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Matrix interpolation in the direction of the third dimension

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Ano on 19 Jun 2019
Commented: Ano on 28 Jun 2019
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
John D'Errico on 24 Jun 2019
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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Answers (1)

Gert Kruger
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
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);
Cfit{x, y} = fit( (1:N)', temp_ar', 'poly2');
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);
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?!

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