what does this code do ?

   r1=r1(:,1:length(r1)-1)

Answer 1

[Adam]

It removes the last element of r1 in a rather over the top manner. Basically the same as:

r1(end) = [];

if r1 is a vector.

Edit:

As pointed out by John D'Errico below and added here to correct the answer, since r1 is a matrix rather than a vector

r(:,end) = [];

is the way to achieve the equivalent and remove the final column as oppose to just the final element as the example above would do for a vector.

See John's comment below for more detail.

[John D'Errico]

Be careful. The indicated code from the OP deletes the last column of a matrix, or if it is a row vector, the final element. I do agree that the operation was done in an over-the-top manner.

r = magic(3)
r =
   8     1     6
   3     5     7
   4     9     2

r(end) = []
r =
     8     3     4     1     5     9     6     7

If your goal is to actually remove the last column of a matrix, you would be better off doing it like this:

r = magic(3);
r(:,end) = []
r =
     8     1
     3     5
     4     9

[Adam]

Ah yes, I missed the double indexing.