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how to pick out alternating columns and rows in a matrix?
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg551] how to pick out alternating columns and rows in a matrix?
*From*: Richard Q. Chen <chen at fractal.eng.yale.edu>
*Date*: Wed, 15 Mar 95 13:24:59 EST
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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