78 lines
2.4 KiB
C++
78 lines
2.4 KiB
C++
#ifndef ADAPTIVESIMPSONINTEGRATE_H
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#define ADAPTIVESIMPSONINTEGRATE_H
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namespace AdaptiveSimpsonIntegrate {
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#include <armadillo>
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#include <cmath>
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#include <iostream>
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//#include <iomanip>
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// 定义被积函数：y = A*exp(-(x-P)²/(2*delt²)) + H/(1+exp((x-P)/W)) + C
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struct FitFunction {
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// 拟合公式的参数
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double A; // 高斯项振幅
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double P; // 中心位置
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double delt; // 高斯项宽度
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double H; // Sigmoid项高度
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double W; // Sigmoid项宽度
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double C; // 常数项
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// 重载()运算符，计算给定点x的函数值
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double operator()(double x) const {
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// 高斯项：A*exp(-(x-P)²/(2*delt²))
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double gaussian_term = A * ::std::exp(-::std::pow(x - P, 2) / (2 * ::std::pow(delt, 2)));
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// Sigmoid项：H/(1+exp((x-P)/W))
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double sigmoid_term = H / (1 + ::std::exp((x - P) / W));
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// 常数项 + 两项之和
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return gaussian_term + sigmoid_term + C;
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}
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};
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// 辛普森积分核心计算（单区间）
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template<typename Func>
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double simpson(double a, double b, const Func& f) {
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double h = (b - a) / 2.0;
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double fa = f(a), fb = f(b), fc = f(a + h);
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return h * (fa + 4 * fc + fb) / 3.0;
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}
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// 自适应辛普森积分（递归实现，控制精度）
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template<typename Func>
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double adaptive_simpson(double a, double b, double eps, const Func& f,
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double whole, double fa, double fb, double fc, int depth) {
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// 防止递归过深（避免栈溢出）
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if (depth > 20) return whole;
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double c = (a + b) / 2.0;
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double h = (b - a) / 4.0;
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double fd = f(a + h), fe = f(b - h);
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// 计算左右子区间的辛普森值
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double left = simpson(a, c, f);
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double right = simpson(c, b, f);
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// 精度判断：满足则返回，不满足则递归细分
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if (::std::abs(left + right - whole) <= 15 * eps) {
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return left + right + (left + right - whole) / 15.0;
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}
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return adaptive_simpson(a, c, eps/2, f, left, fa, fc, fd, depth+1) +
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adaptive_simpson(c, b, eps/2, f, right, fc, fb, fe, depth+1);
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}
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// 积分入口函数（对外接口）
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template<typename Func>
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double integrate(Func f, double a, double b, double eps = 1e-8) {
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double c = (a + b) / 2.0;
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double fa = f(a), fb = f(b), fc = f(c);
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double whole = simpson(a, b, f);
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return adaptive_simpson(a, b, eps, f, whole, fa, fb, fc, 0);
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}
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}
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#endif // ADAPTIVESIMPSONINTEGRATE_H
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