Inserting Ones at pseudo-fixed Intervals - matlab

Question

I have the following row vector:
A = zeros(1,200);
I'd like to insert a '1' every 2-3 columns until I have exactly 80 ones in total that are approximately evenly spaced - as opposed to having fixed spacing - with the first 2 columns being zeros.
e.g.
0 0 1 0 1 0 0 1 0 0 1 0 1 ...
It would be nice if the combination could be permuted as well so that more than one row vector satisfies the criteria.
Thanks!

Answer 1

You could use repelem (run-length encoding) to do this. The way that repelem works is that we have two inputs: the values and the number of times each value is repeated.
For example
values = [0 1];
repeats = [1 2];
repelem(values, repeats)
% 0 1 1
We can also have duplicate values in the values array
values = [0 1 0 1];
repeats = [2 1 1 1];
repelem(values, repeats)
% 0 0 1 0 1
We can utilize this to solve your problem.
First we construct the values matrices to simply alternate between 0 and 1 meaning that we want the expanded matrix to contain some 0's followed by a 1, some 0's followed by a 1, etc.
values = ~mod(1:80, 2);
% 0 1 0 1 0 1 0 1 ....
In your case, the number of times each 0 is going to be repeated is going to be either 1 or 2. Each 1 however, is only going to be repeated once. To make this happen we use rand to pick randomly between 1 and 2 repeats. Then we assign all the repeats for 1 values to be a single repeat.
repeats = randi([1 2], size(values));
% Make sure that the 1's are always only repeated once
repeats(values) = 1;
We use 80 entries in the repeats and values arrays just to make sure that we end up with at least 80 values in the final (expanded) array.
Now apply the repelem and keep only the first 80 values
result = repelem(values, repeats);
result = result(1:80);
% 0 1 0 0 1 0 0 1 0 1 0 0 1

Answer 2

You can do this with a few standard functions and array indexing. Something like this ...
A = zeros(1,200);
ixs = round(cumsum(2 + rand(200,1)));
A(ixs(ixs<200))=1;
%Sample result here, first 20 entries: 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1
What we're doing here is:
Setting up the A array (this is clear)
Defining an oversized array of index values to set to one (more on that below)
Then using that index to set values to one, trimming the oversize.
In terms of creating the index ixs, in innermost portion (2 + rand(200,1)) creates a 200x1 array of values between 2 and 3. Using cumsum generates the cumulative sum of this array, and then round rounds the values to an integer, which can be used for indexing. For example, the first 10 values is ixs look like this, for a particular run:
>> ixs(1:10)'
ans =
3 5 8 11 13 16 18 20 22 24
Since the number of 1 values will vary each time, I set this up to be oversized. That is, the last few values are [487 489 491 497 500], larger than the actual size required. This is why the values need to be trimmed with applying the index.

Answer 3

A = zeros(1,200);
idx = cumsum(1 + randi(2,80,1)); % This is the main trick
A(idx) = 1;
cumsum(1 + randi(2,80,1)) gets you the indexes for exactly 80 elements in A which need to be switched to 1 spaced by 2 or 3 (randomly)