Python Integration, Interpolation, and Curve Fitting 

After all these year, you video is still amazingly helpful! Thank you for your hard work

Really enjoyed your clear tutorial. I'm using this to help me fit spectra peaks from astronomical data to gaussian curves. Will hopefully impress my professor. Much thanks!

Thank you very much! I couldn't find this anywhere , you saved me

A very good video, just what I needed to quickly get going on a work problem I currently have, using nothing but the packages that already come installed in anaconda. Good work.

Thanks for the positive feedback. The code is available at this website: ignite.byu.edu/che263/lectureNotes/ This includes all lecture notes. If you back up to che263 you can see other course materials. The integration, interpolation, and curve fitting slides are now separate, but much of the content is the same. Not all notes are posted; they get added as the semester progresses. You can find slides from previous semesters here: ignite.byu.edu/che263/lectureNotes/old.html

Hello, would it be possible to get a pdf of the data shown on the video?

Great video, very well explained thanks

This was a superb tutorial, I was wondering if you have or can make a video explaining how to make the r squared value for the curve fitted function you made at 14:08

As a Python newbie, I found this tutorial fantastic for an analysis I am currently undertaking. What is missing though, is the code necessary for goodness of fit. I can't figure out how to do this - can anybody help?

Nice Thx.

Very nice explained

I have a question about the last fitting you did. Those command lines make the fit with minimum squares? (sorry for my english)

What if the function have been integrated by .quad and sub into another non-analytical function to get two sets of array, and I want to do curve fitting of that with test data?

I like it, but I was looking for some tutorials that explain me how can I use the covariance matrix, that in your tutorial is reported at the end of it as "extras" in the "curve_fit" output, and still I can't find anyone who explain me it

Great stuff! thx!

GRACIAS!!!!

How about using numpy corrcoef? at curve fitting id just enter p3 as parameter of it

Thank you. Is there a downloadable of this notebook?

At the end of the function, why do you put dx, has it any use?

Where I can found that example notebook?

import numpy as np import matplotlib.pyplot as plt % matplotlib inline from scipy.integrate import quad def f(x): return 3.0*x*x+ 1.0 xlo=0 xhi=1 I, err=quad(f,xlo, xhi) print("I =", I) print("err =", err) from scipy.interpolate import interp1d x_given= np.linspace(0,10,10) y_given=np.cos(x_given**2.0/8.0) xx= np.linspace(0,10,1000) yy=np.cos(xx**2.0/8.0) plt.plot(x_given, y_given, "o", label="given data") plt.plot(xx, yy, ":", label="perf") plt.legend(loc='best') x_i=np.linspace(0,10,1000) f_linear=interp1d(x_given, y_given) y_li=f_linear(x_i) f_spline=interp1d(x_given, y_given, kind='cubic') y_is=f_spline(x_i) #plot plt.plot(x_given, y_given, "o", label='given data') plt.plot(x_i,y_li, '-', label='linear') plt.plot(x_i,y_is, '--', label='spline') plt.plot(xx, yy, ":", label='perf') plt.legend(loc='best') x_given=np.array([0.,1.,2.,3.,4.,5.]) y_given=np.array([0.,0.8,0.9,1.0,-0.8,-1.0]) x_p=np.linspace(-2.0,6.0,100) p_3=np.polyfit(x_given, y_given,3) y_p=np.polyval(p_3,x_p) plt.plot(x_given, y_given, "o") plt.plot(x_p, y_p, '-') plt.legend(['data','polyfit'], loc='best') plt.ylim(-2,2) from scipy.optimize import * def f(x,a,b,c): return a*np.exp(-b*x)+c x_given=np.linspace(0,4,50) y_given=f(x_given,2.5,1.3,0.5)+0.2*np.random.normal(size=len(x_given)) params,extras=curve_fit(f,x_given, y_given) print('a=%g, b=%g, c=%g' %(params[0], params[1], params[2])) y_fit=f(x_given,params[0], params[1], params[2]) #plots plt.plot(x_given, y_given, "o") plt.plot(x_given, y_fit, "-") plt.legend(['data', 'fit'], loc='best')