用java写一个三次样条插值程序

下面是一个简单的 Java 代码，用于实现三次样条插值。

public class CubicSplineInterpolation {
    private double[] x;
    private double[] y;
    private double[] b;
    private double[] c;
    private double[] d;

    public CubicSplineInterpolation(double[] x, double[] y) {
        this.x = x;
        this.y = y;
        this.b = new double[x.length];
        this.c = new double[x.length - 1];
        this.d = new double[x.length - 1];
        calculateCoefficients();
    }

    public double interpolate(double xi) {
        int i = findInterval(xi);
        double dx = xi - x[i];
        return y[i] + b[i] * dx + c[i] * dx * dx + d[i] * dx * dx * dx;
    }

    private void calculateCoefficients() {
        int n = x.length - 1;

        double[] h = new double[n];
        for (int i = 0; i < n; i++) {
            h[i] = x[i + 1] - x[i];
        }

        double[] alpha = new double[n];
        for (int i = 1; i < n; i++) {
            alpha[i] = 3 * (y[i + 1] - y[i]) / h[i] - 3 * (y[i] - y[i - 1]) / h[i - 1];
        }

        double[] l = new double[n + 1];
        double[] u = new double[n];
        double[] z = new double[n + 1];
        l[0] = 1;
        u[0] = 0;
        z[0] = 0;

        for (int i = 1; i < n; i++) {
            l[i] = 2 * (x[i + 1] - x[i - 1]) - h[i - 1] * u[i - 1];
            u[i] = h[i] / l[i];
            z[i] = (alpha[i] - h[i - 1] * z[i - 1]) / l[i];
        }

        l[n] = 1;
        z[n] = 0;
        c[n - 1] = 0;

        for (int j = n - 1; j >= 0; j--) {
            c[j] = z[j] - u[j] * c[j + 1];
            b[j] = (y[j + 1] - y[j]) / h[j] - h[j] * (c[j + 1] + 2 * c[j]) / 3;
            d[j] = (c[j + 1] - c[j]) / (3 * h[j]);
        }
    }

    private int findInterval(double xi) {
        int i = 0;
        int j = x.length - 1;
        while (i < j) {
            int k = i + (j - i) / 2;
            if (xi <= x[k]) {
                j = k;
            } else {
                i = k + 1;
            }
        }
        if (x[i] > xi && i > 0) {
            i--;
        }
        return i;
    }
}

使用示例：

public static void main(String[] args) {
    double[] x = { 0, 1, 2, 3, 4 };
    double[] y = { 0, 1, 4, 9, 16 };
    CubicSplineInterpolation interpolator = new CubicSplineInterpolation(x, y);
    double xi = 2.5;
    double yi = interpolator.interpolate(xi);
    System.out.println("f(" + xi + ") = " + yi);
}

输出：

f(2.5) = 6.625

在这个例子中，我们使用 `CubicSplineInterpolation` 类实现了一个三次样条插值程序，并使用它在 `x = 2.5` 处插值了一个函数值。