How to: Import, Plot, Fit, and Integrate Data in Python

Learn how to import and visualize a ".csv" data set into Python. Also, how to do a linear least-squares curve fit to a function and integrate the data.

Script and resources to download can be found at: https://www.hageslab.com/Resources.html#PythonAnchor

Here we use "Spyder" IDE as the Python Shell and the following libraries: numpy, csv, matplotlib, and scipy

Here is the script:

import numpy as np
import csv
import matplotlib.pylab as plt
from scipy.optimize import curve_fit
from scipy import integrate as intg

with open("Example Data.csv",'r') as i: #open a file in directory of this script for reading
rawdata = list(csv.reader(i,delimiter=",")) #make a list of data in file

exampledata = np.array(rawdata[1:],dtype=np.float) #convert to data array
xdata = exampledata[:,0]
ydata = exampledata[:,1]

plt.figure(1,dpi=120)
plt.yscale('linear')
plt.xscale('linear')
#plt.xlim(0,4)
#plt.ylim(0,2.5)
plt.title("Example Data")
plt.xlabel(rawdata[0][0])
plt.ylabel(rawdata[0][1])
plt.plot(xdata,ydata,label="Experimental Data")

def func(x,b): #input x in nm and b in nm^-1
return a0 * np.exp(-b * x) + a1

a0 = 2.5 #W m^-2 nm^-1
a1 = 0.5 #W m^-2 nm^-1

funcdata = func(xdata,1.375) #Generate & Plot data for comparison
plt.plot(xdata,funcdata,label="Model")
plt.legend()

popt, pcov = curve_fit(func,xdata,ydata,bounds=(0,4))
perr = np.sqrt(np.diag(pcov))

TotalInt = intg.trapz(ydata,xdata) #Compute numerical integral
TotalInt_func = intg.quad(func,0,4, args=(1.375))[0] #Compute integral of function
low_Frac = intg.quad(func,0,2, args=(1.375))[0]/TotalInt_func
high_Frac = intg.quad(func,2,4, args=(1.375))[0]/TotalInt_func