If I have a function that the independent variable is the upper limit of an definite integral of a mathematical model. This mathematical model has the parameters I want to do regression. This mathematical model is nonlinear and can be complicated.

1. How can I solve this?

2. if the output of my function is then be processed， can it be curve_fit?

There is a simplified case

import scipy.optimize as sp
from scipy.integrate import quad
import numpy as np
number = 100def f(x,a,b,c):return 500*a*x+b*cdef curvefit(d,a,b,c):return quad(f,0,d,args=(a,b,c))[0]x_linear = np.linspace(0.001,0.006,number)
y_linear = 23.33*x_linear + 0.02*(np.random.random(number)-0.5)
parameter = sp.curve_fit(curvefit,x_linear,y_linear)

x and y _linear are number I made up.

d in curvefit() is now x_linear that is a list, and is the upper limit in quad().

The error shows ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

I know quad() requires upper limit to be float.

The error is raised inside the function scipy.integrate.quad because d is a numpy.array and not a scalar. The function given to scipy.optimize.curve_fit take the independent variable (x_linear in your case) as first argument.

The quick and dirty fix is to modify curvefit to compute the definite integral for each value in d:

def curvefit(xs,a,b,c):return [quad(f,0,x,args=(a,b,c))[0] for x in xs]