Most efficient way to put vector on the off-diagonal of the blocks of a block matrix
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I have two vectors each of the same length, and I want to put these vectors on the diagonal parts of each block of a matrix. Let's say my two vectors are and , both are of length , I am trying to construct an matrix that looks like
For example if my vectors were v = [1 2 3 4 5 6 7 8 9 8 7 6] and u = [9 8 7 6 5 4 3 2 1 2 3 4] then I would mant a matrix that looks like
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
9 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 8 0 3 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 6 0 5 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 5 0 6 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 3 0 8 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 2 0 9 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 2 0 7 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 6;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0;
]
I would like to know what an efficient way of doing this, particularly with sparse arrays I could create this matrix.
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Stephen23
2023 年 5 月 23 日
編集済み: Stephen23
2023 年 5 月 23 日
v = [1,2,3,4,5,6,7,8,9,8,7,6];
u = [9,8,7,6,5,4,3,2,1,2,3,4];
L = sqrt(numel(v));
vM = reshape(v,fix(L),[]);
uM = reshape(u,fix(L),[]);
vM(end+1,:) = 0;
uM(end+1,:) = 0;
vM([2:end,1],:) = vM;
N = ceil(L).^2;
M = spdiags([uM(:),vM(:)],[-1,1],N,N);
Checking:
full(M)
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その他の回答 (2 件)
David Goodmanson
2023 年 5 月 24 日
編集済み: David Goodmanson
2023 年 5 月 24 日
Hi David,
MODIFIED
see Dyuman's comment to sensibly shorten this original code.
n = 4;
v = [1 2 3 4 5 6 7 8 9 8 7 6]; % length n*(n-1)
u = [9 8 7 6 5 4 3 2 1 2 3 4];
vv = [reshape(v,n-1,n); zeros(1,n)];
vv = vv(:);
vv(end) = [];
uu = [reshape(u,n-1,n); zeros(1,n)];
uu = uu(:);
uu(end) = [];
M = diag(vv,1) + diag(uu,-1)
you can cut even more lines using the code below but at the cost of transparancy, so I think Dyuman's version is the best one.
n = 4;
v = [1 2 3 4 5 6 7 8 9 8 7 6];
u = [9 8 7 6 5 4 3 2 1 2 3 4];
uv = [reshape([v u],n-1,2*n);zeros(1,2*n)];
M = diag(uv(1:n^2-1),1) + diag(uv(n^2+1:2*n^2-1),-1)
1 件のコメント
Dyuman Joshi
2023 年 5 月 24 日
You can use indexing to shorten the code by 2 lines -
n = 4;
v = [1 2 3 4 5 6 7 8 9 8 7 6]; % length n*(n-1)
u = [9 8 7 6 5 4 3 2 1 2 3 4];
vv = [reshape(v,n-1,n); zeros(1,n)];
vv = vv(1:end-1);
uu = [reshape(u,n-1,n); zeros(1,n)];
uu = uu(1:end-1);
M = diag(vv,1) + diag(uu,-1)
John D'Errico
2023 年 5 月 23 日
The most efficient way? SPDIAGS.
help spdiags
For example, to create a 6x6 sparse matrix, with an upper and lower diagonal elements as vectors of length 5, we do this:
V1 = randi(10,[5,1]); % Just some random numbers.
V2 = randi(10,[5,1]);
A = spdiags([[V1;nan],[nan;V2]],[-1,1],6,6)
full(A)
spy(A)
Note that I padded an extra element, a NaN in this case, at the beginning of V2 and the end of V1.
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