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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: [mg66286] Re: Extract any diagonal from a square matrix...
  • From: "Ray Koopman" <koopman at sfu.ca>
  • Date: Mon, 8 May 2006 00:46:01 -0400 (EDT)
  • References: <e3js8r$8kh$1@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

This follows your basic approach, but with two changes:
1. The method of specifying the diagonal is:
   e = 2 -- 2nd superdiagonal
       1 -- 1st superdiagonal
       0 -- main diagonal
      -1 -- 1st subdiagonal
      -2 -- 2nd subdiagonal
     etc...
2. The matrix can be rectangular.
   For superdiagonals, drop the first e columns.
   For subdiagonals, drop the first -e rows.
   Tr can take it from there.

takediag[a_?MatrixQ, 0] := Tr[a, List]

takediag[a_?MatrixQ, e_Integer?Positive]/; e < Length@a[[1]] :=
  Tr[Drop[#,e]&/@a], List]

takediag[a_?MatrixQ, e_Integer?Negative]/; -e < Length@a :=
  Tr[Drop[a,-e], List]


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