Python Integration, Interpolation, and Curve Fitting

iPython Notebook, using numpy and scipy interpolation, integration, and curve fitting functions

[mokus]

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

[jawnvawn]

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!

[jimwest]

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.

[AlexOmbla]

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

[yurivendruscolo]

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

[clivemayo]

Great video, very well explained thanks

[skfkfkd]

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

[davidmckinnon]

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?

[MartinezF]

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

[stefanofedele]

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

[shobanasanthanagopalan]

Thank you. Is there a downloadable of this notebook?

[frankelindddd]

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?

[Satenc]

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

[aamira]

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

[Passco]

Where I can found that example notebook?

[sambad]

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)


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')