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]])
