How to extract a number of diagonals of a matrix

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

Answer 1

[Star Strider]

The diag function can do everything you want. You just have to ask it!

[S. David]

I need a 2d+1 loops with this function like:

FNew=zeros(N);
for d=-3:3
FNew=diag(diag(F,d),d); % F is the original matrix
end

Is there a way without using a for loop?

[Star Strider]

Every time I’ve needed to do something like that, I used a loop.

I don’t understand the nested diag call. You only need to call it once. You’re apparently also not saving FNew. You need to save it in a cell array, e.g. ‘FNew{d} = ...’ if you want to use it later. (Cell array because they’re not all the same lengths.)

[S. David]

According to MATLAB help:

1- D = diag(v,k) places the elements of vector v on the kth diagonal. k=0 represents the main diagonal, k>0 is above the main diagonal, and k<0 is below the main diagonal.

2- x = diag(A,k) returns a column vector of the elements on the kth diagonal of A.

I need to put the kth diagonal of F (diag(F,d) from point 2) on the kth diagonal of FNew (FNew=diag(diag(F,d),d) from point 1). It works just fine.

Some times I need to include a large number of diagonals, and I was thinking of doing it without for loop if possible.

[Star Strider]

OK. But if the kth diagional of FNew is the kth diagonal of F, why not just do:

FNew = F;

What am I missing here?

[S. David]

I want to create from F (whose elements are not zero) a new matrix that has 2d+1 diagonals that are the same diagonals of F, while all other elements in FNew are set to zero.

[Star Strider]

I’m lost. F is (4x4), so that means FNew is (10x10) with zeros along its diagonals that aren’t congruent with the sizes of the diagonals of F?

[Cedric]

I may be wrong, but as far as I understand, he just wants to create a band matrix Fnew based on F.

[Star Strider]

That makes sense.

[S. David]

Thanks Cedric Wannaz. Yes it is a banded matrix from F, that is the term.

[Star Strider]

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.

Answer 2

[Cedric]

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.

[S. David]

Interesting!!

[Cedric]

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.

[S. David]

I needed it full, because I need to left-multiply an N-by-1 vector by it for signal processing.

Answer 3

[Sean de Wolski]

Or triu and tril

x = magic(10);
n = 3;
x = x(tril(ones(size(x)),n)&triu(ones(size(x)),-n))

[S. David]

Still I want the new matrix to be N-by-N by nulling all elements not in the selected diagonals.