Integration in python

Question

The code I have written to integrate is giving wrong results.I get the c_0,c_1,...c_4 to be zeros! What am I doing wrong? I am using simply 0.7.6 on a mac.

from numpy import *
from matplotlib.pyplot import *
from sympy import *
x = Symbol('x')
f = 1.0*sin(np.pi * x)
phi_0 = 1.0
phi_1 = 1.0*x
phi_2 = 1./2*(3*x**2-1)
phi_3 = 1./2*(5*x**3-3*x)
phi_4 = 1./8*(35*x**4-30*x**2+3)
c_0 = integrate(f*phi_0, (x, -1.0, 1.0))
c_1 = integrate(f*phi_1, (x, -1.0, 1.0))
c_2 = integrate(f*phi_2, (x, -1.0, 1.0))
c_3 = integrate(f*phi_3, (x, -1.0, 1.0))
c_4 = integrate(f*phi_4, (x, -1.0, 1.0))
print c_0
print c_1
print c_2
print c_3
print c_4

smichr · Accepted Answer · 2015-04-22 17:51:22Z

1

Other than the need to import numpy as np, I don't see any problems in the most recent version (0.7.6). Some values are zero (as expected due to symmetry consideration) but others are not:

>>> print c_0
0
>>> print c_1
0.636619772367581
>>> print c_2
0
>>> print c_3
-0.330926260628403
>>> print c_4
0

answered Apr 22, 2015 at 17:51

smichr

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4 Comments

MAS Over a year ago

I get zeros for all @smichr .

smichr Over a year ago

For me, >>> sympy.__version__ -> '0.7.6-git'. What do you get?

smichr Over a year ago

Also, check your value of np.pi. It is possible that it got set to 0 which would then make your f zero, too.

MAS Over a year ago

how can I check my version? I typed "sympy.__version__ -> " in my code but got an error. @smichr

dparadis28 · Accepted Answer · 2015-04-22 17:54:38Z

1

I agree with smichr. Everything appears to be fine as long as your import numpy. You can also use scipy but that is dependent on your preferences and needs.

from scipy.integrate import quad

quad(lambda x: x**2, 0, 1)

answered Apr 22, 2015 at 17:54

dparadis28

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4 Comments

MAS Over a year ago

can I define x**2 prior to calling quad?

dparadis28 Over a year ago

Yeah that's not a problem. For example lets say f(x) was defined to be x**2, you can say quad(f, -1, 1) and it should integrate that for you

MAS Over a year ago

how should I define f. before I would define x as symbolic variable and then define f. Now what should I use? lambda? @dparadis28

dparadis28 Over a year ago

You could use lambdas or define a function (ex: def f(x): return x**2) and use f as an arg for the quad function as shown above; quad(f, -1, 1). Does this help point you in the right direction?

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