I was wondering how one can represent a sum in python without loops like here
where we have:
def rosen(x):
"""The Rosenbrock function"""
return sum(100.0*(x[1:]-x[:-1]**2.0)**2.0 + (1-x[:-1])**2.0)
My function is the following: V(theta) = Sum(i=1->N)[a0*(cos(i*theta)]
Thank you in advance for your help :):)
Your formula is:
V(theta) = Sum(i=1->N)[a0*(cos(i*theta)]
which means: sum all values of a0*(cos(i*theta) for a given value theta in the range 1 to and including N.
This becomes something like this in Python:
def V(theta, N):
return sum(a0*(cos(i*theta)) for i in range(1, N + 1))
Note that you have to pass theta and N to the function. Also note that we are using N + 1 to make sure N is included (as range iterates over the values until, but not including, the last value).
something like:
def V(theta,N):
return sum(a0*(cos(i*theta) for i in range(1,N+1))
print V(theta,N)
or you can use lambda:
V =lambda theta,N : sum(a0*(cos(i*theta) for i in range(1,N+1))
print V(theta,N)
Your shown example uses no math functions, just basic arithmetical operations. That's why it works as shown, but math.cos doesn't support lists and so will not work this way.
If you really want to get around without any for, you should use numpy. Numpy's math functions support lists (actually arrays).
This way you can write something like:
from numpy import *
def fun(theta):
return a0*sum(cos(arange(1,N+1)*theta))
Should you be doing a lot of this kind of calculations, it is best to use numpy.
