Integrate with scipy

Question

I want to integrate x**(-2/3)*(x-1)**(1/3) from 0~1, I had changed variables and use Simpson rule to solve it before,and now I want to try some quicker methods.

my code:

x1 = lambda x: x**(-2/3)*(x-1)**(1/3)
integrate.quad(x1,0,1)

Error:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/lib/python3/dist-packages/scipy/integrate/quadpack.py", line 281, in quad
    retval = _quad(func,a,b,args,full_output,epsabs,epsrel,limit,points)
  File "/usr/lib/python3/dist-packages/scipy/integrate/quadpack.py", line 345, in _quad
    return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)
quadpack.error: Supplied function does not return a valid float.

How can I solve it?

yeah,it is a singularity.It is ok to integrate just `lambda x: x**(-2/3)`, quad function can deal with the singularities, but I have no idea with this one. — ShaoHui, Mar 12 '16 at 06:18
Are you sure that your function work right? Because `x**(-2/3)` and `x**(-2./3.)` is different functions. — Aleksei Shestakov, Mar 12 '16 at 06:21
@AlexeiShestakov in Python 2 only. In Python 3 they are the same — awesoon, Mar 12 '16 at 06:22

score 3 · Accepted Answer · edited May 23 '17 at 11:59

3

Even though the heading says Integrate with numpy, I suppose you mean scipy.. Your problem is that you have complex numbers in your function. For example, the part (x-1)**(1/3) becomes complex for x in [0, 1), but scipy.integrate.quad does not handle complex numbers. See e.g. Use scipy.integrate.quad to integrate complex numbers for more information.

edited May 23 '17 at 11:59

Community

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answered Mar 12 '16 at 06:36

Anders

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Integrate with scipy

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