Collapsing matrix into columns

Question

I have a 2D matrix where the № of columns is always a multiple of 3 (e.g. 250×27) - due to a repeating organisation of the results (A,B,C, A,B,C, A,B,C, and so forth). I wish to reshape this matrix to create a new matrix with 3 columns - each containing the aggregated data for each type (A,B,C) (e.g. 2250×3).

So in a matrix of 250×27, all the data in columns 1,4,7,10,13,16,19,22,25 would be merged to form the first column of the resulting reshaped matrix.

The second column in the resulting reshaped matrix would contain all the data from columns 2,5,8,11,14,17,20,23,26 - and so forth.

Is there a simple way to do this in MATLAB? I only know how to use reshape if the columns I wanted to merge were adjacent (1,2,3,4,5,6) rather than non-adjacent (1,4,7,10,13,16) etc.

Answer 1

Shameless steal from @Divakar:

B = reshape( permute( reshape(A,size(A,1),3,[]), [1,3,2]), [], 3 );

Answer 2

Let A be your matrix. You can save every third column in one matrix like: (Note that you don't have to save them as matrices separately but it makes this example easier to read).

A = rand(27); %as test
B = A(:,1:3:end);
C = A(:,2:3:end);
D = A(:,3:3:end);

Then you use reshape:

B = reshape(B,[],1);
C = reshape(C,[],1);
D = reshape(D,[],1);

And finally put it all together:

A = [B C D];

Answer 3

You can just treat every set of columns as a single item and do three reshapes together. This should do the trick:

[save as "reshape3.m" file in your Matlab folder to call it as a function]

function out = reshape3(in)
    [~,C]=size(in); % determine number of columns
    if mod(C,3) ~=0 
        error('ERROR: Number of rows must be a multiple of 3')
    end

    R_out=numel(in)/3; % number of rows in output

    % Reshape columns 1,4,7 together as new column 1, column 2,5,8 as new col 2 and so on
    out=[reshape(in(:,1:3:end),R_out,1), ...
        reshape(in(:,2:3:end),R_out,1), ...
        reshape(in(:,3:3:end),R_out,1)];
end

Answer 4

Lets suppose you have a 3x6 matrix A

A = [1 2 3 4 5 6;6 5 4 3 2 1;2 3 4 5 6 7]
A =

     1     2     3     4     5     6
     6     5     4     3     2     1
     2     3     4     5     6     7

you extract the size of the matrix

b =size(A)

and then extract each third column for a single row

c1 = A((1:b(1)),[1:3:b(2)])
c2 = A((1:b(1)),[2:3:b(2)])
c3 = A((1:b(1)),[3:3:b(2)])

and put them in one matrix

A_result = [c1(:) c2(:) c3(:)]

A_result =

     1     2     3
     6     5     4
     2     3     4
     4     5     6
     3     2     1
     5     6     7