Can someone explain this example of deleting elements from a matrix in MATLAB?

Question

The following example appears in the MATLAB tutorial:

X = [16  2 13;
     5  11  8;
     9   7 12;
     4  14  1]

Using a single subscript deletes a single element, or sequence of elements, and reshapes the remaining elements into a row vector. So:

X(2:2:10) = []

results in:

X = [16 9 2 7 13 12 1]

Mysteriously, the entire 2nd row and the first two elements in the 4th row have been deleted, but I can't see the correspondence between the position of the deleted elements and the index vector 2:2:10. Can someone please explain?

Answer 1

The example you gave shows "linear indexing". When you have a multidimensional array and you give it a single scalar or vector, it indexes along each column from top to bottom and left to right. Here's an example of indexing into each dimension:

mat = [1 4 7;...
       2 5 8;...
       3 6 9];
submat = mat(1:2,1:2);

"submat" will contain the top left corner of the matrix: [1 4; 2 5]. This is because the first 1:2 in the subindex accesses the first dimension (rows) and the second 1:2 accesses the second dimension (columns), extracting a 2-by-2 square. If I don't supply an index for each dimension, separated by commas, but instead just one index, MATLAB will index into the matrix as though it were one big column vector:

submat = mat(3,3);  % "Normal" indexing: extracts element "9"
submat = mat(9);    % Linear indexing: also extracts element "9"
submat = mat([1 5 6]);  % Extracts elements "1", "5", and "6"

The MATLAB documentation can explain further.

Answer 2

It's very simple.

It basically starts from the second element in this example and goes upto tenth element (column wise) in steps of 2 and deletes corresponding elements. The remaining elements result in a row vector.