spline_interpolation.cc

#include "spline_interpolation.h"
#include <complex>
#include <iostream>
#include <fstream>
#include <vector>
#include <complex>
#include <numeric>
#include <cmath>
#include <math.h>

std::complex<double> spline (const double& t, const std::vector<std::complex<double>>& data) {
  //double a11, a12, a21, a22, a23, a32, a33, b1, b2, b3, k0, k1, k2, a_2, b_2, x0, y0, x1, y1, x2, y2;
  double a11, a12, a21, a22, a23, a32, a33, b1, b2, b3, k1, k2, a_2, b_2, x0, y0, x1, y1, x2, y2;
  //if ((t>1) && t<data.size()-1){
  x0 = (int)(t)-1;
  y0 = data[x0].real();
  x1 = (int)(t);
  y1 = data[x1].real();
  x2 = (int)(t)+1;
  y2 = data[x2].real();
  a11 = 2.0/(x1-x0);
  a12 = 1.0/(x1-x0);
  a21 = a12;
  a22 = 2.0*(1.0/(x1-x0)+ 1.0/(x2-x1));
  a23 = 1.0/(x2-x1);
  a32 = a23;
  a33 = 2.0/(x2-x1);
  b1 = 3.0*((y1-y0)/pow((x1-x0),2));
  b2 = 3.0*((y1-y0)/pow((x1-x0),2)+(y2-y1)/pow((x2-x1),2));
  b3 = 3.0*((y2-y1)/pow((x2-x1),2));
  size_t ccounter=0;
  double D = (a11*a22*a33)-(a11*a23*a32+a12*a21*a33);
  //k0 =((-a12*a33*b2 - b1*a23*a32)-(-a12*a23*b3 - b1*a22*a33) )/D;
  k1 =((-a11*a23*b3 -b1*a21*a33) - (-a11*a33*b2))/D;
  k2 = ((-a11*a32*b2 - a12*a21*b3) - (-a11*a22*b3 - b1*a21*a32))/D;
  a_2 =  k1*(x2-x1)-(y2-y1);
  b_2 = -k2*(x2-x1)+(y2-y1);
  auto q2 = [&x1,&x2,&y1,&y2,&a_2,&b_2,&ccounter](double x) {
    double t = (x-x1)/(x2-x1);
    return (1-t)*y1+t*y2+t*(1.0-t)*(a_2*(1.0-t)+b_2*t);
  }; 
  return std::complex<double>(q2(t),0.0); 
  // }
  //else
  //  return data[int(t)]; 
}