MATLAB: Interpolating data in a better way

interp1interpolation

I will simplify this down, as my data is huge. I have about 100 sets of data smaller than the one I am going up to; each one of them vary in size. IE 3×6 or 9×9. I need to interpolate it up to say 20×20. Names of variables were changed for simplicity also.

A 3×3 raw data would look like this, and cannot change (easily) as I am importing from an edit locked file.

rawdata=[1 7 3 ;8 9 6; 2 2 5];

Here is how am currently going about it.

g_raw = size(rawdata);

xg_g = linspace(1,20,g_raw(1));

yg_g = linspace(1,20,g_raw(2));

interp_x_g = interp1(xg_g, g_raw, 1:20); %doing one direction

interp_y_g = interp1(yg_g, interp_x_g', 1:20)'; %tackling other direction with a transpose and transpose back

interpolated_g = interp_y_g(:); %making into a vector for plotting vs another vector

It works in a sense, but comes out very choppy. Is there a better way? I have been using MatLab for about a week and getting the hang of it. I just do not understand everything in the help files. IE I could not get polyfit to work in my loops. Not sure if I should be using interp2 or 3? All help is appreciated, even if it is just correcting syntax or general advice.

Cheers!

Walt

Best Answer

Yeah, try interp2 -- sotoo

[nr,nc]=size(rawdata);
[X,Y] = meshgrid(1:nr,1:nc);   % the original array mesh
[Xq,Yq] = meshgrid(linspace(1,nr,20),linspace(1,nr,20));  % the 20X copy
Vq = interp2(X,Y,rawdat,Xq,Yq);

Related Solutions

MATLAB: Can I make a spline both smoothing and periodic

This FEX file advertises all kinds of convenient options for constraining spline fits,

http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling

You need the Optimization Toolbox, though.

MATLAB: Fast interp1 with ‘spline’

Well, the simple answer is to not use interp1. Just use spline and then ppval.

The problem is that for a spline interpolant, every time you call interp1, it must effectively call spline inside on your data. By calling spline once, this makes it more efficient.

For example...

x = linspace(-1,1,100);
y = exp(x);
xev = rand(1,1000)*2 - 1;
S = spline(x,y);
timeit(@() interp1(x,y,xev,'spline'))
ans =
    0.0003005
timeit(@() ppval(S,xev))
ans =
   0.00025177

Not as big of a difference as I thought it might be, but some.

You MIGHT also gain some time if you are willing to pre-interpolate the function to a finer interval, so that then you could do linear interpolation. Since linear interpolant will be faster to do, this should see some gain too.

x = linspace(-1,1,10);
y = exp(x);
xfine = linspace(-1,1,1000);
yfine = interp1(x,y,xfine,'spline');
xev = rand(1,1000)*2 - 1;
timeit(@() interp1(x,y,xev,'spline'))
ans =
   0.00028546
timeit(@() interp1(xfine,yfine,xev))
ans =
   0.00022313

You can also see some gain by using pchip instead of spline, as that is a faster way to build the spline, though sometimes not quite as smooth.

timeit(@() interp1(x,y,xev,'pship'))
ans =
   0.00026064

Finally I recall seeing some tools on the file exchange that tried to give a speedup for interp1, but they were mostly for linear interpolation.

Finally, while you could certainly use a mexfile to improve the time, that presumes that your skills are sufficient to write a spline interpolant, and to do so efficiently in C. I'm afraid that compiled MATLAB code would gain you nothing here.

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