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  1. /// @file     power_regression_approximation.cpp
  2. /// @author   Vo Hoang Anh, <spyofgame200@gmail.com>
  3. /// @brief    This is a simple implementation of the power regression approximation
  4. ///           With given array (x[]) and (y[]) at same size (n)
  5. ///           It will find constant (a), (b) that provides
  6. ///           Approximation function f(x) = a * x[i] ^ b ~ y[i] 
  7. ///           
  8. /// @license  Public domain.
  9.  
  10. #include <iostream>
  11. #include <iomanip>
  12. #include <cmath>
  13.  
  14. using namespace std;
  15.  
  16. /// Size limitation
  17. const int LIM = 1e6 + 16;
  18.  
  19. /// Given array
  20. int n;
  21. long double x[LIM], y[LIM];
  22.  
  23. /// Constant need to find
  24. long double a, b;
  25.  
  26. /// set it to (-1) if you only need the approximation function
  27. /// Number of digits after decimal points of (a) and (b)
  28. int w = 15;
  29.  
  30. /// First min(k, n) number to be comparing f(x[i]) vs (y[i])
  31. int k = 0;
  32.  
  33. /// Funtion: a * x^b ~ y
  34. long double f(long double x) { return a * pow(x, b); }
  35. int main()
  36. {
  37.     /// Input array
  38.     cin >> n;
  39.     for (int i = 1; i <= n; ++i) cin >> x[i];
  40.     for (int i = 1; i <= n; ++i) cin >> y[i];
  41.  
  42.     /// Detail information
  43.     cin >> w >> k;
  44.  
  45.     /// Precalculating
  46.     long double sigma_ln_x = 0;
  47.     long double sigma_ln_y = 0;
  48.     long double sigma_ln_xx = 0;
  49.     long double sigma_ln_xy = 0;
  50.     for (int i = 1; i <= n; ++i)
  51.     {
  52.         long double tx = log(x[i]);
  53.         long double ty = log(y[i]);
  54.         sigma_ln_x += tx;
  55.         sigma_ln_y += ty;
  56.         sigma_ln_xx += tx * tx;
  57.         sigma_ln_xy += tx * ty;
  58.     }
  59.  
  60.     /// Power approximation constant
  61.     b = ((n * sigma_ln_xy) - (sigma_ln_x * sigma_ln_y))
  62.       / ((n * sigma_ln_xx) - (sigma_ln_x * sigma_ln_x));
  63.  
  64.     /// Base approximation constant
  65.     a = exp((sigma_ln_y - b * sigma_ln_x) / n);
  66.  
  67.     /// Output such function
  68.     cout << setprecision(w) << "Approximation Function: f(x) =   " << a << " * x ^(" << b << ")" << endl;
  69.  
  70.     /// Incase you dont need error
  71.     if (w == -1) return 0;
  72.  
  73.     /// Calculating error
  74.     long double Sigma_error_value_down = 0;
  75.     long double Sigma_error_value_up   = 0;
  76.     long double Sigma_error_percent_down = 0;
  77.     long double Sigma_error_percent_up   = 0;
  78.     long double Sigma_error_value   = 0;
  79.     long double Sigma_error_percent = 0;
  80.  
  81.     k = min(k, n);
  82.     if (k) cout << "\nComparing f(x[i]) vs y[i]:\n";
  83.     for (int i = 1; i <= n; ++i)
  84.     {
  85.         long double Error_value = y[i] - f(x[i]);
  86.         long double Error_percent = Error_value / y[i] * 100;
  87.         if (i <= k) /// Comparing f(x[i]) vs (y[i])
  88.         {
  89.             cout << "At: " << setw(6) << i << " | ";
  90.             cout << setprecision(w) << fixed << "<" << f(x[i]) << " -> " << y[i] << ">   =   ";
  91.             cout << setprecision(w) << fixed << Error_value << " ~ " << Error_percent << " %" << endl;
  92.         } 
  93.  
  94.         if (Error_value < 0)   Sigma_error_value_down   += Error_value;
  95.         if (Error_value > 0)   Sigma_error_value_up     += Error_value;
  96.         Sigma_error_value   += fabs(Error_value);
  97.  
  98.         if (Error_percent < 0) Sigma_error_percent_down += Error_percent;
  99.         if (Error_percent > 0) Sigma_error_percent_up   += Error_percent;
  100.         Sigma_error_percent += fabs(Error_percent);
  101.     }
  102.  
  103.     /// Average error
  104.     long double Average_error_value_down   = Sigma_error_value_down   / n;
  105.     long double Average_error_value_up     = Sigma_error_value_up     / n;
  106.     long double Average_error_value        = Sigma_error_value        / n;
  107.     long double Average_error_percent_down = Sigma_error_percent_down / n;
  108.     long double Average_error_percent_up   = Sigma_error_percent_up   / n;
  109.     long double Average_error_percent      = Sigma_error_percent      / n;
  110.  
  111.     /// Output error
  112.     cout << "\nFunction Errors: " << setprecision(4) << Average_error_percent << "%\n";
  113.     cout << "Sigma_error_value_down      " << " = " << setprecision(w) << fixed << Sigma_error_value_down     << endl;
  114.     cout << "Sigma_error_value_up        " << " = " << setprecision(w) << fixed <<  Sigma_error_value_up       << endl;
  115.     cout << "Sigma_error_value           " << " = " << setprecision(w) << fixed <<  Sigma_error_value          << endl;
  116.     cout << "Average_error_value_down    " << " = " << setprecision(w) << fixed <<  Average_error_value_down   << endl;
  117.     cout << "Average_error_value_up      " << " = " << setprecision(w) << fixed <<  Average_error_value_up     << endl;
  118.     cout << "Average_error_value         " << " = " << setprecision(w) << fixed <<  Average_error_value        << endl;
  119.     cout << "Sigma_error_percent_down    " << " = " << setprecision(w) << fixed <<  Sigma_error_percent_down   << "%" << endl;
  120.     cout << "Sigma_error_percent_up      " << " = " << setprecision(w) << fixed <<  Sigma_error_percent_up     << "%" << endl;
  121.     cout << "Sigma_error_percent         " << " = " << setprecision(w) << fixed <<  Sigma_error_percent        << "%" << endl;
  122.     cout << "Average_error_percent_down  " << " = " << setprecision(w) << fixed <<  Average_error_percent_down << "%" << endl;
  123.     cout << "Average_error_percent_up    " << " = " << setprecision(w) << fixed <<  Average_error_percent_up   << "%" << endl;
  124.     cout << "Average_error_percent       " << " = " << setprecision(w) << fixed <<  Average_error_percent      << "%" << endl;
  125.     return 0;
  126. }
Success #stdin #stdout 0.01s 5840KB
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Approximation Function: f(x) =   1.99878336369307 * x ^(1.00994314580507)

Function Errors: 2.115%
Sigma_error_value_down       = -1.377347561865178
Sigma_error_value_up         = 1.395349195411709
Sigma_error_value            = 2.772696757276887
Average_error_value_down     = -0.137734756186518
Average_error_value_up       = 0.139534919541171
Average_error_value          = 0.277269675727689
Sigma_error_percent_down     = -10.794383823268997%
Sigma_error_percent_up       = 10.356983554896431%
Sigma_error_percent          = 21.151367378165428%
Average_error_percent_down   = -1.079438382326900%
Average_error_percent_up     = 1.035698355489643%
Average_error_percent        = 2.115136737816543%
https://ideone.com/mmoWxJ
Power Regression Approximation
language:
C++14 (gcc 8.3)
created:
3 years ago
visibility:
public

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