Creating nested structure from flat, for Mathematica expressions
BeginPackage["Unflatten`"] | |
Unflatten::usage = "Unflatten[h[elems], posints, heads] creates a nested structure by wrapping | |
the elements in positions intervals posints in heads heads"; | |
UnflattenNested::usage = "UnflattenNested[expr, {startposlist, endposlist}, head] wraps elements | |
of expr at positions starting at startposlist_i and ending at endposlist_i in head head"; | |
Begin["`Private`"] | |
ClearAll[listSplit,reconstructIntervals,groupElements,groupPositions,processPosList,groupElementsNested]; | |
listSplit[x_List, lengthlist_List,headlist_List]:= | |
MapThread[ | |
#1@@Take[x,#2]&, | |
{headlist,Transpose[{Most[#]+1,Rest[#]}&[FoldList[Plus,0,lengthlist]]]} | |
]; | |
reconstructIntervals[listlen_Integer,ints_List]:= | |
Module[{missed,startint,lastint}, | |
startint = If[ints[[1,1]]==1,{},{1,ints[[1,1]]-1}]; | |
lastint = If[ints[[-1,-1]]==listlen, {},{ints[[-1,-1]]+1,listlen}]; | |
missed = | |
Map[ | |
If[#[[2,1]]-#[[1,2]]>1,{#[[1,2]]+1,#[[2,1]]-1},{}]&, | |
Partition[ints,2,1] | |
]; | |
missed = Join[missed,{lastint}]; | |
Prepend[Flatten[Transpose[{ints,missed}],1],startint] | |
]; | |
groupElements[ | |
lst_List,poslist_List,headlist_List | |
] /; And[OrderedQ[Flatten[Sort[poslist]]],Length[headlist]==Length[poslist]]:= | |
Module[{totalheadlist,allints,llist}, | |
totalheadlist = | |
Append[ | |
Flatten[Transpose[{Array[Sequence&,{Length[headlist]}],headlist}],1], | |
Sequence | |
]; | |
allints = reconstructIntervals[Length[lst],poslist]; | |
llist = Map[If[#==={},0,1-Subtract@@#]&,allints]; | |
listSplit[lst, llist,totalheadlist] | |
]; | |
(* To work on general heads, we need this *) | |
groupElements[h_[x__],poslist_List,headlist_List]:= | |
h[Sequence@@groupElements[{x},poslist,headlist]]; | |
(* If we have a single head *) | |
groupElements[expr_,poslist_List,head_]:= | |
groupElements[expr,poslist,Table[head,{Length[poslist]}]]; | |
groupPositions[plist_List]:= | |
Reap[Sow[Last[#],{Most[#]}]&/@plist,_,List][[2]]; | |
processPosList::unmtch = "The starting and ending position lists `1` and `2` don't match"; | |
processPosList[{openlist_List,closelist_List}]:= | |
Module[{opengroup,closegroup,poslist}, | |
{opengroup,closegroup} = groupPositions/@{openlist,closelist}; | |
poslist = Transpose[Transpose[Sort[#]]&/@{opengroup,closegroup}]; | |
If[UnsameQ @@ poslist[[1]], | |
Message[processPosList::unmtch,openlist,closelist]; | |
{}, | |
(* else *) | |
Transpose[{poslist[[1,1]],Transpose/@ Transpose[poslist[[2]]]}] | |
] | |
]; | |
groupElementsNested[nested_,{openposlist_List,closeposlist_List},head_]/;Head[head]=!=List:= | |
Fold[ | |
Function[{x,y},MapAt[groupElements[#,y[[2]],head]&,x,{y[[1]]}]], | |
nested, | |
Sort[processPosList[{openposlist,closeposlist}],Length[#2[[1]]] < Length[#1[[1]]]&] | |
]; | |
Unflatten[args___]:= groupElements[args]; | |
UnflattenNested[args___]:=groupElementsNested[args] | |
End[] | |
EndPackage[] |
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Hi, is this equivalent to the new
ArrayReshape
?