MATLAB: How to assign parts of a main matrix equal to the indexed sub matrices

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In matlab if we have a main matrix

A=[1 2 1 2;3 4 3 4;1 2 1 2;3 4 3 4]

which is a 4*4 matrix divided into 2*2 sub blocks. If we want to get all the i'th values (1st,2nd,3rd,4th) of each sub matrix indexed to a single matrix.i.e., what I have to do to get the output as :

AA(1)=[1 1;1 1] ;
AA(2)=[2 2;2 2] ;
AA(3)=[3 3;3 3]; 
AA(4)=[4 4;4 4]

what if the size of main matrix is large say 512*348?

Best Answer

This will work for any size matrix:

cat(3,...
    A(1:2:end,1:2:end),...
    A(1:2:end,2:2:end),...
    A(2:2:end,1:2:end),...
    A(2:2:end,2:2:end))

If you want an arbitrary number of i-th submatrices, then use reshape and permute.

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MATLAB: How can enlarge a matrix

If you have MATLAB R2015a (or more recent) then you can use repelem.

Otherwise you could try this FEX submission:

http://de.mathworks.com/matlabcentral/fileexchange/24536-expand

Or else you have to calculate it yourself, the easiest way is to use kron:

>> m = [1,2;3,4];
>> n = 5;
>> kron(m,ones(n))
ans =
     1     1     1     1     1     2     2     2     2     2
     1     1     1     1     1     2     2     2     2     2
     1     1     1     1     1     2     2     2     2     2
     1     1     1     1     1     2     2     2     2     2
     1     1     1     1     1     2     2     2     2     2
     3     3     3     3     3     4     4     4     4     4
     3     3     3     3     3     4     4     4     4     4
     3     3     3     3     3     4     4     4     4     4
     3     3     3     3     3     4     4     4     4     4
     3     3     3     3     3     4     4     4     4     4

MATLAB: How to assign values of each sub matrix from main matriix into another matrix

Assuming that the number of input matrix rows/columns are exact multiples of the number of submatrix rows/columns, then this does the job quite nicely:

A = [1,2,1,2;3,4,3,4;1,2,1,2;3,4,3,4] % input array
[Ar,Ac] = size(A);
Nr = 2; % submatrix rows


Nc = 2; % submatrix columns


Sr = Ar/Nr;
Sc = Ac/Nc;
C = cell(Sr,Sc); % preallocate output cell array
for Kr = 1:Sr
    for Kc = 1:Sc
        C{Kr,Kc} = A(Kr:Sr:end,Kc:Sc:end);
    end
end

You can easily concatenate the cell array contents into one numeric array:

Z = cat(3,C{:})

There are probably ways of doing this using reshape and permute, but the loop is easier to understand and is likely reasonably efficient anyway. Tested on the matrix from the original question:

>> A = [1,2,1,2;3,4,3,4;1,2,1,2;3,4,3,4]
A =
   1   2   1   2
   3   4   3   4
   1   2   1   2
   3   4   3   4
>> Nr = 2; % submatrix rows
>> Nc = 2; % submatrix columns
...
>> C{:}
ans =
   1   1
   1   1
ans =
   3   3
   3   3
ans =
   2   2
   2   2
ans =
   4   4
   4   4

And a larger example:

>> A = [1,2,3,4,1,2,3,4;5,6,7,8,5,6,7,8];
>> A = [A;A;A;A]
A =
   1   2   3   4   1   2   3   4
   5   6   7   8   5   6   7   8
   1   2   3   4   1   2   3   4
   5   6   7   8   5   6   7   8
   1   2   3   4   1   2   3   4
   5   6   7   8   5   6   7   8
   1   2   3   4   1   2   3   4
   5   6   7   8   5   6   7   8
>> Nr = 4; % submatrix rows
>> Nc = 2; % submatrix columns
...
>> C{:}
ans =
   1   1
   1   1
   1   1
   1   1
ans =
   5   5
   5   5
   5   5
   5   5
ans =
   2   2
   2   2
   2   2
   2   2
ans =
   6   6
   6   6
   6   6
   6   6
ans =
   3   3
   3   3
   3   3
   3   3
ans =
   7   7
   7   7
   7   7
   7   7
ans =
   4   4
   4   4
   4   4
   4   4
ans =
   8   8
   8   8
   8   8
   8   8

Best Answer

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MATLAB: How to assign values of each sub matrix from main matriix into another matrix

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