# Matrix interpolation in the direction of the third dimension

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Ano on 19 Jun 2019
Commented: Ano on 28 Jun 2019
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!
John D'Errico on 24 Jun 2019

Gert Kruger on 19 Jun 2019
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.
Ano on 28 Jun 2019
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?!