Applying function to all elements of the list of list












3












$begingroup$


Let's say we have a following list:



{{{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4}, {1,2, 3, 4, 5}}, {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4,5}}, {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4,5}}, {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}}.



Now, I've written this simple function:



TransformToPoints[{a_}] := 
If[First[a] == 1,
{First[a] = 0, Last[a] = Last[a] + 1},
{First[a] = First[a] - 1, Last[a] = Last[a] + 1}]


so basically that function takes in a list and transforms it to the list of 2 elements, where those 2 elements are produced as described in the function. Now, I'd like to apply this function to all the elements of lists inside the big list above (which is usually much, much bigger) so the new list would look as follows:



{{{0,2},{2,4},{4,6},{0,3},{0,6}},{{0,2},{2,4},{4,6},{2,5},{0,6}},...,{{0,2},{2,4},{4,6},{0,5},{0,6}}}



What would be the quickest way to do that?










share|improve this question











$endgroup$

















    3












    $begingroup$


    Let's say we have a following list:



    {{{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4}, {1,2, 3, 4, 5}}, {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4,5}}, {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4,5}}, {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}}.



    Now, I've written this simple function:



    TransformToPoints[{a_}] := 
    If[First[a] == 1,
    {First[a] = 0, Last[a] = Last[a] + 1},
    {First[a] = First[a] - 1, Last[a] = Last[a] + 1}]


    so basically that function takes in a list and transforms it to the list of 2 elements, where those 2 elements are produced as described in the function. Now, I'd like to apply this function to all the elements of lists inside the big list above (which is usually much, much bigger) so the new list would look as follows:



    {{{0,2},{2,4},{4,6},{0,3},{0,6}},{{0,2},{2,4},{4,6},{2,5},{0,6}},...,{{0,2},{2,4},{4,6},{0,5},{0,6}}}



    What would be the quickest way to do that?










    share|improve this question











    $endgroup$















      3












      3








      3





      $begingroup$


      Let's say we have a following list:



      {{{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4}, {1,2, 3, 4, 5}}, {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4,5}}, {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4,5}}, {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}}.



      Now, I've written this simple function:



      TransformToPoints[{a_}] := 
      If[First[a] == 1,
      {First[a] = 0, Last[a] = Last[a] + 1},
      {First[a] = First[a] - 1, Last[a] = Last[a] + 1}]


      so basically that function takes in a list and transforms it to the list of 2 elements, where those 2 elements are produced as described in the function. Now, I'd like to apply this function to all the elements of lists inside the big list above (which is usually much, much bigger) so the new list would look as follows:



      {{{0,2},{2,4},{4,6},{0,3},{0,6}},{{0,2},{2,4},{4,6},{2,5},{0,6}},...,{{0,2},{2,4},{4,6},{0,5},{0,6}}}



      What would be the quickest way to do that?










      share|improve this question











      $endgroup$




      Let's say we have a following list:



      {{{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4}, {1,2, 3, 4, 5}}, {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4,5}}, {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4,5}}, {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}}.



      Now, I've written this simple function:



      TransformToPoints[{a_}] := 
      If[First[a] == 1,
      {First[a] = 0, Last[a] = Last[a] + 1},
      {First[a] = First[a] - 1, Last[a] = Last[a] + 1}]


      so basically that function takes in a list and transforms it to the list of 2 elements, where those 2 elements are produced as described in the function. Now, I'd like to apply this function to all the elements of lists inside the big list above (which is usually much, much bigger) so the new list would look as follows:



      {{{0,2},{2,4},{4,6},{0,3},{0,6}},{{0,2},{2,4},{4,6},{2,5},{0,6}},...,{{0,2},{2,4},{4,6},{0,5},{0,6}}}



      What would be the quickest way to do that?







      list-manipulation






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Jan 14 at 19:35









      Mr.Wizard

      231k294761049




      231k294761049










      asked Jan 14 at 16:39









      amator2357amator2357

      997




      997






















          2 Answers
          2






          active

          oldest

          votes


















          5












          $begingroup$

          An alternative way to define your transformation function:



          tToP[lst_List] := #[[{1, -1}]] + {-1, 1} & /@ lst;

          list = {{{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {3, 4}, {1,2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}};

          tToP /@ list



          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}},

          {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}},

          {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}




          Alternatively, you can use Map[tToP, list, 1].






          share|improve this answer









          $endgroup$













          • $begingroup$
            Thank you @kglr, I really like it ! I'll accept your answer since it uses this unintuitive (at least to me) approach.
            $endgroup$
            – amator2357
            Jan 14 at 21:23










          • $begingroup$
            @amator2357, thank you for the accept.
            $endgroup$
            – kglr
            Jan 14 at 21:33



















          5












          $begingroup$

          First of all, you can't do assignment to variables that you entered into the function in this case. It's not necessary either, just define your function as follows (notice that I also fixed your matching pattern):



          Clear[TransformToPoints]
          TransformToPoints[a_List] := If[First[a] == 1, {0, Last[a] + 1}, {First[a] - 1, Last[a] + 1}]


          To apply the function to all elements of the big list, just use Map. However, you don't want to map onto the first level but the second level down, so this is what you do:



          Map[
          TransformToPoints,
          {
          {{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}
          },
          {2} (* map onto the 2nd level*)
          ]




          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}}, {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}}, {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}








          share|improve this answer











          $endgroup$













          • $begingroup$
            Thank you so much!
            $endgroup$
            – amator2357
            Jan 14 at 17:44











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          2 Answers
          2






          active

          oldest

          votes








          2 Answers
          2






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          5












          $begingroup$

          An alternative way to define your transformation function:



          tToP[lst_List] := #[[{1, -1}]] + {-1, 1} & /@ lst;

          list = {{{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {3, 4}, {1,2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}};

          tToP /@ list



          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}},

          {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}},

          {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}




          Alternatively, you can use Map[tToP, list, 1].






          share|improve this answer









          $endgroup$













          • $begingroup$
            Thank you @kglr, I really like it ! I'll accept your answer since it uses this unintuitive (at least to me) approach.
            $endgroup$
            – amator2357
            Jan 14 at 21:23










          • $begingroup$
            @amator2357, thank you for the accept.
            $endgroup$
            – kglr
            Jan 14 at 21:33
















          5












          $begingroup$

          An alternative way to define your transformation function:



          tToP[lst_List] := #[[{1, -1}]] + {-1, 1} & /@ lst;

          list = {{{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {3, 4}, {1,2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}};

          tToP /@ list



          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}},

          {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}},

          {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}




          Alternatively, you can use Map[tToP, list, 1].






          share|improve this answer









          $endgroup$













          • $begingroup$
            Thank you @kglr, I really like it ! I'll accept your answer since it uses this unintuitive (at least to me) approach.
            $endgroup$
            – amator2357
            Jan 14 at 21:23










          • $begingroup$
            @amator2357, thank you for the accept.
            $endgroup$
            – kglr
            Jan 14 at 21:33














          5












          5








          5





          $begingroup$

          An alternative way to define your transformation function:



          tToP[lst_List] := #[[{1, -1}]] + {-1, 1} & /@ lst;

          list = {{{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {3, 4}, {1,2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}};

          tToP /@ list



          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}},

          {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}},

          {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}




          Alternatively, you can use Map[tToP, list, 1].






          share|improve this answer









          $endgroup$



          An alternative way to define your transformation function:



          tToP[lst_List] := #[[{1, -1}]] + {-1, 1} & /@ lst;

          list = {{{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {3, 4}, {1,2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4,5}},
          {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}};

          tToP /@ list



          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}},

          {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}},

          {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}},

          {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}




          Alternatively, you can use Map[tToP, list, 1].







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Jan 14 at 17:53









          kglrkglr

          184k10202418




          184k10202418












          • $begingroup$
            Thank you @kglr, I really like it ! I'll accept your answer since it uses this unintuitive (at least to me) approach.
            $endgroup$
            – amator2357
            Jan 14 at 21:23










          • $begingroup$
            @amator2357, thank you for the accept.
            $endgroup$
            – kglr
            Jan 14 at 21:33


















          • $begingroup$
            Thank you @kglr, I really like it ! I'll accept your answer since it uses this unintuitive (at least to me) approach.
            $endgroup$
            – amator2357
            Jan 14 at 21:23










          • $begingroup$
            @amator2357, thank you for the accept.
            $endgroup$
            – kglr
            Jan 14 at 21:33
















          $begingroup$
          Thank you @kglr, I really like it ! I'll accept your answer since it uses this unintuitive (at least to me) approach.
          $endgroup$
          – amator2357
          Jan 14 at 21:23




          $begingroup$
          Thank you @kglr, I really like it ! I'll accept your answer since it uses this unintuitive (at least to me) approach.
          $endgroup$
          – amator2357
          Jan 14 at 21:23












          $begingroup$
          @amator2357, thank you for the accept.
          $endgroup$
          – kglr
          Jan 14 at 21:33




          $begingroup$
          @amator2357, thank you for the accept.
          $endgroup$
          – kglr
          Jan 14 at 21:33











          5












          $begingroup$

          First of all, you can't do assignment to variables that you entered into the function in this case. It's not necessary either, just define your function as follows (notice that I also fixed your matching pattern):



          Clear[TransformToPoints]
          TransformToPoints[a_List] := If[First[a] == 1, {0, Last[a] + 1}, {First[a] - 1, Last[a] + 1}]


          To apply the function to all elements of the big list, just use Map. However, you don't want to map onto the first level but the second level down, so this is what you do:



          Map[
          TransformToPoints,
          {
          {{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}
          },
          {2} (* map onto the 2nd level*)
          ]




          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}}, {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}}, {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}








          share|improve this answer











          $endgroup$













          • $begingroup$
            Thank you so much!
            $endgroup$
            – amator2357
            Jan 14 at 17:44
















          5












          $begingroup$

          First of all, you can't do assignment to variables that you entered into the function in this case. It's not necessary either, just define your function as follows (notice that I also fixed your matching pattern):



          Clear[TransformToPoints]
          TransformToPoints[a_List] := If[First[a] == 1, {0, Last[a] + 1}, {First[a] - 1, Last[a] + 1}]


          To apply the function to all elements of the big list, just use Map. However, you don't want to map onto the first level but the second level down, so this is what you do:



          Map[
          TransformToPoints,
          {
          {{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}
          },
          {2} (* map onto the 2nd level*)
          ]




          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}}, {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}}, {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}








          share|improve this answer











          $endgroup$













          • $begingroup$
            Thank you so much!
            $endgroup$
            – amator2357
            Jan 14 at 17:44














          5












          5








          5





          $begingroup$

          First of all, you can't do assignment to variables that you entered into the function in this case. It's not necessary either, just define your function as follows (notice that I also fixed your matching pattern):



          Clear[TransformToPoints]
          TransformToPoints[a_List] := If[First[a] == 1, {0, Last[a] + 1}, {First[a] - 1, Last[a] + 1}]


          To apply the function to all elements of the big list, just use Map. However, you don't want to map onto the first level but the second level down, so this is what you do:



          Map[
          TransformToPoints,
          {
          {{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}
          },
          {2} (* map onto the 2nd level*)
          ]




          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}}, {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}}, {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}








          share|improve this answer











          $endgroup$



          First of all, you can't do assignment to variables that you entered into the function in this case. It's not necessary either, just define your function as follows (notice that I also fixed your matching pattern):



          Clear[TransformToPoints]
          TransformToPoints[a_List] := If[First[a] == 1, {0, Last[a] + 1}, {First[a] - 1, Last[a] + 1}]


          To apply the function to all elements of the big list, just use Map. However, you don't want to map onto the first level but the second level down, so this is what you do:



          Map[
          TransformToPoints,
          {
          {{1}, {3}, {5}, {1, 2}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4}, {1, 2, 3, 4, 5}},
          {{1}, {3}, {5}, {1, 2, 3}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {3, 4, 5}, {1, 2, 3, 4, 5}}, {{1}, {3}, {5}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}
          },
          {2} (* map onto the 2nd level*)
          ]




          {{{0, 2}, {2, 4}, {4, 6}, {0, 3}, {0, 6}}, {{0, 2}, {2, 4}, {4,
          6}, {2, 5}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0, 4}, {0, 6}}, {{0,
          2}, {2, 4}, {4, 6}, {2, 6}, {0, 6}}, {{0, 2}, {2, 4}, {4, 6}, {0,
          5}, {0, 6}}}









          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Jan 15 at 9:12

























          answered Jan 14 at 17:02









          Sjoerd SmitSjoerd Smit

          3,670715




          3,670715












          • $begingroup$
            Thank you so much!
            $endgroup$
            – amator2357
            Jan 14 at 17:44


















          • $begingroup$
            Thank you so much!
            $endgroup$
            – amator2357
            Jan 14 at 17:44
















          $begingroup$
          Thank you so much!
          $endgroup$
          – amator2357
          Jan 14 at 17:44




          $begingroup$
          Thank you so much!
          $endgroup$
          – amator2357
          Jan 14 at 17:44


















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