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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: [mg66294] Re: [mg66279] Extract any diagonal from a square matrix...
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Mon, 8 May 2006 00:46:22 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

Change the definition of d to be symmetric:

2 -- 2nd superdiagonal 
1 -- 1st superdiagonal 
0 --  main diagonal 
-1 -- 1st subdiagonal 
-2 -- 2nd subdiagonal

DiagonalT[a_List, d_Integer] := 
  Module[{r=If[d>0,0,-d],
          c=If[d>0,d,0]},
        Table[a[[k+r,k+c]],
          {k,1,Length[a]-Abs[d]}]]/;
      Abs[d]<Length[a];


Bob Hanlon

---- 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;
> ...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
> 


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