fork download
copy 
  1. #include <iostream>
  2. #include <cmath>
  3. #include <vector>
  4. #include <fstream>
  5.  
  6. // Funkcja 1: exp(x) * cos(0.5 * x^2)
  7. double func1(double x) {
  8.     return std::exp(x) * std::cos(0.5 * x * x);
  9. }
  10.  
  11. // Funkcja 2: 1 / (12 * x^2 + 1)
  12. double func2(double x) {
  13.     return 1.0 / (12.0 * x * x + 1.0);
  14. }
  15.  
  16. // Generowanie węzłów Czebyszewa
  17. std::vector<double> chebyshevNodes(int degree, double a, double b) {
  18.     std::vector<double> nodes(degree);
  19.     for (int i = 0; i < degree; ++i) {
  20.         double cos_theta = std::cos(M_PI * (2.0 * i + 1) / (2.0 * degree));
  21.         nodes[i] = 0.5 * (a + b) + 0.5 * (b - a) * cos_theta;
  22.     }
  23.     return nodes;
  24. }
  25.  
  26. // Obliczanie współczynników wielomianu Czebyszewa
  27. std::vector<double> chebyshevCoefficients(int degree, double a, double b, double (*func)(double)) {
  28.     std::vector<double> nodes = chebyshevNodes(degree, a, b);
  29.     std::vector<double> coeffs(degree, 0.0);
  30.  
  31.     for (int k = 0; k < degree; ++k) {
  32.         double sum = 0.0;
  33.         for (int j = 0; j < degree; ++j) {
  34.             sum += func(nodes[j]) * std::cos(M_PI * k * (2.0 * j + 1) / (2.0 * degree));
  35.         }
  36.         coeffs[k] = (2.0 / degree) * sum;
  37.     }
  38.  
  39.     coeffs[0] *= 0.5; // Współczynnik dla T_0(x)
  40.     return coeffs;
  41. }
  42.  
  43. // Obliczanie wartości wielomianu Czebyszewa
  44. double chebyshevPolynomial(const std::vector<double>& coeffs, double x, double a, double b) {
  45.     double t = (2.0 * x - (a + b)) / (b - a); // Przekształcenie na [-1, 1]
  46.     double y = 0.0;
  47.     double T_k_minus_2 = 1.0;
  48.     double T_k_minus_1 = t;
  49.  
  50.     for (size_t k = 0; k < coeffs.size(); ++k) {
  51.         if (k == 0) {
  52.             y += coeffs[k] * T_k_minus_2;
  53.         } else if (k == 1) {
  54.             y += coeffs[k] * T_k_minus_1;
  55.         } else {
  56.             double T_k = 2.0 * t * T_k_minus_1 - T_k_minus_2;
  57.             y += coeffs[k] * T_k;
  58.             T_k_minus_2 = T_k_minus_1;
  59.             T_k_minus_1 = T_k;
  60.         }
  61.     }
  62.  
  63.     return y;
  64. }
  65.  
  66. int main() {
  67.     // Parametry
  68.     double a1 = 0.0, b1 = 3.0;
  69.     double a2 = -2.0, b2 = 2.0;
  70.     std::vector<int> degrees = {3, 10, 40};
  71.  
  72.     // Pliki wynikowe
  73.     std::ofstream file1("func1.dat");
  74.     std::ofstream file2("func2.dat");
  75.  
  76.     for (int degree : degrees) {
  77.         std::vector<double> coeffs1 = chebyshevCoefficients(degree, a1, b1, func1);
  78.         std::vector<double> coeffs2 = chebyshevCoefficients(degree, a2, b2, func2);
  79.  
  80.         for (double x = a1; x <= b1; x += 0.01) {
  81.             double approx1 = chebyshevPolynomial(coeffs1, x, a1, b1);
  82.             file1 << x << " " << func1(x) << " " << approx1 << "\n";
  83.         }
  84.  
  85.         for (double x = a2; x <= b2; x += 0.01) {
  86.             double approx2 = chebyshevPolynomial(coeffs2, x, a2, b2);
  87.             file2 << x << " " << func2(x) << " " << approx2 << "\n";
  88.         }
  89.  
  90.         file1 << "\n\n";
  91.         file2 << "\n\n";
  92.     }
  93.  
  94.     file1.close();
  95.     file2.close();
  96.  
  97.     std::cout << "Dane zapisane do plikow func1.dat i func2.dat. Wykresy mozna rysowac za pomoca Gnuplot." << std::endl;
  98.     return 0;
  99. }
  100.  
Success #stdin #stdout 0s 5276KB
comments (?)
stdin
copy 
Standard input is empty
stdout
copy 
Dane zapisane do plikow func1.dat i func2.dat. Wykresy mozna rysowac za pomoca Gnuplot.
https://ideone.com/5Mv3Kz
language:
C++ (gcc 8.3)
created:
1 day ago
visibility:
public

Share or Embed source code

Discover > Sphere Engine API

The brand new service which powers Ideone!

Discover > IDE Widget

Widget for compiling and running the source code in a web browser!