机器学习 番外篇 05 numpy之矩阵运算

矩阵运算

# 给定一个向量，让所有元素*2

import numpy as np
l=np.arange(5)
a=np.array(2*e for e in l)
a

>>>array(<generator object <genexpr> at 0x10ee9e830>, dtype=object)

l

>>>array([0, 1, 2, 3, 4])

l*2

>>>array([0, 2, 4, 6, 8])

l / 2

>>>array([0. , 0.5, 1. , 1.5, 2. ])

l //2

>>>array([0, 0, 1, 1, 2])

l

>>>array([0, 1, 2, 3, 4])

np.abs(l)

>>>array([0, 1, 2, 3, 4])

np.cos(l)

>>>array([ 1.        ,  0.54030231, -0.41614684, -0.9899925 , -0.65364362])

np.exp(l)

>>>array([ 1.        ,  2.71828183,  7.3890561 , 20.08553692, 54.59815003])

np.power(3,l) # l^3

>>>array([ 1,  3,  9, 27, 81])

np.log2(l)

/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in log2
  """Entry point for launching an IPython kernel.

>>>array([     -inf, 0.       , 1.       , 1.5849625, 2.       ])

矩阵运算

aa=np.arange(4).reshape(2,2)
aa

>>>array([[0, 1],
       [2, 3]])

b=np.full((2,2),10)

b

>>>array([[10, 10],
       [10, 10]])

aa+b

>>>array([[10, 11],
       [12, 13]])

aa-b

>>>array([[-10,  -9],
       [ -8,  -7]])

# 矩阵乘法
aa.dot(b)

>>>array([[10, 10],
       [50, 50]])

# 矩阵转置
aa.T

>>>array([[0, 2],
       [1, 3]])

向量和矩阵的运算

v=np.array([1,2])

aa

>>>array([[0, 1],
       [2, 3]])

v+aa

>>>array([[1, 3],
       [3, 5]])

np.vstack([v]*aa.shape[0]) # [v]*2

>>>array([[1, 2],
       [1, 2]])

# 扩展
np.tile(v,(2,1))

>>>array([[1, 2],
       [1, 2]])

v*aa

>>>array([[0, 2],
       [2, 6]])

# 矩阵的逆
np.linalg.inv(aa)

>>>array([[-1.5,  0.5],
       [ 1. ,  0. ]])

# 伪逆矩阵
pinvaa=np.linalg.pinv(aa)

pinvaa

>>>array([[-1.50000000e+00,  5.00000000e-01],
       [ 1.00000000e+00,  4.21097322e-17]])