Elementary matrices in Matlab

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Tim david
Tim david 2022-2-2
编辑： DGM 2022-2-17
I am very new to MATLAB, and I am trying to create a numerical scheme to solve a differential equation. However I am having trouble implementing matrices. I was wondering if anyone can help with constructing a following NxN matrix?
I am sure there is a better way to implement, but the following works
N=10
tod=zeros(N)
for k=1:(N-1)
tod(k, k+1)=-2
end
for k=1:(N-2)
tod(k, k+2)=1
end
tod_2=zeros(N)
for k=1:(N-1)
tod_2(k, k+1)=2
end
for k=1:(N-2)
tod_2(k, k+2)=-1
end
tran=transpose(tod_2)
Final=tran+tod

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回答（3 个）

DGM
DGM 2022-2-2
编辑：DGM 2022-2-17
Ran in:
(EDIT to fix misread)
Here's one way:
n = 8;
z = zeros(1,n-3);
R = toeplitz([0 2 -1 z],[0 -2 1 z])
R = 8×8
0 -2 1 0 0 0 0 0 2 0 -2 1 0 0 0 0 -1 2 0 -2 1 0 0 0 0 -1 2 0 -2 1 0 0 0 0 -1 2 0 -2 1 0 0 0 0 -1 2 0 -2 1 0 0 0 0 -1 2 0 -2 0 0 0 0 0 -1 2 0
  5 个评论
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DGM
DGM 2022-2-3
Oof . I totally overlooked that.
Stephen23
Stephen23 2022-2-3
@DGM: add it to your answer, no one will look in these comments.

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John D'Errico
John D'Errico 2022-2-2
Ran in:
So many ways to do this. DGM showed a great way using toeplitz. But there are others. For example, you could use diag.
n = 5;
R = diag(ones(n-2,1),2) - 2*diag(ones(n-1,1),1); R = R + R'
R = 5×5
0 -2 1 0 0 -2 0 -2 1 0 1 -2 0 -2 1 0 1 -2 0 -2 0 0 1 -2 0
Or use spdiags, creating the matrix directly. Since your matrix is banded, if n is at all large, then you truly want to learn to use sparse matrices.
n = 10;
R = spdiags(ones(n,1)*[1 -2 -2 1],[-2 -1 1 2],n,n);
R is now a sparse matrix, so it will offer great advantages in computing when n grows large.
spy(R)
full(R)
ans = 10×10
0 -2 1 0 0 0 0 0 0 0 -2 0 -2 1 0 0 0 0 0 0 1 -2 0 -2 1 0 0 0 0 0 0 1 -2 0 -2 1 0 0 0 0 0 0 1 -2 0 -2 1 0 0 0 0 0 0 1 -2 0 -2 1 0 0 0 0 0 0 1 -2 0 -2 1 0 0 0 0 0 0 1 -2 0 -2 1 0 0 0 0 0 0 1 -2 0 -2 0 0 0 0 0 0 0 1 -2 0
I could probably have used tools like meshgrid, tril and triu.
Voss
Voss 2022-2-2
Ran in:
Here's one way you can do it (and it produces the correct matrix too):
N = 10;
R = zeros(N);
R(2:N+1:end-N) = 2;
R(3:N+1:end-2*N) = -1;
R(N+1:N+1:end-1) = -2;
R(2*N+1:N+1:end-2) = 1;
R
R = 10×10
0 -2 1 0 0 0 0 0 0 0 2 0 -2 1 0 0 0 0 0 0 -1 2 0 -2 1 0 0 0 0 0 0 -1 2 0 -2 1 0 0 0 0 0 0 -1 2 0 -2 1 0 0 0 0 0 0 -1 2 0 -2 1 0 0 0 0 0 0 -1 2 0 -2 1 0 0 0 0 0 0 -1 2 0 -2 1 0 0 0 0 0 0 -1 2 0 -2 0 0 0 0 0 0 0 -1 2 0

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