Matrix interpolation in the direction of the third dimension

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!

[Matt J]

It's not clear what you are doing, because ...

and the use of polyfit needs vectors

... polyfit doesn't do interpolation, it does curve fitting.

which is not provided in interp1

... interp1 doesn't do curve fitting, it does interpolation.

[Jan]

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

[John D'Errico]

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

Answer 1

[Gert Kruger]

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.

[John D'Errico]

Ano's answer moved to a comment:

Hello !

Thank you very much for your reply!

The code you proposed seems like exactly what I have been looking for, but when I perform a small test the new added matrices (the interpolated ones) differ greatly from the original values. Here is an example of the resylts I get

CM{1} =[1 4; 5 6];
CM{2}= [1 5; 8 9]; 
CM{3}= [1 3; 2 11];

while the obtained matrix A is such that

A(:,:,1) =
    1.0000   -7.7188
  -30.1563   12.0938
A(:,:,2) =
    1.0000  -56.7187
 -177.1563    5.0938

Note that A(:,:,1) must be inserted between CM{1} and CM{2} , while A(:,:,2) must be inserted between CM{2} and CM{3} . the difference between the entries of A and CM is big while they must in my case represent the same final matrix (2x2x5). any ideas ?!

Best regards!

[Gert Kruger]

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]

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?!