多项式函数拟合

import torch
import matplotlib.pyplot as plt
import numpy as np

#生成一个人工数据集
def create(w,b,sample):
    x = torch.normal(0,1,size=(sample,len(w)))
    y = w[0]*x + w[1]*(x**2) +w[2] * (x**3) + b
    y += torch.normal(0,0.01,y.shape)
    return x,y


t_w=torch.tensor([1.2,-3.4,5.6])
t_b=5

plt.Figure()
features,lables=create(t_w,t_b,20)
plt.plot(features,lables,'r+')
plt.show()


w=torch.normal(0,0.01,t_w.shape,requires_grad=True)
b=torch.zeros(1,requires_grad=True)
lr=0.025

def net(x,w,b):
    return  (w[0]*x + w[1]*(x**2) +w[2] * (x**3) + b)

def sgd(params,lr):
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad
            param.grad.zero_()

def Loss(y_hat,y):
    return (y_hat-y)**2/2/len(y)

def Train(x,y,w,b,lr):
    for epoch in range(100):
        y_hat=net(x,w,b)
        l=Loss(y_hat,y).sum()
        l.backward()
        sgd([w,b],lr)
        print('loss=%.4f' % l)

Train(features,lables,w,b,lr)
w=w.detach().numpy()
b=b.detach().numpy()
print(w,b)

与需要拟合的多项式接近