[Python] NumPy Indexing

程式語言：Python
Package：numpy
官方文件

簡介：NumPy indexing 的使用

Indexing

ndarrays indexing 的方法，即是 x[obj]
obj 的型態會影響賦於的 array 是 view 還是 copy
  • view：與其他 array 共用空間，改值會互相影響
  • copy：與其他 array 不共用空間，改值不會互相影響
import numpy as np

x = np.array([[ 0, 1, 2],
              [ 3, 4, 5],
              [ 6, 7, 8],
              [ 9, 10, 11]])
view = x[1:2, 1:3]
copy = x[1:2, [1, 2]]
print(view) # [[4 5]]
view[0] = 100
print(view) # [[100 100]]
print(x)
# [[  0   1   2]
 # [  3 100 100]
 # [  6   7   8]
 # [  9  10  11]]
print(copy) # [[4 5]]
copy[0] = 200
print(copy) # [[200 200]]
print(x)
# [[  0   1   2]
 # [  3 100 100]
 # [  6   7   8]
 # [  9  10  11]]

Basic Slicing and Indexing

  • view 型態
  • obj
    • slice object (start:stop:step)
      import numpy as np

x = np.array([1, 2, 3, 4])
view = x[-1::-1]
print(view) # [4 3 2 1]
view[0] = 100
print(x) # [  1   2   3 100]
    • an integer
      import numpy as np

x = np.array([[1, 2], [3, 4]])
view = x[:, 1]
print(view) # [2 4]
view[0] = 100
print(x)
# [[  1 100]
#  [  3   4]]
    • a tuple of slice objects and integers
      import numpy as np

x = np.array([[1, 2], [3, 4]])
view = x[(slice(0,2), 1)] # 等同 x[0:2, 1]
print(view) # [2 4]
view[0] = 100
print(x)
# [[  1 100]
#  [  3   4]]
    • ... (Ellipsis)，表示剩餘的其他維度，等同 (:, :, :, ...)，甚至可能為空 
      import numpy as np

x = np.array([[1, 2], [3, 4]])
view = x[..., 1]
print(view) # [2 4]
view[0] = 100
print(x)
# [[  1 100]
#  [  3   4]]
    • np.newaxis
      import numpy as np

x = np.array([[1, 2], [3, 4]])
# 等同 view = x[:, None]
view = x[:, np.newaxis]
print(view.shape) # (2, 1, 2)
print(view)
# [[[1 2]]
#  [[3 4]]]
view[0] = 100
print(x)
# [[100 100]
#  [  3   4]]
  • dimension
    • 若為 integer， \(D = D - 1\)，np.newaxis 則 \(D = D + 1\)
      import numpy as np

x = np.ones((1, 2, 3, 4, 5, 6))
print(x.shape)                   # (1, 2, 3, 4, 5, 6)
print(x[:].shape)                # (1, 2, 3, 4, 5, 6)
print(x[:, 1].shape)             # (1, 3, 4, 5, 6)
print(x[:, 0:1].shape)           # (1, 1, 3, 4, 5, 6)
print(x[0:1, ...].shape)         # (1, 2, 3, 4, 5, 6)
print(x[:, :, np.newaxis].shape) # (1, 2, 1, 3, 4, 5, 6)
    • 若 x[obj] 的 \(D = 1\) 則回傳 scalar，此時不影響原 array
      import numpy as np

x = np.array([1, 2, 3, 4])
view = x[0]
print(type(view)) # <class 'numpy.int32'>
view = 100
print(x) # [1 2 3 4]
  • 等效表示
    • In python
      x[(exp1, exp2, ..., expN)] == x[exp1, exp2, ..., expN]
    • 只有 interger 可拆分
      import numpy as np

x = np.arange(120).reshape((2, 3, 4, 5))
print(x[0, ..., 1:2, 0, 0]) # [20]
print(x[0][..., 1:2, 0, 0]) # [20]
print(x[0][...][1:2][0, 0]) # [20 21 22 23 24]
print(x[0][...][1:2][0][0]) # [20 21 22 23 24]
print(x)
# [[[[  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]]]]

Advanced Indexing

  • copy 型態
  • obj
    • integers (broadcasting 經常使用，後述會再說明)
      import numpy as np

x = np.arange(9).reshape(3, 3)
copy = x[[1, 2], [0, 1]]
print(copy) # [3 7]
copy[0] = 100
print(x) 
# [[0 1 2]
#  [3 4 5]
#  [6 7 8]]
    • boolean ndarrays (前幾個 \(D\) 需一致)，等同 x[obj.nonzero()] 
      import numpy as np

x = np.arange(9).reshape(3, 3)
copy = x[np.array([[True, False, True],
                   [False, True, False],
                   [False, False, False]])]
print(copy) # [0 2 4]
copy[0] = 100
print(x) 
# [[0 1 2]
#  [3 4 5]
#  [6 7 8]]
  • dimension
    • integers 依組合不同，會得到不同的結果
      import numpy as np

x = np.arange(90).reshape((10, 9))
print(x.shape) # (10, 9)

# 等同 x.take([[1, 2]], axis=1)
result = x[:, [[1, 2]], ...]
print(result.shape) # (10, 1, 2)

# 等同 x.take([[1, 2]], axis=0)
result = x[..., [[1, 2]], :]
print(result.shape) # (1, 2, 9)

result = x[[1, 2], ..., [0]]
print(result.shape) # (2, )

result = x[[1, 2]]
print(result.shape) # (2, 9)

      import numpy as np

x = np.arange(10*9*8*7).reshape((10, 9, 8, 7))
print(x.shape) # (10, 9, 8, 7)

# 等同 x.take([[1, 2]], axis=1)
result = x[:, [[1, 2]], ...]
print(result.shape) # (10, 1, 2, 8, 7)

# 等同 x.take([[1, 2]], axis=2)
result = x[..., [[1, 2]], :]
print(result.shape) # (10, 9, 1, 2, 7)

result = x[:, [1, 2], [0], :]
print(result.shape) # (10, 2, 7)

result = x[:, [1, 2], :, [0]]
print(result.shape) # (2, 10, 8)

result = x[[1, 2], [0]]
print(result.shape) # (2, 8, 7)
    • boolean array 依 obj 的 dimension 決定，\(D = D_x - D_{obj} +1\)
      import numpy as np

x = np.arange(60).reshape(3, 4, 5)
print(x.shape) # (3, 4, 5)
print(x[x>15].shape) # (44,)
print(x[[True, True, False]].shape) # (2, 4, 5)
ind = np.array([[True, True, False, True],
                [True, True, False, True],
                [True, True, False, False]])
print(x[ind].shape) # (8, 5)

Broadcasting

  • 規則
    • dimension 相同
    • dimension=1 自動延展
  • 平常範例
    import numpy as np

x = np.arange(6).reshape(2,3)
y = np.arange(3).reshape(3,1)

z = x*y # operands could not be broadcast together with shapes (2,3) (3,1)

    import numpy as np

x = np.arange(3).reshape(3,1)
y = np.arange(3).reshape(3,1)

z = x*y
print(x.shape) # (3, 1)
print(y.shape) # (3, 1)
print(z.shape) # (3, 3)

    import numpy as np

x = np.arange(3).reshape(1,3)
y = np.arange(3).reshape(3,1)

z = x*y
print(x.shape) # (1, 3)
print(y.shape) # (3, 1)
print(z.shape) # (3, 3)

    import numpy as np

x = np.arange(3)
y = np.arange(3).reshape(3,1)

z = x*y
print(x.shape) # (3, )
print(y.shape) # (3, 1)
print(z.shape) # (3, 3)
  • index 範例
    import numpy as np

x = np.array([[ 0,  1,  2],
              [ 3,  4,  5],
              [ 6,  7,  8],
              [ 9, 10, 11]])

rows = np.array([0, 3], dtype=np.intp)
columns = np.array([0, 2], dtype=np.intp)

rowsT = rows[:, np.newaxis]
print("rows.shape {}, columns.shape {}".format(rowsT.shape, columns.shape))
# rows.shape (2, 1), columns.shape (2,)

print(x.shape) # (4, 3)

# 以下兩者等價
print(x[rowsT, columns].shape) # (2, 2)
print(x[np.ix_(rows, columns)].shape) # (2, 2)

Field Access

  • view 型態
  • obj
    • strings
      import numpy as np

x = np.zeros((2,2), dtype=[('a', np.int32), ('b', np.float64, (3,3))])
print(x)
# [[(0, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])
#   (0, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])]
#  [(0, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])
#   (0, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])]]

print(x['a'].shape) # (2, 2)
print(x['a'].dtype) # dtype('int32')
print(x['b'].shape) # (2, 2, 3, 3)
print(x['b'].dtype) # dtype('float64')

view = x['a']
print(view)
# [[0 0]
#  [0 0]]

view[0] = 100
print(x)
# [[(100, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])
#   (100, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])]
#  [(  0, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])
#   (  0, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])]]

Flat Iterator indexing

  • view 型態
  • 範例
    import numpy as np

x = np.zeros((2,2))
print(x)
# [[ 0.  0.]
#  [ 0.  0.]]

view = x.flat
print(view[:])
# [ 0.  0.  0.  0.]

view[0] = 100
print(x)
# [[ 100.    0.]
#  [   0.    0.]]

Note

  • 可用內建的 slice 
    # 等同 x[1:10:5,::-1] 
obj = (slice(1,10,5), slice(None,None,-1))
x[obj]
  • 不同情況，會得到不同的結果 view, copy , scalar
    import numpy as np

x = np.arange(9).reshape(3,3)
print(x)
# [[0 1 2]
 # [3 4 5]
 # [6 7 8]]

copy = x[(1,2),]
print(copy)
# [[3 4 5]
 # [6 7 8]]
copy[0] = 100
print(x)
# [[0 1 2]
 # [3 4 5]
 # [6 7 8]]

# 等同 view = x[1,2]
scalar = x[(1,2)] 
print(scalar)
# 5
scalar = 200
print(x)
# [[0 1 2]
 # [3 4 5]
 # [6 7 8]]

copy = x[[1,2]] 
print(copy)
# [[3 4 5]
 # [6 7 8]]
copy[0] = 300
print(x)
# [[0 1 2]
 # [3 4 5]
 # [6 7 8]]

view = x[[1,slice(None)]] 
print(view)
# [3 4 5]
view[0] = 400
print(x)
# [[  0   1   2]
 # [400   4   5]
 # [  6   7   8]]
  • NumPy indexing 建議 type 為 intp
    import numpy as np

ind = np.array([[0, 0],
                [3, 3]], dtype=np.intp)
  • advanced indexing 若 index 超出範圍，並不會出現 IndexError
    import numpy as np

x = np.zeros((8, 8))
print(x[[], [100]]) # 不會出現錯誤

參考

Numpy 笔记(二): 多维数组的切片(slicing)和索引(indexing)
numpy 中的 broadcasting（广播）机制

留言

張貼留言