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]])