python
1.python中数组和矩阵乘法及使用总结
- 对数组的运算
import numpy as np
a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
a = np.mat(a)
a
--->>
matrix([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
b = np.array([[7, 8, 9],[4, 5, 6],[1, 2, 3]])
b = np.mat(b)
b
--->>
matrix([[7, 8, 9],
[4, 5, 6],
[1, 2, 3]])
a + b#矩阵的加减运算和数组运算一致，在对应位置相加减
--->>
matrix([[ 8, 10, 12],
[ 8, 10, 12],
[ 8, 10, 12]])
a * b#矩阵的乘用*即可表示
--->>
matrix([[ 18, 24, 30],
[ 54, 69, 84],
[ 90, 114, 138]])
b * a
--->>
matrix([[102, 126, 150],
[ 66, 81, 96],
[ 30, 36, 42]])
np.dot(b, a)# 使用dot与*的效果一样
--->>
matrix([[102, 126, 150],
[ 66, 81, 96],
[ 30, 36, 42]])
np.dot(a, b)
--->>
matrix([[ 18, 24, 30],
[ 54, 69, 84],
[ 90, 114, 138]])
c = np.array([1, 2, 3])#构建一个一行三列的数组
c
--->>
array([1, 2, 3])
a * c# 不符合矩阵运算规则
--->>
ValueError Traceback (most recent call last)
<ipython-input-19-fc01a05f2628> in <module>()
----> 1 a * c
/home/icrclsc/anaconda3/lib/python3.5/site-packages/numpy/matrixlib/defmatrix.py in __mul__(self, other)
307 if isinstance(other, (N.ndarray, list, tuple)) :
308 # This promotes 1-D vectors to row vectors
--> 309 return N.dot(self, asmatrix(other))
310 if isscalar(other) or not hasattr(other, '__rmul__') :
311 return N.dot(self, other)
ValueError: shapes (3,3) and (1,3) not aligned: 3 (dim 1) != 1 (dim 0)
c * a
--->>
matrix([[30, 36, 42]])
np.dot(c, a)# 与矩阵运算一致
--->>
matrix([[30, 36, 42]])
np.dot(a, c)# 自动将a转换成3行1列参与运算,返回结果格式已经变为1行3列而非3行一列的矩阵
--->>
matrix([[14, 32, 50]])
c =c.reshape(3, 1)
c
--->>
array([[1],
[2],
[3]])
a * c
--->>
matrix([[14],
[32],
[50]])
c * a
--->>
ValueError Traceback (most recent call last)
<ipython-input-25-608e57f1304c> in <module>()
----> 1 c * a
/home/icrclsc/anaconda3/lib/python3.5/site-packages/numpy/matrixlib/defmatrix.py in __rmul__(self, other)
313
314 def __rmul__(self, other):
--> 315 return N.dot(other, self)
316
317 def __imul__(self, other):
ValueError: shapes (3,1) and (3,3) not aligned: 1 (dim 1) != 3 (dim 0)
- 矩阵求逆，转置，求迹
a.T# a 的转置
--->>
matrix([[1, 4, 7],
[2, 5, 8],
[3, 6, 9]])
a.H# a的共轭转置
--->>
matrix([[1, 4, 7],
[2, 5, 8],
[3, 6, 9]])
b = np.eye(3)
b
--->>
array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])
b = b * 3
b
--->>
array([[3., 0., 0.],
[0., 3., 0.],
[0., 0., 3.]])
b = np.mat(b)
b
matrix([[3., 0., 0.],
[0., 3., 0.],
[0., 0., 3.]])
b.I
matrix([[0.33333333, 0. , 0. ],
[0. , 0.33333333, 0. ],
[0. , 0. , 0.33333333]])
np.trace(b)
9.0
