Re: copying a variable

*To*: mathgroup at smc.vnet.net*Subject*: [mg92345] Re: copying a variable*From*: "Szabolcs HorvÃt" <szhorvat at gmail.com>*Date*: Sat, 27 Sep 2008 22:24:39 -0400 (EDT)*References*: <gbl303$m03$1@smc.vnet.net> <48DE179F.5090201@gmail.com>

I still don't understand completely what you are doing, but I will try to give some suggestions below. I hope they will be useful. On Sat, Sep 27, 2008 at 18:06, ramiro <ramiro.barrantes at uvm.edu> wrote: > Hi Szabolcs, > > I just tried with expressions and it looks great. I think I was just > treating the DownValues as a kind of hash table (inspired a bit by the > mathematica paclets) I think this is an important step in defining how I > will work with tree (I work with evolutionary trees in biology). So here > are two questions as I'm afraid I'm missing mathematica tricks: > > 1) If I want to find out the ancestor of a node, would it be best to a) just > traverse the tree every time (maybe the speed won't be an issue), b) do some > combination of Position, etc. to figure it out; c) keep a separate record > of definitions (like the one I had) of who's the ancestor and the children > of who. The easiest (but not necessarily fastest) way to do this is to traverse the complete tree and use pattern matching: Let us define an example tree to work on: tree = "a"["b"["A", "B"], "C", "c"["d"["D"], "E"], "F"] This is what it looks like (I'm assuming that you have Mathematica 6): TreeForm[tree] This function finds parents of all occurrences of a node: allParents[tree_, node_] := Cases[tree, par_[___, node, ___] :> par, {0, Infinity}] Perhaps every node has only a single occurrence, so it would be better to stop searching as soon as we find it: firstParent[tree_, node_] := First@Cases[tree, par_[___, node, ___] :> par, {0, Infinity}, 1] This is the list of all child nodes: In[23]:= children = Level[tree, {-1}] Out[23]= {"A", "B", "C", "D", "E", "F"} And these are their parents: In[24]:= firstParent[tree, #] & /@ children Out[24]= {"b", "b", "a", "d", "c", "a"} If you need to find certain child nodes very frequently by their names, you could create an index of their positions: In[25]:= (# -> First@Position[tree, #] &) /@ children Out[25]= {"A" -> {1, 1}, "B" -> {1, 2}, "C" -> {2}, "D" -> {3, 1, 1}, "E" -> {3, 2}, "F" -> {4}} For a large tree we can make a dispatch table (see Dispatch) of this list of rules for fast lookup. Here I treated the end child nodes differently from those nodes that can have children themselves. If they should be equivalent, then you could work with expressions like "a"["b"[], "c"["d"[], "e"[]]] instead. > > 2) What if I want to do an operation on a tree, I was thinking about reading > the tree and then making "definitions" of children, ancestors, etc. (just > because I am going to use those many times), then making the operation > somehow and outputting the tree again as an expression. e.g. > > reroot[treeX_]:=Module[{definitions}, > definition = "read all the tree data, ancestors, children, root, etc." > based on treeX > .... reroot the tree > > make a new expression based on rerooted tree > output expression > ] You can use Delete, Insert, ReplacePart, Cases, DeleteCases, Replace, etc. to manipulate trees. For example, ReplacePart[tree, 0 -> "x"] replaces the root of the tree with "x". "x"[tree] attaches tree to a new root "x". > > Thanks for helping. Any suggestions or comments much appreciated. >

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