Python中的矩阵操作

Numpy

通过观察Python的自有数据类型，我们可以发现Python原生并不提供多维数组的操作，那么为了处理矩阵，就需要使用第三方提供的相关的包。

NumPy 是一个非常优秀的提供矩阵操作的包。NumPy的主要目标，就是提供多维数组，从而实现矩阵操作。

NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of positive integers. In NumPy dimensions are called axes.

基本操作

#######################################
# 创建矩阵
#######################################
from numpy import array as matrix, arange

# 创建矩阵
a = arange(15).reshape(3,5)
a

# Out[10]:
# array([[0., 0., 0., 0., 0.],
#        [0., 0., 0., 0., 0.],
#        [0., 0., 0., 0., 0.]])

b = matrix([2,2])
b

# Out[33]: array([2, 2])

c = matrix([[1,2,3,4,5,6],[7,8,9,10,11,12]], dtype=int)
c

# Out[40]:
# array([[ 1,  2,  3,  4,  5,  6],
#        [ 7,  8,  9, 10, 11, 12]])

#######################################
# 创建特殊矩阵
#######################################
from numpy import zeros, ones,empty

z = zeros((3,4))
z

# Out[43]:
# array([[0., 0., 0., 0.],
#        [0., 0., 0., 0.],
#        [0., 0., 0., 0.]])

o = ones((3,4))
o

# Out[46]:
# array([[1., 1., 1., 1.],
#        [1., 1., 1., 1.],
#        [1., 1., 1., 1.]])

e = empty((3,4))
e

# Out[47]:
# array([[0., 0., 0., 0.],
#        [0., 0., 0., 0.],
#        [0., 0., 0., 0.]])

#######################################
# 矩阵数学运算
#######################################
from numpy import array as matrix, arange

a = arange(9).reshape(3,3)
a

# Out[10]:
# array([[0, 1, 2],
#        [3, 4, 5],
#        [6, 7, 8]])

b = arange(3)
b

# Out[14]: array([0, 1, 2])

a + b

# Out[12]:
# array([[ 0,  2,  4],
#        [ 3,  5,  7],
#        [ 6,  8, 10]])

a - b

# array([[0, 0, 0],
#        [3, 3, 3],
#        [6, 6, 6]])

a * b

# Out[11]:
# array([[ 0,  1,  4],
#        [ 0,  4, 10],
#        [ 0,  7, 16]])

a < 5

# Out[12]:
# array([[ True,  True,  True],
#        [ True,  True, False],
#        [False, False, False]])

a ** 2

# Out[13]:
# array([[ 0,  1,  4],
#        [ 9, 16, 25],
#        [36, 49, 64]], dtype=int32)

a += 3
a

# Out[17]:
# array([[ 3,  4,  5],
#        [ 6,  7,  8],
#        [ 9, 10, 11]])

#######################################
# 矩阵内置操作
#######################################
from numpy import array as matrix, arange

a = arange(9).reshape(3,3)
a

# Out[10]:
# array([[0, 1, 2],
#        [3, 4, 5],
#        [6, 7, 8]])

a.max()

# Out[23]: 8

a.min()

# Out[24]: 0

a.sum()

# Out[25]: 36

#######################################
# 矩阵索引、拆分、遍历
#######################################
from numpy import array as matrix, arange

a = arange(25).reshape(5,5)
a

# Out[9]:
# array([[ 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]])

a[2,3]      # 取第3行第4列的元素

# Out[3]: 13

a[0:3,3]    # 取第1到3行第4列的元素

# Out[4]: array([ 3,  8, 13])

a[:,2]      # 取所有第二列元素

# Out[7]: array([ 2,  7, 12, 17, 22])

a[0:3,:]    # 取第1到3行的所有列

# Out[8]:
# array([[ 0,  1,  2,  3,  4],
#        [ 5,  6,  7,  8,  9],
#        [10, 11, 12, 13, 14]])

a[-1]   # 取最后一行

# Out[10]: array([20, 21, 22, 23, 24])

for row in a:   # 逐行迭代
    print(row)

# [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]

for element in a.flat:  # 逐元素迭代，从左到右，从上到下
    print(element)

# 0
# 1
# 2
# 3
# ...

#######################################
# 改变矩阵
#######################################
from numpy import array as matrix, arange

b = arange(20).reshape(5,4)

b

# Out[18]:
# array([[ 0,  1,  2,  3],
#        [ 4,  5,  6,  7],
#        [ 8,  9, 10, 11],
#        [12, 13, 14, 15],
#        [16, 17, 18, 19]])

b.ravel()

# Out[16]:
# array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
#        17, 18, 19])

b.reshape(4,5)

# Out[17]:
# array([[ 0,  1,  2,  3,  4],
#        [ 5,  6,  7,  8,  9],
#        [10, 11, 12, 13, 14],
#        [15, 16, 17, 18, 19]])

b.T     # reshape 方法不改变原矩阵的值，所以需要使用  .T  来获取改变后的值

# Out[19]:
# array([[ 0,  4,  8, 12, 16],
#        [ 1,  5,  9, 13, 17],
#        [ 2,  6, 10, 14, 18],
#        [ 3,  7, 11, 15, 19]])

#######################################
# 合并矩阵
#######################################
from numpy import array as matrix,newaxis
import numpy as np

d1 = np.floor(10*np.random.random((2,2)))
d2 = np.floor(10*np.random.random((2,2)))

d1

# Out[7]:
# array([[1., 0.],
#        [9., 7.]])

d2

# Out[9]:
# array([[0., 0.],
#        [8., 9.]])

np.vstack((d1,d2))  # 按列合并

# Out[10]:
# array([[1., 0.],
#        [9., 7.],
#        [0., 0.],
#        [8., 9.]])

np.hstack((d1,d2))  # 按行合并

# Out[11]:
# array([[1., 0., 0., 0.],
#        [9., 7., 8., 9.]])

np.column_stack((d1,d2)) # 按列合并

# Out[13]:
# array([[1., 0., 0., 0.],
#        [9., 7., 8., 9.]])

c1 = np.array([11,12])
c2 = np.array([21,22])

np.column_stack((c1,c2))

# Out[14]:
# array([[11, 21],
#        [12, 22]])

c1[:,newaxis]   # 添加一个“空”列

# Out[18]:
# array([[11],
#        [12]])

np.hstack((c1,c2))

# Out[27]: array([11, 12, 21, 22])

np.hstack((c1[:,newaxis],c2[:,newaxis]))

# Out[28]:
# array([[11, 21],
#        [12, 22]])

参考

1. NumPy官方文档