Combining different elements of array in Numpy while doing vector operations

Question

I have a function f which I am using to evolve a Numpy array z repeatedly. Thus my code looks like this:

for t in range(100):
    z = f(z)

However, now I want to combine elements of array while evolving. For example, in simple Python, I would like to do something like this:

N = len(z)
for t in range(100):
    for i in range(len(z)):
         z_new[i] = f(z[i]) + z[(i-1)%N] + z[(i+1)%N]
    z = z_new

How can achieve the same thing in Numpy vector operations so that I wouldn't have to compromise with the great speed that Numpy gives me?

Thanks in advance

When i is the index of the last element, what will z[i+1] be? — wwii
– wwii, Commented Jun 19, 2015 at 7:03
I actually use modulo. So the actual entries are z[(i-1)%N] and z[(i+1)%N] so that z[i+1] = z[0] when i is last element. Also, here N = len(z). — Peaceful
– Peaceful, Commented Jun 19, 2015 at 7:05
Slices are the fastest way to index your array, eg z[1:]-z[:-1]. If you have to wrap around you will have to use slower advanced indexing or concatenation. Look at the internals of roll. Look also at take and put. — hpaulj
– hpaulj, Commented Jun 19, 2015 at 8:49

wwii · Accepted Answer · 2015-06-19 15:42:35Z

2

You can roll the data back and forth to achieve the same result.

Z = f(z)
Z = np.roll(Z, 1) + z
Z = np.roll(Z, -2) + z
z = np.roll(Z, 1)

I had also first thought about slicing but went with np.roll when I found it.

Prompted by @hpaulj's comment I came up with a slice solution:

q = np.array([1,2,3,4,5])
Q = f(q)
# operate on the middle
Q[1:] += q[:-1]
Q[:-1] += q[1:]
# operate on the ends
Q[0] += q[-1]
Q[-1] += q[0]

q = Q.copy()

edited Jun 19, 2015 at 15:42

answered Jun 19, 2015 at 7:30

wwii

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1 Comment

Peaceful Over a year ago

Actually my real task is much more complicated but I think this wonderful roll function should do the job. Thanks

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