Linear regression

#本次采用pytorch实现
#探究房屋状况的俩个因素,房龄和面积
#公式 price = w(area)*area+w(age)*age+b

#损失函数:用于衡量价格预测值与真实值之间的误差,通常我们会选取一个非负数作为误差，且数值越小表示误差越小
#优化函数 ->直接用公式表达出来。这类解叫作解析解
#        ->只能通过优化算法有限次迭代模型参数来尽可能降低损失函数的值。这类解叫作数值解
#优化函数的有以下两个步骤：
#        (i)初始化模型参数，一般来说使用随机初始化；
#        (ii)我们在数据上迭代多次，通过在负梯度方向移动参数来更新每个参数。

#本次采用随机梯度下降

#从零开始的实现
import torch
import time

# 初始化变量 a, b 作为 1000 维向量,进行demo
n = 1000
a = torch.ones(n)
b = torch.ones(n)

# 定义一个计时器类来记录时间
class Timer(object):
    """Record multiple running times."""
    def __init__(self):
        self.times = []
        self.start()

    def start(self):
        # start the timer
        self.start_time = time.time()

    def stop(self):
        # stop the timer and record time into a list
        self.times.append(time.time() - self.start_time)
        return self.times[-1]

    def avg(self):
        # calculate the average and return
        return sum(self.times)/len(self.times)

    def sum(self):
        # return the sum of recorded time
        return sum(self.times)

#使用for循环按元素逐一做标量加法timer = Timer()
timer = Timer()
c = torch.zeros(n)
for i in range(n):
    c[i] = a[i] + b[i]
'%.9f sec' % timer.stop()

#使用torch来将两个向量直接做矢量加法
timer.start()
d = a + b
'%.9f sec' % timer.stop()
#结果很明显,后者比前者运算速度更快。因此，我们应该尽可能采用矢量计算，以提升计算效率

#线性回归模型从零开始的实现
# 导入包和模块
import torch
from IPython import display
from matplotlib import pyplot as plt
import numpy as np
import random

print(torch.__version__)

#生成数据集,根据之上的公式生成1,000个数据,特征为2
# 设置输入特征编号
num_inputs = 2
# set example number
num_examples = 1000

# 设置真实权重和偏差以生成相应的标签
true_w = [2, -3.4]
true_b = 4.2

features = torch.randn(num_examples, num_inputs,
                      dtype=torch.float32) 
# 返回一个符合均值为0，方差为1的正态分布（标准正态分布）中填充随机数的张量
labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
labels += torch.tensor(np.random.normal(0, 0.01, size=labels.size()),
                       dtype=torch.float32)

#使用图像来展示生成的数据
plt.scatter(features[:, 1].numpy(), labels.numpy(), 1);

#读取数据集
def data_iter(batch_size, features, labels):
    num_examples = len(features)
    indices = list(range(num_examples))
    random.shuffle(indices)  # 随机读取10个样本
    for i in range(0, num_examples, batch_size):
        j = torch.LongTensor(indices[i: min(i + batch_size, num_examples)]) # 最后一次可能不够整批
        #使用坐标形式存储稀疏矩阵
        yield  features.index_select(0, j), labels.index_select(0, j)
        #return

batch_size = 10

for X, y in data_iter(batch_size, features, labels):
    print(X, '\n', y)
    break

#初始化模型参数
w = torch.tensor(np.random.normal(0, 0.01, (num_inputs, 1)), dtype=torch.float32)
b = torch.zeros(1, dtype=torch.float32)

w.requires_grad_(requires_grad=True)
b.requires_grad_(requires_grad=True)

#定义模型
def linreg(X, w, b):
    return torch.mm(X, w) + b
#torch.mm是两个矩阵相乘，即两个二维的张量相乘

#定义损失函数
def squared_loss(y_hat, y): 
    return (y_hat - y.view(y_hat.size())) ** 2 / 2

#定义优化函数
def sgd(params, lr, batch_size): 
    for param in params:
        param.data -= lr * param.grad / batch_size #使用 .data 操作无梯度轨迹的参数

# 超参数初始化
lr = 0.03
num_epochs = 5

net = linreg
loss = squared_loss

# 训练
for epoch in range(num_epochs):  # 训练num_epochs次
    # 在每个 epoch 中，dataset 中的所有样本都将被使用一次
    
    # X 是特征，y 是批次样本的标签
    for X, y in data_iter(batch_size, features, labels):
        l = loss(net(X, w, b), y).sum()  
        # calculate the gradient of batch sample loss 
        l.backward()  
        # 使用小批量随机梯度下降迭代模型参数
        sgd([w, b], lr, batch_size)  
        # reset parameter gradient
        w.grad.data.zero_()
        b.grad.data.zero_()
    train_l = loss(net(features, w, b), labels)
    print('epoch %d, loss %f' % (epoch + 1, train_l.mean().item()))

w, true_w, b, true_b

#线性回归模型使用pytorch的简洁实现
import torch
from torch import nn
import numpy as np
torch.manual_seed(1)

print(torch.__version__)
torch.set_default_tensor_type('torch.FloatTensor')

#读取数据集
import torch.utils.data as Data

batch_size = 10

# combine featues and labels of dataset
dataset = Data.TensorDataset(features, labels)

# put dataset into DataLoader
data_iter = Data.DataLoader(
    dataset=dataset,            # torch TensorDataset format
    batch_size=batch_size,      # mini batch size
    shuffle=True,               # whether shuffle the data or not
    num_workers=2,              # read data in multithreading
)
for X, y in data_iter:
    print(X, '\n', y)
    break

#定义模型
class LinearNet(nn.Module):
    def __init__(self, n_feature):
        super(LinearNet, self).__init__()      # 调用父函数来初始化
        self.linear = nn.Linear(n_feature, 1)  # 函数原型：`torch.nn.Linear(in_features, out_features,bias=True)

    def forward(self, x):
        y = self.linear(x)
        return y
    
net = LinearNet(num_inputs) #实例化
print(net)

#初始化多层网络的方法
# 方法一
net = nn.Sequential(
    nn.Linear(num_inputs, 1)
    # other layers can be added here
    )

# 方法二
net = nn.Sequential()
net.add_module('linear', nn.Linear(num_inputs, 1))
# net.add_module ......

# 方法三
from collections import OrderedDict
net = nn.Sequential(OrderedDict([
          ('linear', nn.Linear(num_inputs, 1))
          # ......
        ]))

print(net)
print(net[0])

#初始化模型参数
from torch.nn import init

init.normal_(net[0].weight, mean=0.0, std=0.01)
init.constant_(net[0].bias, val=0.0)  # or you can use `net[0].bias.data.fill_(0)` to modify it directly

for param in net.parameters():
    print(param)

#定义损失函数
loss = nn.MSELoss()    # nn 内置平方损失函数
                       # function prototype: `torch.nn.MSELoss(size_average=None, reduce=None, reduction='mean')`

#定义优化函数
import torch.optim as optim

optimizer = optim.SGD(net.parameters(), lr=0.03)   # built-in random gradient descent function
print(optimizer)  # function prototype: `torch.optim.SGD(params, lr=, momentum=0, dampening=0, weight_decay=0, nesterov=False)`

#训练
num_epochs = 3
for epoch in range(1, num_epochs + 1):
    for X, y in data_iter:
        output = net(X)
        l = loss(output, y.view(-1, 1))
        optimizer.zero_grad() # reset gradient, equal to net.zero_grad()
        l.backward()
        optimizer.step()
    print('epoch %d, loss: %f' % (epoch, l.item()))

#结果比较
dense = net[0]
print(true_w, dense.weight.data)
print(true_b, dense.bias.data)