Question

I’m trying to solve numerically an equation using Python2.7. This is the whole code:

from sympy import *
from sympy import Symbol
from sympy.solvers import nsolve
from scipy import *
from pylab import *
import numpy as np

# Symbols
theta = Symbol('theta')
phi = Symbol('phi')
phi0 = Symbol('phi0')
H0 = Symbol('H0')
# Constants
a = 0.05 
b = 0.05**2/(8*pi*1e-7)
c= 0.001/(4*pi*1e-7)
phi0 = 60*pi/180 
H0 = -0.03/(4*pi*1e-7)
def m(theta,phi):
    return np.array([sin(theta)*cos(phi), sin(theta)*cos(phi), cos(phi)])
def h(phi0):
    return np.array([cos(phi0), sin(phi0), 0])
def k(theta,phi,phi0):
    return np.vdot(m(theta,phi),h(phi0))
def F(theta,phi,phi0,H0): 
    return -(a*H0)*k(theta,phi,phi0)+b*(cos(theta)**2)+c*(sin(2*theta)**2)+sin(theta)**4*sin(2*phi)**2
def F_phi(theta,phi,phi0,H0):
    return simplify(diff(F(theta,phi,phi0,H0),phi))
def G(phi):
    return F_phi(pi/2,phi,phi0,H0)
solution = nsolve(G(phi), phi)
print solution

and this is the traceback that I have:

Traceback (most recent call last):
File "Test.py", line 33, in <module>
solution = nsolve(G(phi), phi)
File "Test.py", line 32, in G
return F_phi(pi/2,phi,phi0,H0)
File "Test.py", line 30, in F_phi
return simplify(diff(F(theta,phi,phi0,H0),phi))
File "Test.py", line 28, in F
return -(a*H0)*k(theta,phi,phi0)+b*(cos(theta)**2)+c*(sin(2*theta)**2)+sin(theta)**4*sin(2*phi)**2
File "Test.py", line 26, in k
return np.vdot(m(theta,phi),h(phi0))
File "Test.py", line 22, in m
return np.array([sin(theta)*cos(phi), sin(theta)*cos(phi), cos(phi)])
AttributeError: cos

I am using the sympy, numpy and pylab libraries. So, I don’t get a problem with the cos function. Any help?

Answer 1

The problem is using star imports instead of importing each package under a different namespace.

This imports function sympy.functions.elementary.trigonometric.cos under the cos name:

from sympy import *

After that, you import <ufunc 'cos'> under the name cos, overwriting the previous definition:

from scipy import *

Then, it overwrites the previous cos function by another copy of exactly the same function (from the matplotlib package):

from pylab import *

This also imports the same <ufunc 'cos'> but under the np.cos name. This is the proper way to import things:

import numpy as np

In the end, you’re left with a copy of the cos function that knows how to apply itself to floats, not sympy objects. When you try to apply that function to sympy objects like phi you get the AttributeError. All in all, the solution to this particular problem is to fix the imports and know if you want the functions from sympy or the ones from numpy.