MATLAB: Better method to interpn when one grid is fixed

interpn n-d interpolation improvement dimensions

I currently have a n-D sized database, and I'm using interpn to interpolate values from it. However, I do not interpolate on the last dimension, as I'm using the database to interpolate between 1xn solutions. The database is very large, and I am interpolating on it many times, so I'm looking for a faster solution. I believe there should be a faster solution since I'm not necessarily "interpolating" between values on the last dimension. Below is an example of my current method that I am looking to improve:

Example:

database=rand([4,4,2,3,8,6,2,6,5500]);
interpGrids={[1000 2000 4000 7000],[-5 -2 2 5],[0 1],[-5 0 5],[-20 -15 -5 0 5 10 15 20],[10 20 30 40 50 60],[-5 0],[.1 .2 .3 .4 .5 1],1:5500};
ngGriddedData=cell(1,9);
[ngGriddedData{:}]=ndgrid(interpGrids{:});
tic
solution=interpn(ngGriddedData{:},database,3000,1,1,2,-17,35,-4,.35,1:5500);
toc

Many many thanks for any suggestions. I'll be sure to send some good computing karma your way.

– Sean

Best Answer

Hi Sean,

You can use the griddedInterpolant function, which provides performance improvements for repeated queries to the interpolant.

F = griddedInterpolant(interpGrids,database);
tic 
solution2 = F({3000,1,1,2,-17,35,-4,.35,1:5500});
toc

Related Solutions

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.

MATLAB: GriddedInterpolant not a built-In Functions on a GPU

I'm not sure what you're asking, but if you're asking "am I right that I have to rewrite my code?" then yes, you are right.

Best Answer

Related Solutions

MATLAB: Fast interp1 with ‘spline’

MATLAB: GriddedInterpolant not a built-In Functions on a GPU

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