Data')

popt, pcov = curve_fit(data_model, x, y)

fit_line = [data_model(time, popt[0], popt[1], popt[2], popt[3]) for time in x]
ax.plot(x, fit_line, label='Fit')

So far so good, curve_fit can detect the number of parameters in the lambdify expression, but I actually need to fit to an integral of the function about each point as the data is not instantaneous.

Is it possible to use a starred expression like

def fit_func(x, *inputs):
    # find the average value of the model about each point
    return [integrate.quad(data_model, _x - 1 / 2, _x + 1 / 2, args=inputs)[0] for _x in x]

and use curve_fit like so

popt, pcov = curve_fit(fit_func, x, y)

At the moment I get the error ValueError: Unable to determine number of fit parameters.