How can I make a NumberLineLogPlot'?












4












$begingroup$


I have a piecewise function that is defined in logarithmic intervals, i.e., the different pieces are defined on



{{1. <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}}


I'd like to visualize the different domains on a number line.
NumberLinePlot, of course, works, but it looks clumsy as the plot is fully dominated by the last domain an the first one is barely visible:



NumberLinePlot[{{1. <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}}, {x, 1, 1000}]


enter image description here



So I can use something along the lines of



NumberLinePlot[

  {{Log[10, 1] <= x <= Log[10, 10]}, 

   {Log[10, 10] <= x <= Log[10, 100]}, 

   {Log[10, 100] <= x <= Log[10, 1000]}}, 

  {x, Log[10, 1], Log[10, 1000]}]


which results in a much more pleasantly balanced plot:



enter image description here



However, now the number line ticks show the exponents — so in essence I'd like something like NumberLineLogPlot, but that doesn't exist.



I tried to recreate something like that by abusing LogLogPlot



Show[

  MapThread[

    LogLogPlot[#1, #2, PlotStyle -> #3] &, 

    {{1, 2, 4}, {x, #[[1, 1]], #[[1, 3]]} & /@ dx , {Red, Green, Blue}}], 

  PlotRange -> Automatic, Frame -> {{False, False}, {True, False}}]


Which leads to something like



enter image description here



which is better in terms of the logarithmic x-axis but is quite clumsy in other ways.



Any ideas how to implement a NumberLineLogPlot nicely?






piecewise ticks numberlineplot loglogplot







share|improve this question











$endgroup$

















    4












    $begingroup$


    I have a piecewise function that is defined in logarithmic intervals, i.e., the different pieces are defined on



    {{1. <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}}


    I'd like to visualize the different domains on a number line.
    NumberLinePlot, of course, works, but it looks clumsy as the plot is fully dominated by the last domain an the first one is barely visible:



    NumberLinePlot[{{1. <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}}, {x, 1, 1000}]


    enter image description here



    So I can use something along the lines of



    NumberLinePlot[
    
  {{Log[10, 1] <= x <= Log[10, 10]}, 
    
   {Log[10, 10] <= x <= Log[10, 100]}, 
    
   {Log[10, 100] <= x <= Log[10, 1000]}}, 
    
  {x, Log[10, 1], Log[10, 1000]}]


    which results in a much more pleasantly balanced plot:



    enter image description here



    However, now the number line ticks show the exponents — so in essence I'd like something like NumberLineLogPlot, but that doesn't exist.



    I tried to recreate something like that by abusing LogLogPlot



    Show[
    
  MapThread[
    
    LogLogPlot[#1, #2, PlotStyle -> #3] &, 
    
    {{1, 2, 4}, {x, #[[1, 1]], #[[1, 3]]} & /@ dx , {Red, Green, Blue}}], 
    
  PlotRange -> Automatic, Frame -> {{False, False}, {True, False}}]


    Which leads to something like



    enter image description here



    which is better in terms of the logarithmic x-axis but is quite clumsy in other ways.



    Any ideas how to implement a NumberLineLogPlot nicely?






    piecewise ticks numberlineplot loglogplot







    share|improve this question











    $endgroup$















      4












      4








      4





      $begingroup$


      I have a piecewise function that is defined in logarithmic intervals, i.e., the different pieces are defined on



      {{1. <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}}


      I'd like to visualize the different domains on a number line.
      NumberLinePlot, of course, works, but it looks clumsy as the plot is fully dominated by the last domain an the first one is barely visible:



      NumberLinePlot[{{1. <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}}, {x, 1, 1000}]


      enter image description here



      So I can use something along the lines of



      NumberLinePlot[
      
  {{Log[10, 1] <= x <= Log[10, 10]}, 
      
   {Log[10, 10] <= x <= Log[10, 100]}, 
      
   {Log[10, 100] <= x <= Log[10, 1000]}}, 
      
  {x, Log[10, 1], Log[10, 1000]}]


      which results in a much more pleasantly balanced plot:



      enter image description here



      However, now the number line ticks show the exponents — so in essence I'd like something like NumberLineLogPlot, but that doesn't exist.



      I tried to recreate something like that by abusing LogLogPlot



      Show[
      
  MapThread[
      
    LogLogPlot[#1, #2, PlotStyle -> #3] &, 
      
    {{1, 2, 4}, {x, #[[1, 1]], #[[1, 3]]} & /@ dx , {Red, Green, Blue}}], 
      
  PlotRange -> Automatic, Frame -> {{False, False}, {True, False}}]


      Which leads to something like



      enter image description here



      which is better in terms of the logarithmic x-axis but is quite clumsy in other ways.



      Any ideas how to implement a NumberLineLogPlot nicely?






      piecewise ticks numberlineplot loglogplot







      share|improve this question











      $endgroup$




      I have a piecewise function that is defined in logarithmic intervals, i.e., the different pieces are defined on



      {{1. <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}}


      I'd like to visualize the different domains on a number line.
      NumberLinePlot, of course, works, but it looks clumsy as the plot is fully dominated by the last domain an the first one is barely visible:



      NumberLinePlot[{{1. <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}}, {x, 1, 1000}]


      enter image description here



      So I can use something along the lines of



      NumberLinePlot[
      
  {{Log[10, 1] <= x <= Log[10, 10]}, 
      
   {Log[10, 10] <= x <= Log[10, 100]}, 
      
   {Log[10, 100] <= x <= Log[10, 1000]}}, 
      
  {x, Log[10, 1], Log[10, 1000]}]


      which results in a much more pleasantly balanced plot:



      enter image description here



      However, now the number line ticks show the exponents — so in essence I'd like something like NumberLineLogPlot, but that doesn't exist.



      I tried to recreate something like that by abusing LogLogPlot



      Show[
      
  MapThread[
      
    LogLogPlot[#1, #2, PlotStyle -> #3] &, 
      
    {{1, 2, 4}, {x, #[[1, 1]], #[[1, 3]]} & /@ dx , {Red, Green, Blue}}], 
      
  PlotRange -> Automatic, Frame -> {{False, False}, {True, False}}]


      Which leads to something like



      enter image description here



      which is better in terms of the logarithmic x-axis but is quite clumsy in other ways.



      Any ideas how to implement a NumberLineLogPlot nicely?






      piecewise ticks numberlineplot loglogplot




      piecewise ticks numberlineplot loglogplot






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Feb 3 at 15:13









      m_goldberg

      87.7k872198




      87.7k872198










      asked Feb 3 at 13:00









      Oliver JennrichOliver Jennrich

      887411




      887411






















          2 Answers
          2






          active

          oldest

          votes


















          4












          $begingroup$

          Use the option Ticks



          intervals = {{1 <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}};
          

          
logIntervals = intervals /. {n_?NumericQ :> Log10[n]}
          

          
(* {{0 <= x <= 1}, {1 <= x <= 2}, {2 <= x <= 3}} *)
          

          
NumberLinePlot[logIntervals, {x, 0, 3}, 
          
 Ticks -> {({Log10[#], #} & /@ 
          
    {1, 2, 5, 10, 20, 50, 100, 200, 500, 1000}), None}]


          enter image description here






          share|improve this answer









          $endgroup$













          • $begingroup$
            Nice one! I particularly like the trick with the patternreplacement for the Log
            $endgroup$
            – Oliver Jennrich
            Feb 3 at 15:32



















          0












          $begingroup$

          You can also transform intervals into a list of lists and use ListLinePlot with the option ScalingFunctions:



          lst = MapIndexed[Thread[{#[[1]], #2[[1]]/2}] &, intervals /. LessEqual -> ({#, #3} &)]; 
          
Show[ListLinePlot[lst, ScalingFunctions -> {{Log[10, #] &, 10^# &}, None},
          
   Joined -> #] & /@ {True, False}, AspectRatio -> 1/5, Axes -> {True, False}]


          enter image description here






          share|improve this answer









          $endgroup$













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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            4












            $begingroup$

            Use the option Ticks



            intervals = {{1 <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}};
            

            
logIntervals = intervals /. {n_?NumericQ :> Log10[n]}
            

            
(* {{0 <= x <= 1}, {1 <= x <= 2}, {2 <= x <= 3}} *)
            

            
NumberLinePlot[logIntervals, {x, 0, 3}, 
            
 Ticks -> {({Log10[#], #} & /@ 
            
    {1, 2, 5, 10, 20, 50, 100, 200, 500, 1000}), None}]


            enter image description here






            share|improve this answer









            $endgroup$













            • $begingroup$
              Nice one! I particularly like the trick with the patternreplacement for the Log
              $endgroup$
              – Oliver Jennrich
              Feb 3 at 15:32
















            4












            $begingroup$

            Use the option Ticks



            intervals = {{1 <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}};
            

            
logIntervals = intervals /. {n_?NumericQ :> Log10[n]}
            

            
(* {{0 <= x <= 1}, {1 <= x <= 2}, {2 <= x <= 3}} *)
            

            
NumberLinePlot[logIntervals, {x, 0, 3}, 
            
 Ticks -> {({Log10[#], #} & /@ 
            
    {1, 2, 5, 10, 20, 50, 100, 200, 500, 1000}), None}]


            enter image description here






            share|improve this answer









            $endgroup$













            • $begingroup$
              Nice one! I particularly like the trick with the patternreplacement for the Log
              $endgroup$
              – Oliver Jennrich
              Feb 3 at 15:32














            4












            4








            4





            $begingroup$

            Use the option Ticks



            intervals = {{1 <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}};
            

            
logIntervals = intervals /. {n_?NumericQ :> Log10[n]}
            

            
(* {{0 <= x <= 1}, {1 <= x <= 2}, {2 <= x <= 3}} *)
            

            
NumberLinePlot[logIntervals, {x, 0, 3}, 
            
 Ticks -> {({Log10[#], #} & /@ 
            
    {1, 2, 5, 10, 20, 50, 100, 200, 500, 1000}), None}]


            enter image description here






            share|improve this answer









            $endgroup$



            Use the option Ticks



            intervals = {{1 <= x <= 10}, {10 <= x <= 100}, {100 <= x <= 1000}};
            

            
logIntervals = intervals /. {n_?NumericQ :> Log10[n]}
            

            
(* {{0 <= x <= 1}, {1 <= x <= 2}, {2 <= x <= 3}} *)
            

            
NumberLinePlot[logIntervals, {x, 0, 3}, 
            
 Ticks -> {({Log10[#], #} & /@ 
            
    {1, 2, 5, 10, 20, 50, 100, 200, 500, 1000}), None}]


            enter image description here







            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered Feb 3 at 14:39









            Bob HanlonBob Hanlon

            60.8k33597




            60.8k33597












            • $begingroup$
              Nice one! I particularly like the trick with the patternreplacement for the Log
              $endgroup$
              – Oliver Jennrich
              Feb 3 at 15:32


















            • $begingroup$
              Nice one! I particularly like the trick with the patternreplacement for the Log
              $endgroup$
              – Oliver Jennrich
              Feb 3 at 15:32
















            $begingroup$
            Nice one! I particularly like the trick with the patternreplacement for the Log
            $endgroup$
            – Oliver Jennrich
            Feb 3 at 15:32




            $begingroup$
            Nice one! I particularly like the trick with the patternreplacement for the Log
            $endgroup$
            – Oliver Jennrich
            Feb 3 at 15:32











            0












            $begingroup$

            You can also transform intervals into a list of lists and use ListLinePlot with the option ScalingFunctions:



            lst = MapIndexed[Thread[{#[[1]], #2[[1]]/2}] &, intervals /. LessEqual -> ({#, #3} &)]; 
            
Show[ListLinePlot[lst, ScalingFunctions -> {{Log[10, #] &, 10^# &}, None},
            
   Joined -> #] & /@ {True, False}, AspectRatio -> 1/5, Axes -> {True, False}]


            enter image description here






            share|improve this answer









            $endgroup$


















              0












              $begingroup$

              You can also transform intervals into a list of lists and use ListLinePlot with the option ScalingFunctions:



              lst = MapIndexed[Thread[{#[[1]], #2[[1]]/2}] &, intervals /. LessEqual -> ({#, #3} &)]; 
              
Show[ListLinePlot[lst, ScalingFunctions -> {{Log[10, #] &, 10^# &}, None},
              
   Joined -> #] & /@ {True, False}, AspectRatio -> 1/5, Axes -> {True, False}]


              enter image description here






              share|improve this answer









              $endgroup$
















                0












                0








                0





                $begingroup$

                You can also transform intervals into a list of lists and use ListLinePlot with the option ScalingFunctions:



                lst = MapIndexed[Thread[{#[[1]], #2[[1]]/2}] &, intervals /. LessEqual -> ({#, #3} &)]; 
                
Show[ListLinePlot[lst, ScalingFunctions -> {{Log[10, #] &, 10^# &}, None},
                
   Joined -> #] & /@ {True, False}, AspectRatio -> 1/5, Axes -> {True, False}]


                enter image description here






                share|improve this answer









                $endgroup$



                You can also transform intervals into a list of lists and use ListLinePlot with the option ScalingFunctions:



                lst = MapIndexed[Thread[{#[[1]], #2[[1]]/2}] &, intervals /. LessEqual -> ({#, #3} &)]; 
                
Show[ListLinePlot[lst, ScalingFunctions -> {{Log[10, #] &, 10^# &}, None},
                
   Joined -> #] & /@ {True, False}, AspectRatio -> 1/5, Axes -> {True, False}]


                enter image description here







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered Feb 4 at 4:24









                kglrkglr

                189k10206424




                189k10206424






























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