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  1. #include <iostream>
  2. #include <vector>
  3. #include <cmath>
  4.  
  5. double eps, a, b, tab_step;
  6.  
  7. std::vector<double> root_segs;
  8.  
  9. double f(double x) {
  10.   return sqrt(4.0*x+7.0) - 3.0 * cos(x);
  11. }
  12.  
  13. double fprime(double x) {
  14.   return 3 * sin(x) + 2.0/sqrt(4*x+7);
  15. }
  16.  
  17. void in_par() {
  18.   //std::cin >> tab_step >> eps;
  19.   //std::cin >> a >> b;
  20.   a = -1.5; b = 2;
  21.   eps = 1e-8; tab_step = 0.01;
  22. }
  23.  
  24. void print_seg(int i) {
  25.   std::cout << "[" << root_segs[i] << ", " << (root_segs[i]+tab_step) << "]";
  26. }
  27.  
  28. void sep() {
  29.   for (double x = a; x <= b; x += tab_step)
  30.     if (f(x) * f(x + tab_step) <= 0)
  31.       root_segs.push_back(x);
  32.   if (!root_segs.size()) {
  33.     std::cout << "No roots present in requested segment, terminating\n";
  34.     exit(0);
  35.   }
  36.   std::cout << "Root separation yielded following segments:" << std::endl;
  37.   print_seg(0);
  38.   for (int i = 1; i < root_segs.size(); i++)
  39.     std::cout << ", ", print_seg(i);
  40.   std::cout << std::endl;
  41. }
  42.  
  43. void bisect(double l, double r) {
  44.   std::cout << "Bisection method; [" << l << ", " << r << "]: ";
  45.   int step = 0;
  46.   while (r - l > 2 * eps) {
  47.     ++step;
  48.     double mid = (l + r) / 2.0;
  49.     if (f(mid) * f(r) < 0)
  50.       l = mid;
  51.     else
  52.       r = mid;
  53.   }
  54.   double ans = (r+l)/2.0;
  55.   std::cout
  56.     << step << " steps, ans " << ans
  57.     << ", |r| = " << fabs(f(ans))
  58.     << ", fsl = " << (r-l)
  59.     << std::endl;
  60. }
  61.  
  62. void newton(double xs) {
  63.   std::cout << "Newton's method; x_0 = " << xs << "; ";
  64.   int steps = 0;
  65.   double nx = xs, px = xs;
  66.   do {
  67.     ++steps;
  68.     px = nx;
  69.     nx = nx - f(nx) / fprime(nx);
  70.   } while (nx - px > eps);
  71.   std::cout
  72.     << steps << " steps, ans " << nx
  73.     << ", |r| = " << fabs(f(nx))
  74.     << std::endl;
  75. }
  76.  
  77. void mod_newton(double xs) {
  78.   std::cout << "Modified Newton's method; x_0 = " << xs << "; ";
  79.   int steps = 0;
  80.   double nx = xs, px = xs;
  81.   double fpr0 = fprime(xs);
  82.   do {
  83.     ++steps;
  84.     px = nx;
  85.     nx = nx - f(nx) / fpr0;
  86.   } while (nx - px > eps);
  87.   std::cout
  88.     << steps << " steps, ans " << nx
  89.     << ", |r| = " << fabs(f(nx))
  90.     << std::endl;
  91. }
  92.  
  93. void secant(double k, double l) {
  94.   std::cout << "Secant method; x_0 = " << k << ", x_1 = " << l;
  95.   int steps = 0;
  96.   while (fabs(k - l) > eps) {
  97.     ++steps;
  98.     double fs = f(l);
  99.     double n = l - fs * ((l - k) / (fs - f(k)));
  100.     k = l; l = n;
  101.   }
  102.   std::cout
  103.     << ", " << steps
  104.     << " steps, ans " << l
  105.     << ", |r| = " << fabs(f(l))
  106.     << std::endl;
  107. }
  108.  
  109. int main(int argc, char** argv) {
  110.   std::cout << "LW 1: numerical methods of solving nonlinear equations\n";
  111.   std::cout << "Variant 4, f(x) := sqrt(4*x + 7) - 3*cos(x)\n";
  112.  
  113.   std::cout.precision(10);
  114.   in_par();
  115.  
  116.   std::cout
  117.     << "A = " << a << "; B = " << b
  118.     << "; h = " << tab_step
  119.     << "; eps = " << eps << std::endl;
  120.  
  121.   std::cout << std::endl;
  122.   sep();
  123.   std::cout << std::endl;
  124.   for (int i = 0; i < root_segs.size(); i++)
  125.     bisect(root_segs[i], root_segs[i] + tab_step);
  126.   for (int i = 0; i < root_segs.size(); i++)
  127.     newton(root_segs[i]);
  128.   for (int i = 0; i < root_segs.size(); i++)
  129.     mod_newton(root_segs[i]);
  130.   for (int i = 0; i < root_segs.size(); i++)
  131.     secant(root_segs[i], root_segs[i] + tab_step);
  132.  
  133.   return 0;
  134. }
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