The colon notation used in multidimensional array

I have come across the following notation in MATLAB

    y(:, :, :, 2) = y(:, :, :, 1);

    y(:, 1, :, 4) = y(:, 1, :, 3);

I have no clue what it means?

I know for matrix A(:,1) and A(1,:) means extract first column and first row respectively. But the above is not clear to me.

Thanks.

Answer 1

[Adam]

It is just an extension of what you already know, but for multi-dimensional arrays. You can no longer use terms like 'rows' and 'columns' unless you have n ever more creative names for each dimension, but the logic is the same. Take all data from the dimensions that have a : and only the specified data from the dimensions which you give an exact index for.

Personally I rarely if ever use arrays of dimensionality higher than 3 because I like to be able to visualise what indexing means and since I can't visualise beyond a 3d cube I easily get confused. That said, the logic works the same whether it can be visualised intuitively or not!

[DM]

wait so does A(:,1) mean take all rows and first column, or just first column? Because your statement Take all data from the dimensions that have a : and only the specified data from the dimensions which you give an exact index for. confused me.

[Adam]

A(:,1) says take all rows, 1st column.

My statement may not have been worded perfectly, but it should be interpreted as a 1 (or a 6 or 34 or whatever) as an index will take just the data for that specific index into that dimension. Any dimension where you specify a : takes all data from that dimension.

[DM]

But it gives me just second column not all rows. See example below

 A=[2, 3, 4; 0, 5, 7]
  A =
     2   3   4
     0   5   7
  > A(:, 2)
  ans =
     3
     5

[Adam]

It gives you all rows of the 2nd column. It's basically like a filter. It would give you all rows, but you told it to only give you column 2 so all other elements of the rows are thrown away.

Answer 2

[Guillaume]

The colon is exactly the same as writing 1:end. In your example, naming the dimensions y, x, z, and t

y(:, :, :, 2) = y(:, :, :, 1);

copy all the values at t = 1 to t = 2 and

y(:, 1, :, 4) = y(:, 1, :, 3);

copy all the values at x = 1 and t = 3 to x = 1 and t = 4.