用ｃ＋＋写一个分段连续线性函数的拟合,并画出图像

以下是一种基于最小二乘法的分段连续线性函数拟合方法的C++代码，并附带绘图功能。

#include <iostream>
#include <vector>
#include <fstream>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include "gnuplot_i.hpp" // 需要安装 gnuplot_i 库

using namespace std;

// 定义分段线性函数
class PiecewiseLinearFunction {
private:
    vector<double> breakpoints; // 分段点
    vector<double> slopes; // 斜率

public:
    // 添加分段点和对应的斜率
    void AddSegment(double x, double slope) {
        breakpoints.push_back(x);
        slopes.push_back(slope);
    }

    // 计算函数值
    double operator()(double x) const {
        if (breakpoints.empty()) {
            return 0.0;
        }
        size_t i = upper_bound(breakpoints.begin(), breakpoints.end(), x) - breakpoints.begin();
        i = min(i, breakpoints.size() - 1);
        return slopes[i] * (x - breakpoints[i]) + operator()(breakpoints[i]);
    }

    // 返回所有分段点
    vector<double> GetBreakpoints() const {
        return breakpoints;
    }
};

// 最小二乘法拟合
PiecewiseLinearFunction FitPiecewiseLinearFunction(const vector<double>& x, const vector<double>& y, int num_segments) {
    PiecewiseLinearFunction f;

    // 初始化分段点
    vector<double> breakpoints(num_segments + 1);
    for (int i = 0; i <= num_segments; i++) {
        breakpoints[i] = x.front() + i * (x.back() - x.front()) / num_segments;
    }

    // 迭代优化
    for (int iter = 0; iter < 10; iter++) {
        // 计算每个分段的斜率
        vector<double> slopes(num_segments);
        for (int i = 0; i < num_segments; i++) {
            double sum_x = 0.0, sum_y = 0.0, sum_xy = 0.0, sum_xx = 0.0;
            int count = 0;
            for (int j = 0; j < x.size(); j++) {
                if (breakpoints[i] <= x[j] && x[j] < breakpoints[i+1]) {
                    sum_x += x[j];
                    sum_y += y[j];
                    sum_xy += x[j] * y[j];
                    sum_xx += x[j] * x[j];
                    count++;
                }
            }
            if (count > 0) {
                slopes[i] = (count * sum_xy - sum_x * sum_y) / (count * sum_xx - sum_x * sum_x);
            }
        }

        // 更新分段点位置
        for (int i = 1; i < num_segments; i++) {
            double delta = 0.0;
            int count = 0;
            for (int j = 0; j < x.size(); j++) {
                if (breakpoints[i-1] <= x[j] && x[j] < breakpoints[i+1]) {
                    delta += y[j] - (slopes[i-1] * (x[j] - breakpoints[i-1]) + slopes[i] * (breakpoints[i] - x[j]));
                    count++;
                }
            }
            if (count > 0) {
                delta /= count;
                breakpoints[i] += delta;
            }
        }
    }

    // 添加分段点和对应的斜率到函数对象中
    for (int i = 0; i < num_segments; i++) {
        f.AddSegment(breakpoints[i], slopes[i]);
    }
    f.AddSegment(breakpoints.back(), slopes.back());

    return f;
}

int main() {
    // 生成测试数据
    const int num_points = 100;
    vector<double> x(num_points), y(num_points);
    for (int i = 0; i < num_points; i++) {
        x[i] = 5.0 * i / num_points;
        y[i] = sin(x[i]);
    }

    // 拟合分段线性函数
    const int num_segments = 5;
    PiecewiseLinearFunction f = FitPiecewiseLinearFunction(x, y, num_segments);

    // 输出分段点
    vector<double> breakpoints = f.GetBreakpoints();
    for (int i = 0; i < breakpoints.size(); i++) {
        cout << "breakpoint " << i << " = " << breakpoints[i] << endl;
    }

    // 绘制图像
    Gnuplot gp;
    gp << "plot '-' with points title 'data', '-' with lines title 'fit'\n";
    gp.send1d(make_tuple(x, y));
    vector<double> fit_x(200), fit_y(200);
    for (int i = 0; i < fit_x.size(); i++) {
        fit_x[i] = 5.0 * i / fit_x.size();
        fit_y[i] = f(fit_x[i]);
    }
    gp.send1d(make_tuple(fit_x, fit_y));

    return 0;
}

运行程序后，会输出拟合出的分段点位置，同时会弹出一个图像窗口，显示原始数据和拟合结果。可以根据需要调整拟合的分段数目和迭代次数。