Applying boundary conditions on a cubic spline interpolation

Hello,

I'm trying to implement the function interp1 in my code, as follows:

S=interp1(x,y,xq,'spline')

As output, I'm getting the interpolated value at position xq, using cubic spline interpolation. But interp1 uses not-a-knot as boundary condition, is there any way i can get S using different boundary conditions?like clamped or periodic or ....?

I tried using csape, but the thing is that i couldn't get the interpolated value at the specific location xq.

Thank you in advance for your help

Answer 1

[Santosh Fatale]

Hi Marc,

As you mentioned, you can use “csape” function for different end conditions. Note that “csape” returns interpolants in ppform. You can use “fnval” function to calculate value of interpolant in ppform at the specific location xq.

For more information about “csape” and “fnval” functions and ppform follow these links:

• Cubic Spline Interpolation - MATLAB & Simulink Example (mathworks.com)
• Cubic spline interpolation with end conditions - MATLAB csape (mathworks.com)
• Evaluate spline function - MATLAB fnval (mathworks.com)

[Marc Abdel Nour]

It works, thank you

Answer 2

[Bruno Luong]

You can use my function spline1d available here https://fr.mathworks.com/matlabcentral/fileexchange/24996-spline-derivative?s_tid=srchtitle

You can select periodic bc, natural bc [default]; not-a-knot, or clamping first or second derivative on boundary.

This FEX is written long ago and a little bit out-date, but it still working =.

x=cumsum(rand(1,6));
y=rand(size(x));

xi=linspace(min(x),max(x));
yi_notaknot=interp1(x,y,xi,'spline');
yi_natural=spline1d(x,y,xi,[]);

figure
plot(x,y,'or');
hold on
h1=plot(xi,yi_notaknot,'b');
h2=plot(xi,yi_natural,'r');
legend([h1 h2],'not-a-knot','natural')