梯度下降法

// 梯度下降法.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。
//

#include "pch.h"
#include <iostream>
#define maxn 105
#include <cmath>
#include <algorithm>
#include<fstream>
#include <cstdio>
using namespace std;

int n, m;  //n个特征(因子),m个数据
double theta[maxn];//参数集
double temp[maxn];
double data[maxn][maxn];//数据集
double Y[maxn];//结果集
double hx[maxn];
const double eps = 1e-9;//1*10的-9次方
double alpha = 0.001;
double ave[maxn];
void Mean_Normaliazation()
{
	
	for (int i = 0;i <= n;++i)
	{
		double maxim = -1e9;
		double minum = 1e9;
		double tmp = 0;
		for (int j = 1;j <= m;++j)
		{
			tmp += ::data[j][i];
		}
		tmp /= m;
		double mb = 0;
		for (int j = 1;j <= m;++j)
		{
			mb += (::data[j][i] - tmp)*(::data[j][i] - tmp);
		}
		mb /= m;
		mb = sqrt(mb);
		for (int j = 1;j <= m;++j)
		{
			::data[j][i] = (::data[j][i] - tmp) / mb;
		}
	}
	double maxim = -1e9;
	/*double tmp=0;
	for(int i=1;i<=m;++i)
	{
		maxim=max(Y[i],maxim);
		tmp+=Y[i];
	}
	tmp/=m;
	for(int i=1;i<=m;++i)
	{
		Y[i]=(Y[i]-tmp)/maxim;
	}*/
}
double h(int x)//计算假设函数
{
	double res = 0;
	for (int i = 0;i <= n;++i)
	{
		res += theta[i] * ::data[x][i];
	}
	return res;
}
double J_theta()//计算cost function
{
	double res = 0;
	for (int i = 1;i <= m;++i)
	{
		res += (h(i) - Y[i])*(h(i) - Y[i]);
	}
	res = res / (2 * m);
	return res;
}
double f(int x)//求偏导数
{
	double res = 0;
	for (int i = 1;i <= m;++i)
	{
		res += hx[i] * ::data[i][x];
	}
	res /= m;
	return res;
}
void Gradient_Descent()//梯度下降
{
	for (int i = 1;i <= m;++i)
	{
		::data[i][0] = 1;
	}
	for (int i = 0;i <= n;++i)
	{
		theta[i] = 1;//初始化
	}
	double now, nex;
	do
	{
		now = J_theta();
		for (int i = 1;i <= m;++i)
		{
			hx[i] = h(i) - Y[i];
		}
		for (int i = 0;i <= n;++i)
		{
			temp[i] = theta[i] - alpha * f(i);
		}
		for (int i = 0;i <= n;++i)
		{
			theta[i] = temp[i];
		}
		nex = J_theta();
		//cout<<J_theta()<<endl;
	} while (abs(nex - now) > eps);
}
int main()
{
	ifstream fin("E:\\iris.data.txt");//读入文本文件内的数据
	//freopen("in.txt", "r", stdin);
	cout << "请输入特征数、数据个数";
	cin >> n >> m;
	for (int i = 1;i <= m;++i)
	{
		for (int j = 1;j <= n;++j)
		{
			cin >> ::data[i][j];
		}
	}
	for (int i = 1;i <= m;++i)
	{
		cin >> Y[i];
	}
	Mean_Normaliazation();
	Gradient_Descent();
	for (int i = 0;i <= n;++i)
	{
		cout << theta[i];
		//printf("%.2lf\n", theta[i]);
	}
	return 0;
}