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.
