Python中的矩阵操作
Numpy
通过观察Python的自有数据类型，我们可以发信啊Python原生并不提供多为数组的操作，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
- NumPy官方文档