1D interpolation with non-monotonic scattered data

Question

Kim 2014-10-20

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https://ww2.mathworks.cn/matlabcentral/answers/159322-1d-interpolation-with-non-monotonic-scattered-data

回答： AlexL 2022-7-19

I cant figure out how do 1D interpolation with scattered data. I know how to get it working with 2D interpolation, but scatteredinterpolant only works with 2D or more. Thank you for your help!

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Answer 1

Andrei Bobrov 2014-10-20

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https://ww2.mathworks.cn/matlabcentral/answers/159322-1d-interpolation-with-non-monotonic-scattered-data#answer_155847

编辑：Andrei Bobrov 2014-10-20

在 MATLAB Online 中打开

Use griddedInterpolant-class

small example:

x = rand(30,2); % you data
x1 = sortrows(x,1);
F = griddedInterpolant(x1(:,1),x1(:,2));
out = F(xinput);

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Kim 2014-10-20

I just tried it and I got the following message: Error using griddedInterpolant The grid vectors are not strictly monotonic increasing.

Andrei Bobrov 2014-10-20

please see small example in my answer

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Answer 2

Riley 2016-10-5

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https://ww2.mathworks.cn/matlabcentral/answers/159322-1d-interpolation-with-non-monotonic-scattered-data#answer_237592

在 MATLAB Online 中打开

Just ran into this same issue, however the solution posted seems to avoid tackling an important detail here- griddedInterpolant, unlike scatteredInterpolant, doesn't remove repeated index points (at least, on 2015a). For example:

x = rand(30,2); % clean data
x1 = sortrows(x,1);
F = griddedInterpolant(x1(:,1),x1(:,2)); % this is fine
x_repeat = x1(:,1);x_repeat(2) =  x_repeat(3); % introduce a repeated index point
F = griddedInterpolant(x_repeat,x1(:,2)); %produces an error

compare that to the scatteredInterpolant class-

x = rand(30,3); % clean data
x1 = sortrows(x,1);
x_repeat = x1(:,1:2);x_repeat(2,:) =  x_repeat(3,:); % introduce a repeated index point
F = scatteredInterpolant(x_repeat,x1(:,3)); %rather than throwing an error, shows a warning and cleans your data for you

however, as scatteredInterpolant requires at least 2 dimensions for its indices, this doesn't work for 1d interpolation. Clearly at this point you can add your own cleaning method, but if you are using this class chances are you are trying to avoid writing that sort of code in the first place. As such, here's a hack I used to use the scatteredInterpolant cleaning method on a 1d data set-

xi = rand(30,1);%indices
x = sort(xi);
v = rand(30,1);% values
xq = [0.5 0.6];% query indices
x(2) = x(3);% the repeated index
Fs = scatteredInterpolant(x*ones(1,2),v);%make 1d into 2d
%note that the sane thing to do doesn't work: vq = Fs(xq'*ones(1,2)) produces an empty vector
F = griddedInterpolant(Fs.Points(:,1),Fs.Values);
vq = F(xq);