Help understanding interp2?

Can someone explain to me how interp2(X,Y,V,Xq,Yq) works? I've read the matlab docs, but they aren't very clear. Can anyone explain how it works more plainly?

Answer 1

[John D'Errico]

Interp2 is a tool that allows you to interpolate on a gridded domain. So a grid based on meshgrid, in the (x,y) plane. The presumption is you have some array V, that defines V(x,y).

Xq and Yq are now a list of points to interpolate over that grid.

Interp2 is NOT there to interpolate over scattered data points, thus a point cloud in the (x,y) plane. That purpose is served by tools like griddata and scatteredInterpolant.

[Troy McClure]

So what I'm trying to do is implement interp2 in C, which I can't do until I know what interp2 does, but I'm still having trouble understanding what you mean by a couple points here.

So if V, X, and Y are all 2D arrays, are you saying the value at V[1][1] contains the output of the function V(X[1][1], Y[1][1])? If so, I don't understand why X and Y are even needed by interp2.

Secondly, are you saying Xq contains the X components of a list of points and Yq contains the Y components of that same list of points? So the 1st query point would be Xq[1],Yq[1]?

I'm also not sure what is meant by "interpolate over a grid". V(X,Y) does not appear to define a grid but a 1D array since for each set of 2 inputs (a point) it gives a single output. What grid is being interpolated over?

[John D'Errico]

[x,y] = meshgrid(0:2,0:3)
x =
     0     1     2
     0     1     2
     0     1     2
     0     1     2
y =
     0     0     0
     1     1     1
     2     2     2
     3     3     3
     
z = x.^2 + y.^2
z =
     0     1     4
     1     2     5
     4     5     8
     9    10    13

Given only the gridded lattice in the (x,y) plane, you have created z(x,y). Do you accept that?

Interp2 alllows you to compute z(1.5,2.3), given only the information in the arrays x, y, and z. This is called interpolation. Of course it will not be exact, but a relatively coarse approximation, since the true underlying function is not known. (At least it is not known to interp2.)

interp2(x,y,z,1.5,2.3)
ans =
            8
            
1.5^2 + 2.3^2
ans =
         7.54

As I said, not a perfect approximation, but the default for interp2 is a tensor product linear interpolant. A spline interpolant will do better.

interp2(x,y,z,1.5,2.3,'spline')
ans =
         7.54

Since the function was truly quadratic, logically a cubic spline interpolant would do pretty well.

If none of this still makes any sense, then you need to do some serious reading about interpolation in multiple dimensions.

[Troy McClure]

Thanks, this is a really good breakdown.

Answer 2

[madhan ravi]

V(X,Y) -> function Xq & Yq are query points

query points -> what would be the functions value at these points.

[Troy McClure]

Not sure I understand still. Which 2 variables are being interpolated between and what value is being used to do the interpolation?