Create matrix by repeatedly overlapping a vector

Question

I\'m having great difficulty coding the following in MATLAB: Suppose you have the following vector:

a   
b
c
d
e
f
g
h
...

Specifying an (e

Answer 1

Short answer

bsxfun is your friend in this case. The following one-liner (assuming you know L and v is your vector) does what you want

v(bsxfun(@plus, [0:L-1]', 1:L/2:numel(v)-L))

Explanation

To try it out and understand it, lets have a further look. The idea is to first create a vector that determines, where the windows start in the v vector. Windows start every L/2 entries (L is even, so we can divide). But how many windows fit? We can rely on MATLAB to figure this out by saying:

start_offset = 1:L/2:numel(v)-L;

Here we just only need to specify that

• first window is at at index 1
• windows start every L/2 entries
• the last window should start at least L entries before the end of the v vector. So that the last window fist in there.

Now, the rest of the example:

v = 'a':'z';
L = 4;

% indices in every output matrix column are contiguous
% and the difference between first and last is `L-1`
id1 = [0:L-1]';

% start_offset determines where in the input vector v every window starts.
% windows start every L/2 entries. The last entry that fits will start
% at some index, from which we can still use L subsequent indices to access v
start_offset = 1:L/2:numel(v)-L;

% calculate how many entries were dropped from v
% from number of elements in v subtract the largest index value used
dropped = numel(v) - (start_offset+L-1);

% window indices are created using bsxfun and singleton expansion.
% Every window's indices are given by [0:L-1] + window start index
idx = bsxfun(@plus, id1, start_offset);

v(x)

ans =

  acegikmoqsu
  bdfhjlnprtv
  cegikmoqsuw
  dfhjlnprtvx