使用EIGEN实现曲线拟合

• QR分解与最小二乘
• Eigen解线性方程组

double polyeval(Eigen::VectorXd coeffs, double x) {
  double result = 0.0;
  for (int i = 0; i < coeffs.size(); i++) {result += coeffs[i]*pow(x, i);}
  return result;
}

Eigen::VectorXd polyfit(Eigen::VectorXd xvals, Eigen::VectorXd yvals, int order) {
  assert(xvals.size() == yvals.size());
  assert(order >= 1 && order <= xvals.size() - 1);
  Eigen::MatrixXd A(xvals.size(), order + 1);
  for (int i = 0; i < xvals.size(); i++) {
    A(i, 0) = 1.0;
  }
  for (int j = 0; j < xvals.size(); j++) {
    for (int i = 0; i < order; i++) {
      A(j, i + 1) = A(j, i) * xvals(j);
    }
  }
  auto Q = A.householderQr();
  auto result = Q.solve(yvals);
  return result;
}

Eigen::VectorXd xvals(6);
Eigen::VectorXd yvals(6);
xvals << 9.261977, -2.06803, -19.6663, -36.868, -51.6263, -66.3482;
yvals << 5.17,     -2.25,    -15.306,  -29.46,  -42.85,   -57.6116;
auto coeffs= polyfit(xvals,yvals,3);
std::cout<< "Y(16)=" << polyeval(coeffs,16) << endl;

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