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MathGroup Archive 2006

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Re: Extract any diagonal from a square matrix...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66289] Re: [mg66279] Extract any diagonal from a square matrix...
  • From: "Carl K. Woll" <carlw at wolfram.com>
  • Date: Mon, 8 May 2006 00:46:08 -0400 (EDT)
  • References: <200605070350.XAA08508@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

hawkmoon269 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;
> ...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.
> 
> Any thoughts...?
> 
> h

First, I would use

1 -- 1st superdiagonal
0 -- main diagonal
-1 -- 1st subdiagonal

etc.

To find these diagonals, I would implement your idea as follows:

diag[mat_,d_]:=
Tr[PadLeft[m, Dimensions[m] + If[d > 0, {0, -d}, {d, 0}]],List]

Carl Woll
Wolfram Research


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