Fixing curve with python error
I am trying to put my data into (cos(x))^n
. A dollar is n
in theory 2, but my data should give me about 1.7. When I define a fitting function and try curve_fit
, I get the error
def f(x,a,b,c):
return a+b*np.power(np.cos(x),c)
param, extras = curve_fit(f, x, y)
This is my data
x y error
90 3.3888756187 1.8408898986
60 2.7662844365 1.6632150903
45 2.137309503 1.4619540017
30 1.5256883339 1.2351875703
0 1.4665463518 1.2110104672
The error looks like this:
/usr/local/lib/python3.5/dist-packages/ipykernel_launcher.py:4: RuntimeWarning: Invalid value found after including cwd from sys.path.
/usr/lib/python3/dist-packages/scipy/optimize/minpack.py:690: Optimization Warning: Parameter covariance cannot be estimated
category = OptimizeWarning)
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The problem is that it cos(x)
can become negative and then cos(x) ^ n
undefined. Illustration:
np.cos(90)
-0.44807361612917013
and for example
np.cos(90) ** 1.7
nan
This results in two error messages.
It works great if you modify your model eg. before a + b * np.cos(c * x + d)
. Then the graph looks like this:
The code can be found below with some inline comments:
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
def f(x, a, b, c, d):
return a + b * np.cos(c * x + d)
# your data
xdata = [90, 60, 45, 30, 0]
ydata = [3.3888756187, 2.7662844365, 2.137309503, 1.5256883339, 1.4665463518]
# plot data
plt.plot(xdata, ydata, 'bo', label='data')
# fit the data
popt, pcov = curve_fit(f, xdata, ydata, p0=[3., .5, 0.1, 10.])
# plot the result
xdata_new = np.linspace(0, 100, 200)
plt.plot(xdata_new, f(xdata_new, *popt), 'r-', label='fit')
plt.legend(loc='best')
plt.show()
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