Re: Sort a List, in a List of Lists of Lists

*To*: mathgroup at smc.vnet.net*Subject*: [mg113822] Re: Sort a List, in a List of Lists of Lists*From*: "Nasser M. Abbasi" <nma at 12000.org>*Date*: Sun, 14 Nov 2010 06:10:08 -0500 (EST)*References*: <ibl9g2$b8a$1@smc.vnet.net> <4CDF2000.5080209@12000.org>*Reply-to*: nma at 12000.org

On 11/13/2010 3:32 PM, Nasser M. Abbasi wrote: > > one way: > > ------------------ > a={{{1,2},{2,1},{1,1}},{{1,1},{1,1},{1,2}},{{2,1},{2,2},{1,2}},{{2,2},{1,2},{2,2}},{{1,1},{2,1},{1,2}},{{1,2},{2,2},{2,2}}}; > > {nRow,nCol,nPages}=Dimensions[a]; > Map[Sort,Flatten[a,1]]; > Partition[%, nCol] > ------------------ > > Out[138]= {{{1,2},{1,2},{1,1}},{{1,1},{1,1},{1,2}},{{1,2},{2,2},{1,2}},{{2,2},{1,2},{2,2}},{{1,1},{1,2},{1,2}},{{1,2},{2,2},{2,2}}} > ps. In the above, {nRow,nCol,nPages}=Dimensions[a] should really be {nPages,nRow,nCol}=Dimensions[a]; If you really want to do this in a more 'obvious' way, you can simply Sort each row in each page by 'hand' as in --------------- Table[ Sort[ a[[k,j]] ], {k,1,nPages},{j,1,nRow}] -------------- Out[407]= {{{1,2},{1,2},{1,1}},{{1,1},{1,1},{1,2}},{{1,2},{2,2},{1,2}},{{2,2},{1,2},{2,2}},{{1,1},{1,2},{1,2}},{{1,2},{2,2},{2,2}}} There is nothing wrong with this. It says go over each page in the 3D structure, sort each row. The nice thing is that the result will have the same shape as the original 3D matrix. So no need to reshape it using Parition. I think of a 3D matrix as made up of a book, the number of pages is the size of the third dimension, and each page in the matrix has size nRow,nCol. nRow tells how many lines on the page, nCol tells how many columns in the page. nPages actually is the first entry returned by Dimensions, not the third. so, in 3D, when writing A[[ 1,2 ]] the '1' is the page number, and '2' will be the row number on that page. in 2D, A[[ 1,2 ]] then '1' is the row number, and '2' is the column number. There is only one page, so no entry for it. For 3D, A[[1,2,3]] means page 1, row 2 on that page, column 3 on that page. For 4D matrix, A[[ n,p,i,j ]] is n'th book, p page in that book,mathgroup at smc.vnet.net i'th row on that page, j'th column For 5D matrix A[[ m,n,p,i,j ]] is m library, n book in that library, p page in that book, i row on that page, and j column. etc... If you think of the lists as the above, everything becomes very clear and easy. At leat for me. I do not like to think of lists as nested and levels and such. I always try to look at a list as arrays and matrices, and look at what dimensions it has, and go from there. --Nasser

**Follow-Ups**:**SetAttributes[CenterDot, Flat]***From:*"Dave Snead" <dsnead6@charter.net>