Matrix Manipulations - How to achieve these specific forms?

Dear Community,

I am struggling to achieve two distinct forms of matrices.

1) I want to build a matrix with the following form and dimensions of [8760 x 2*8760]

(1 1 0 0 0 0 ...
0 0 1 1 0 0 ...
0 0 0 0 1 1 ...
...)

2) I want to build a matrix with the following form and dimensions of [2*8760 x 2*8760]

(0 0 0 0 0 0 ...
  5 8 0 0 0 0 ...
  0 0 0 0 0 0 ...
  5 8 5 8 0 0 ...
  ...)

I just can't make that work, also I am fairly new to Matlab. I really hope somebody can see a solution here.

Thanks a lot, Mathias

[Stephen23]

Note: see Jos's answer if you actually want those matrices.

Answer 1

[Jos (10584)]

Bruno's and KSSV's answers do not create the matrices you asked for, or am I mistaken? Anyways, here are my suggestions:

N = 4 ; % small example, rather than N=8760

M1 = kron(eye(N), [1 1])
%     1     1     0     0     0     0     ...
%     0     0     1     1     0     0     ...
%     0     0     0     0     1     1     ...
%     ...

M2 = kron(tril(ones(N)), [0 0 ; 5 8])
%     0     0     0     0     0     ...
%     5     8     0     0     0     ...
%     0     0     0     0     0     ...
%     5     8     5     8     0     ...
%     ...

[Stephen23]

+1 this actually gives the matrices shown in the question.

[Bruno Luong]

I'm not 100% convinced since in the example of (2) given by OP we can't see a 2x2 block far below the diagonal, so there is still a confusion whereas the lower-diagonal or 2-diagonal by block is needed.

In anycase he/she gets the receipt to build the matrix.

Answer 2

[Bruno Luong]

>> A=diag(ones(1,5),0)+diag(ones(1,4),-1)

A =

     1     0     0     0     0
     1     1     0     0     0
     0     1     1     0     0
     0     0     1     1     0
     0     0     0     1     1

>> kron(A,[2 3; 5 8])

ans =

     2     3     0     0     0     0     0     0     0     0
     5     8     0     0     0     0     0     0     0     0
     2     3     2     3     0     0     0     0     0     0
     5     8     5     8     0     0     0     0     0     0
     0     0     2     3     2     3     0     0     0     0
     0     0     5     8     5     8     0     0     0     0
     0     0     0     0     2     3     2     3     0     0
     0     0     0     0     5     8     5     8     0     0
     0     0     0     0     0     0     2     3     2     3
     0     0     0     0     0     0     5     8     5     8

>>

[Mathias Dirksmeier]

Perfect, both work!

[Mathias Dirksmeier]

Still, the second matrix (if I put 0 0 instead of 2 3) should give what I was looking for. The first one does not though...

[Bruno Luong]

The first question is easily extrapolated (I did not give the answer for the first question)

FirstQuestionMat =diag(ones(1,5),0)+diag(ones(1,4),+1)

If you claim my solution for the second quetion is good, then Jos's answer is not, and vice-versa.

Look again the results, and be clear in you mind.

Better learn the technique rather than take the answer as it is.

[Mathias Dirksmeier]

Sorry, you are right. Your solution does not solve my problem.

Answer 3

[KSSV]

Read about diag

N = 10 ;

A = diag(ones(N,1))+diag(ones(N-1,1),-1) ;

[Mathias Dirksmeier]

Thanks!