CODEWITHSUNDEEP
pythonscipynumerical-integrationquad
user1171835
user1171835

Reputation: 1281

Integration using quadrature

I have been having a few issues using the quadrature function in python 2.7 (part of the scipy.integrate module). The equation I am trying to integrate is simply:

x/(d^2) - (x^2)

The integration is between limits a and b. However, I need to do the integration at 40 different values of d and am not sure how to pass in the second argument so as to loop the integration over the values of d. Any help would be much appreciated and is quadrature the best way to evaluate this problem.

Upvotes: 4

Views: 265

Answers (3)

Nico Schlömer
Nico Schlömer

Reputation: 58721

If you want exact symbolic integration, you'll need to turn to SymPy. Try

import sympy

x = sympy.Symbol('x')
a = sympy.Symbol('a')
b = sympy.Symbol('b')
d = sympy.Symbol('d')

res = sympy.integrate(x / (d**2 - x**2), (x, a, b))
print(res)

This returns

log(a**2 - d**2)/2 - log(b**2 - d**2)/2

which you can most easily use to evaluate your data.

Upvotes: 0

Adobe
Adobe

Reputation: 13467

from numpy import arange
from scipy.integrate import quad
beg = 0.
end = 4.
res = []
for d in arange(1., 40.):
    res.append(quad(lambda x: x/(d**2.)-(x**2.), beg, end))

You can then access the results by

print res[0]

or even

print res

Upvotes: 2

NPE
NPE

Reputation: 500157

In [9]: from scipy.integrate import quad

In [10]: a = 0

In [11]: b = 1

In [12]: [quad(lambda x, d: x/(d**2)-x**2, a, b, args=d) for d in range(2, 5)]
Out[12]: 
[(-0.20833333333333334, 2.3717550132075781e-15),
 (-0.27777777777777773, 3.0886887822595405e-15),
 (-0.30208333333333337, 3.3546344203581545e-15)]

Change the for d in range(2, 5) as required.

Upvotes: 4

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