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I want to fit a curve to my experimental dataset, and I do not really know how to do it. I have been looking for possibilities, and I came across curve_fit (and also least_suqares), which seems to be up for the task, but I am still very much unfamiliar with how it works, as I struggle to get it into my thick head. I started my attempt by defining the initial values:

import numpy as np
import math
from scipy.optimize import curve_fit, least_squares

f_exp = np.array([1, 1.6, 2.7, 4.4, 7.3, 12, 20, 32, 56, 88, 144, 250000])
e_exp = np.array([7.15, 7.30, 7.20, 7.25, 7.26, 7.28, 7.32, 7.25, 7.35, 7.34, 7.37, 13.55])

n_e_exp = len(e_exp)

ezero     = 7.15
einf      = 13.55
fc        = np.arange(1,11000,1000)
alpha     = np.arange(0,1.1,0.1)

log_f_mod = np.arange(-3, 6.5, 0.5)
f_mod     = 10 ** log_f_mod

n_f_mod   = len(f_mod)
n_fc      = len(fc)
n_alpha   = len(alpha)  

x         = np.zeros((n_f_mod, n_fc))
for j in range(n_f_mod):
        for k in range(n_fc):
            x[j,k] = np.log(f_mod[j] / fc[k])

Notice that x is function of fc. Now, I define the function I want to run using either curve_fit, least_squares, or some other function that is more suitable: 

def c_c_eRI(einf, ezero, alpha, x):
    eR    = einf + 1/2 * (ezero - einf) * (1 - np.sinh((1 - alpha) * x) / (np.cosh((1 - alpha) * x) + np.cos(alpha * math.pi / 2))) 
    eI    = np.abs(1/2 * (ezero - einf) * np.cos(alpha * math.pi / 2) / (np.cosh((1 - alpha) * x) + np.sin(alpha * math.pi / 2)))
    eRI   = np.sqrt(eR ** 2 + eI ** 2)
    return eRI

At this point, I tried to make it work without any luck by:

fit = curve_fit(c_c_eRI, f_exp, e_exp)
  • Is there a way to use a function (e.g. curve_fit, least_squares, or some other) to fit the curve to the experimental data and simultaneously provide the value of the independent variables that are alpha and fc (which x is a function of) that are used to achieve the fit itself?

In other words, the aim is to find the values of alpha and fc (which x is a function of) that provides the best possible fit to f_exp versus e_exp in a similar manner as the EXCEL solver finds the minimum squared residuals by varying alpha and fc.

The end goal is to plot f_exp vs. e_exp as well as the fitted curve using matplotlib -- I am also a bit lost on how to do this.

I do apologize for the lack of a more generalized example.

naughty_waves
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1 Answers1

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If I understood your example correctly, I think you just have to change your function definition to

def c_c_eRI(x, einf, ezero, alpha):
    ...

From the curve_fit docs: The model function, f(x, …). It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments.

Richard Fitzhugh
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  • Thank you, @Richard Fitzhugh. I had failed to mention that both `alpha` and `fc` (which `x` is a function of) are independent variables -- I rectified it by editing it as soon as I realized, sorry for that and thank you for pointing it out. Do you by any chance know how I can obtain the values for `alpha` and `fc` that are used for the best fit? – naughty_waves Mar 27 '19 at 20:48
  • After looking at your code, I'm not sure what you're trying to accomplish. It seems to me that you have experimental data for a 1D function (f_exp vs e_exp) and you're trying to fit this 1D experimental data to an equation with 2 independent variables? So like a function plotted over the Cartesian plane? It's not possible to fit 1D data to a 2D function. So I think either you have only 1 independent variable, or you're trying to do something that's not really possible. – Richard Fitzhugh Mar 28 '19 at 14:51
  • If you really want to fit a function with multiple independent variables, [here's how to do it](https://stackoverflow.com/questions/28372597/python-curve-fit-with-multiple-independent-variables?rq=1), but you need data to match what you're trying to fit. – Richard Fitzhugh Mar 28 '19 at 14:54
  • Thank you, @Richard Fitzhugh. I may very well be trying to do something impossible, and I am also terrible at explaining what I want to do. I thought it would be simple to find the values of `fc` and `alpha` that provides the best fit but I guess I am out of my depth. – naughty_waves Apr 27 '19 at 14:29