numpy模块轴（axis）的一些用法说明，以及相关矩阵堆叠（concatenate, hstack, vstack, dstack, stack）用法的说明

Love The Way You Lie 2023-08-17 16:04 8阅读 0赞

# 轴含义说明 #

axis的含义：由此可以看出，通过不同的axis，numpy会沿着不同的方向进行操作：

如果不设置，那么对所有的元素操作；如果axis=0，则沿着纵轴进行操作；axis=1，则沿着横轴进行操作。

但这只是简单的二位数组，如果是多维的呢？可以总结为一句话：

设axis=i，则numpy沿着第i个下标变化的放向进行操作。

例如刚刚的例子，可以将表示为：

import numpy as np
    data = np.array([[1,2],[3,4]])

data = [
                                [a00, a01],
                                [a10, a11]
                                ]，

所以axis=0时，沿着第0个下标变化的方向进行操作，也就是a00->a10, a01->a11，

也就是纵坐标的方向，axis=1时也类似。下面我们举一个四维的求sum的例子来验证一下：

data = np.random.randint(0, 5, [4,3,2,3])
    print data

[[[[4 3 0]
       [0 4 0]]
    
      [[3 2 1]
       [2 0 3]]
    
      [[2 2 4]
       [1 2 0]]]
    
    
     [[[0 2 4]
       [2 4 0]]
    
      [[4 2 4]
       [0 4 0]]
    
      [[3 0 3]
       [4 1 1]]]
    
    
     [[[0 2 0]
       [3 3 3]]
    
      [[4 3 2]
       [3 2 3]]
    
      [[0 2 4]
       [0 3 2]]]
    
    
     [[[2 2 0]
       [0 2 2]]
    
      [[2 3 3]
       [1 2 4]]
    
      [[0 1 0]
       [1 0 1]]]]

print "axis=0"
    #numpy验证第0维的方向来求和，也就是第一个元素值=a0000+a1000+a2000+a3000=11,
    #第二个元素=a0001+a1001+a2001+a3001=5，同理可得最后的结果如下：
    print data.sum(axis=0)
    print "axis=1"
    print data.sum(axis=1)
    print "axis=2"
    print data.sum(axis=2)
    #当axis=3时，numpy验证第3维的方向来求和，也就是第一个元素值=a0000+a0001+a0002=5,
    #第二个元素=a0010+a0011+a0012=7，同理可得最后的结果如下：
    print "axis=3"
    print data.sum(axis=3)

axis=0
    [[[13  6  9]
      [ 7  4  5]]
    
     [[12  9 11]
      [ 6 10  1]]
    
     [[ 8 13 12]
      [ 9  6  6]]]
    axis=1
    [[[10  9  8]
      [ 5  3  4]]
    
     [[ 9  7 10]
      [ 5  4  2]]
    
     [[ 9  5 10]
      [ 8  5  3]]
    
     [[ 5  7  4]
      [ 4  8  3]]]
    axis=2
    [[[5 4 3]
      [5 1 3]
      [5 7 6]]
    
     [[4 1 4]
      [4 7 4]
      [6 3 4]]
    
     [[7 2 4]
      [5 4 3]
      [5 4 6]]
    
     [[4 3 3]
      [4 7 2]
      [1 5 2]]]
    axis=3
    [[[ 9  3]
      [ 8  1]
      [10  8]]
    
     [[ 5  4]
      [12  3]
      [ 9  4]]
    
     [[ 9  4]
      [ 6  6]
      [ 9  6]]
    
     [[ 5  5]
      [ 6  7]
      [ 5  3]]]

# 相关矩阵堆叠（concatenate, hstack, vstack, dstack, stack）用法的说明 #

arr=[np.random.randn(2,3) for _ in range(5)]
    print arr
    print arr[0].shape

[array([[-0.80612405,  0.31055887, -0.442608  ],
           [-0.53218701,  1.73229849,  0.87374842]]), array([[ 2.30505457,  0.2061082 , -1.02476858],
           [ 0.01919642, -0.62611687, -0.35686779]]), array([[ 1.8560166 ,  0.61116091,  0.80456681],
           [-0.11137362, -1.22763138, -0.4134618 ]]), array([[-0.6849199 ,  0.09698213,  0.82980694],
           [-1.12956127, -0.33650792,  0.34616903]]), array([[ 1.78424831,  0.09591247, -0.19971545],
           [ 0.62067279, -1.21686687, -2.0698592 ]])]
    (2, 3)

## np.stack ##

将两个矩阵沿着一个新指定的轴堆起来  
更专业的英语说明：  
np.stack  
Join a sequence of arrays along a new axis.  
The axis parameter specifies the index of the new axis in the dimensions of the result.  
For example, if axis=0 it will be the first dimension and if axis=-1 it will be the last dimension.

print "axis=0"
    print np.stack(arr,axis=0)
    print "previous: "+str(arr[0].shape)+" now: "+str(np.stack(arr,axis=0).shape)
    print "axis=1"
    print np.stack(arr,axis=1)
    print "previous: "+str(arr[0].shape)+" now: "+str(np.stack(arr,axis=1).shape)
    print "axis=2"
    print np.stack(arr,axis=2)
    print "previous: "+str(arr[0].shape)+" now: "+str(np.stack(arr,axis=2).shape)

axis=0
    [[[-0.80612405  0.31055887 -0.442608  ]
      [-0.53218701  1.73229849  0.87374842]]
    
     [[ 2.30505457  0.2061082  -1.02476858]
      [ 0.01919642 -0.62611687 -0.35686779]]
    
     [[ 1.8560166   0.61116091  0.80456681]
      [-0.11137362 -1.22763138 -0.4134618 ]]
    
     [[-0.6849199   0.09698213  0.82980694]
      [-1.12956127 -0.33650792  0.34616903]]
    
     [[ 1.78424831  0.09591247 -0.19971545]
      [ 0.62067279 -1.21686687 -2.0698592 ]]]
    previous: (2, 3) now: (5, 2, 3)
    axis=1
    [[[-0.80612405  0.31055887 -0.442608  ]
      [ 2.30505457  0.2061082  -1.02476858]
      [ 1.8560166   0.61116091  0.80456681]
      [-0.6849199   0.09698213  0.82980694]
      [ 1.78424831  0.09591247 -0.19971545]]
    
     [[-0.53218701  1.73229849  0.87374842]
      [ 0.01919642 -0.62611687 -0.35686779]
      [-0.11137362 -1.22763138 -0.4134618 ]
      [-1.12956127 -0.33650792  0.34616903]
      [ 0.62067279 -1.21686687 -2.0698592 ]]]
    previous: (2, 3) now: (2, 5, 3)
    axis=2
    [[[-0.80612405  2.30505457  1.8560166  -0.6849199   1.78424831]
      [ 0.31055887  0.2061082   0.61116091  0.09698213  0.09591247]
      [-0.442608   -1.02476858  0.80456681  0.82980694 -0.19971545]]
    
     [[-0.53218701  0.01919642 -0.11137362 -1.12956127  0.62067279]
      [ 1.73229849 -0.62611687 -1.22763138 -0.33650792 -1.21686687]
      [ 0.87374842 -0.35686779 -0.4134618   0.34616903 -2.0698592 ]]]
    previous: (2, 3) now: (2, 3, 5)

## np.hstack， np.vstack, np.dstack ##

*  np.hstack  
    将两个矩阵水平方向（行所在的轴）堆起来Stack arrays in sequence horizontally (column wise),  
    等同于 *np.concatenate(arr,axis=1)*
 *  np.vstack  
    矩阵沿着垂直的方向堆叠，Stack arrays in sequence vertically (row wise)  
    等同于 *np.concatenate(arr,axis=0)*
 *  np.dstack  
    矩阵沿着深度方向堆叠，即第三个轴 Stack arrays in sequence depth wise (along third dimension)

print np.hstack(arr)
    print "previous: "+str(arr[0].shape)+" now: "+str(np.hstack(arr).shape)
    print np.vstack(arr)
    print "previous: "+str(arr[0].shape)+" now: "+str(np.vstack(arr).shape)
    print np.dstack(arr)
    print "previous: "+str(arr[0].shape)+" now: "+str(np.dstack(arr).shape)

[[-0.80612405  0.31055887 -0.442608    2.30505457  0.2061082  -1.02476858
       1.8560166   0.61116091  0.80456681 -0.6849199   0.09698213  0.82980694
       1.78424831  0.09591247 -0.19971545]
     [-0.53218701  1.73229849  0.87374842  0.01919642 -0.62611687 -0.35686779
      -0.11137362 -1.22763138 -0.4134618  -1.12956127 -0.33650792  0.34616903
       0.62067279 -1.21686687 -2.0698592 ]]
    previous: (2, 3) now: (2, 15)
    [[-0.80612405  0.31055887 -0.442608  ]
     [-0.53218701  1.73229849  0.87374842]
     [ 2.30505457  0.2061082  -1.02476858]
     [ 0.01919642 -0.62611687 -0.35686779]
     [ 1.8560166   0.61116091  0.80456681]
     [-0.11137362 -1.22763138 -0.4134618 ]
     [-0.6849199   0.09698213  0.82980694]
     [-1.12956127 -0.33650792  0.34616903]
     [ 1.78424831  0.09591247 -0.19971545]
     [ 0.62067279 -1.21686687 -2.0698592 ]]
    previous: (2, 3) now: (10, 3)
    [[[-0.80612405  2.30505457  1.8560166  -0.6849199   1.78424831]
      [ 0.31055887  0.2061082   0.61116091  0.09698213  0.09591247]
      [-0.442608   -1.02476858  0.80456681  0.82980694 -0.19971545]]
    
     [[-0.53218701  0.01919642 -0.11137362 -1.12956127  0.62067279]
      [ 1.73229849 -0.62611687 -1.22763138 -0.33650792 -1.21686687]
      [ 0.87374842 -0.35686779 -0.4134618   0.34616903 -2.0698592 ]]]
    previous: (2, 3) now: (2, 3, 5)

## np.concatenate用法 ##

将几个矩阵沿着不同的轴堆起来 Join a sequence of arrays along an existing axis.

print "axis=0"
    print np.concatenate(arr,axis=0)
    print "previous: "+str(arr[0].shape)+" now: "+str(np.concatenate(arr,axis=0).shape)
    print "axis=1"
    print np.concatenate(arr,axis=1)
    print "previous: "+str(arr[0].shape)+" now: "+str(np.concatenate(arr,axis=1).shape)

axis=0
    [[-0.80612405  0.31055887 -0.442608  ]
     [-0.53218701  1.73229849  0.87374842]
     [ 2.30505457  0.2061082  -1.02476858]
     [ 0.01919642 -0.62611687 -0.35686779]
     [ 1.8560166   0.61116091  0.80456681]
     [-0.11137362 -1.22763138 -0.4134618 ]
     [-0.6849199   0.09698213  0.82980694]
     [-1.12956127 -0.33650792  0.34616903]
     [ 1.78424831  0.09591247 -0.19971545]
     [ 0.62067279 -1.21686687 -2.0698592 ]]
    previous: (2, 3) now: (10, 3)
    axis=1
    [[-0.80612405  0.31055887 -0.442608    2.30505457  0.2061082  -1.02476858
       1.8560166   0.61116091  0.80456681 -0.6849199   0.09698213  0.82980694
       1.78424831  0.09591247 -0.19971545]
     [-0.53218701  1.73229849  0.87374842  0.01919642 -0.62611687 -0.35686779
      -0.11137362 -1.22763138 -0.4134618  -1.12956127 -0.33650792  0.34616903
       0.62067279 -1.21686687 -2.0698592 ]]
    previous: (2, 3) now: (2, 15)