python - 如何有效地连接 numpy 中的许多 arange 调用？

Question

我想在 cnt 值的向量上对像 numpy.arange(0, cnt_i) 这样的调用进行向量化，并像下面的代码片段那样连接结果:

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

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

不幸的是，由于临时数组和列表理解循环，上面的代码内存效率非常低。

有没有办法在 numpy 中更有效地做到这一点？

Answer 1

这是一个完全向量化的函数:

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

这是@Developer 的答案的变体，它只调用一次 arange:

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

这是原始版本，写成一个函数:

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

演示:

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])

使用更大的计数数组比较时序:

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