How to extract vectors from a given condition matrix in Octave

Question

I'm trying to extract a matrix with two columns. The first column is the data that I want to group into a vector, while the second column is information about the group.

A =
1   1
2   1
7   2
9   2
7   3
10  3
13  3
1   4
5   4
17  4
1   5
6   5

the result that i seek are

A1 =
1
2

A2 =
7 
9 

A3 =
7 
10
13

A4=
1 
5 
17

A5 =
1 
6 

as an illustration, I used the eval function but it didn't give the results I wanted

Answer 1

Assuming that you don't actually need individually named separated variables, the following will put the values into separate cells of a cell array, each of which can be an arbitrary size and which can be then retrieved using cell index syntax. It makes used of logical indexing so that each iteration of the for loop assigns to that cell in B just the values from the first column of A that have the correct number in the second column of A.

num_cells = max (A(:,2));

B = cell (num_cells,1);

for idx = 1:max(A(:,2))
  B(idx) = A((A(:,2)==idx),1);
end

B =
{
  [1,1] =

     1
     2

  [2,1] =

     7
     9

  [3,1] =

      7
     10
     13

  [4,1] =

      1
      5
     17

  [5,1] =

     1
     6

}

Cell arrays are accessed a bit differently than normal numeric arrays. Array indexing (with ()) will return another cell, e.g.:

>> B(1)
ans =
{
  [1,1] =

     1
     2

}

To get the contents of the cell so that you can work with them like any other variable, index them using {}.

>> B{1}
ans =

   1
   2

How it works:

Use max(A(:,2)) to find out how many array elements are going to be needed. A(:,2) uses subscript notation to indicate every value of A in column 2.

Create an empty cell array B with the right number of cells to contain the separated parts of A. This isn't strictly necessary, but with large amounts of data, things can slow down a lot if you keep adding on to the end of an array. Pre-allocating is usually better.

For each iteration of the for loop, it determines which elements in the 2nd column of A have the value matching the value of idx. This returns a logical array. For example, for the third time through the for loop, idx = 3, and:

>> A_index3 = A(:,2)==3
A_index3 =

  0
  0
  0
  0
  1
  1
  1
  0
  0
  0
  0
  0

That is a logical array of trues/falses indicating which elements equal 3. You are allowed to mix both logical and subscripts when indexing. So using this we can retrieve just those values from the first column:

 A(A_index3, 1)
ans =

    7
   10
   13

we get the same result if we do it in a single line without the A_index3 intermediate placeholder:

>> A(A(:,2)==3, 1)
ans =

    7
   10
   13

Putting it in a for loop where 3 is replaced by the loop variable idx, and we assign the answer to the idx location in B, we get all of the values separated into different cells.