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Re: how to pick out alternating columns and rows in a matrix?
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg577] Re: [mg551] how to pick out alternating columns and rows in a matrix?
*From*: hannibal at caesar.physik.uni-oldenburg.de (L. Hannibal)
*Date*: Mon, 20 Mar 1995 10:33:28 +0100 (NFT)
> eng.yale.edu>
> To: mathgroup at christensen.cybernetics.net
> Subject: [mg551] how to pick out alternating columns and rows in a matrix?
> Content-Length: 1249
>
>
> Hi,
> Suppose I have a matrix of even dimensions, I would like
> to form a matrix consisting of only the odd rows and columns of the
> matrix. A concrete example may make my request clearer:
>
> In[2]:= MatrixForm[u=Array[a,{6,6}]]
>
> Out[2]//MatrixForm= a[1, 1] a[1, 2] a[1, 3] a[1, 4] a[1, 5] a[1, 6]
>
> a[2, 1] a[2, 2] a[2, 3] a[2, 4] a[2, 5] a[2, 6]
>
> a[3, 1] a[3, 2] a[3, 3] a[3, 4] a[3, 5] a[3, 6]
>
> a[4, 1] a[4, 2] a[4, 3] a[4, 4] a[4, 5] a[4, 6]
>
> a[5, 1] a[5, 2] a[5, 3] a[5, 4] a[5, 5] a[5, 6]
>
> a[6, 1] a[6, 2] a[6, 3] a[6, 4] a[6, 5] a[6, 6]
>
> I would like to pick out the 1st, 3rd and 5th rows and columns.
> My current solution is embarassingly contorted. I would like to see
> some more elegant solutions to this.
>
> Here is what I did:
>
> In[3]:= First /@ Partition[Flatten[u],2];
>
> In[4]:= Transpose[Partition[%,3]];
>
> In[5]:= First /@ Partition[Flatten[%],2];
>
> In[6]:= Transpose[Partition[%,3]];
>
> In[7]:= MatrixForm[%]
>
> Out[7]//MatrixForm= a[1, 1] a[1, 3] a[1, 5]
>
> a[3, 1] a[3, 3] a[3, 5]
>
> a[5, 1] a[5, 3] a[5, 5]
>
> Thanks for any help.
>
> Richard
>
>
Richard,
odd[u_]:=Array[u[[2 #1 -1,2 #2-1]]&,
{Ceiling[Length[u]/2],Ceiling[Length[u[[1]]]/2]}]
works on any rectangular matrix.
Ludger.
*************************
Ludger Hannibal
Carl v. Ossitzky Universitaet
Oldenburg,
Germany
************************
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