How to do cubic interpolation from given sets of data ?

I'm new to matlab. I'm trying to learn how to do cubic interpolation from given sets of data for example x=[0 1 8 12 27] and y=[1 2 3 4 5] I know matlab has some functions that do cubic interpolation but I don't understand how to to implement them with data sets. I've tried using references from the site and other sources but I can't seem to find any guidance for this.

Answer 1

[Star Strider]

The interp1 function with the 'pchip' method is the easiest way to do this (for me, anyway).

From the documentation:

• 'pchip' Shape-preserving piecewise cubic interpolation.

The Code —

x=[0 1 8 12 27];
y=[1 2 3 4 5];

xi = linspace(min(x), max(x));
yi = interp1(x, y, xi, 'pchip');

figure(1)
plot(xi, yi)
hold on
plot(x, y, 'pr', 'MarkerFaceColor','g')
hold off
grid

[Herp Derp]

Can this be done with the spline function ?

[Star Strider]

Yes. It gives a different result from that of interp1.

The Code —

yi = spline(x,y,xi);

figure(2)
plot(xi, yi, '-m')
hold on
plot(x, y, 'pc', 'MarkerFaceColor','r')
hold off
grid

[Herp Derp]

I'm a bit new to this topic. If they are both suppose to do cubic spline interpolations why are their graphs different ?

[Star Strider]

They’re not all ‘cubic spline’ interpolations. I wasn’t clear on what you intended by ‘cubic interpolation’. This now covers every option I can find.

The spline function will give the same result with interp1 with the 'spline' method:

x=[0 1 8 12 27];
y=[1 2 3 4 5];

xi = linspace(min(x), max(x));
yi = interp1(x, y, xi, 'spline');

figure(1)
plot(xi, yi)
hold on
plot(x, y, 'pr', 'MarkerFaceColor','g')
hold off
grid