integral_approximation.cpp

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#include <cassert>     
#include <cmath>       
#include <cstdint>
#include <functional>  
#include <iostream>    

namespace math {
double integral_approx(double lb, double ub,
                       const std::function<double(double)>& func,
                       double delta = .0001) {
    double result = 0;
    uint64_t numDeltas = static_cast<uint64_t>((ub - lb) / delta);
    for (int i = 0; i < numDeltas; i++) {
        double begin = lb + i * delta;
        double end = lb + (i + 1) * delta;
        result += delta * (func(begin) + func(end)) / 2;
    }
    return result;
}

void test_eval(double approx, double expected, double threshold) {
    assert(approx >= expected * (1 - threshold));
    assert(approx <= expected * (1 + threshold));
}

}  // namespace math
 
static void test() {
    double test_1 = math::integral_approx(
        3.24, 7.56, [](const double x) { return log(x) + exp(x) + x; });
    std::cout << "Test Case 1" << std::endl;
    std::cout << "function: log(x) + e^x + x" << std::endl;
    std::cout << "range: [3.24, 7.56]" << std::endl;
    std::cout << "value: " << test_1 << std::endl;
    math::test_eval(test_1, 1924.80384023549, .001);
    std::cout << "Test 1 Passed!" << std::endl;
    std::cout << "=====================" << std::endl;
 
    double test_2 = math::integral_approx(0.023, 3.69, [](const double x) {
        return x * x + cos(x) + exp(x) + log(x) * log(x);
    });
    std::cout << "Test Case 2" << std::endl;
    std::cout << "function: x^2 + cos(x) + e^x + log^2(x)" << std::endl;
    std::cout << "range: [.023, 3.69]" << std::endl;
    std::cout << "value: " << test_2 << std::endl;
    math::test_eval(test_2, 58.71291345202729, .001);
    std::cout << "Test 2 Passed!" << std::endl;
    std::cout << "=====================" << std::endl;
 
    double test_3 = math::integral_approx(
        10.78, 24.899, [](const double x) { return x * x * x - x * x + 378; });
    std::cout << "Test Case 3" << std::endl;
    std::cout << "function: x^3 - x^2 + 378" << std::endl;
    std::cout << "range: [10.78, 24.899]" << std::endl;
    std::cout << "value: " << test_3 << std::endl;
    math::test_eval(test_3, 93320.65915078377, .001);
    std::cout << "Test 3 Passed!" << std::endl;
    std::cout << "=====================" << std::endl;
 
    double test_4 = math::integral_approx(
        .101, .505,
        [](const double x) { return cos(x) * tan(x) * x * x + exp(x); },
        .00001);
    std::cout << "Test Case 4" << std::endl;
    std::cout << "function: cos(x)*tan(x)*x^2 + e^x" << std::endl;
    std::cout << "range: [.101, .505]" << std::endl;
    std::cout << "value: " << test_4 << std::endl;
    math::test_eval(test_4, 0.566485986311631, .001);
    std::cout << "Test 4 Passed!" << std::endl;
    std::cout << "=====================" << std::endl;
 
    double test_5 = math::integral_approx(
        -1, 1, [](const double x) { return exp(-1 / (x * x)); });
    std::cout << "Test Case 5" << std::endl;
    std::cout << "function: e^(-1/x^2)" << std::endl;
    std::cout << "range: [-1, 1]" << std::endl;
    std::cout << "value: " << test_5 << std::endl;
    math::test_eval(test_5, 0.1781477117815607, .001);
    std::cout << "Test 5 Passed!" << std::endl;
}

int main() {
    test();  // run self-test implementations
    return 0;
}