Interpolate matrices for different times in Matlab

I have computed variables stored in a matrix for a specific time vector. Now I want to interpolate between those whole matrices for a new time vector to get the matrices for the desired new time vector.

I've came up with the following solution but it seems clunky and computational demanding:

    clear all;

    a(:,:,1) = [1 1 1;2 2 2;3 3 3]; % Matrix 1
    a(:,:,2) = [4 4 4;6 6 6;8 8 8]; % Matrix 2

    t1 = [1 2]; % Old time vector

    t2 = [1 1.5 2]; % New time vector

    % Interpolation for each matrix element
    for r = 1:1:size(a,2)
    for c = 1:1:size(a,1)
    tab(:) = a(r,c,:);
    tabInterp(r,c,:) = interp1(t1,tab(:),t2);
    end
    end

The result is and should be:

    [2.5000    2.5000    2.5000
        4.0000    4.0000    4.0000
        5.5000    5.5000    5.5000]

Any thoughts?

Answer 1

[Stephen23]

Simpler in just one line and more efficient without all of those intermediate variables:

>> a(:,:,1) = [1 1 1;2 2 2;3 3 3];
>> a(:,:,2) = [4 4 4;6 6 6;8 8 8];
>> b = permute(interp1([1,2],permute(a,[3,2,1]),[1,1.5,2]),[3,2,1])
b(:,:,1) =
   1   1   1
   2   2   2
   3   3   3
b(:,:,2) =
   2.5000   2.5000   2.5000
   4.0000   4.0000   4.0000
   5.5000   5.5000   5.5000
b(:,:,3) =
   4   4   4
   6   6   6
   8   8   8

And compared to your original code:

>> isequal(tabInterp,b)
ans = 1

[mldmnn]

That is even better than the other answer! Nice to learn from experts!

Answer 2

[Ameer Hamza]

You can use interp3 as follow:

clear all;
a(:,:,1) = [1 1 1;2 2 2;3 3 3]; % Matrix 1
a(:,:,2) = [4 4 4;6 6 6;8 8 8]; % Matrix 2
t1 = [1 2]; % Old time vector
t2 = [1 1.5 2]; % New time vector
% Interpolation for each matrix element
[X, Y, Z] = meshgrid(1:size(a,1), 1:size(a,2), t1);
[X2, Y2, Z2] = meshgrid(1:size(a,1), 1:size(a,2), t2);
tabInterp = interp3(X,Y,Z,a,X2,Y2,Z2);

[mldmnn]

It works very well. Thank you! Didn't think about using interp3 for this issue.

[Ameer Hamza]

You are welcome.