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第三章 数组的操作-变形

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数组操作

更改形状

在对数组进行操作时，为了满足格式和计算的要求通常会改变其形状。

  • numpy.ndarray.shape表示数组的维度，返回一个元组，这个元组的长度就是维度的数目，即ndim属性（秩）。

例：通过修改shape属性来改变数组的形状。

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import numpy as np

x = np.array([1, 2, 9, 4, 5, 6, 7, 8])
print(x.shape) #(8,)
x.shape = [2, 4]
print(x)
#[[1 2 9 4]
# [5 6 7 8]]
  • numpy.ndarray.flat 将数组转换为一维的迭代器，可以用for访问数组每一个元组。
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import numpy as np
x = np.array([[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]])
y = x.flat
print(y)# <numpy.flatiter object at 0x0000020F9BA10C60>
for i in y:
    print(i, end = ' ')
# 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
y[3] = 0
print(x)
# [[11 12 13  0 15]
#  [16 17 18 19 20]
#  [21 22 23 24 25]
#  [26 27 28 29 30]
#  [31 32 33 34 35]]

修改迭代器中的元素，原数组中对应元素也相应改变。

  • numpy.ndarray.flatten([order = ‘C’])将数组的副本转换为一维数组，并返回。
    • order：‘C’ — 按行，’F’—按列，’A’—原顺序，’K’—元素在内存中的出现顺序。

例：flatten()函数返回的是拷贝。

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import numpy as np

x = np.array([[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]])
y = x.flatten(order='F')
print(y)
# [11 16 21 26 31 12 17 22 27 32 13 18 23 28 33 14 19 24 29 34 15 20 25 30
#  35]

y[3] = 0
print(x)
# [[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]]
  • numpy.ravel(a, order = ‘C’) Return a contiguous flattened array.

例：ravel()返回的是视图。

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import numpy as np

x = np.array([[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]])
y = np.ravel(x)
print(y)
# [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]

y[3] = 0
print(x)
# [[11 12 13  0 15]
#  [16 17 18 19 20]
#  [21 22 23 24 25]
#  [26 27 28 29 30]
#  [31 32 33 34 35]

例：order=F 就是拷贝

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x = np.array([[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]])

y = np.ravel(x, order='F')
print(y)
# [11 16 21 26 31 12 17 22 27 32 13 18 23 28 33 14 19 24 29 34 15 20 25 30
#  35]

y[3] = 0
print(x)
# [[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]]
  • numpy.reshape(a, newshape[, order = ‘C’])在不更改数据的情况下为数组赋予新的形状。

例：reshape()函数当参数newshape = [rows,-1]时，将根据行数自动确定列数；newshape = [-1,column]时，将根据行数自动确定行数。

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import numpy as np

x = np.arange(12)
y = np.reshape(x, [3, 4])
print(y.dtype)  # int32
print(y)
# [[ 0  1  2  3]
#  [ 4  5  6  7]
#  [ 8  9 10 11]]

y = np.reshape(x, [3, -1])
print(y)
# [[ 0  1  2  3]
#  [ 4  5  6  7]
#  [ 8  9 10 11]]

y = np.reshape(x,[-1,3])
print(y)
# [[ 0  1  2]
#  [ 3  4  5]
#  [ 6  7  8]
#  [ 9 10 11]]

y[0, 1] = 10
print(x)
# [ 0 10  2  3  4  5  6  7  8  9 10 11]（改变x去reshape后y中的值，x对应元素也改变）

例：reshape()函数当参数newshape = -1时，表示将数组降为一维。

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import numpy as np

x = np.random.randint(12, size=[2, 2, 3])
print(x)
# [[[11  9  1]
#   [ 1 10  3]]
# 
#  [[ 0  6  1]
#   [ 4 11  3]]]
y = np.reshape(x, -1)
print(y)
# [11  9  1  1 10  3  0  6  1  4 11  3]

数组转置

  • numpy.transpose(a, axes = None) Permute the dimensions of an array.
  • numpy.ndarray.T Same as self.transpose(),except that self is returned if self.ndim < 2.
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import numpy as np

x = np.random.rand(5, 5) * 10
x = np.around(x, 2)
print(x)
# [[6.74 8.46 6.74 5.45 1.25]
#  [3.54 3.49 8.62 1.94 9.92]
#  [5.03 7.22 1.6  8.7  0.43]
#  [7.5  7.31 5.69 9.67 7.65]
#  [1.8  9.52 2.78 5.87 4.14]]
y = x.T
print(y)
# [[6.74 3.54 5.03 7.5  1.8 ]
#  [8.46 3.49 7.22 7.31 9.52]
#  [6.74 8.62 1.6  5.69 2.78]
#  [5.45 1.94 8.7  9.67 5.87]
#  [1.25 9.92 0.43 7.65 4.14]]
y = np.transpose(x)
print(y)
# [[6.74 3.54 5.03 7.5  1.8 ]
#  [8.46 3.49 7.22 7.31 9.52]
#  [6.74 8.62 1.6  5.69 2.78]
#  [5.45 1.94 8.7  9.67 5.87]
#  [1.25 9.92 0.43 7.65 4.14]]

更改维度

当创建一个数组之后，还可以给它增加一个维度，这在矩阵计算中经常会用到。

  • numpy.newaxis = None None的别名，对索引数组很有用。

例：很多工具包在进行计算时都会先判断输入数据的维度是否满足要求，如果输入数据达不到指定的维度时，可以使用newaxis参数来增加一个维度。

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import numpy as np

x = np.array([1, 2, 9, 4, 5, 6, 7, 8])
print(x.shape)  # (8,)
print(x)  # [1 2 9 4 5 6 7 8]

y = x[np.newaxis, :]
print(y.shape)  # (1, 8)
print(y)  # [[1 2 9 4 5 6 7 8]]

y = x[:, np.newaxis]
print(y.shape)  # (8, 1)
print(y)
# [[1]
#  [2]
#  [9]
#  [4]
#  [5]
#  [6]
#  [7]
#  [8]]
  • numpy.squeeze(a, axis = None) 从数组的形状中删除单维度条目，即把shape中为1的维度去掉。
    • a表示输入的数组；
    • axis用于指定需要删除的维度，但是指定的维度必须为单维度，否则将会报错；
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import numpy as np

x = np.arange(10)
print(x.shape)  # (10,)
x = x[np.newaxis, :]
print(x.shape)  # (1, 10)
y = np.squeeze(x)
print(y.shape)  # (10,)
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import numpy as np

x = np.array([[[0], [1], [2]]])
print(x.shape)  # (1, 3, 1)
print(x)
# [[[0]
#   [1]
#   [2]]]

y = np.squeeze(x)
print(y.shape)  # (3,)
print(y)  # [0 1 2]

y = np.squeeze(x, axis=0)
print(y.shape)  # (3, 1)
print(y)
# [[0]
#  [1]
#  [2]]

y = np.squeeze(x, axis=2)
print(y.shape)  # (1, 3)
print(y)  # [[0 1 2]]

y = np.squeeze(x, axis=1)#欲删除的维度不为1，报错。
# ValueError: cannot select an axis to squeeze out which has size not equal to one

数组组合

如果要将两份数据组合到一起，就需要拼接操作。

  • numpy.concatenate((a1, a2, …), axis = 0, out = None) Join a sequence of arrays along an existing axis.

例：连接沿现有轴的数组序列（原来x，y都是一维的，拼接后的结果也是一维的）

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import numpy as np

x = np.array([1, 2, 3])
y = np.array([7, 8, 9])
z = np.concatenate([x, y])
print(z)
# [1 2 3 7 8 9]

z = np.concatenate([x, y], axis=0)
print(z)
# [1 2 3 7 8 9]

例：原来x，y都是二维的，拼接后的结果也是二维的。

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import numpy as np

x = np.array([1, 2, 3]).reshape(1, 3)
y = np.array([7, 8, 9]).reshape(1, 3)
z = np.concatenate([x, y])
print(z)
# [[ 1  2  3]
#  [ 7  8  9]]
z = np.concatenate([x, y], axis=0)
print(z)
# [[ 1  2  3]
#  [ 7  8  9]]
z = np.concatenate([x, y], axis=1)
print(z)
# [[ 1  2  3  7  8  9]]

例：x，y在原来的维度上进行拼接。

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import numpy as np

x = np.array([[1, 2, 3], [4, 5, 6]])
y = np.array([[7, 8, 9], [10, 11, 12]])
z = np.concatenate([x, y])
print(z)
# [[ 1  2  3]
#  [ 4  5  6]
#  [ 7  8  9]
#  [10 11 12]]
z = np.concatenate([x, y], axis=0)
print(z)
# [[ 1  2  3]
#  [ 4  5  6]
#  [ 7  8  9]
#  [10 11 12]]
z = np.concatenate([x, y], axis=1)
print(z)
# [[ 1  2  3  7  8  9]
#  [ 4  5  6 10 11 12]]
  • numpy.stack(array, axis = 0, out = None) Join a sequence of arrays along a new axis.

例：沿着新的轴加入一系列数组（stack为增加维度的拼接）。

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import numpy as np

x = np.array([1, 2, 3])
y = np.array([7, 8, 9])
z = np.stack([x, y])
print(z.shape)  # (2, 3)
print(z)
# [[1 2 3]
#  [7 8 9]]

z = np.stack([x, y], axis=1)
print(z.shape)  # (3, 2)
print(z)
# [[1 7]
#  [2 8]
#  [3 9]]
  • numpy.vstack(tup)Stack arrays in sequence vertically (row wise).
  • numpy.hstack(tup)Stack arrays in sequence horizontally (column wise).

hstack(),vstack()分别表示水平和竖直的拼接方式。在数据维度等于1时，比较特殊。而当维度大于或等于2时，它们的作用相当于concatenate，用于在已有轴上进行操作。

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import numpy as np

a = np.hstack([np.array([1, 2, 3, 4]), 5])
print(a)  # [1 2 3 4 5]

a = np.concatenate([np.array([1, 2, 3, 4]), 5])
print(a)
# all the input arrays must have same number of dimensions, but the array at index 0 has 1 dimension(s) and the array at index 1 has 0 dimension(s)

数组拆分

  • numpy.split(ary, indices_or_sections, axis = 0) Split an array into multiple sub-arrays as views into ary.

例：拆分数组

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import numpy as np

x = np.array([[11, 12, 13, 14],
              [16, 17, 18, 19],
              [21, 22, 23, 24]])
y = np.split(x, [1, 3]) #[1, 3]表示在第1行和第3行进行拆分
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19],
#        [21, 22, 23, 24]]), array([], shape=(0, 4), dtype=int32)]

y = np.split(x, [1, 3], axis=1)
print(y)
# [array([[11],
#        [16],
#        [21]]), array([[12, 13],
#        [17, 18],
#        [22, 23]]), array([[14],
#        [19],
#        [24]])]
  • numpy.vsplit(ary, indices_or_sections) Split an array into multiple sub-arrays vertically (row-wise).

例：水平切分是把数组按照宽度切分。

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import numpy as np

x = np.array([[11, 12, 13, 14],
              [16, 17, 18, 19],
              [21, 22, 23, 24]])
y = np.vsplit(x, 3)# 切成三分
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19]]), array([[21, 22, 23, 24]])]

y = np.vsplit(x, [1])# 在下标1处切分
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19],
#        [21, 22, 23, 24]])]

y = np.vsplit(x, [1, 3])# 在下标1 3处切分
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19],
#        [21, 22, 23, 24]]), array([], shape=(0, 4), dtype=int32)]
  • numpy.hsplit(ary, indices_or_sections) Split an array into multiple sub-arrays horizontally (column-wise).

例：垂直切分是把数组按照高度切分

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import numpy as np

x = np.array([[11, 12, 13, 14],
              [16, 17, 18, 19],
              [21, 22, 23, 24]])
y = np.hsplit(x, 2)#切成两份
print(y)
# [array([[11, 12],
#        [16, 17],
#        [21, 22]]), array([[13, 14],
#        [18, 19],
#        [23, 24]])]


y = np.hsplit(x, [3])#在下标3处切分
print(y)
# [array([[11, 12, 13],
#        [16, 17, 18],
#        [21, 22, 23]]), array([[14],
#        [19],
#        [24]])]

y = np.hsplit(x, [1, 3])#在下标1 3处切分
print(y)
# [array([[11],
#        [16],
#        [21]]), array([[12, 13],
#        [17, 18],
#        [22, 23]]), array([[14],
#        [19],
#        [24]])]

数组平铺

  • numpy.tile(A, reps) Construct an array by repeating A the number of times given by reps.

tile是瓷砖的意思，顾名思义，这个函数就是把数组像瓷砖一样铺展开来。

例：将原矩阵横向、纵向地复制。

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import numpy as np

x = np.array([[1, 2], [3, 4]])
print(x)
# [[1 2]
#  [3 4]]

y = np.tile(x, (1, 3))
print(y)
# [[1 2 1 2 1 2]
#  [3 4 3 4 3 4]]

y = np.tile(x, (3, 1))
print(y)
# [[1 2]
#  [3 4]
#  [1 2]
#  [3 4]
#  [1 2]
#  [3 4]]

y = np.tile(x, (3, 3))
print(y)
# [[1 2 1 2 1 2]
#  [3 4 3 4 3 4]
#  [1 2 1 2 1 2]
#  [3 4 3 4 3 4]
#  [1 2 1 2 1 2]
#  [3 4 3 4 3 4]]
  • numpy.repeat(a, repeats, axis=None) Repeat elements of an array.
    • axis=0，沿着y轴复制，实际上增加了行数。
    • axis=1，沿着x轴复制，实际上增加了列数。
    • repeats，可以为一个数，也可以为一个矩阵。
    • axis=None时就会flatten当前矩阵，实际上就是变成了一个行向量。

例：重复数组的元素

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import numpy as np

x = np.repeat(3, 4)
print(x)  # [3 3 3 3]

x = np.array([[1, 2], [3, 4]])
y = np.repeat(x, 2)
print(y)
# [1 1 2 2 3 3 4 4]

y = np.repeat(x, 2, axis=0)
print(y)
# [[1 2]
#  [1 2]
#  [3 4]
#  [3 4]]

y = np.repeat(x, 2, axis=1)
print(y)
# [[1 1 2 2]
#  [3 3 4 4]]

y = np.repeat(x, [2, 3], axis=0)
print(y)
# [[1 2]
#  [1 2]
#  [3 4]
#  [3 4]
#  [3 4]]

y = np.repeat(x, [2, 3], axis=1)
print(y)
# [[1 1 2 2 2]
#  [3 3 4 4 4]]

添加和删除元素

  • numpy.unique(ar, return_index=False, return_inverse=False,return_counts=False, axis=None) Find the unique elements of an array
    • return_index：the indices of the input array that give the unique values
    • return_inverse：the indices of the unique array that reconstruct the input array
    • return_counts：the number of times each unique value comes up in the input array

例：查找数组的唯一元素。

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a=np.array([1,1,2,3,3,4,4])
b=np.unique(a,return_counts=True)
print(b[0][list(b[1]).index(1)])
#2