Run interpolation for several datasets at once

Hello,

My code is performing interpolation of gridded data. My Sample values "V" are stored within an 3D array.

X and Y values are given within corresponding 3D arrays. The third dimension stores basically the different datasets (there are N different cases).

e.g.

X(:, :, 1) Y(:, :, 1) V(:, :, 1) -> Dataset 1

X(:, :, 2) Y(:, :, 2) V(:, :, 2) -> Dataset 2 (...)

The points I want to interpolate my data to (xglobal, yglobal) are constant for all Datasets.

In the end the Interpolated data is stored again within an 3D Array.

for i=1:N
      x_Wake = x(:,:,i);
      y_Wake = y(:,:,i);
      V = Vi(:,:,i);
globaldata = griddata(x_Wake, y_Wake, Vi, xglobal, yglobal);
matV(:,:,i) = V;
end

This is part of a rountine so this step is time critical - which is the reason why I want to get rid of the loop and

Interpolate all datasets at once. I tried using griddedinterpolant - but I couldn't make it work.

Thanks in advance for any help/ ideas provided!

Best wishes

DS

[Matt J]

Don't you mean,

matV(:,:,i) = globalData;

[Matt J]

Is there any pattern to the way x(:,:,i) and y(:,:,i) change from slice to slice?

[DS]

1st:

Yeah you're right - sticking to my notation it should be:

Vi = V(:,:,i);

Sorry about that.

2nd:

The only pattern is that all elements of x and y are within the limits of xglobal and yglobal

It might be that they are simmilar but that depends heavily on the case which is modeled so shouldn't be taken into account too much

[Matt J]

It might be that they are simmilar but that depends heavily on the case which is modeled so shouldn't be taken into account too much

So, for example, the spacing between x(m,n,i) and x(m+1,n,i) is not constant with i?

[DS]

ah sorry - thats what you meant!

x and y used to be both vectors with constant spacing (x and y have their own spacing constant). which have been meshed.

Nevertheless they're different from dataset to dataset (the spacing remains constant).

Answer 1

[Matt J]

x and y used to be both vectors with constant spacing (x and y have their own spacing constant). which have been meshed.

Let's forget the mesh. I will now pretend x and y are the original vectors, and likewise I will assume xglobal and yglobal are grid vectors. There is never any reason in Matlab to mesh vectors purely for the purposes of interpolation.

Nevertheless they're different from dataset to dataset (the spacing remains constant).

If so, then there is some translation vector [tx(i),ty(i)] such that for each i x and y can be written

x=x0+tx(i);
y=y0+ty(i);

Then, the interpolation loop can be done more efficiently as,

F=griddedInterpolant({x0,y0,1:N},Vi);

L=length(xglobal)

[XY,Z]=ndgrid([xglobal(:);yglobal(:)],1:N);

X=XY(1:L,:)-tx(:).';
Y=XY(l+1:end,:)-ty(:).';

matV= reshape( F([X(:),Y(:),Z(:)])   , size(Vi));

[DS]

Thank you for your commitment!

Your first comment helped me to get this point 300xfaster.

Then I discovered some cases where my vectors stopped being uniform- your second comment helped me as a basis to get the job done.

I have to say - nice community around here. I'm new to programming so that was really instructive information for me.

Thanks a bunch.

DS

Answer 2

[Matt J]

If it's gridded interpolation, you shouldn't be using griddata. You should be using interp2.

for i=1:N
      x_Wake = x(:,:,i);
      y_Wake = y(:,:,i);
      V = Vi(:,:,i);
    globaldata = interp2(x_Wake, y_Wake, Vi, xglobal, yglobal);

end

It would also speed things up if you have x_Wake and y_Wake be grid vectors instead of a full grid.