This is a notebook of integration, alias, note for Numerical Recipe.



In [33]:

    
import numpy as np
from scipy import integrate

Equally spaced abscissas

Example: f(x)=(x-1)^2 from 0 to 2.



In [34]:

    
def ftest(x):
    return (x-1)**2



In [35]:

    
ftest(0)









    Out[35]:





1



In [36]:

    
ftest(2)









    Out[36]:





1



In [37]:

    
integrate.romberg(ftest,0,2)









    Out[37]:





0.66666666666666663

Trapezoidal Rule



In [38]:

    
2*(ftest(0)+ftest(2))/2









    Out[38]:





2



In [39]:

    
np.trapz([ftest(0),ftest(2)],x=[0,2])









    Out[39]:





2.0

Simpson's Rule



In [40]:

    
1*(ftest(0)/3+4*ftest(1)/3+ftest(2)/3)









    Out[40]:





0

Simpson's 3/8 Rule



In [41]:

    
2/3*(3*ftest(0)/8+9*ftest(2/3)/8+9*ftest(4/3)/8+3*ftest(2)/8)









    Out[41]:





0

Extended Trapezoidal Rule



In [42]:

    
intExtTrap=1/2*(ftest(0)+ftest(2))



In [43]:

    
for seg in range(1,199):
    intExtTrap = intExtTrap+ftest(0.01*seg)



In [44]:

    
intExtTrap= intExtTrap*0.01
print(intExtTrap)



In [45]:

    
delExtTrap3=0.01
intExtTrap3=5/12*ftest(0)+13/12*ftest(delExtTrap3)+13/12*ftest(2-delExtTrap3)+5/12*ftest(2)



In [46]:

    
for seg in range(1,197):
    intExtTrap3 = intExtTrap3 + ftest(delExtTrap3+seg*delExtTrap3)



In [47]:

    
intExtTrap3=(intExtTrap3)*delExtTrap3
print(intExtTrap3)

Gaussian Quadratures



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