%matplotlib inline
import sympy
import numpy as np
import matplotlib.pyplot as plt
from sympy.abc import x as a,y as b

# 模拟函数 y=3x-1

#自变量
x=np.linspace(-5,5,num=1000)
#加入噪声
noise=np.random.rand(len(x))*2-1
#因变量
y=3*x-1+noise

plt.figure(figsize=(10,10))
plt.scatter(x,y,s=1)

y=ax+b  #目标函数

e=1/2*Σ([axi+b]-yi)^2   #代价函数，求使得代价函数为最小值时，对应的a和b

对a求偏导->Σ(axi+b-yi)*xi

对b求偏导->Σ(axi+b-yi)

result=sympy.solve([
  np.sum((a*x+b-y)*x),
  np.sum(a*x+b-y)],[a,b])
print(result)	#{x: 3.01182977621975, y: -1.00272253325765}

plt.figure(figsize=(10,10))
plt.scatter(x,y,s=1)
plt.plot(x,result[a]*x+result[b],c='red')

print(type(a),type(b))	#<class 'sympy.core.symbol.Symbol'> <class 'sympy.core.symbol.Symbol'>

# 注意这里覆盖了sympy.abc的a和b
# 设定a和b的起始点
a,b=0.1,0.1

#步长，也称作学习率
alpha=0.00001

#循环一千次结束
for i in range(1000):
  a-=alpha*np.sum((a*x+b-y)*x)
  b-=alpha*np.sum(a*x+b-y)

print(a,b)	#3.0118297762197526 -1.002674927350334

plt.figure(figsize=(10,10))
plt.scatter(x,y,s=1)
plt.plot(x,a*x+b,c='black')

print(type(a),type(b))	#<class 'numpy.float64'> <class 'numpy.float64'>