I have the following data for x and y:
x y
1.71 0.0
1.76 5.0
1.81 10.0
1.86 15.0
1.93 20.0
2.01 25.0
2.09 30.0
2.20 35.0
2.32 40.0
2.47 45.0
2.65 50.0
2.87 55.0
3.16 60.0
3.53 65.0
4.02 70.0
4.69 75.0
5.64 80.0
7.07 85.0
9.35 90.0
13.34 95.0
21.43 100.0
For the above data, I am trying to fit the data in the form:
However, there are certain uncertainties associated with x and y, where x has uncertainty of 50% of x and y has a fixed uncertainty. I am trying to determine the uncertainty in the fit parameters with this uncertainties package. But, I am having issues with curve fitting with scipy optimize's curve fit function. I get the following error:
minpack.error: Result from function call is not a proper array of floats.
How do I fix the following error and determine the uncertainty of the fit parameters (a,b and n)?
MWE
from __future__ import division
import numpy as np
import re
from scipy import optimize, interpolate, spatial
from scipy.interpolate import UnivariateSpline
from uncertainties import unumpy
def linear_fit(x, a, b):
return a * x + b
uncertainty = 0.5
y_error = 1.2
x = np.array([1.71, 1.76, 1.81, 1.86, 1.93, 2.01, 2.09, 2.20, 2.32, 2.47, 2.65, 2.87, 3.16, 3.53, 4.02, 4.69, 5.64, 7.07, 9.35, 13.34, 21.43])
x_uncertainty = x * uncertainty
x = unumpy.uarray(x, x_uncertainty)
y = np.array([0.0, 5.0, 10.0, 15.0, 20.0, 25.0, 30.0, 35.0, 40.0, 45.0, 50.0, 55.0, 60.0, 65.0, 70.0, 75.0, 80.0, 85.0, 90.0, 95.0, 100.0])
y = unumpy.uarray(y, y_error)
n = np.arange(0, 5, 0.005)
coefficient_determination_on = np.empty(shape = (len(n),))
for j in range(len(n)):
n_correlation = n[j]
x_fit = 1 / ((x) ** n_correlation)
y_fit = y
fit_a_raw, fit_b_raw = optimize.curve_fit(linear_fit, x_fit, y_fit)[0]
x_prediction = (fit_a_raw / ((x) ** n_correlation)) + fit_b_raw
y_residual_squares = np.sum((x_prediction - y) ** 2)
y_total_squares = np.sum((y - np.mean(y)) ** 2)
coefficient_determination_on[j] = 1 - (y_residual_squares / y_total_squares)