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]])