numpy轴操作
今天讲点干货的东西,关于numpy中轴操作(axes)的内容。
在numpy中有些函数支持axes参数,比如max、min、mean等,关于其轴的处理可能很容易给人感觉云里雾里的,毕竟高维之后还真不好确定。
这里先以一个简单例子进行说明:
>>> import numpy as np
>>> np.random.seed(42)
>>> a = np.arange(120)
>>> a
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,
26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51,
52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64,
65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77,
78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90,
91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103,
104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116,
117, 118, 119])
>>> np.random.shuffle(a)
>>> a
array([ 44, 47, 4, 55, 26, 64, 73, 10, 40, 107, 18, 62, 11,
36, 89, 91, 109, 0, 88, 104, 65, 45, 31, 70, 42, 12,
15, 114, 76, 97, 24, 78, 22, 96, 56, 110, 30, 53, 118,
9, 33, 25, 69, 28, 98, 85, 5, 90, 68, 39, 49, 35,
16, 66, 34, 113, 7, 43, 72, 67, 83, 27, 19, 95, 100,
8, 13, 84, 3, 17, 38, 117, 6, 77, 111, 94, 54, 50,
80, 46, 81, 61, 116, 79, 93, 41, 58, 48, 101, 57, 75,
32, 112, 59, 63, 105, 37, 29, 115, 1, 52, 21, 2, 23,
103, 99, 87, 108, 74, 86, 82, 119, 20, 60, 71, 106, 14,
92, 51, 102])
接下来对其进行重塑让其成为4维向量:
>>> b = a.reshape(2,3,4,5)
>>> b.shape
(2, 3, 4, 5)
假设现在要进行max操作,那么每个轴其结果是什么呢?
带着这个问题,我们先将变量打印出来,再对其进行分解:
>>> b
array([[[[ 44, 47, 4, 55, 26],
[ 64, 73, 10, 40, 107],
[ 18, 62, 11, 36, 89],
[ 91, 109, 0, 88, 104]],
[[ 65, 45, 31, 70, 42],
[ 12, 15, 114, 76, 97],
[ 24, 78, 22, 96, 56],
[110, 30, 53, 118, 9]],
[[ 33, 25, 69, 28, 98],
[ 85, 5, 90, 68, 39],
[ 49, 35, 16, 66, 34],
[113, 7, 43, 72, 67]]]
[[[ 83, 27, 19, 95, 100],
[ 8, 13, 84, 3, 17],
[ 38, 117, 6, 77, 111],
[ 94, 54, 50, 80, 46]],
[[ 81, 61, 116, 79, 93],
[ 41, 58, 48, 101, 57],
[ 75, 32, 112, 59, 63],
[105, 37, 29, 115, 1]],
[[ 52, 21, 2, 23, 103],
[ 99, 87, 108, 74, 86],
[ 82, 119, 20, 60, 71],
[106, 14, 92, 51, 102]]]
>>> b[0]
array([[[ 44, 47, 4, 55, 26],
[ 64, 73, 10, 40, 107],
[ 18, 62, 11, 36, 89],
[ 91, 109, 0, 88, 104]],
[[ 65, 45, 31, 70, 42],
[ 12, 15, 114, 76, 97],
[ 24, 78, 22, 96, 56],
[110, 30, 53, 118, 9]],
[[ 33, 25, 69, 28, 98],
[ 85, 5, 90, 68, 39],
[ 49, 35, 16, 66, 34],
[113, 7, 43, 72, 67]]])
>>> b[1]
array([[[ 83, 27, 19, 95, 100],
[ 8, 13, 84, 3, 17],
[ 38, 117, 6, 77, 111],
[ 94, 54, 50, 80, 46]],
[[ 81, 61, 116, 79, 93],
[ 41, 58, 48, 101, 57],
[ 75, 32, 112, 59, 63],
[105, 37, 29, 115, 1]],
[[ 52, 21, 2, 23, 103],
[ 99, 87, 108, 74, 86],
[ 82, 119, 20, 60, 71],
[106, 14, 92, 51, 102]]])
而第1维b.max(axis=0)的过程实际上就是每个子矩阵中相同位置选最大的值。比如在b[0]中第1行第1个元素是44,而b[1]相同位置上元素是83,因此第1行第1个元素自然是83。同理第1行第2个元素是47,以此类推最后1个元素是102,从而得到最终的结果。因此其结果为:
>>> b.max(axis=0)
array([[[ 83, 47, 19, 95, 100],
[ 64, 73, 84, 40, 107],
[ 38, 117, 11, 77, 111],
[ 94, 109, 50, 88, 104]],
[[ 81, 61, 116, 79, 93],
[ 41, 58, 114, 101, 97],
[ 75, 78, 112, 96, 63],
[110, 37, 53, 118, 9]],
[[ 52, 25, 69, 28, 103],
[ 99, 87, 108, 74, 86],
[ 82, 119, 20, 66, 71],
[113, 14, 92, 72, 102]]])
那么按照第2维度进行max处理呢,此时我们取出b[0]中每一组第1行:
>>> b[0][:,0]
array([[44, 47, 4, 55, 26],
[65, 45, 31, 70, 42],
[33, 25, 69, 28, 98]])
那么第2维的比较就是相应44,65,33中谁的值最大,自然是65获胜了。接着下1个是47,再下一个是69,以此类推得到b[0]中每一组的最大值。同理b[1]中也进行相同的操作。
>>> b.max(axis=1)
array([[[ 65, 47, 69, 70, 98],
[ 85, 73, 114, 76, 107],
[ 49, 78, 22, 96, 89],
[113, 109, 53, 118, 104]],
[[ 83, 61, 116, 95, 103],
[ 99, 87, 108, 101, 86],
[ 82, 119, 112, 77, 111],
[106, 54, 92, 115, 102]]])
之后是第3维的比较,那就继续分解下去,于是有:
>>> b[0][0]
array([[ 44, 47, 4, 55, 26],
[ 64, 73, 10, 40, 107],
[ 18, 62, 11, 36, 89],
[ 91, 109, 0, 88, 104]])
此时要比较的就是从44,64,18,91中找出最大值,自然91是最大的,下一个元素是109,再下一个是11,之后是88和107了。因此其结果为:
>>> b.max(axis=2)
array([[[ 91, 109, 11, 88, 107],
[110, 78, 114, 118, 97],
[113, 35, 90, 72, 98]],
[[ 94, 117, 84, 95, 111],
[105, 61, 116, 115, 93],
[106, 119, 108, 74, 103]]])
最后是第4维最值的比较,直接就是比较每行中每列值谁最大了:
>>> b[0][0][0]
array([44, 47, 4, 55, 26])
>>> b[0][0][1]
array([ 64, 73, 10, 40, 107])
可以看到其最值为55,之后是107。因此其结果为:
>>> b.max(axis=3)
array([[[ 55, 107, 89, 109],
[ 70, 114, 96, 118],
[ 98, 90, 66, 113]],
[[100, 84, 117, 94],
[116, 101, 112, 115],
[103, 108, 119, 106]]])
换句话说整个过程就是要找到需要比较的组,逐步分解从而可以轻松得到结果。
同样该方法也可以用于mean、min等函数中。至于其结果的维度,可以将shape值对应位的值去掉即可,如:
>>> b.max(axis=0).shape == b.shape[1:]
True
>>> b.max(axis=1).shape == b.shape[:1] + b.shape[2:]
True
...
True
原因很简单,因为对应维度都用于比较了,结果对应维度就降维了,直接被忽略了。
