Spline Toolbox

Periodic Data

We know that the sine function is -periodic. To check how well our interpolant does on that score, we compute, e.g., the difference in the value of its first derivative at the two endpoints,

• diff(fnval(fnder(cs),[0 4*pi]))
  ans = -.0307
  

which is not so good. If you prefer to get an interpolant whose first and second derivatives at the two endpoints, 0 and 4*pi, match, use instead the command cspape which permits specification of many different kinds of end conditions, including periodic end conditions. So, use instead

• pcs = csape(x,y,'periodic');
  

for which we get

• diff(fnval(fnder(pcs),[0 4*pi]))
  ans = -2.2204e-016
  

as the difference of end slopes. Even the difference in end second derivatives is small:

• diff(fnval(fnder(pcs,2),[0 4*pi]))
  ans = -1.4017e-014
  

Cubic Spline Interpolation

Other End Conditions