How can I replace the upper off diagonal(super diagonal) and lower off diagonal(sub diagonal) of a matrix?
16 views (last 30 days)
Show older comments
Given a symmetric tridiagonal matrix T generated by
n=5;
p=1;
q=1.7;
r=1;
T=full(gallery('tridiagonal',n,p,q,r));
T=[1.8 1 0 0 0;1 1.8 0 0 0;0 1 1.8 1 0;0 0 1 1.8 1;0 0 0 1 1.8]
How do I change the 1 1 1 1 on both upper and lower off diagonal to 1 0 1 0? What if n is arbitrary, is there any code that fix the off diagonals to a desired vector?
0 Comments
Answers (5)
the cyclist
on 13 Aug 2024
% Arbitrary size
N=5;
% Example input
A = rand(N); % NxN random matrix
disp(A)
% Vector to set as the sub- or superdiagonal
v = rand(N-1,1); % The length of v should be one less than the number of rows/columns in A
% Set the subdiagonal to the values in v
A(sub2ind(size(A), 2:N, 1:(N-1))) = v;
% Set the superdiagonal to the values in v
A(sub2ind(size(A), 1:(N-1), 2:N)) = v;
% Display the updated matrix
disp(A)
0 Comments
David Goodmanson
on 13 Aug 2024
Edited: David Goodmanson
on 13 Aug 2024
Hello Olawale
m = rand(5,5)
m1 = diag(m,1) % original upper diagonal
a = [2 3 4 5]' % new upper diagonal elements
mnew = m - diag(m1,1) + diag(a,1)
and the lower diagonal works the same way with 1 replaced by -1 everywhere.
1 Comment
John D'Errico
on 13 Aug 2024
Certainly the preferred solution almost always. Far cleaner. Easy on the eyes, to read, to debug. Code that you can follow is important one day in the future, when you will need to change it.
The only reason why an indexing solution would be preferred is if the matrices were large, AND if the time cost was significant, so you were doing this operation sufficiently often to matter.
Naga
on 13 Aug 2024
Hello Olawale,
To modify the off-diagonal elements of the symmetric tridiagonal matrix T to a specified pattern, you can use indexing to directly set these values. Below is a MATLAB code snippet that demonstrates how to change the off-diagonal elements to 1 0 1 0 for the given matrix T.
for i = 1:length(desired_vector)
if i <= n-1
T(i, i+1) = desired_vector(i); % Upper off-diagonal
T(i+1, i) = desired_vector(i); % Lower off-diagonal
end
end
0 Comments
See Also
Categories
Find more on Operating on Diagonal Matrices in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!