线性回归

//线性回归
#include <iostream>
#include <math.h>
#include <fstream>
#include <process.h>

using namespace std;

class regression
{
private:
 int i, n;
 double a, b, sum_x, sum_y, sum_xsq, sum_xy, rsq, rsq_num, rsq_denom;
 double *y_model, *x, *y;

public:
 regression()
 {
  sum_x = 0.0;
  sum_y = 0.0;
  sum_xsq = 0.0;
  sum_xy = 0.0;
  rsq_num = 0.0;
  rsq_denom = 0.0;
 }
 void regression_input();
 void sline();
 void exp1();
 void exp2();
 void exp3();
 void power();
 void logarithmic();
 void square_root();
 void one_third();
 void inverse();
 void summations();
 void r_sq();
 ~regression()
 {
  delete[] x, y, y_model;
 }
};

void main()
{
 int choice;
 cout << "\n可用下列方程拟合：" << endl;
 cout << "\n1. 直线：Y = A * X + B" << endl;
 cout << "\n2. 指数1：Y = A * (B ^ X)" << endl;
 cout << "\n3. 指数2：Y = A * EXP(B * X)" << endl;
 cout << "\n4. 指数3：Y = A * EXP(X) + B" << endl;
 cout << "\n5. 幂函数：Y = A * (X ^ B)" << endl;
 cout << "\n6. 对数函数：Y = A * LN(X) + B" << endl;
 cout << "\n7. 平方根函数：Y = A * SQRT(X) + B" << endl;
 cout << "\n8. 1/3次幂函数：Y = A * (X ^ 0.33) + B" << endl;
 cout << "\n9. 反比函数：Y = A / X + B" << endl;
 cout << "\n输入你的选择（1 - 9）";
 cin >> choice;
 regression curvefit;
 curvefit.regression_input();
 if (choice == 1) {curvefit.sline();}
 if (choice == 2) {curvefit.exp1();}
 if (choice == 3) {curvefit.exp2();}
 if (choice == 4) {curvefit.exp3();}
 if (choice == 5) {curvefit.power();}
 if (choice == 6) {curvefit.logarithmic();}
 if (choice == 7) {curvefit.square_root();}
 if (choice == 8) {curvefit.one_third();}
 if (choice == 9) {curvefit.inverse();}
}

void regression::regression_input()
{
 ifstream fin("regression.dat");
 fin >> n;
 x = new double[n];
 y = new double[n];
 y_model = new double[n];
 for (i = 0; i < n; i++)
 {
  fin >> x[i] >> y[i];
 }
 fin.close();
}

void regression::sline()
{
 summations();
 a = (n * sum_xy - sum_x * sum_y) / (n * sum_xsq - pow(sum_x, 2));
 b = (sum_y - a * sum_x) / n;
 cout << "\n拟合直线：Y = A * X + B" << endl;
 cout << "\nA = " << a << " B = " << b;
 for (i = 0; i < n; i ++)
 {
  y_model[i] = a * x[i] + b;
 }
 r_sq();
}

void regression::exp1()
{
 for (i = 0; i < n; i++)
 {
  if (y[i] <= 0.0)
  {
   cout << "\n不可能拟合指数函数，失败..." << endl;
   exit(0);
  }
 }
 for (i = 0; i < n; i++)
 {
  y[i] = log(y[i]);
 }
 summations();
 b = (n * sum_xy - sum_x * sum_y) / (n * sum_xsq - pow(sum_x, 2));
 a = (sum_y - b * sum_x) / n;
 a = exp(a);
 b = exp(b);
 cout << "\n拟合指数函数1：Y  = A * (B ^ X)" << endl;
 cout << "\nA = " << a << " B = " << b;
 for (i = 0; i < n; i++)
 {
  y_model[i] = log(b) * x[i] + log(a);
 }
 r_sq();
}

void regression::exp2()
{
 for (i = 0; i < n; i++)
 {
  if (y[i] <= 0.0)
  {
   cout << "\n不可能拟合指数函数，失败..." << endl;
   exit(0);
  }
 }
 for (i = 0; i < n; i++)
 {
  y[i] = log(y[i]);
 }
 summations();
 b = (n * sum_xy - sum_x * sum_y) / (n * sum_xsq - pow(sum_x, 2));
 a = (sum_y - b * sum_x) / n;
 a = exp(a);
 cout << "\n拟合指数函数2：Y  = A * EXP(B * X)" << endl;
 cout << "\nA = " << a << " B = " << b;
 for (i = 0; i < n; i++)
 {
  y_model[i] = b * x[i] + log(a);
 }
 r_sq();
}

void regression::exp3()
{
 for (i = 0; i < n; i++)
 {
  x[i] = exp(x[i]);
 }
 summations();
 a = (n * sum_xy - sum_x * sum_y) / (n * sum_xsq - pow(sum_x, 2));
 b = (sum_y - a * sum_x) / n;
 cout << "\n拟合指数函数3：Y  = A * EXP(X) + B" << endl;
 cout << "\nA = " << a << " B = " << b;
 for (i = 0; i < n; i++)
 {
  y_model[i] = a * x[i] + b;
 }
 r_sq();
}

void regression::power()
{
 for (i = 0; i < n; i++)
 {
  if ((y[i] <= 0.0) || (x[i] <= 0.0))
  {
   cout << "\n不可能拟合幂函数，失败..." << endl;
   exit(0);
  }
 }
 for (i = 0; i < n; i++)
 {
  y[i] = log(y[i]);
  x[i] = log(x[i]);
 }
 summations();
 b = (n * sum_xy - sum_x * sum_y) / (n * sum_xsq - pow(sum_x, 2));
 a = (sum_y - b * sum_x) / n;
 a = exp(a);
 cout << "\n拟合幂函数：Y = A * (X ^ B)" << endl;
 cout << "\nA = " << a << " B = " << b;
 for (i = 0; i < n; i++)
 {
  y_model[i] = b * x[i] + log(a);
 }
 r_sq();
}

void regression::logarithmic()
{
 for (i = 0; i < n; i++)
 {
  if (x[i] <= 0.0)
  {
   cout << "\n不可能拟合对数函数，失败..." << endl;
   exit(0);
  }
 }
 for (i = 0; i < n; i++)
 {
  x[i] = log(x[i]);
 }
 summations();
 a = (n * sum_xy - sum_x * sum_y) / (n * sum_xsq - pow(sum_x, 2));
 b = (sum_y - a * sum_x) / n;
 cout << "\n拟合对数函数：Y = A * LN(X) + B" << endl;
 cout << "\nA = " << a << " B = " << b;
 for (i = 0; i < n; i++)
 {
  y_model[i] = a * x[i] + b;
 }
 r_sq();
}

void regression::square_root()
{
 for (i = 0; i < n; i++)
 {
  if (x[i] < 0.0)
  {
   cout << "\n不可能拟合平方根函数，失败..." << endl;
   exit(0);
  }
 }
 for (i = 0; i < n; i++)
 {
  x[i] = sqrt(x[i]);
 }
 summations();
 a = (n * sum_xy - sum_x * sum_y) / (n * sum_xsq - pow(sum_x, 2));
 b = (sum_y - a * sum_x) / n;
 cout << "\n拟合平方根函数：Y = A * SQRT(X) + B" << endl;
 cout << "\nA = " << a << " B = " << b;
 for (i = 0; i < n; i++)
 {
  y_model[i] = a * x[i] + b;
 }
 r_sq();
}

void regression::one_third()
{
 for (i = 0; i < n; i++)
 {
  if (x[i] < 0.0)
  {
   cout << "\n不可能拟合1/3次幂函数，失败..." << endl;
   exit(0);
  }
 }
 for (i = 0; i < n; i++)
 {
  x[i] = pow(x[i], 0.33);
 }
 summations();
 a = (n * sum_xy - sum_x * sum_y) / (n * sum_xsq - pow(sum_x, 2));
 b = (sum_y - a * sum_x) / n;
 cout << "\n拟合1/3次幂函数：Y = A * (X ^ 0.33) + B" << endl;
 cout << "\nA = " << a << " B = " << b;
 for (i = 0; i < n; i++)
 {
  y_model[i] = a * x[i] + b;
 }
 r_sq();
}

void regression::inverse()
{
 for (i = 0; i < n; i++)
 {
  if (x[i] == 0.0)
  {
   cout << "\n不可能拟合反比函数，失败..." << endl;
   exit(0);
  }
 }
 for (i = 0; i < n; i++)
 {
  x[i] = 1.0 / x[i];
 }
 summations();
 a = (n * sum_xy - sum_x * sum_y) / (n * sum_xsq - pow(sum_x, 2));
 b = (sum_y - a * sum_x) / n;
 cout << "\n拟合反比函数：Y = A / X + B" << endl;
 cout << "\nA = " << a << " B = " << b;
 for (i = 0; i < n; i++)
 {
  y_model[i] = a * x[i] + b;
 }
 r_sq();
}

void regression::summations()
{
 for (i = 0; i < n; i++)
 {
  sum_x += x[i];
  sum_y += y[i];
  sum_xsq += pow(x[i], 2);
  sum_xy += x[i] * y[i];
 }
}

void regression::r_sq()
{
 for (i = 0; i < n; i++)
 {
  rsq_num += pow((y_model[i] - sum_y / n), 2);
  rsq_denom += pow((y[i] - sum_y / n), 2);
 }
 rsq = rsq_num / rsq_denom;
 cout << "\nr^2 = " << rsq << endl;
}