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ggkogkou 2021-10-28 00:18:51 +03:00 committed by GitHub
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1 changed files with 18 additions and 19 deletions
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numerical_methods/midpoint_integral_method.cpp
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@ -1,8 +1,8 @@
/**
* @file
* @brief A numerical method for easy [approximation of
* integrals](https://en.wikipedia.org/wiki/Midpoint_method) \details The idea
* is to split the interval into N of intervals and use as interpolation points
* integrals](https://en.wikipedia.org/wiki/Midpoint_method)
* @details The idea is to split the interval into 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].
@ -20,7 +20,6 @@
*/
#include <cassert> /// for assert
#include <cmath> /// for math functions
#include <cmath>
#include <cstdlib> /// for std::atof
#include <functional> /// for std::function
#include <iostream> /// for IO operations
@ -33,7 +32,7 @@
namespace numerical_methods {
/**
* @namespace midpoint_rule
* \brief Contains the function of the midpoint method implementation
* @brief Contains the function of the midpoint method implementation
*/
namespace midpoint_rule {
/*!
@ -77,11 +76,8 @@ double midpoint(const int N, const double h, const double a,
return evaluate_integral;
}
} // namespace midpoint_rule
} // namespace numerical_methods
/**
* \brief A function f(x) that will be used to test the method
* @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)
*/
@ -93,8 +89,11 @@ double k(double x) { return std::sqrt(2 * std::pow(x, 3) + 3); }
/** @brief Another test function */
double l(double x) { return x + std::log(2 * x + 1); }
} // namespace midpoint_rule
} // namespace numerical_methods
/**
* \brief Self-test implementations
* @brief Self-test implementations
* @param N is the number of intervals
* @param h is the step
* @param a is x0
@ -106,25 +105,25 @@ static void test(int N, double h, double a, double b,
bool used_argv_parameters) {
// Call midpoint() for each of the test functions f, g, k, l
// Assert with two decimal point precision
double result_f = numerical_methods::midpoint_rule::midpoint(N, h, a, f);
double result_f = numerical_methods::midpoint_rule::midpoint(N, h, a, numerical_methods::midpoint_rule::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 = numerical_methods::midpoint_rule::midpoint(N, h, a, g);
double result_g = numerical_methods::midpoint_rule::midpoint(N, h, a, numerical_methods::midpoint_rule::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 = numerical_methods::midpoint_rule::midpoint(N, h, a, k);
double result_k = numerical_methods::midpoint_rule::midpoint(N, h, a, numerical_methods::midpoint_rule::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 = numerical_methods::midpoint_rule::midpoint(N, h, a, l);
double result_l = numerical_methods::midpoint_rule::midpoint(N, h, a, numerical_methods::midpoint_rule::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
@ -146,7 +145,7 @@ int main(int argc, char** argv) {
bool used_argv_parameters =
false; // If argv parameters are used then the assert must be omitted
// for the tst cases
// for the test cases
// Get user input (by the command line parameters or the console after
// displaying messages)
@ -170,7 +169,7 @@ int main(int argc, char** argv) {
// Find the step
h = (b - a) / N;
test(N, h, a, b, used_argv_parameters); /// run self-test implementations
test(N, h, a, b, used_argv_parameters); // run self-test implementations
return 0;
}