Create a double identity matrix matlab

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Afluo Raoual
Afluo Raoual 2022 年 3 月 11 日
編集済み: John D'Errico 2022 年 3 月 11 日
If we have an identity matrix of dimensions (M*M) we use:
M=12;
K=eye(M);
But how can we obtain this matrix in general way: (it means double the identity)
K =
1 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0 0
0 0 1 1 0 0 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0 0 0
0 0 0 0 1 1 0 0 0 0 0 0
0 0 0 0 0 1 1 0 0 0 0 0
0 0 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 1 1 0 0 0
0 0 0 0 0 0 0 0 1 1 0 0
0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 1 1

採用された回答

John D'Errico
John D'Errico 2022 年 3 月 11 日
編集済み: John D'Errico 2022 年 3 月 11 日
There are many basic ways, some not so basic. Perhaps my favorite is just:
n = 8;
A = triu(tril(ones(n)),-1)
A = 8×8
1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1
Here is another easy one:
A = eye(n) + diag(ones(n-1,1),-1)
A = 8×8
1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1
And yet another cute one is:
A = toeplitz([1 1,zeros(1,n-2)],[1,zeros(1,n-1)])
A = 8×8
1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1
Oh, wait. This next one is just too pretty to disregard:
flip(hankel([zeros(1,n-2),1 1]))
ans = 8×8
1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1
Of course, if n is seriously large, then you would want to create the result as a sparse matrix. Now spdiags is clearly a great solution.
n = 30;
A = spdiags(ones(n,2),[-1,0],n,n);
spy(A)
Actually, 30 is not at all large in context, but I made n only 30 so you could see that it worked. For a sparse matrix to be truly valuable, I'd only worry about it if n was on the order of 1000 or more.
The trick to solving such a problem in MATLAB is to get used to understanding how the various matrix tools can be used, and some experience in seeing how elements are stored in matrices. That helps you to see the many possible solutions to such a problem. Already in my mind I can see at least one other fairly simple solution. No, two more, at least. I could use meshgrid, maybe use indexing, or god forbid, a loop. Nah, skip the loop. Other ways should be there too.

その他の回答 (3 件)

KSSV
KSSV 2022 年 3 月 11 日
M=12;
K=eye(M);
K(2:1+size(K,1):end) = 1
K = 12×12
1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0

Ive J
Ive J 2022 年 3 月 11 日
Maybe not the best way, but works:
% taken from doc kron
n = 12;
I = speye(n, n);
E = sparse(2:n, 1:n-1, 1, n, n);
K = full(I + E)
K = 12×12
1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0

Sugar Daddy
Sugar Daddy 2022 年 3 月 11 日
Daddy is here for help
M = 12;
K = transpose(eye(M)+triu(circshift(eye(M),1,2)))
K = 12×12
1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0

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