numpy -- 数组转置和轴对换

重塑

import numpy as np

arr = np.arange(15).reshape((3,5))
print(arr)

[[ 0  1  2  3  4]
 [ 5  6  7  8  9]
 [10 11 12 13 14]]

arr = np.arange(15).reshape(3,5)
print(arr)

[[ 0  1  2  3  4]
 [ 5  6  7  8  9]
 [10 11 12 13 14]]

转置

arr = np.arange(18).reshape((3,6))
print(arr)

[[ 0  1  2  3  4  5]
 [ 6  7  8  9 10 11]
 [12 13 14 15 16 17]]

print(arr.T)

[[ 0  6 12]
 [ 1  7 13]
 [ 2  8 14]
 [ 3  9 15]
 [ 4 10 16]
 [ 5 11 17]]

矩阵相乘

print(np.dot(arr.T,arr))

[[180 198 216 234 252 270]
 [198 219 240 261 282 303]
 [216 240 264 288 312 336]
 [234 261 288 315 342 369]
 [252 282 312 342 372 402]
 [270 303 336 369 402 435]]

transpose

arr = np.arange(16).reshape(2,2,4)
print(arr)

[[[ 0  1  2  3]
  [ 4  5  6  7]]

 [[ 8  9 10 11]
  [12 13 14 15]]]

print(arr.transpose((1,0,2)))

[[[ 0  1  2  3]
  [ 8  9 10 11]]

 [[ 4  5  6  7]
  [12 13 14 15]]]

详细解释：

arr数组的内容为

- a[0][0] = [0, 1, 2, 3]

- a[0][1] = [4, 5, 6, 7]

- a[1][0] = [8, 9, 10, 11]

- a[1][1] = [12, 13, 14, 15]

transpose的参数为坐标，正常顺序为(0, 1, 2, ... , n - 1)，

现在传入的为(1, 0, 2)代表a[x][y][z] = a[y][x][z]，第0个和第1个坐标互换。原本shape是 2 2 4 传入后，还是2 2 4 shape不变

- a'[0][0] = a[0][0] = [0, 1, 2, 3]

- a'[0][1] = a[1][0] = [8, 9, 10, 11]

- a'[1][0] = a[0][1] = [4, 5, 6, 7]

- a'[1][1] = a[1][1] = [12, 13, 14, 15]

print(arr.transpose((2,1,0)))  #原来100， 001

[[[ 0  8]
  [ 4 12]]

 [[ 1  9]
  [ 5 13]]

 [[ 2 10]
  [ 6 14]]

 [[ 3 11]
  [ 7 15]]]

详细解释：

arr数组的内容为

- a[0][0][0] = [0]

- a[0][0][1] = [1]

- a[0][0][2] = [2]

- a[0][0][3] = [3]

---

- a[0][1][0] = [4]

- a[0][1][1] = [5]

- a[0][1][2] = [6]

- a[0][1][3] = [7]

---

- a[1][0][0] = [8]

- a[1][0][1] = [9]

- a[1][0][2] = [10]

- a[1][0][3] = [11]

---

- a[1][1][0] = [12]

- a[1][1][1] = [13]

- a[1][1][2] = [14]

- a[1][1][3] = [15]

transpose的参数为坐标，正常顺序为(0, 1, 2, ... , n - 1)，

现在传入的为(2, 1, 0)代表a[x][y][z] = a[z][y][x]，第0个和第2个坐标互换。原来shape是 2 2 4 变化后为4 2 2 shape产生变化

- a'[0][0][0] = a[0][0][0] = [0]

- a'[0][0][1] =a[1][0][0] = [8]

- a'[0][1][0] =a[0][1][0] = [4]

- a'[0][1][1] =a[1][1][0] = [12]

---

- a'[1][0][0] = a[0][0][1] = [1]

- a'[1][0][1] =a[1][0][1] = [9]

- a'[1][1][0] =a[0][1][1] = [5]

- a'[1][1][1] =a[1][1][1] = [13]

---

- a'[2][0][0] = a[0][0][2] = [2]

- a'[2][0][1] =a[1][0][2] = [10]

- a'[2][1][0] =a[0][1][2] = [6]

- a'[2][1][1] =a[1][1][2] = [14]

---

- a'[3][0][0] = a[0][0][3] = [3]

- a'[3][0][1] =a[1][0][3] = [11]

- a'[3][1][0] =a[0][1][3] = [7]

- a'[3][1][1] =a[1][1][3] = [15]