python - Vectorizing a Numpy slice operation

Question

Say I have a Numpy vector,

A = zeros(100)

and I divide it into subvectors by a list of breakpoints which index into A, for instance,

breaks = linspace(0, 100, 11, dtype=int)

So the i-th subvector would be lie between the indices breaks[i] (inclusive) and breaks[i+1] (exclusive). The breaks are not necessarily equispaced, this is only an example. However, they will always be strictly increasing.

Now I want to operate on these subvectors. For instance, if I want to set all elements of the i-th subvector to i, I might do:

for i in range(len(breaks) - 1):
    A[breaks[i] : breaks[i+1]] = i

Or I might want to compute the subvector means:

b = empty(len(breaks) - 1)
for i in range(len(breaks) - 1):
    b = A[breaks[i] : breaks[i+1]].mean()

And so on.

How can I avoid using for loops and instead vectorize these operations?

Answer 1

You can use simple np.cumsum -

import numpy as np

# Form zeros array of same size as input array and 
# place ones at positions where intervals change
A1 = np.zeros_like(A)
A1[breaks[1:-1]] = 1

# Perform cumsum along it to create a staircase like array, as the final output
out = A1.cumsum()

Sample run -

In [115]: A
Out[115]: array([3, 8, 0, 4, 6, 4, 8, 0, 2, 7, 4, 9, 3, 7, 3, 8, 6, 7, 1, 6])

In [116]: breaks
Out[116]: array([ 0,  4,  9, 11, 18, 20])

In [142]: out
Out[142]: array([0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]..)

---

If you want to have mean values of those subvectors from A, you can use np.bincount -

mean_vals = np.bincount(out, weights=A)/np.bincount(out)

If you are looking to extend this functionality and use a custom function instead, you might want to look into MATLAB's accumarray equivalent for Python/Numpy: accum whose source code is available here.