using curve_fit function from scipy python

Question

I am confused on how this function is supposed to work. I am trying to fit a line of best fit for the data sets of xdata and ydata. This code produces errors, but I do not understand how the curve_fit function is supposed to work or if I have used the right terms for what I wanted to do. xdata and ydata plotted on a graph produces a curved patter, going up, and then dropping down. Any help much appreciated.

#define xdata dnd ydata 
xdata = np.array([-2,-1.64,-1.33,-0.7,0,0.45,1.2,1.64,2.32,2.9])
ydata = np.array([0.699369,0.700462,0.695354,1.03905,1.97389,2.41143,1.91091,0.919576,-0.730975,-
1.42001]) 



# get the curve fit funtion 
from scipy.optimize import curve_fit
def func(xdata, p1, p2):
    return p1*np.cos(p2*xdata) + p2*np.sin(p1*xdata)


popt, pcov = curve_fit(func, xdata, ydata)


#plot code for data points 
plot.plot(xdata,ydata,"bo",label="Xdata and Ydata")
plot.plot(popt,pcov,"r--",label="Curve of Best Fit")
plot.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
plot.show()

This currently produces a straight line which is not the curve of best fit for the data. I am trying to mirror the data pattern as best as possible, and currently I am nowhere close.

Answer 1

What you were missing:

1. As I said in my comments you needed np.cos and np.sin . The reason for that is because xdata and ydata are numpy arrays of (10,) shape. Therefore Python can't recognize that, it needs to be (10,1)
2. You need to define a linspace for the data, it's called xfine in the below example

---

Here's a working example:

import numpy as np
import matplotlib.pyplot as qt
from scipy.optimize import curve_fit

#define xdata dnd ydata 
xdata = np.array([-2,-1.64,-1.33,-0.7,0,0.45,1.2,1.64,2.32,2.9])
ydata = np.array([0.699369,0.700462,0.695354,1.03905,1.97389,2.41143,1.91091,0.919576,-0.730975,-
1.42001]) 

def func(xdata, p1, p2):
    return p1*np.cos(p2*xdata) + p2*np.sin(p1*xdata)

xfine = np.linspace(xdata.min(), xdata.max(), 100)

popt, pcov = curve_fit(func, xdata, ydata)

plt.plot(xdata, ydata, '.');
plt.plot(xfine, func(xfine, popt[0], popt[1]),'r-')

Answer 2

You need to use numpy.cos instead of math.cos to handle vectors:

def func(xdata, p1, p2):
    return p1*np.cos(p2*xdata) + p2*np.sin(p1*xdata)

And you need to generate fit curve like this:

xfit = np.linspace(xdata[0], xdata[-1], 100)
yfit = func(xfit, *popt)
plt.plot(xdata, ydata)
plt.plot(xfit, yfit)
plt.show()