Re: Insulating data from code

*To*: mathgroup at smc.vnet.net*Subject*: [mg66532] Re: Insulating data from code*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Fri, 19 May 2006 03:39:31 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <e4ekai$9av$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Ray Koopman wrote: >>From time to time I've wanted to partition the first level of one > list, say A, the same way that another list, say B, is partitioned. > One way to do this is > > copyPartition[A_List, B_List] /; Length@A >= Length@Flatten@B := > Module[{i = 0}, Map[A[[++i]]&,B,{-1}]] > > But all the methods I've thought of have a pointer that functions > something like i in the above code. I'd like to eliminate the pointer, > because in the unlikely event that A contains an unevaluated symbol > that is the same as the name of the pointer with $ appended -- e.g., > i$, if the pointer is i -- then in the returned list that symbol will > have a numeric value assigned to it. Unique[i] doesn't help. The > only solution I see is the probabilistic one of giving the pointer a > strange (random?) name that hopefully would be very unlikely to show > up as data. But that would be giving up. Does anyone have any ideas? > Hi Ray, Please find hereunder a function that solve the problem of conflicting local name in the lists. In[1]:= copyPartition2[A_List, B_List] /; Length[A] >= Length[Flatten[B]] := Module[{start, end}, start = FoldList[Plus, 1, Length /@ B]; end = start - 1; start = Most[start]; end = Rest[end]; ((A[[#1]] & ) /@ Range[First[#1], Last[#1]] & ) /@ Transpose[{start, end}]] In[2]:= listA = {1, 2, 3, 4, 5, 6, 7, i$25, i$26, i$27}; listB = {{a, b}, {2, 6, 1.4, 5/3}, {i}, {a, b, c}}; In[4]:= copyPartition2[listA, listB] Out[4]= {{1, 2}, {3, 4, 5, 6}, {7}, {i$25, i$26, i$27}} Below, you will find some details about how the function works: In[5]:= start = FoldList[Plus, 1, Length /@ listB] Out[5]= {1, 3, 7, 8, 11} In[6]:= end = start - 1 Out[6]= {0, 2, 6, 7, 10} In[7]:= start = Most[start] Out[7]= {1, 3, 7, 8} In[8]:= end = Rest[end] Out[8]= {2, 6, 7, 10} In[9]:= Transpose[{start, end}] Out[9]= {{1, 2}, {3, 6}, {7, 7}, {8, 10}} In[10]:= (Range[First[#1], Last[#1]] & ) /@ Transpose[{start, end}] Out[10]= {{1, 2}, {3, 4, 5, 6}, {7}, {8, 9, 10}} In[11]:= ((listA[[#1]] & ) /@ Range[First[#1], Last[#1]] & ) /@ Transpose[{start, end}] Out[11]= {{1, 2}, {3, 4, 5, 6}, {7}, {i$25, i$26, i$27}} Best regards, Jean-Marc