numpy模塊軸（axis）的一些用法說明，以及相關矩陣堆疊（concatenate, hstack, vstack, dstack, stack）用法的說明

軸含義說明

axis的含義：由此可以看出，通過不同的axis，numpy會沿着不同的方向進行操作：

如果不設置，那麼對所有的元素操作；如果axis=0，則沿着縱軸進行操作；axis=1，則沿着橫軸進行操作。

但這只是簡單的二位數組，如果是多維的呢？可以總結爲一句話：

設axis=i，則numpy沿着第i個下標變化的放向進行操作。

例如剛剛的例子，可以將表示爲：

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

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

所以axis=0時，沿着第0個下標變化的方向進行操作，也就是a00->a10, a01->a11，

也就是縱座標的方向，axis=1時也類似。下面我們舉一個四維的求sum的例子來驗證一下：

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驗證第0維的方向來求和，也就是第一個元素值=a0000+a1000+a2000+a3000=11,
#第二個元素=a0001+a1001+a2001+a3001=5，同理可得最後的結果如下：
print data.sum(axis=0)
print "axis=1"
print data.sum(axis=1)
print "axis=2"
print data.sum(axis=2)
#當axis=3時，numpy驗證第3維的方向來求和，也就是第一個元素值=a0000+a0001+a0002=5,
#第二個元素=a0010+a0011+a0012=7，同理可得最後的結果如下：
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]]]

相關矩陣堆疊（concatenate, hstack, vstack, dstack, stack）用法的說明

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

將兩個矩陣沿着一個新指定的軸堆起來
更專業的英語說明：
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
  將兩個矩陣水平方向（行所在的軸）堆起來Stack arrays in sequence horizontally (column wise),
  等同於 np.concatenate(arr,axis=1)
• np.vstack
  矩陣沿着垂直的方向堆疊，Stack arrays in sequence vertically (row wise)
  等同於 np.concatenate(arr,axis=0)
• np.dstack
  矩陣沿着深度方向堆疊，即第三個軸 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

將幾個矩陣沿着不同的軸堆起來 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)