global name 'sqrt' not defined

Question

I've created a function, potential(x,K,B,N), where x,K,B are numpy arrays and N is an integer. I'm trying to test the function in iPython but I keep getting the error "global name 'sqrt' not defined".

Here's a look at my code:

def potential(x,K,B,N):

    x = x.reshape((3,N),order='F')

U_b = 0.0
for i in xrange(0,N-1):
    for j in xrange(i+1,N):
        if K[i,j] == 1.0:
            U_b += sum((x[:,i]-x[:,j])**2)
U_b = 0.5*U_b

U_a = 0.0
for i in xrange(0,N-2):
    for j in xrange(i+1,N-1):
        for l in xrange(j+1,N):
            if B[i,j,l] == 1.0:
                U_a += B[i,j,l]*sum((x[:,i]-x[:,j])*(x[:,j]-x[:,l]))/(sqrt(sum((x[:,i]-x[:,j])**2))*sqrt(sum((x[:,j]-x[:,l])**2)))
U_a = -U_a

U_r = 0.0
d = 0.0
for i in xrange(0,N-1):
    for j in xrange(i+1,N):
        d = sqrt(sum((x[:,i]-x[:,j])**2))
        if d > sqrt(0.2):
            U_r += (1.0/6.0)*(1/(d**6))
        else:
            U_r += -0.2**(-7.0/2.0)*d + (7.0/6.0)*(0.2)**(-3)

return U_b + U_a + U_r

I've tried using from math import * but that doesn't seem to help. Any suggestions would be greatly appreciated!

Answer 1

Add the missing line:

from numpy import sqrt 

(or in non-NumPy code from math import sqrt. Note that these are two different functions:numpy.sqrt also accepts vectors and arrays , but plain math.sqrt doesn't)

I've tried using from math import * but that doesn't seem to help.

(Possibly you did that after defining the function. Anyway, fuhgeddaboutit, just reload the code in a clean session, it will work.)

UPDATES:

• strictly, in Python you're supposed to do import package not from package import identifier1 [,identifier2, identifier3...] and never from package import *. But from package import identifier1 is ok when judiciously used, if you don't overdo it, and locally inside a function. If it's unambiguous, and you're going to be doing a lot of it, it shortens the code e.g. sqrt() instead of math.sqrt(), log instead of math.log10()

• sqrt is not a builtin in Python, unlike R. So yes in Python you need either from numpy import sqrt or import math or from math import sqrt before you can use it.

Answer 2

Since you tagged numpy,

import numpy as np

Then use np.sqrt instead of sqrt. Always works.