Re: Extract any diagonal from a square matrix...
- To: mathgroup at smc.vnet.net
- Subject: [mg66398] Re: Extract any diagonal from a square matrix...
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 11 May 2006 02:16:09 -0400 (EDT)
- Organization: The University of Western Australia
- References: <e3js8r$8kh$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <e3js8r$8kh$1 at smc.vnet.net>, "hawkmoon269" <rson at new.rr.com>
wrote:
> Trying to put a function together that extracts any one of the
> diagonals from a square matrix. Right now I have this --
>
> DiagonalT[a_List, d_Integer] :=
> Tr[Take[Which[Positive[d], a, Negative[d], Transpose[a]],
> {1, Length[a] - Abs[d] + 1}, {Abs[d], Length[a]}], List]
>
> This works, but I thought there might be something less cumbersome.
> Essentially, the function constructs a submatrix of the matrix so that
> the requested diagonal from the matrix becomes the main diagonal of the
> submatrix, which is then retrieved. D is the diagonal to retrieve,
> where d =
>
> 3 -- 2nd superdiagonal
> 2 -- 1st superdiagonal
> 1 -- main diagonal
> -2 -- 1st subdiagonal
> -3 -- 2nd subdiagonal
>
> etc...
>
> Some other things I've considered --
>
> ...rotating the elements of each row until column 1 becomes the
> requested diagonal;
Along these lines you can use MapIndexed:
RotateRight /@ MapIndexed[RotateLeft, m]
> ...dropping elements from each row until the first or last element in
> each row becomes the next element in the requested diagonal;
> ...flattening the matrix and then using Range and Part to retrieve the
> requested diagonal.
Defining
Diagonals[m_] := MapIndexed[Take[#1, #2[[1]]] &,
Reverse[Transpose[RotateRight /@ MapIndexed[RotateLeft, m]]]]
then for square matrices,
Reverse @ Diagonals[m]
gives the list of superdiagonals, and
Diagonals[Transpose[m]]
gives the list of subdiagonals.
Cheers,
Paul
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