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Create midpoint_integral_method.cpp

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ggkogkou
2021-10-28 12:30:25 +03:00
committed by GitHub
parent 068e6d8169
commit 42df777a15
1 changed files with 25 additions and 13 deletions
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38
numerical_methods/midpoint_integral_method.cpp
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@@ -23,6 +23,7 @@
#include <cstdlib> /// for std::atof
#include <functional> /// for std::function
#include <iostream> /// for IO operations
#include <stdint> /// for integer allocation
#include <map> /// for std::map container
/**
@@ -38,17 +39,16 @@ namespace numerical_methods {
*/
namespace midpoint_rule {
/**
* @fn double midpoint(const int N, const double h, const double a, const
* @fn double midpoint(const std::int32_t N, const double h, const double a, const
* std::function<double (double)>& func)
* \brief Main function for implementing the Midpoint Integral Method
* implementation
* @brief Main function for implementing the Midpoint Integral Method implementation
* @param N is the number of intervals
* @param h is the step
* @param a is x0
* @param func is the function that will be integrated
* @returns the result of the integration
*/
double midpoint(const int N, const double h, const double a,
double midpoint(const std::int32_t N, const double h, const double a,
const std::function<double(double)>& func) {
std::map<int, double>
data_table; // Contains the data points, key: i, value: f(xi)
@@ -57,16 +57,16 @@ double midpoint(const int N, const double h, const double a,
// Create the data table
// Loop from x0 to xN-1
double temp = NAN;
for (int i = 0; i < N; i++) {
for (std::uint8_t i = 0; i < N; i++) {
temp = func(xi + h / 2); // find f(xi+h/2)
data_table.insert(std::pair<int, double>(i, temp)); // add i and f(xi)
data_table.insert(std::pair<std::int32_t, double>(i, temp)); // add i and f(xi)
xi += h; // Get the next point xi for the next iteration
}
// Evaluate the integral.
// Remember: {f(x0+h/2) + f(x1+h/2) + ... + f(xN-1+h/2)}
double evaluate_integral = 0;
for (int i = 0; i < N; i++) evaluate_integral += data_table.at(i);
for (std::uint8_t i = 0; i < N; i++) evaluate_integral += data_table.at(i);
// Multiply by the coefficient h
evaluate_integral *= h;
@@ -83,14 +83,26 @@ double midpoint(const int N, const double h, const double a,
/**
* @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)
* @returns the value of the dependent variable yi = f(xi) = sqrt(xi) + ln(xi)
*/
double f(double x) { return std::sqrt(x) + std::log(x); }
/** @brief Another test function */
/**
* @brief A function g(x) that will be used to test the method
* @param x The independent variable xi
* @returns the value of the dependent variable yi = g(xi) = e^(-xi) * (4 - xi^2)
*/
double g(double x) { return std::exp(-x) * (4 - std::pow(x, 2)); }
/** @brief Another test function */
/**
* @brief A function k(x) that will be used to test the method
* @param x The independent variable xi
* @returns the value of the dependent variable yi = k(xi) = sqrt(2*xi^3 + 3)
*/
double k(double x) { return std::sqrt(2 * std::pow(x, 3) + 3); }
/** @brief Another test function */
/**
* @brief A function l(x) that will be used to test the method
* @param x The independent variable xi
* @returns the value of the dependent variable yi = l(xi) = xi + ln(2*xi + 1)
*/
double l(double x) { return x + std::log(2 * x + 1); }
} // namespace midpoint_rule
@@ -105,7 +117,7 @@ double l(double x) { return x + std::log(2 * x + 1); }
* @param used_argv_parameters is 'true' if argv parameters are given and
* 'false' if not
*/
static void test(int N, double h, double a, double b,
static void test(std::int32_t 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
@@ -145,7 +157,7 @@ static void test(int N, double h, double a, double b,
* @returns 0 on exit
*/
int main(int argc, char** argv) {
int N = 16; /// Number of intervals to divide the integration interval.
std::int32_t 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