如何采样一个numpy数组并有效地对每个采样执行计算? [英] How to sample a numpy array and perform computation on each sample efficiently?
问题描述
假设我有一个1d数组,我想用一个移动的窗口进行采样,并在窗口内将每个元素除以第一个元素.
Assume I have a 1d array, what I want is to sample with a moving window and within the window divide each element by the first element.
例如,如果我有[2, 5, 8, 9, 6]
并且窗口大小为3,则结果将为
For example if I have [2, 5, 8, 9, 6]
and a window size of 3, the result will be
[[1, 2.5, 4],
[1, 1.6, 1.8],
[1, 1.125, 0.75]].
我现在要做的基本上是一个for循环
What I'm doing now is basically a for loop
import numpy as np
arr = np.array([2., 5., 8., 9., 6.])
window_size = 3
for i in range(len(arr) - window_size + 1):
result.append(arr[i : i + window_size] / arr[i])
等
当数组很大时,它会很慢,我想知道是否有更好的方法?我想无法解决O(n ^ 2)的复杂性,但是也许numpy有一些我不知道的优化.
When the array is large it is quite slow, I wonder whether there's better ways? I guess there is no way around the O(n^2) complexity, but perhaps numpy has some optimizations that I don't know of.
推荐答案
这是使用的矢量化方法broadcasting
-
N = 3 # Window size
nrows = a.size-N+1
a2D = a[np.arange(nrows)[:,None] + np.arange(N)]
out = a2D/a[:nrows,None].astype(float)
我们还可以使用 NumPy strides
来提高效率提取滑动窗口,就像这样-
We can also use NumPy strides
for a more efficient extraction of sliding windows, like so -
n = a.strides[0]
a2D = np.lib.stride_tricks.as_strided(a,shape=(nrows,N),strides=(n,n))
样品运行-
In [73]: a
Out[73]: array([4, 9, 3, 6, 5, 7, 2])
In [74]: N = 3
...: nrows = a.size-N+1
...: a2D = a[np.arange(nrows)[:,None] + np.arange(N)]
...: out = a2D/a[:nrows,None].astype(float)
...:
In [75]: out
Out[75]:
array([[ 1. , 2.25 , 0.75 ],
[ 1. , 0.33333333, 0.66666667],
[ 1. , 2. , 1.66666667],
[ 1. , 0.83333333, 1.16666667],
[ 1. , 1.4 , 0.4 ]])
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