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 ************************