splineInteg

This is well-defined only modulo an (n-1)-order polynomial.

import almafa.engine.func-1;


  xy = [-100,4; 8,93; 42,-88; 444, 827];
  xmin = min(xy[...;0]);
  xmax = max(xy[...;0]);
  eps = (xmax-xmin)/200;
  xmin -= 2*eps;
  xmax += 2*eps;
  x = xmin..eps..xmax;

  p = splineInterp(xy);
  print("The interpolating normal cubic spline").title()
  plot(x, (@(x) splineEval(p,x))(#x))
  print("Inverting 2nd derivative").title()
  s = splineInteg(splineDiff(p,2), 2);
  plot(x, (@(x) splineEval(s,x))(#x))
  print("The difference to the original spline should be a linear:")
  d = splineAdd(s, splineNeg(p))
  plot(x, (@(x) splineEval(d,x))(#x))

splineInteg(s)