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How do I transpose the first and deepest levels of an arbitrarily nested array?

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How do I transpose the first and deepest levels of an arbitrarily nested array?



The Next CEO of Stack OverflowA question about transforming one List into two Lists with additional requirementsEmulating R data frame getters with UpValuesQuickly pruning elements in one structured array that exist in a separate unordered array`Part` like `Delete`: How to delete list of columns or arbitrarily deeper levelsHow to mesh a region using adaptive cubic elementsHow to efficiently Flatten nested lists while preserving select levels?Distribute elements of one line across arbitrary dimension of another listDeep level nested list addition`Transpose` nested `Association`How to extract the first element in nested lists










6












$begingroup$


Is there a straightforward way to convert



arr = 
 a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b
;


to:



a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b


?



I need to swap the first and last dimension. Which should in principle be possible, because, although arr does not have a fixed structure, the 'bottom' is always uniform:



Level[arr, -2]



a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b



Had Transpose/Flatten/MapThread accepted a negative level specification, it would have been easy. That is not the case.



One can think about that question as: How do I create arr2 so that arr[[whatever__, y_]] == arr2[[y, whatever__]]?



EDIT:



In general Level[arr, -2] should be a rectangular array, but rows do not need to be the same.



So this:



a1, b1, a2, b2, a3, b3, a4, b4, a5, b5, a6, b6, a7,b7 ;


should end up:



 a1, a2, a3, a4, a5, a6, a7 , ...;





list-manipulation







share|improve this question











$endgroup$











  • $begingroup$
    Not a solution, but Flatten[MapIndexed[RotateRight[#2] -> #1 &, arr, -1]] gives you a list of rules of what needs to be constructed. I don't know of a way to construct it though: SparseArray does not construct ragged structures.
    $endgroup$
    – Roman
    11 hours ago










  • $begingroup$
    Maybe something along the lines of arr /. a,b->a,a,b->b? Or perhaps more generally, arr /. a_?VectorQ :> First@a, a_?VectorQ :> Last@a?
    $endgroup$
    – Carl Woll
    11 hours ago











  • $begingroup$
    Does your list always contain a,b at the lowest level, or can there be anything there as long as they're all of same length?
    $endgroup$
    – Roman
    11 hours ago











  • $begingroup$
    @Roman Level[arr, -2]` should be a rectangular array but rows do not need to be the same.
    $endgroup$
    – Kuba♦
    11 hours ago










  • $begingroup$
    @Kuba maybe you can come up with a recursion that constructs the result from the list of rules I gave 4 lines up? That would be a handy tool to have in any case.
    $endgroup$
    – Roman
    11 hours ago
















6












$begingroup$


Is there a straightforward way to convert



arr = 
 a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b
;


to:



a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b


?



I need to swap the first and last dimension. Which should in principle be possible, because, although arr does not have a fixed structure, the 'bottom' is always uniform:



Level[arr, -2]



a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b



Had Transpose/Flatten/MapThread accepted a negative level specification, it would have been easy. That is not the case.



One can think about that question as: How do I create arr2 so that arr[[whatever__, y_]] == arr2[[y, whatever__]]?



EDIT:



In general Level[arr, -2] should be a rectangular array, but rows do not need to be the same.



So this:



a1, b1, a2, b2, a3, b3, a4, b4, a5, b5, a6, b6, a7,b7 ;


should end up:



 a1, a2, a3, a4, a5, a6, a7 , ...;





list-manipulation







share|improve this question











$endgroup$











  • $begingroup$
    Not a solution, but Flatten[MapIndexed[RotateRight[#2] -> #1 &, arr, -1]] gives you a list of rules of what needs to be constructed. I don't know of a way to construct it though: SparseArray does not construct ragged structures.
    $endgroup$
    – Roman
    11 hours ago










  • $begingroup$
    Maybe something along the lines of arr /. a,b->a,a,b->b? Or perhaps more generally, arr /. a_?VectorQ :> First@a, a_?VectorQ :> Last@a?
    $endgroup$
    – Carl Woll
    11 hours ago











  • $begingroup$
    Does your list always contain a,b at the lowest level, or can there be anything there as long as they're all of same length?
    $endgroup$
    – Roman
    11 hours ago











  • $begingroup$
    @Roman Level[arr, -2]` should be a rectangular array but rows do not need to be the same.
    $endgroup$
    – Kuba♦
    11 hours ago










  • $begingroup$
    @Kuba maybe you can come up with a recursion that constructs the result from the list of rules I gave 4 lines up? That would be a handy tool to have in any case.
    $endgroup$
    – Roman
    11 hours ago














6












6








6





$begingroup$


Is there a straightforward way to convert



arr = 
 a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b
;


to:



a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b


?



I need to swap the first and last dimension. Which should in principle be possible, because, although arr does not have a fixed structure, the 'bottom' is always uniform:



Level[arr, -2]



a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b



Had Transpose/Flatten/MapThread accepted a negative level specification, it would have been easy. That is not the case.



One can think about that question as: How do I create arr2 so that arr[[whatever__, y_]] == arr2[[y, whatever__]]?



EDIT:



In general Level[arr, -2] should be a rectangular array, but rows do not need to be the same.



So this:



a1, b1, a2, b2, a3, b3, a4, b4, a5, b5, a6, b6, a7,b7 ;


should end up:



 a1, a2, a3, a4, a5, a6, a7 , ...;





list-manipulation







share|improve this question











$endgroup$




Is there a straightforward way to convert



arr = 
 a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b
;


to:



a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b


?



I need to swap the first and last dimension. Which should in principle be possible, because, although arr does not have a fixed structure, the 'bottom' is always uniform:



Level[arr, -2]



a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b



Had Transpose/Flatten/MapThread accepted a negative level specification, it would have been easy. That is not the case.



One can think about that question as: How do I create arr2 so that arr[[whatever__, y_]] == arr2[[y, whatever__]]?



EDIT:



In general Level[arr, -2] should be a rectangular array, but rows do not need to be the same.



So this:



a1, b1, a2, b2, a3, b3, a4, b4, a5, b5, a6, b6, a7,b7 ;


should end up:



 a1, a2, a3, a4, a5, a6, a7 , ...;





list-manipulation




list-manipulation






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 1 hour ago









J. M. is slightly pensive♦

98.7k10311467




98.7k10311467










asked 11 hours ago









Kuba♦Kuba

107k12210531




107k12210531











  • $begingroup$
    Not a solution, but Flatten[MapIndexed[RotateRight[#2] -> #1 &, arr, -1]] gives you a list of rules of what needs to be constructed. I don't know of a way to construct it though: SparseArray does not construct ragged structures.
    $endgroup$
    – Roman
    11 hours ago










  • $begingroup$
    Maybe something along the lines of arr /. a,b->a,a,b->b? Or perhaps more generally, arr /. a_?VectorQ :> First@a, a_?VectorQ :> Last@a?
    $endgroup$
    – Carl Woll
    11 hours ago











  • $begingroup$
    Does your list always contain a,b at the lowest level, or can there be anything there as long as they're all of same length?
    $endgroup$
    – Roman
    11 hours ago











  • $begingroup$
    @Roman Level[arr, -2]` should be a rectangular array but rows do not need to be the same.
    $endgroup$
    – Kuba♦
    11 hours ago










  • $begingroup$
    @Kuba maybe you can come up with a recursion that constructs the result from the list of rules I gave 4 lines up? That would be a handy tool to have in any case.
    $endgroup$
    – Roman
    11 hours ago

















  • $begingroup$
    Not a solution, but Flatten[MapIndexed[RotateRight[#2] -> #1 &, arr, -1]] gives you a list of rules of what needs to be constructed. I don't know of a way to construct it though: SparseArray does not construct ragged structures.
    $endgroup$
    – Roman
    11 hours ago










  • $begingroup$
    Maybe something along the lines of arr /. a,b->a,a,b->b? Or perhaps more generally, arr /. a_?VectorQ :> First@a, a_?VectorQ :> Last@a?
    $endgroup$
    – Carl Woll
    11 hours ago











  • $begingroup$
    Does your list always contain a,b at the lowest level, or can there be anything there as long as they're all of same length?
    $endgroup$
    – Roman
    11 hours ago











  • $begingroup$
    @Roman Level[arr, -2]` should be a rectangular array but rows do not need to be the same.
    $endgroup$
    – Kuba♦
    11 hours ago










  • $begingroup$
    @Kuba maybe you can come up with a recursion that constructs the result from the list of rules I gave 4 lines up? That would be a handy tool to have in any case.
    $endgroup$
    – Roman
    11 hours ago
















$begingroup$
Not a solution, but Flatten[MapIndexed[RotateRight[#2] -> #1 &, arr, -1]] gives you a list of rules of what needs to be constructed. I don't know of a way to construct it though: SparseArray does not construct ragged structures.
$endgroup$
– Roman
11 hours ago




$begingroup$
Not a solution, but Flatten[MapIndexed[RotateRight[#2] -> #1 &, arr, -1]] gives you a list of rules of what needs to be constructed. I don't know of a way to construct it though: SparseArray does not construct ragged structures.
$endgroup$
– Roman
11 hours ago












$begingroup$
Maybe something along the lines of arr /. a,b->a,a,b->b? Or perhaps more generally, arr /. a_?VectorQ :> First@a, a_?VectorQ :> Last@a?
$endgroup$
– Carl Woll
11 hours ago





$begingroup$
Maybe something along the lines of arr /. a,b->a,a,b->b? Or perhaps more generally, arr /. a_?VectorQ :> First@a, a_?VectorQ :> Last@a?
$endgroup$
– Carl Woll
11 hours ago













$begingroup$
Does your list always contain a,b at the lowest level, or can there be anything there as long as they're all of same length?
$endgroup$
– Roman
11 hours ago





$begingroup$
Does your list always contain a,b at the lowest level, or can there be anything there as long as they're all of same length?
$endgroup$
– Roman
11 hours ago













$begingroup$
@Roman Level[arr, -2]` should be a rectangular array but rows do not need to be the same.
$endgroup$
– Kuba♦
11 hours ago




$begingroup$
@Roman Level[arr, -2]` should be a rectangular array but rows do not need to be the same.
$endgroup$
– Kuba♦
11 hours ago












$begingroup$
@Kuba maybe you can come up with a recursion that constructs the result from the list of rules I gave 4 lines up? That would be a handy tool to have in any case.
$endgroup$
– Roman
11 hours ago





$begingroup$
@Kuba maybe you can come up with a recursion that constructs the result from the list of rules I gave 4 lines up? That would be a handy tool to have in any case.
$endgroup$
– Roman
11 hours ago











3 Answers
3






active

oldest

votes


















8












$begingroup$

arr = a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b;

SetAttributes[f1, Listable]
Apply[f1, arr, 0, -3] /. f1 -> List



a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b







share|improve this answer









$endgroup$




















    3












    $begingroup$

    This is what the list at the lowest level looks like:



    el = First@Level[list, -2];


    Using this, we can solve it with a rules-based approach:



    list /. el -> # & /@ el


    or a recursive approach like this:



    walk[lists : __List, i_] := walk[#, i] & /@ lists
    walk[atoms : __, i_] := i
    walk[list, #] & /@ el





    share|improve this answer









    $endgroup$




















      2












      $begingroup$

      Terrible solution using Table but works:



      Table[Map[#[[i]] &, arr, -2], i, Last[Dimensions[Level[arr, -2]]]]





      share|improve this answer









      $endgroup$













        Your Answer





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        3 Answers
        3






        active

        oldest

        votes








        3 Answers
        3






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes









        8












        $begingroup$

        arr = a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b;

        SetAttributes[f1, Listable]
        Apply[f1, arr, 0, -3] /. f1 -> List



        a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b







        share|improve this answer









        $endgroup$

















          8












          $begingroup$

          arr = a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b;

          SetAttributes[f1, Listable]
          Apply[f1, arr, 0, -3] /. f1 -> List



          a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b







          share|improve this answer









          $endgroup$















            8












            8








            8





            $begingroup$

            arr = a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b;

            SetAttributes[f1, Listable]
            Apply[f1, arr, 0, -3] /. f1 -> List



            a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b







            share|improve this answer









            $endgroup$



            arr = a, b, a, b, a, b, a, b, a, b, a, b, a, b, a, b;

            SetAttributes[f1, Listable]
            Apply[f1, arr, 0, -3] /. f1 -> List



            a, a, a, a, a, a, a, a, b, b, b, b, b, b, b, b








            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered 11 hours ago









            andre314andre314

            12.3k12352




            12.3k12352





















                3












                $begingroup$

                This is what the list at the lowest level looks like:



                el = First@Level[list, -2];


                Using this, we can solve it with a rules-based approach:



                list /. el -> # & /@ el


                or a recursive approach like this:



                walk[lists : __List, i_] := walk[#, i] & /@ lists
                walk[atoms : __, i_] := i
                walk[list, #] & /@ el





                share|improve this answer









                $endgroup$

















                  3












                  $begingroup$

                  This is what the list at the lowest level looks like:



                  el = First@Level[list, -2];


                  Using this, we can solve it with a rules-based approach:



                  list /. el -> # & /@ el


                  or a recursive approach like this:



                  walk[lists : __List, i_] := walk[#, i] & /@ lists
                  walk[atoms : __, i_] := i
                  walk[list, #] & /@ el





                  share|improve this answer









                  $endgroup$















                    3












                    3








                    3





                    $begingroup$

                    This is what the list at the lowest level looks like:



                    el = First@Level[list, -2];


                    Using this, we can solve it with a rules-based approach:



                    list /. el -> # & /@ el


                    or a recursive approach like this:



                    walk[lists : __List, i_] := walk[#, i] & /@ lists
                    walk[atoms : __, i_] := i
                    walk[list, #] & /@ el





                    share|improve this answer









                    $endgroup$



                    This is what the list at the lowest level looks like:



                    el = First@Level[list, -2];


                    Using this, we can solve it with a rules-based approach:



                    list /. el -> # & /@ el


                    or a recursive approach like this:



                    walk[lists : __List, i_] := walk[#, i] & /@ lists
                    walk[atoms : __, i_] := i
                    walk[list, #] & /@ el






                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered 11 hours ago









                    C. E.C. E.

                    50.9k399205




                    50.9k399205





















                        2












                        $begingroup$

                        Terrible solution using Table but works:



                        Table[Map[#[[i]] &, arr, -2], i, Last[Dimensions[Level[arr, -2]]]]





                        share|improve this answer









                        $endgroup$

















                          2












                          $begingroup$

                          Terrible solution using Table but works:



                          Table[Map[#[[i]] &, arr, -2], i, Last[Dimensions[Level[arr, -2]]]]





                          share|improve this answer









                          $endgroup$















                            2












                            2








                            2





                            $begingroup$

                            Terrible solution using Table but works:



                            Table[Map[#[[i]] &, arr, -2], i, Last[Dimensions[Level[arr, -2]]]]





                            share|improve this answer









                            $endgroup$



                            Terrible solution using Table but works:



                            Table[Map[#[[i]] &, arr, -2], i, Last[Dimensions[Level[arr, -2]]]]






                            share|improve this answer












                            share|improve this answer



                            share|improve this answer










                            answered 10 hours ago









                            RomanRoman

                            4,0161022




                            4,0161022



























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                                2013 GY136 Descoberta | Órbita | Referências Menu de navegação«List Of Centaurs and Scattered-Disk Objects»«List of Known Trans-Neptunian Objects»

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                                Objetos do disco dispersoObjetos transnetunianos objeto transnetunianodisco dispersoSistema Solarcorpo celesteressonância orbitalplanetaplanetamagnitude absolutadiâmetro9 de abril2013Outer Solar System Origins Surveyórbitaexcentricidadesemieixo maiorUAperiélioSolafélio 2013 GY136 Data da descoberta 9 de abril de 2013 Descoberto por Outer Solar System Origins Survey Categoria Transnetuniano Objeto do disco disperso Elementos orbitais Semieixo maior 55,961 UA Perélio 32,595 UA Afélio 79,327 UA Excentricidade 0,418 Inclinação 10,9° Características físicas Dimensões 133 km Magnitude absoluta 7,6 ver 2013 GY 136 , também escrito como 2013 GY136 , é um objeto transnetuniano que está localizado no disco disperso, uma região do Sistema Solar. Este corpo celeste está em uma ressonância orbital de 2:5 com o planeta planeta. Ele possui uma magnitude absoluta de 7,6 [ 1 ] e tem um diâmetro estimad...
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                                Metrô de Los Teques Índice Linhas | Estações | Ver também | Referências Ligações externas | Menu de navegação«INSTITUCIÓN»«Mapa de rutas»originalMetrô de Los TequesC.A. Metro Los Teques |Alcaldía de Guaicaipuro – Sitio OficialGobernacion de Mirandaeeeeeee

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                                Metrô de Los TequesFundações na Venezuela em 2006 metropolitanoLos TequesGuaicaipuroMirandaGoverno da VenezuelaLinha 1Linha 2estaçõesLinha 1Linha 2IndependenciaSan AntonioLinha 3GuaicaipuroLibertadorEstação Las AdjuntasMetrô de Caracasalgarismocorestaçõesnomecorestaçõesestações Metrô de Los Teques Uma das composições que operam no sistema. Informações Proprietário Governo da Venezuela Local [[ Los Teques, Miranda]] País variant = Tipo de transporte Metropolitano Número de linhas 2 Número de estações 5 Website [1] Funcionamento Início de funcionamento 3 de novembro de 2006 (12 anos) [ 1 ] Operadora(s) C. A. Metro Los Teques Dados técnicos Extensão do sistema 11,2 km Bitola Bitola padrão (1435 mm) Velocidade máxima 80 km/h ...
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