How to extract a number of diagonals of a matrix
18 views (last 30 days)
Show older comments
Hello all,
I have an N-by-N matrix. I want to extract the main diagonal and d diagonals to its right and d diagonals to its left and null all other elements. How can I do that?
Thanks
0 Comments
Accepted Answer
Star Strider
on 6 Jun 2014
10 Comments
Star Strider
on 7 Jun 2014
Thank you. Please add your vote to Cedric’s answer.
I didn’t catch the banded matrix. It’s been a while since I encountered them.
More Answers (2)
Cedric
on 7 Jun 2014
Edited: Cedric
on 7 Jun 2014
Sparse, SPDIAGS - Here is a version using sparse matrices and SPDIAGS
Original, dense matrix:
>> N = 5 ;
>> A = randi( 10, N, N )
A =
9 1 2 2 7
10 3 10 5 1
2 6 10 10 9
10 10 5 8 10
7 10 9 10 7
Define diag ID "amplitude":
>> d = 1 ; % => -1,0,1 => band of width 3.
Build band sparse matrix:
>> Aband = spdiags( spdiags(A, -d:d), -d:d, N, N )
Aband =
(1,1) 9
(2,1) 10
(1,2) 1
(2,2) 3
(3,2) 6
(2,3) 10
(3,3) 10
(4,3) 5
(3,4) 10
(4,4) 8
(5,4) 10
(4,5) 10
If you needed to have it full despite the large amount of 0s (for large values of N):
>> Aband = full( Aband )
Aband =
9 1 0 0 0
10 3 10 0 0
0 6 10 10 0
0 0 5 8 10
0 0 0 10 7
Note that there is a processing time overhead when you deal with sparse matrices, which is compensated by the gain in efficiency (when N is large) due to the fact that only non-zero elements are stored/processed. For small values of N though, I would consider Star Strider's solution based on a loop with full matrices, or the solution below.
Dense, TRIL - Here is another "dense" solution based on TRIL and logical indexing (I am using the same A as above, and I display intermediary steps so you can see the logic):
>> id = logical( tril( ones(N), d ))
id =
1 1 0 0 0
1 1 1 0 0
1 1 1 1 0
1 1 1 1 1
1 1 1 1 1
>> id = id & id.'
id =
1 1 0 0 0
1 1 1 0 0
0 1 1 1 0
0 0 1 1 1
0 0 0 1 1
>> A(~id) = 0
A =
9 1 0 0 0
10 3 10 0 0
0 6 10 10 0
0 0 5 8 10
0 0 0 10 7
If you really need to optimize your code, I'd advise you to implement the 4 or 5 solutions presented in this thread, and time them specifically for your case.
3 Comments
Cedric
on 7 Jun 2014
Note that most built-ins in MATLAB support sparse matrices, so if N is large and d is small in comparison, it is in your interest not to transform back to full unless really needed.
Sean de Wolski
on 6 Jun 2014
Or triu and tril
x = magic(10);
n = 3;
x = x(tril(ones(size(x)),n)&triu(ones(size(x)),-n))
See Also
Categories
Find more on Sparse 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!