Question

For a matrix A (4 rows, 1000 columns). I want to group the columns of the matrix A which have the same value for the third line. so I must have sub matrix with a third row that contains the same value.

for example:

if:

A =

     1     4     5     2     2     2     2     1     1     5
     1     4     5     4     4     2     2     4     5     2
     3     3     3     3     4     1     3     5     3     4
     4     5     5     5     4     1     5     5     5     5

then

A1 =

     1     4     5     2     2     1
     1     4     5     4     2     5
     3     3     3     3     3     3
     4     5     5     5     5     5

A2 =

     2     5
     4     2
     4     4
     4     5

A3 =

     2
     2
     1
     1

the result can be in the form of a cell.

Answer 1

You can make the assignment in a single line using ACCUMARRAY:

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

out = accumarray(A(3,:)', (1:size(A,2)), [], @(x){A(:,x)} );

With this, out{i} contains all columns of A where the third row of A equals i (and empty in case there is no valid column).

If you want out{i} to contain columns corresponding to the i-th smallest unique value in the third row of A, you can use GRP2IDX from the statistics toolbox first:

[idx,correspondingEntryInA] = grp2idx(A(3,:)'); %'#
out = accumarray(idx, (1:size(A,2)), [], @(x){A(:,x)} );

Here, out{i} contains the columns corresponding to correspondingEntryInA(i).