Python知识(6)--numpy做矩阵运算

矩阵运算

论numpy中matrix 和 array的区别：http://blog.csdn.net/vincentlipan/article/details/20717163

matrix 和 array的差别： Numpy matrices必须是2维的,但是 numpy arrays (ndarrays) 可以是多维的（1D，2D，3D····ND）. Matrix是Array的一个小的分支，包含于Array。所以matrix 拥有array的所有特性。

1.基本运算

import numpy as np

a = np.array([[-1,2],[2,3]])
b = np.array([[3,4],[4,5]])
print '\n a:\n',a
print '\n b:\n',b

##转置
print '\n a transpose:\n',a.T

##共扼矩阵
#print '\n a H:\n',a.I

##逆矩阵
print '\n a inv:\n',np.linalg.inv(a) # 求逆

##转置
print '\n a transpose:\n',a.T

# a + b，矩阵相加
print "\n a+b: \n",a+b

# a - b，矩阵相减
print "\n a-b: \n",a-b

#2x2 矩阵，矩阵相乘
print "\n a mul b:\n",a.dot(b.T)

#2x3矩阵，矩阵点乘
print "\n a dot b: \n",a*b

#2x3矩阵，矩阵点除
print "\n a/b \n:",a/np.linalg.inv(b)

#求迹
print "\n a trace",np.trace(a) 

#特征，特征向量
eigval,eigvec = np.linalg.eig(a) 
#eigval = np.linalg.eigvals(a) #直接求解特征值

print "\n a eig value:\n",eigval,
print'\n a eig vector:\n',eigvec

运算结果：

a:
[[-1  2]
 [ 2  3]]

 b:
[[3 4]
 [4 5]]

 a transpose:
[[-1  2]
 [ 2  3]]

 a inv:
[[-0.42857143  0.28571429]
 [ 0.28571429  0.14285714]]

 a transpose:
[[-1  2]
 [ 2  3]]

 a+b: 
[[2 6]
 [6 8]]

 a-b: 
[[-4 -2]
 [-2 -2]]

 a mul b:
[[ 5  6]
 [18 23]]

 a dot b: 
[[-3  8]
 [ 8 15]]

 a/b 
: [[ 0.2  0.5]
 [ 0.5 -1. ]]

 a trace 2

 a eig value:
[-1.82842712  3.82842712] 
 a eig vector:
[[-0.92387953 -0.38268343]
 [ 0.38268343 -0.92387953]]

2.特殊矩阵

import numpy as np
a = np.zeros([4,5]) # all zero
print  '\nall zero \n',a
a = np.ones([7,6]) # all one
print  '\nall one \n',a
a = np.eye(4,7) # 4x7 diagonal
print  '\n4x7 diagonal \n',a
a = np.diag(range(5)) # 5x5 diagonal
print  '\n5x5 diagonal \n',a
a = np.empty((2,3))
print '\nempty \n',a

a = np.arange(10, 30, 5) # array([10, 15, 20, 25]), 1-D
print '\n array([10, 15, 20, 25]), 1-D \n',a
a = np.linspace(0, 2, 9) # 9 numbers from 0 to 2
print '\n9 numbers from 0 to 2 \n',a
a = np.random.random((2,3)) # random matrics
print  '\nrandom matrics \n',a
import numpy as np
a = np.zeros([4,5]) # all zero
print  '\nall zero \n',a
a = np.ones([7,6]) # all one
print  '\nall one \n',a
a = np.eye(4,7) # 4x7 diagonal
print  '\n4x7 diagonal \n',a
a = np.diag(range(5)) # 5x5 diagonal
print  '\n5x5 diagonal \n',a
a = np.empty((2,3))
print '\nempty \n',a
​
a = np.arange(10, 30, 5) # array([10, 15, 20, 25]), 1-D
print '\n array([10, 15, 20, 25]), 1-D \n',a
a = np.linspace(0, 2, 9) # 9 numbers from 0 to 2
print '\n9 numbers from 0 to 2 \n',a
a = np.random.random((2,3)) # random matrics
print  '\nrandom matrics \n',a

运算结果：

all zero 
[[ 0.  0.  0.  0.  0.]
 [ 0.  0.  0.  0.  0.]
 [ 0.  0.  0.  0.  0.]
 [ 0.  0.  0.  0.  0.]]

all one 
[[ 1.  1.  1.  1.  1.  1.]
 [ 1.  1.  1.  1.  1.  1.]
 [ 1.  1.  1.  1.  1.  1.]
 [ 1.  1.  1.  1.  1.  1.]
 [ 1.  1.  1.  1.  1.  1.]
 [ 1.  1.  1.  1.  1.  1.]
 [ 1.  1.  1.  1.  1.  1.]]

4x7 diagonal 
[[ 1.  0.  0.  0.  0.  0.  0.]
 [ 0.  1.  0.  0.  0.  0.  0.]
 [ 0.  0.  1.  0.  0.  0.  0.]
 [ 0.  0.  0.  1.  0.  0.  0.]]

5x5 diagonal 
[[0 0 0 0 0]
 [0 1 0 0 0]
 [0 0 2 0 0]
 [0 0 0 3 0]
 [0 0 0 0 4]]

empty 
[[ 0.06012241  0.30847312  0.20174074]
 [ 0.37654373  0.71036135  0.15586512]]

 array([10, 15, 20, 25]), 1-D 
[10 15 20 25]

9 numbers from 0 to 2 
[ 0.    0.25  0.5   0.75  1.    1.25  1.5   1.75  2.  ]

random matrics 
[[ 0.44052293  0.42283564  0.44825331]
 [ 0.66735609  0.32664018  0.17015328]]