Skip to main content

Threading over a list of lists of lists and a list of atomic expressions


Although I solved the following problem using MapThread, I'm curious about why Thread does not work as I expect it to here.


Given two lists of length n, where the first list is a list of lists of lists and the second is a list of atomic expressions, such as:


list1 = {{{1, 2}, {3, 4, 5}}, {{1, 3, 5}, {9, 8}}};
list2 = {"a", "b"};

and where list1[[n]] can contain 1 or more lists of atomic expressions. I would like to create a single list that places the nth element of the second list at the end of every sublist of list1[[n]], producing:


{{{1, 2, "a"}, {3, 4, 5, "a"}}, {{1, 3, 5, "b"}, {9, 8, "b"}}}


I first tried the following


appendTo[ll_, item_] := Map[Append[#, item] &, ll];
Thread[appendTo[list1, list2]]

But this returns:


{{{1, 2}, {1, 3, 5}}, {{3, 4, 5}, {9, 8}}, {{"a", "b"}, {"a", "b"}}}

even though threading an undefined function seems to produce the right expressions:


Thread[f[a, b]]
{f[{{1, 2}, {3, 4, 5}}, "a"], f[{{1, 3, 5}, {9, 8}}, "b"]}


MapThread works fine:


MapThread[appendTo, {list1, list2}]
{{{1, 2, "a"}, {3, 4, 5, "a"}}, {{1, 3, 5, "b"}, {9, 8, "b"}}}

So why is Thread producing the behavior shown above instead of giving the same result as MapThread?


Threading Rule on the same lists also produces what I expect:


Thread[Rule[list1, list2]]
{{{1, 2}, {3, 4, 5}} -> "a", {{1, 3, 5}, {9, 8}} -> "b"}

Answer




The simple answer: Thread does not have the attribute HoldAll, so its contents are executed before it processes them.


But, it is not quite that simple. If you add HoldAll, you still don't get what you want


Internal`InheritedBlock[{Thread},
SetAttributes[Thread, HoldAll];
Thread[appendTo[list1, list2]]
]
(* {{{1, 2}, {3, 4, 5}, {"a", "b"}}, {{1, 3, 5}, {9, 8}, {"a", "b"}}} *)

which implies that in this form only the first list is threaded over.





Note, I used Internal`InheritedBlock to retain the behavior of Thread while not allowing my modifications to leak.


Comments

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...