How to efficiently concatenate many arange calls in numpy?

Question

I'd like to vectorize calls like numpy.arange(0, cnt_i) over a vector of cnt values and concatenate the results like this snippet:

import numpy
cnts = [1,2,3]
numpy.concatenate([numpy.arange(cnt) for cnt in cnts])

array([0, 0, 1, 0, 1, 2])

Unfortunately the code above is very memory inefficient due to the temporary arrays and list comprehension looping.

Is there a way to do this more efficiently in numpy?

Answer 1

Here's a completely vectorized function:

def multirange(counts):
    counts = np.asarray(counts)
    # Remove the following line if counts is always strictly positive.
    counts = counts[counts != 0]

    counts1 = counts[:-1]
    reset_index = np.cumsum(counts1)

    incr = np.ones(counts.sum(), dtype=int)
    incr[0] = 0
    incr[reset_index] = 1 - counts1

    # Reuse the incr array for the final result.
    incr.cumsum(out=incr)
    return incr

Here's a variation of @Developer's answer that only calls arange once:

def multirange_loop(counts):
    counts = np.asarray(counts)
    ranges = np.empty(counts.sum(), dtype=int)
    seq = np.arange(counts.max())
    starts = np.zeros(len(counts), dtype=int)
    starts[1:] = np.cumsum(counts[:-1])
    for start, count in zip(starts, counts):
        ranges[start:start + count] = seq[:count]
    return ranges

And here's the original version, written as a function:

def multirange_original(counts):
    ranges = np.concatenate([np.arange(count) for count in counts])
    return ranges

Demo:

In [296]: multirange_original([1,2,3])
Out[296]: array([0, 0, 1, 0, 1, 2])

In [297]: multirange_loop([1,2,3])
Out[297]: array([0, 0, 1, 0, 1, 2])

In [298]: multirange([1,2,3])
Out[298]: array([0, 0, 1, 0, 1, 2])

Compare timing using a larger array of counts:

In [299]: counts = np.random.randint(1, 50, size=50)

In [300]: %timeit multirange_original(counts)
10000 loops, best of 3: 114 µs per loop

In [301]: %timeit multirange_loop(counts)
10000 loops, best of 3: 76.2 µs per loop

In [302]: %timeit multirange(counts)
10000 loops, best of 3: 26.4 µs per loop

Answer 2

Try the following for solving memory problem, efficiency is almost the same.

out = np.empty((sum(cnts)))
k = 0
for cnt in cnts:
    out[k:k+cnt] = np.arange(cnt)
    k += cnt

so no concatenation is used.

Answer 3

np.tril_indices pretty much does this for you:

In [28]: def f(c):
   ....:     return np.tril_indices(c, -1)[1]

In [29]: f(10)
Out[29]:
array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 1,
       2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 8])

In [33]: %timeit multirange(range(10))
10000 loops, best of 3: 93.2 us per loop

In [34]: %timeit f(10)
10000 loops, best of 3: 68.5 us per loop

much faster than @Warren Weckesser multirange when the dimension is small.

But becomes much slower when the dimension is larger (@hpaulj, you have a very good point):

In [36]: %timeit multirange(range(1000))
100 loops, best of 3: 5.62 ms per loop

In [37]: %timeit f(1000)
10 loops, best of 3: 68.6 ms per loop