How can I interpolate just one point on a given function while saving time?

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Renato Quartullo
Renato Quartullo 2021-3-19
评论： Michal 2023-8-25
Hi all,
I have a function and I have a collection of N couple of points , namely and respecting the function f. I want to evaluate my function in a single point out of set X, so . Until now I'm using the Matlab function = interp1(,'spline'). But maybe this methods requires a certain computational effort. Since I always evaluate my function on a single point (not a vector of points), is there an alternative function (or method) to interp1 to do this task that allows to save time?
Thank you in advance!
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Renato Quartullo
Renato Quartullo 2021-3-19
编辑：Renato Quartullo 2021-3-19
@Jan The spline method could be an accurate one, any other suggestion? (I tried with a linear interpolation, but it is not sufficient)
@Walter Roberson the vector X represent angles in degree, X = -360:0.5:359.5.
Image Analyst
Image Analyst 2021-3-20
Everything takes computation effort. Please state how long it takes, and how fast you need it to be. You can use tic and toc to time it.

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采纳的回答

Jan
Jan 2021-3-22
3 times faster without overhead, if you fokus on the neighborhood:
X = -360:0.5:359.5;
Y = rand(size(X));
xi = 7.59;
tic
for k = 1:1e4
yi1 = interp1(X, Y, xi,'spline');
end
toc
tic
index = find(xi >= X, 1, 'last');
XX = X(index-8:index+8);
for k = 1:1e4
F = griddedInterpolant(XX, Y(index-8:index+8), 'spline');
yi2 = F(xi);
end
toc
yi1 - yi2 % Of course a difference: RAND are very noisy input data
% Elapsed time is 1.554598 seconds.
% Elapsed time is 0.513496 seconds.

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Walter Roberson
Walter Roberson 2021-3-19
With the X being sorted and known increments, for any xstar you can directly compute the corresponding X bin that does not exceed xstar as xstar*2+721. Call that idx
jdxstart = min(max(1,idx-2), length(X) - 4);
jdx = jdxstart:jdxstart+4;
pp = spline(X(jdx), y(idx))
ystar = ppval(pp, xstar);
That is, we extract X y "near" xstar and spline only there to reduce the work.
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