非扭边界条件下的三次样条曲线插值C++代码，要求使用eigen库

以下是使用Eigen库实现的非扭边界条件下的三次样条曲线插值的C++代码：

#include <iostream>
#include <Eigen/Dense>

using namespace std;
using namespace Eigen;

VectorXd getCoefficients(VectorXd x, VectorXd y)
{
    int n = x.size() - 1;
    VectorXd h = x.tail(n) - x.head(n);
    VectorXd b = (y.tail(n) - y.head(n)).cwiseQuotient(h);
    VectorXd u(n);
    u(1) = 2 * (h(0) + h(1));
    for (int i = 2; i < n; i++)
        u(i) = 2 * (h(i - 1) + h(i)) - h(i - 1) * h(i - 1) / u(i - 1);
    VectorXd v(n);
    v(1) = 6 * (b(1) - b(0));
    for (int i = 2; i < n; i++)
        v(i) = 6 * (b(i) - b(i - 1)) - h(i - 1) * v(i - 1) / u(i - 1);
    VectorXd z(n + 1);
    z(n) = 0;
    for (int i = n - 1; i > 0; i--)
        z(i) = (v(i) - h(i) * z(i + 1)) / u(i);
    z(0) = 0;
    MatrixXd A(n, n);
    A.setZero();
    for (int i = 0; i < n - 1; i++)
    {
        A(i, i) = (h(i) + h(i + 1)) / 3;
        A(i, i + 1) = h(i + 1) / 6;
        A(i + 1, i) = h(i + 1) / 6;
        A(i + 1, i + 1) = (h(i + 1) + h(i + 2)) / 3;
    }
    VectorXd b_prime(n);
    for (int i = 0; i < n; i++)
        b_prime(i) = (y(i + 1) - y(i)) / h(i) - (h(i) * (2 * z(i) + z(i + 1))) / 6;
    VectorXd c = A.colPivHouseholderQr().solve(b_prime);
    VectorXd d(n);
    for (int i = 0; i < n; i++)
        d(i) = (z(i + 1) - z(i)) / (6 * h(i));
    VectorXd coefficients(4 * n);
    for (int i = 0; i < n; i++)
    {
        coefficients.segment(4 * i, 4) << y(i), b(i), c(i), d(i);
    }
    return coefficients;
}

double evaluateSpline(VectorXd coefficients, double x, VectorXd knotVector)
{
    int n = knotVector.size() - 1;
    int i = n - 1;
    while (i >= 0 && x < knotVector(i))
    {
        i--;
    }
    i = min(max(i, 0), n - 1);
    double h = knotVector(i + 1) - knotVector(i);
    double xi = x - knotVector(i);
    double a = coefficients(4 * i);
    double b = coefficients(4 * i + 1);
    double c = coefficients(4 * i + 2);
    double d = coefficients(4 * i + 3);
    return a + b * xi + c * xi * xi + d * xi * xi * xi;
}

int main()
{
    VectorXd x(6);
    x << 0, 1, 2, 3, 4, 5;
    VectorXd y(6);
    y << 0, 1, 0, -1, 0, 1;

    VectorXd coefficients = getCoefficients(x, y);

    VectorXd knotVector(7);
    knotVector << -1, x, 6;

    double x_new = 2.5;
    double y_new = evaluateSpline(coefficients, x_new, knotVector);
    cout << "f(" << x_new << ") = " << y_new << endl;

    return 0;
}

该代码使用了Eigen库中的矩阵操作和线性求解器，实现了非扭边界条件下的三次样条曲线插值。其中，getCoefficients函数用于求解三次样条曲线的系数，evaluateSpline函数用于根据系数和插值节点插值新的数据点。在main函数中，我们先定义了一组数据点x和y，然后使用getCoefficients函数求解系数，再使用evaluateSpline函数插值新的数据点。