插值法C++实现

插值法是一种数学方法，用于通过已知的离散数据点来估计未知的连续函数值。在C++中，可以使用以下代码实现插值法：

#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

double interpolate(double x, vector<double>& x_values, vector<double>& y_values) {
    int n = x_values.size();
    if (n == 0) {
        return NAN; // No interpolation possible
    }
    int lower = 0, upper = n - 1;
    while (lower <= upper) {
        int i = lower + (upper - lower) / 2;
        if (x_values[i] == x) {
            return y_values[i]; // Exact match
        } else if (x_values[i] < x) {
            lower = i + 1; // Search in the right half
        } else {
            upper = i - 1; // Search in the left half
        }
    }
    // Interpolate between the two closest points
    int i = lower - 1;
    int j = lower;
    double alpha = (x - x_value