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Re: how to pick out alternating columns and rows in a matrix?
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg574] Re: [mg551] how to pick out alternating columns and rows in a matrix?
*From*: bob Hanlon <hanlon at pafosu2.hq.af.mil>
*Date*: Sun, 19 Mar 1995 13:42:43
Here is an approach.
Bob Hanlon
---------------
n = 5; u = Array[a, {2n, 2n}];
Fold[ Transpose[ Fold[ Drop, #,
Table[ {-k}, {k, Length[ u ]/2} ] ] ]&,
u, {1, 2} ] // MatrixForm
(* Select odd rows and columns from square matrix *)
a[1, 1] a[1, 3] a[1, 5] a[1, 7] a[1, 9]
a[3, 1] a[3, 3] a[3, 5] a[3, 7] a[3, 9]
a[5, 1] a[5, 3] a[5, 5] a[5, 7] a[5, 9]
a[7, 1] a[7, 3] a[7, 5] a[7, 7] a[7, 9]
a[9, 1] a[9, 3] a[9, 5] a[9, 7] a[9, 9]
n = 4; u = Array[a, {2n, 2n}];
Fold[ Transpose[ Fold[ Drop, #,
Table[ {-k-1}, {k, Length[ u ]/2} ] ] ]&,
u, {1, 2} ] // MatrixForm
(* Select even rows and columns from square matrix *)
a[2, 2] a[2, 4] a[2, 6] a[2, 8]
a[4, 2] a[4, 4] a[4, 6] a[4, 8]
a[6, 2] a[6, 4] a[6, 6] a[6, 8]
a[8, 2] a[8, 4] a[8, 6] a[8, 8]
m = 4; n = 2; u = Array[a, {2m, 2n}];
Transpose[ Fold[ Drop, Transpose[ Fold[ Drop, u,
Table[ {-k}, {k, Length[ u ]/2} ] ] ],
Table[ {-k}, {k, Length[ u[[1]] ]/2} ] ] ] // MatrixForm
(* Select odd rows and columns from even matrix *)
a[1, 1] a[1, 3]
a[3, 1] a[3, 3]
a[5, 1] a[5, 3]
a[7, 1] a[7, 3]
m = 3; n = 5; u = Array[a, {2m, 2n}];
Transpose[Fold[Drop, Transpose[Fold[Drop, u,
Table[{-k-1}, {k, Length[ u ]/2}] ]],
Table[{-k-1}, {k, Length[ u[[1]] ]/2}] ]] // MatrixForm
(* Select even rows and columns from even matrix *)
a[2, 2] a[2, 4] a[2, 6] a[2, 8] a[2, 10]
a[4, 2] a[4, 4] a[4, 6] a[4, 8] a[4, 10]
a[6, 2] a[6, 4] a[6, 6] a[6, 8] a[6, 10]
---------------
On Wed, 15 Mar 1995, Richard Q. Chen wrote:
>
> 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
>
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