diff --git a/numerical_methods/composite_simpson_rule.cpp b/numerical_methods/composite_simpson_rule.cpp deleted file mode 100644 index 05cec9db7..000000000 --- a/numerical_methods/composite_simpson_rule.cpp +++ /dev/null @@ -1,177 +0,0 @@ -#include -#include -#include -#include -#include -#include - -/*! - * @file - * @brief Implementation of the Composite Simpson Rule for the approximation - * - * @details The following is an implementation of the Composite Simpson Rule for the approximation of - * definite integrals. More info -> wiki: https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule - * - * The idea is to split the interval in an EVEN number N of intervals and use as interpolation points the xi - * for which it applies that xi = x0 + i*h, where h is a step defined as h = (b-a)/N where a and b are the - * first and last points of the interval of the integration [a, b]. - * - * We create a table of the xi and their corresponding f(xi) values and we evaluate the integral by the formula: - * I = h/3 * {f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)} - * - * That means that the first and last indexed i f(xi) are multiplied by 1, - * the odd indexed f(xi) by 4 and the even by 2. - * - * In this program there are 4 sample test functions f, g, k, l that are evaluated in the same interval. - * - * Arguments can be passed as parameters from the command line argv[1] = N, argv[2] = a, argv[3] = b - * - * N must be even number and a func) - * @brief Calculate integral or assert if integral is not a number (Nan) - * @param N: number of intervals - * @param h: step - * @param a: x0 - * @param func: choose the function that will be evaluated - * @returns the result of the integration -*/ - double evaluate_by_simpson(int N, double h, double a, std::function func); -} // simspon_method end - -/** - * @fn double f(double x) - * @brief A function f(x) that will be used to test the method - * @param x The independent variable xi - * @returns the value of the dependent variable yi = f(xi) -*/ -double f(double x); -/** - * @brief Another test function -*/ -double g(double x); -/** - * @brief Another test function -*/ -double k(double x); -/** - * @brief Another test function -*/ -double l(double x); - - -int main(int argc, char** argv){ - int N = 16; /// Number of intervals to divide the integration interval. MUST BE EVEN - double a = 1, b = 3; /// Starting and ending point of the integration in the real axis - double h; /// Step, calculated by a, b and N - - bool used_argv_parameters = false; // If argv parameters are used then the assert must be omitted for the tst cases - - // Get user input (by the command line parameters or the console after displaying messages) - if(argc == 4){ - N = std::atoi(argv[1]); - a = (double) std::atof(argv[2]); - b = (double) std::atof(argv[3]); - // Check if a 0 && "N has to be > 0"); - if(N<16 || a!=1 || b!=3) used_argv_parameters = true; - std::cout << "You selected N=" << N << ", a=" << a << ", b=" << b << std::endl; - } - else - std::cout << "Default N=" << N << ", a=" << a << ", b=" << b << std::endl; - - - // Find the step - h = (b-a)/N; - - // Call the functions and find the integral of each function - double result_f = simpson_method::evaluate_by_simpson(N, h, a, f); - assert((used_argv_parameters || (result_f >= 4.09 && result_f <= 4.10)) && "The result of f(x) is wrong"); - std::cout << "The result of integral f(x) on interval [" << a << ", " << b << "] is equal to: " << result_f << std::endl; - - double result_g = simpson_method::evaluate_by_simpson(N, h, a, g); - assert((used_argv_parameters || (result_g >= 0.27 && result_g <= 0.28)) && "The result of g(x) is wrong"); - std::cout << "The result of integral g(x) on interval [" << a << ", " << b << "] is equal to: " << result_g << std::endl; - - double result_k = simpson_method::evaluate_by_simpson(N, h, a, k); - assert((used_argv_parameters || (result_k >= 9.06 && result_k <= 9.07)) && "The result of k(x) is wrong"); - std::cout << "The result of integral k(x) on interval [" << a << ", " << b << "] is equal to: " << result_k << std::endl; - - double result_l = simpson_method::evaluate_by_simpson(N, h, a, l); - assert((used_argv_parameters || (result_l >= 7.16 && result_l <= 7.17)) && "The result of l(x) is wrong"); - std::cout << "The result of integral l(x) on interval [" << a << ", " << b << "] is equal to: " << result_l << std::endl; - - - - return 0; -} - -double simpson_method::evaluate_by_simpson(int N, double h, double a, std::function func){ - std::map data_table; /// Contains the data points. key: i, value: f(xi) - double xi = a; // Initialize xi to the starting point x0 = a - - // Create the data table - double temp; - for(int i=0; i<=N; i++){ - temp = func(xi); - data_table.insert(std::pair(i, temp)); /// add i and f(xi) - xi += h; // Get the next point xi for the next iteration - } - - // Evaluate the integral. - // Remember: f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN) - double evaluate_integral = 0; - for(int i=0; i<=N; i++){ - if(i == 0 || i == N) evaluate_integral += data_table.at(i); - else if(i%2 == 1) evaluate_integral += 4 * data_table.at(i); - else evaluate_integral += 2 * data_table.at(i); - } - - // Multiply by the coefficient h/3 - evaluate_integral *= h/3; - - // If the result calculated is nan, then the user has given wrong input interval. - assert(!std::isnan(evaluate_integral) && "The definite integral can't be evaluated. Check the validity of your input.\n"); - // Else return - return evaluate_integral; -} - -/* ------------- Test sample functions below ---------------------------- -*/ - -// Sample function f(x) = sqrt(x) + log(x) -double f(double x){ - return std::sqrt(x) + std::log(x); -} - -// Sample function g(x) = e^-x * (4 - x^2) -double g(double x){ - return std::exp(-x) * (4 - std::pow(x, 2)); -} - -// Sample function k(x) = sqrt(2x^3+3) -double k(double x){ - return std::sqrt(2*std::pow(x, 3)+3); -} - -// Sample function l(x) = x+ln(2x+1) -double l(double x){ - return x + std::log(2*x+1); -} \ No newline at end of file