Re: Sorting point-arrays by rows and columns, cont.

*To*: mathgroup at smc.vnet.net*Subject*: [mg124081] Re: Sorting point-arrays by rows and columns, cont.*From*: Chris Young <cy56 at comcast.net>*Date*: Sun, 8 Jan 2012 04:24:51 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <je6e3j$q6k$1@smc.vnet.net> <je96m6$j6c$1@smc.vnet.net>

Despite what I said, it seems to be working now. Fold[ ] looks useful for more complicated sorting especially. In[75]:= FoldList[ #1[[Ordering[#1[[All, #2]], All, LessEqual]]] &, hexPts, {1, 2} ] The first list below is hexPts unaltered. The second is hexPts sorted by the x coordinates, i.e., by columns. The third is hexPts sorted by the y coordinates, but with the x-coordinates ordered within each row. Out[75]= { {{0, 0}, {1, 0}, {1/2, Sqrt[3]/2}, {-(1/2), Sqrt[3]/2}, {-1, 0}, {-(1/2), -(Sqrt[3]/2)}, {1/2, -(Sqrt[3]/2)}}, {{-1, 0}, {-(1/2), Sqrt[3]/2}, {-(1/2), -(Sqrt[3]/2)}, {0, 0}, {1/2, Sqrt[3]/2}, {1/2, -(Sqrt[3]/2)}, {1, 0}}, {{-(1/2), -(Sqrt[3]/2)}, {1/2, -(Sqrt[3]/2)}, {-1, 0}, {0, 0}, {1, 0}, {-(1/2), Sqrt[3]/2}, {1/2, Sqrt[3]/2}} } On 2012-01-07 10:27:18 +0000, Chris Young said: > Thanks for the examples with Fold, which I'm going to continue to work > through, but I wasn't able to get it to sort the 2nd elements correctly: > > In[10]:= threes = RandomChoice[Flatten[pts], {10, 3}] > > Out[10]= {{1, 2, 0}, {1, Sqrt[2], 1}, {1, 7, 2}, {1, 1, Sqrt[5]}, {1, > 2, 2}, {0, 4, -1}, {0, 2, 1}, {7, 1, 0}, {1, Sqrt[5], 2}, {0, 2, -1}} > > > (The following doesn't seem to work!! We have Sqrt[5] in the 2nd > coordinate coming before 1 in the last two vectors. > Don't understand why Reverse was needed, and also why {3,1} was used. > What does the {3,1} to?) > > In[35]:= Fold[#1[[Ordering[#1[[All, #2]], All, LessEqual]]] &, threes, > Reverse@{3, 1}] > > Out[35]= {{0, 4, -1}, {0, 2, -1}, {1, 2, 0}, {7, 1, 0}, {0, 2, 1}, {1, > Sqrt[2], 1}, {1, 7, 2}, {1, 2, 2}, {1, Sqrt[5], 2}, {1, 1, Sqrt[5]}}