Matrix interpolation in the direction of the third dimension

Question

Ano 2019-6-19

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评论： Ano 2019-6-28

Hello!

I would like to perform matrix (n x n) interpolation in the direction of the third dimension which is frequency (1 x N), in a way to obtain intermediate matrices which are the interpolated ones. In my case I need to perform quadratic interpolation method which is not provided in interp1, and the use of polyfit together with polyval needs vectors while I have matrices. any ideas how can I proceed? Thank you very much!

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Jan 2019-6-19

@Ano: Please mention, what your inputs are. You can use polyfit to get the scaling factors for each matrix.

John D'Errico 2019-6-24

Please don't add answers just to respond to an answer. Note that multiple people have made COMMENTS. Learn to use them.

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Answer 1

Gert Kruger 2019-6-19

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Here is my attempt at answering your question. I imagine that there are N matrices each with size nxn.

Example matrices:

%%
n = 10;     %Matrix size
N = 5;      %Number of matrices
%% Generate example matrices
for count = 1:N
   CM{count} = rand(n) ; %CM Cell array matrices
end

Then we fit quadratic functions along the third dimension.

%% Generate fits along the third dimension
temp_ar = zeros(1, N);
for x = 1:n
    for y = 1:n
        for z = 1:N
            temp_ar(z) = CM{z}(x, y);
        end
        Cfit{x, y} = fit( (1:N)', temp_ar', 'poly2');        
    end
end

Interpolation is achieved by evaluating the fitted functions:

%% Output matrix generation
%For example output matrix, A, must be 'halfway' between 2nd and 3rd input matrices
A = zeros(n);
z = 2.5;        %Evaluation depth
for x = 1:n
    for y = 1:n
        A(x, y) = Cfit{x, y}(z);        
    end
end

We can test the output matrix, by using the norm:

norm(CM{2} - A)
norm(CM{3} - A)
norm(CM{5} - A)

Note, that the measure of the difference for the first two is less than for the last one, because the matrix A slice is 'further away' from that depth.

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Gert Kruger 2019-6-27

Ano,

the matrices A in my proposed answer is generated from the CM matrices. In my case, when z=1, A=CM{1} and when z=2 then A=CM{2}.

I don't know what you mean by inserted. Do you instead mean that there are new matrices (sample points) which need to be sorted into the CM matrix list?

Ano 2019-6-28

First, thank you very much for your reply, I am grateful for that.

yes, which means that the obtained matrix A at z= 2.5 from your example need to be added into the final version of CM, therefore if I have at the beginning CM defined for 5 frequency samples, and I computed A let say for two additional intermediate samples (i.e., z= 2.5, and z =3.5) my final CM must be defined for 7 samples including the newly interpolated values represented by matrix A. Any suggestions?!

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