Numpy 学习专题（三）—— 数组的变形

前言

• 通常为了满足计算要求，我们会对数组进行形状变化。本模块会用到 numpy 模块，本中 numpy 全部用 np 代替，即 import numpy as np。

一、更改数组形状

numpy.ndarray.shape()

• 该函数可表示数组的形状或修改形状。

x = np.array([1,2,3,4])
print(x.shape)  # (8,)

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

numpy.ndarray.flat()

• 该函数可把数组转换为一维的迭代器，可通过 for 循环输出。此处生成的是视图，故修改一维迭代器的值时，原数组对应位置的值也会改变。

x = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
      
y = x.flat
print(y)  # 

for i in y:
    print(i, end=' ')  # 1 2 3 4 5 6 7 8 9
   
y[3] = 0
print(x) 
# [[1 2 3]
#  [0 5 6]
#  [7 8 9]]

numpy.ndarray.flatten()

• 该函数可把数组转换成一维数组，此处生成的是副本。

x = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
 
y1 = x.flatten(order='C')  # 按行展开
print(y1) # [1 2 3 4 5 6 7 8 9]

y2 = x.flatten(order='F')  # 按列展开
print(y2)  # [1 4 7 2 5 8 3 6 9]

# 改变副本数据，原数组不变
y1[3] = 0
print(x)
# [[1 2 3]
#  [4 5 6]
#  [7 8 9]]

numpy.ravel()

• 该函数可把数组转换成一维数组，即可返回视图，也可返回副本。

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

# 生成视图
y = np.ravel(x)
print(y)  # [1 2 3 4 5 6 7 8 9]

# 改变视图数据，原数组对应位置改变
y[3] = 0
print(x)
# [[1 2 3]
#  [0 5 6]
#  [7 8 9]]

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

# 生成副本
y2 = np.ravel(x, order='F')
print(y2)  # [1 4 7 2 5 8 3 6 9]

# 改变副本数据，原数组不变
y2[3] = 0
print(x)
# [[1 2 3]
#  [4 5 6]
#  [7 8 9]]

numpy.reshape(a, newshape[ ])

• 该函数可把数组转换成任意形状。

x = np.arange(12)

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

# `newshape = [rows,-1]`时，将根据行数自动确定列数
y2 = np.reshape(x, [3, -1])
print(y2)
# [[ 0  1  2  3]
#  [ 4  5  6  7]
#  [ 8  9 10 11]]

# `newshape = [-1, columns]`时，将根据列数自动确定行数
y3 = np.reshape(x, [-1, 3])
print(y3)
# [[ 0  1  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
y[0,1] = 10
print(x)  # [ 0 10  2  3  4  5  6  7  8  9 10 11]

# 参数`newshape = -1`时，表示将数组降为一维
x2 = np.random.randint(12, size=[2, 2, 3])
print(x2)
# [[[11  9  1]
#   [ 1 10  3]]
# 
#  [[ 0  6  1]
#   [ 4 11  3]]]
y4 = np.reshape(x2, -1)
print(y4)
# [11  9  1  1 10  3  0  6  1  4 11  3]

二、数组转置

numpy.transpose(x)

x = np.array([[1, 2, 3], [4, 5, 6]])
y = np.transpose(x)
print(y)
# [[1 4]
#  [2 5]
#  [3 6]]

numpy.ndarray.T

x = np.array([[1, 2, 3], [4, 5, 6]])
y = x.T
print(y)
# [[1 4]
#  [2 5]
#  [3 6]]

三、更改维度

numpy.newaxis

• 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。

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

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

y = x[:, np.newaxis]
print(y.shape)  # (5, 1)
print(y)
# [[1]
#  [2]
#  [3]
#  [4]
#  [5]]

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。 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。

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

# 增加维度
x = x[np.newaxis, :]
print(x.shape)  # (1, 10)

# 删除维度
y = np.squeeze(x)
print(y.shape)  # (10,)

x2 = np.array([[[0], [1], [2]]])
print(x2.shape)  # (1, 3, 1)

y2 = np.squeeze(x2)
print(y2.shape)  #(3,)
print(y2)  # [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)
# ValueError: cannot select an axis to squeeze out which has size not equal to one

四、数组组合

numpy.concatenate()

• 一维拼接

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]

• 二维拼接

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]]

• 复杂类型

x = np.array([[1, 2, 3], [4, 5, 6],[7, 8, 9]])
y = np.array([[10, 11, 12],[13, 14, 15], [16, 17, 18]])

z = np.concatenate([x, y])
print(z)
z = np.concatenate([x, y], axis=0)
print(z)
# [[ 1  2  3]
#  [ 4  5  6]
#  [ 7  8  9]
#  [10 11 12]
#  [13 14 15]
#  [16 17 18]]

z = np.concatenate([x, y], axis=1)
print(z)
# [[ 1  2  3 10 11 12]
#  [ 4  5  6 13 14 15]
#  [ 7  8  9 16 17 18]]

五、数组拆分

numpy.vsplit()

• 垂直切分，把数组按照高度切分

x = np.array([[11, 12, 13, 14],
              [16, 17, 18, 19],
              [21, 22, 23, 24],
              [11, 12, 13, 14]])
              
y = np.vsplit(x, 4)
print(y)
# [array([[11, 12, 13, 14]]), array([[16, 17, 18, 19]]), array([[21, 22, 23, 24]]), array([[11, 12, 13, 14]])]

y2 = np.vsplit(x, 2)
print(y2)
# [array([[11, 12, 13, 14], [16, 17, 18, 19]]), array([[21, 22, 23, 24], [11, 12, 13, 14]])]

numpy.hsplit()

• 水平切分是把数组按照宽度切分

x = np.array([[11, 12, 13, 14],
              [16, 17, 18, 19],
              [21, 22, 23, 24],
              [11, 12, 13, 14]])
y = np.hsplit(x, 4)
print(y)
# [array([[11],
#        [16],
#        [21],
#        [11]]), array([[12],
#        [17],
#        [22],
#        [12]]), array([[13],
#        [18],
#        [23],
#        [13]]), array([[14],
#        [19],
#        [24],
#        [14]])]

y2 = np.hsplit(x, 2)
print(y2)
# [array([[11, 12],
#        [16, 17],
#        [21, 22],
#        [11, 12]]), array([[13, 14],
#        [18, 19],
#        [23, 24],
#        [13, 14]])]

六、数组平铺

numpy.tile(A, reps)

• 将原矩阵横向、纵向地复制

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

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

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

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

numpy.repeat()

• 将原矩阵每行、每列重复复制

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

x = np.array([[1, 2], [3, 4],[5,6]])
print(x)
# [[1 2]
#  [3 4]
#  [5 6]]

# 把原数组降为一维数组，然后复制
y = np.repeat(x, 2)
print(y)
# [1 1 2 2 3 3 4 4 5 5 6 6]

# 按列展开，并复制
y = np.repeat(x, 2, axis=0)
print(y)
# [[1 2]
#  [1 2]
#  [3 4]
#  [3 4]
#  [5 6]
#  [5 6]]

# 按列展开，并指定复制次数
y = np.repeat(x, [1,2, 2], axis=0)
print(y)
# [[1 2]
#  [3 4]
#  [3 4]
#  [3 4]
#  [5 6]
#  [5 6]]

# 按行展开，并指定复制次数
y = np.repeat(x, [2, 3], axis=1)
print(y)
# [[1 1 2 2 2]
#  [3 3 4 4 4]
#  [5 5 6 6 6]]

七、删除重复元素

numpy.unique()

• 对于数组或者列表，unique函数去除其中重复的元素，并按元素由大到小的顺序返回一个新的无元素重复的元组或者列表.

A = [3, 2, 3, 2, 1, 2, 2, 5, 4, 3]  
a = np.unique(A)  

B= (1, 1, 2, 5, 3, 4, 3)  
b= np.unique(B)  

C= ['fgfh','asd','fgfh','asdfds','wrh']  
c= np.unique(C)  

D = np.array([[3, 2, 3, 2],[1,3,1,3]])
d = np.unique(D) 

print(a)  # [1 2 3 4 5]  
print(b)  # [1 2 3 4 5]  
print(c)  # ['asd' 'asdfds' 'fgfh' 'wrh']
print(d)  # [1 2 3]