How to create a specific diagonal Matrix

Hi everyone! I'm trying to find the way to write a generic code to obtain a matrix like the one in this example:

if true
  A=[1 1 1 0 0 0 0 0 0;0 0 0 1 1 1 0 0 0;0 0 0 0 0 0 1 1 1]
end

To be clearer, i need a code to fill my matrix, which dimension is (T,T^2). In the example i have T=3. I need the general code because i need a matrix for each T i set, and it should respect the criteria of the example. This means that i have, for each row, a ones(1,T) vector that starts when the ones vector of the previous row ends. The first row should start with a ones(1,T) vector, as in the example. It is a sort of diagonal matrix i guess. I need it because it is part of the unequality constraints matrix in a linear program i'm developing. Hope someone could help me! thanks a lot in advance!

Answer 1

[Birdman]

Try this:

T=3;
for i=1:T
    A(i,:)=circshift([ones(1,T) zeros(1,T^2-T)],T*(i-1));
end

[Stefano Di Vito]

It worked. Thanks a lot, really!

[Birdman]

You are welcome!

Answer 2

[Stephen23]

That is exactly what blkdiag is for:

>> V = [1,1,1];
>> blkdiag(V,V,V)
ans =
   1   1   1   0   0   0   0   0   0
   0   0   0   1   1   1   0   0   0
   0   0   0   0   0   0   1   1   1

This is much simpler and much more efficient than trying to write your own code using loops. Remember that MATLAB is a high-level language, so loops are often not the best solution.

[Stefano Di Vito]

Thank you, it worked too. But if i had an high T, how would i obtain the right matrix order without typing (V,V,V,....) T-times? forgive my ignorance of course!

[Sean de Wolski]

x = repmat({[ones(1, 3)]}, 1, 3)
blkdiag(x{:})

[Stephen23]

@Stefano Di Vito: using the method that Sean de Wolski showed. It uses a comma-separated list to provide as many input arguments as you want:

https://www.mathworks.com/help/matlab/matlab_prog/comma-separated-lists.html

https://www.mathworks.com/matlabcentral/answers/320713-how-to-operate-on-comma-separated-lists