Linear Interpolation code without using interp1

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Radu-Andrei
Radu-Andrei 2023-10-5
编辑： Matt J 2023-10-5
I need to write a code that does linear interpolation. (without using interp1) My function has 3 inputs (n,x,n2). Vector n contains the sample points, and x contains the corresponding values, x(n). Vector n2 contains the coordinates of the query points. My code is this:
function ynew = interpolate(n,x,n2)
for i = 1:length(n2)
for j = 1:length(n)-1
if n2(i) >= n(j) & n2(i) <= n(j+1)
ynew(i) = x(j) + (x(j+1)-x(j))/(n(j+1)-n(j)) * (n2(i)-n(j));
end
end
end
end
The problem is that it is much slower than interp1(n,x,n2,'linear'). How can I write a code that works faster?
  1 个评论
Matt J
Matt J 2023-10-5
What is the purpose of rewriting interp1? If it is a homework exercise, I don't think speed is supposed to matter.

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回答（3 个）

Torsten
Torsten 2023-10-5
编辑：Torsten 2023-10-5
How can I write a code that works faster?
Allocate ynew = zeros(size(n2)) at the beginning of your code.
Check whether n is monotonically ordered.
Check whether min(n) <= n2 <= max(n).
After you have implemented these three points and you want to speed up your code, edit and understand interp1.
(Means: you shouldn't expect your code to be as fast as a professional code. What you've done on your own is not that bad).
  2 个评论
Radu-Andrei
Radu-Andrei 2023-10-5
Thank you for the suggetions, Torsten. I've tried to look into interp1 but it is a bit overwhelming because there are so many built in functions. At some point interp1 executes this line:
VqLite = matlab.internal.math.interp1(X,V,method,method,Xqcol);
So interp1 uses itself? I don't see the logic.
Torsten
Torsten 2023-10-5
Most probably, interp1.m is only a driver function for the user. The real algorithmic implementation of the interpolation algorithm is hidden in this internal function.

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Matt J
Matt J 2023-10-5
编辑：Matt J 2023-10-5
Ran in:
n=1:8;
x=rand(size(n));
n2=[1.8, 3.2, 6.7];
interp1(n,x,n2)
ans = 1×3
0.1287 0.9405 0.3349
interpolate(n,x,n2)
ans = 1×3
0.1287 0.9405 0.3349
function ynew = interpolate(n,x,n2)
I=discretize(n2,n);
w=(n2-n(I))./(n(I+1)-n(I));
ynew= x(I+1).*w + x(I).*(1-w);
end
Matt J
Matt J 2023-10-5
编辑：Matt J 2023-10-5
function ynew = interpolate(n,x,n2) %Doesn't use interp1
F=griddedInterpolant(n,x);
ynew=F(n2);
end

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