Partial sums and products in numpy

Question

I'm trying to build an array of partial products of the entries of another array in numpy. So far I have:

from numpy.random import dirichlet
from numpy import ones, prod

alpha = ones(100)
p = dirichlet(alpha)

I know I can whatever partial product by slicing my array. For example:

q = prod(p[0:10])

returns the product of the first 10 entries of p .

How could I build the array q so that entry i is the product of the i-1 previous values of p ?

I've tried:

for i in p:
    q[i+1] = prod(p[0:i-1])

however, this throws a numpy.float64 doesn't support item assignment error.

How would I go about building this array? For sums, could I just replace prod with sum ?

Answer 1

You want the NumPy functions cumprod and cumsum

from numpy import cumprod, cumsum
# your code here
q = cumprod(p)
r = cumsum(p)

Documentation

• http://docs.scipy.org/doc/numpy/reference/generated/numpy.cumprod.html
• http://docs.scipy.org/doc/numpy/reference/generated/numpy.cumsum.html

Answer 2

While cumprod is a good simple way of doing this, it would be good to understand why you got an error.

q = prod(p[0:10])  # q is now a float
for i in p:  
    q[i+1] = prod(p[0:i-1])

There are 2 problems with the iteration. i is an item of p , not an index. In fact it probably is a float. q[i+1] does not work because q is a float, not an array.

q=np.zeros(p.size+1)
for i in range(p.size):
    q[i+1]=np.prod(p[:i])

This iteration works. Now q is a large enough array, and i is an integer, a valid index. Where it uses i , i+1 or i-1 is something you can tweak.