如何在numpy中有效地連接多個arange調用？

Question

我想在cnt值的向量上向numpy.arange(0, cnt_i)這樣的調用進行向量化，並像這個片段一樣連接結果：

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，由於臨時數組和列表推導循環，上面的代碼非常低效。

有沒有辦法在numpy中更有效地做到這一點？

Answer 1

這是一個完全矢量化的函數：

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

這里的@開發者回答的變化，只有調用arange一次：

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

這是原始版本，作為函數編寫：

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])

使用更多的計數比較時間：

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

嘗試以下解決內存問題，效率幾乎相同。

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

所以沒有使用連接。

Answer 3

np.tril_indices幾乎為你做了這個：

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

當維度很小時，比@Warren Weckesser multirange快得多。

但是當尺寸更大時變得慢得多（@hpaulj，你有一個很好的觀點）：

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