Partitioning values in a sequence












2












$begingroup$


I have a sequence that forms visible lines when plotted as a graph, what would be a good way to automatically partition the sequence to create a list of sequences, one for each line that is visible when the sequence is plotted?



Here is the start of the sequence:



list = {2,3,5,11,7,23,13,29,41,17,53,37,83,43,89,19,113,131,67,47,73,31,79,173,179,61,191,97,233,239,251,127,139,281,71,293,101,103,107,163,59,359,193,199,137,419,431,443,151,491,509,181,109,277,593,149,307,641,653,659,683,719,241,743,373,761,257,157,263,809,271,409,283,433,911,311,313,953,487,331,499,1013,1019,1031,347,1049,211,269,367,1103,577,167,397,1223,1229,619,1289,223,673,229,461,467,1409,709,1439,1451,727,739,1481,1499,503,1511,1559,1583,1601,401,557,337,853,1733,349,883,197};


Thanks.



cheers,
Jamie






partitions







share|improve this question











$endgroup$












  • $begingroup$
    Possible duplicate of ordering-the-elements-in-a-list-and-separate-them-into-sublists-for-plotting
    $endgroup$
    – MelaGo
    5 hours ago
















2












$begingroup$


I have a sequence that forms visible lines when plotted as a graph, what would be a good way to automatically partition the sequence to create a list of sequences, one for each line that is visible when the sequence is plotted?



Here is the start of the sequence:



list = {2,3,5,11,7,23,13,29,41,17,53,37,83,43,89,19,113,131,67,47,73,31,79,173,179,61,191,97,233,239,251,127,139,281,71,293,101,103,107,163,59,359,193,199,137,419,431,443,151,491,509,181,109,277,593,149,307,641,653,659,683,719,241,743,373,761,257,157,263,809,271,409,283,433,911,311,313,953,487,331,499,1013,1019,1031,347,1049,211,269,367,1103,577,167,397,1223,1229,619,1289,223,673,229,461,467,1409,709,1439,1451,727,739,1481,1499,503,1511,1559,1583,1601,401,557,337,853,1733,349,883,197};


Thanks.



cheers,
Jamie






partitions







share|improve this question











$endgroup$












  • $begingroup$
    Possible duplicate of ordering-the-elements-in-a-list-and-separate-them-into-sublists-for-plotting
    $endgroup$
    – MelaGo
    5 hours ago














2












2








2





$begingroup$


I have a sequence that forms visible lines when plotted as a graph, what would be a good way to automatically partition the sequence to create a list of sequences, one for each line that is visible when the sequence is plotted?



Here is the start of the sequence:



list = {2,3,5,11,7,23,13,29,41,17,53,37,83,43,89,19,113,131,67,47,73,31,79,173,179,61,191,97,233,239,251,127,139,281,71,293,101,103,107,163,59,359,193,199,137,419,431,443,151,491,509,181,109,277,593,149,307,641,653,659,683,719,241,743,373,761,257,157,263,809,271,409,283,433,911,311,313,953,487,331,499,1013,1019,1031,347,1049,211,269,367,1103,577,167,397,1223,1229,619,1289,223,673,229,461,467,1409,709,1439,1451,727,739,1481,1499,503,1511,1559,1583,1601,401,557,337,853,1733,349,883,197};


Thanks.



cheers,
Jamie






partitions







share|improve this question











$endgroup$




I have a sequence that forms visible lines when plotted as a graph, what would be a good way to automatically partition the sequence to create a list of sequences, one for each line that is visible when the sequence is plotted?



Here is the start of the sequence:



list = {2,3,5,11,7,23,13,29,41,17,53,37,83,43,89,19,113,131,67,47,73,31,79,173,179,61,191,97,233,239,251,127,139,281,71,293,101,103,107,163,59,359,193,199,137,419,431,443,151,491,509,181,109,277,593,149,307,641,653,659,683,719,241,743,373,761,257,157,263,809,271,409,283,433,911,311,313,953,487,331,499,1013,1019,1031,347,1049,211,269,367,1103,577,167,397,1223,1229,619,1289,223,673,229,461,467,1409,709,1439,1451,727,739,1481,1499,503,1511,1559,1583,1601,401,557,337,853,1733,349,883,197};


Thanks.



cheers,
Jamie






partitions




partitions






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 13 mins ago









user64494

3,65311122




3,65311122










asked 5 hours ago









Jamie MJamie M

475




475












  • $begingroup$
    Possible duplicate of ordering-the-elements-in-a-list-and-separate-them-into-sublists-for-plotting
    $endgroup$
    – MelaGo
    5 hours ago


















  • $begingroup$
    Possible duplicate of ordering-the-elements-in-a-list-and-separate-them-into-sublists-for-plotting
    $endgroup$
    – MelaGo
    5 hours ago
















$begingroup$
Possible duplicate of ordering-the-elements-in-a-list-and-separate-them-into-sublists-for-plotting
$endgroup$
– MelaGo
5 hours ago




$begingroup$
Possible duplicate of ordering-the-elements-in-a-list-and-separate-them-into-sublists-for-plotting
$endgroup$
– MelaGo
5 hours ago










2 Answers
2






active

oldest

votes


















1












$begingroup$

You could for instance fit a mean polynomial function through the data:



fun = NonlinearModelFit[list, a x^2 + b x + c , {a, b, c}, x] //Normal



-48.3941 + 6.86017 x + 0.0161064 x^2




This will separarate the upper line from the lower line that you can see in the plot:



Show[

 ListLinePlot[list, PlotRange -> All],

 Plot[fun, {x, 0, 125}, PlotRange -> All, PlotStyle -> Red],

 PlotRange -> All]


enter image description here



Then you can simply run through the list and separate it into two lists based on whether the value is above or below the mean fit:



upperLine = {};

lowerLine = {};

Do[

 If[list[[x]] > fun,

   AppendTo[upperLine, {x, list[[x]]}],

   AppendTo[lowerLine, {x, list[[x]]}]];

 , {x, 1, Length[list]}]


The upperLine and lowerLine data sets then look like:



{ListLinePlot[upperLine], ListLinePlot[lowerLine]}


enter image description here



Repeat the process on the lowerLine data to separate the sequences further.






share|improve this answer











$endgroup$





















    2












    $begingroup$

    list = {2, 3, 5, 11, 7, 23, 13, 29, 41, 17, 53, 37, 83, 43, 89, 19, 
    
   113, 131, 67, 47, 73, 31, 79, 173, 179, 61, 191, 97, 233, 239, 251,
    
    127, 139, 281, 71, 293, 101, 103, 107, 163, 59, 359, 193, 199, 
    
   137, 419, 431, 443, 151, 491, 509, 181, 109, 277, 593, 149, 307, 
    
   641, 653, 659, 683, 719, 241, 743, 373, 761, 257, 157, 263, 809, 
    
   271, 409, 283, 433, 911, 311, 313, 953, 487, 331, 499, 1013, 1019, 
    
   1031, 347, 1049, 211, 269, 367, 1103, 577, 167, 397, 1223, 1229, 
    
   619, 1289, 223, 673, 229, 461, 467, 1409, 709, 1439, 1451, 727, 
    
   739, 1481, 1499, 503, 1511, 1559, 1583, 1601, 401, 557, 337, 853, 
    
   1733, 349, 883, 197};
    

    
upper = FindPeaks[list];
    

    
lower = {1, -1} # & /@ FindPeaks[-list];
    

    
ListLinePlot[{list, lower, upper},
    
 PlotStyle -> {LightGray, Blue, Red}]


    enter image description here






    share|improve this answer









    $endgroup$














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      2 Answers
      2






      active

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      2 Answers
      2






      active

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      active

      oldest

      votes






      active

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      1












      $begingroup$

      You could for instance fit a mean polynomial function through the data:



      fun = NonlinearModelFit[list, a x^2 + b x + c , {a, b, c}, x] //Normal



      -48.3941 + 6.86017 x + 0.0161064 x^2




      This will separarate the upper line from the lower line that you can see in the plot:



      Show[
      
 ListLinePlot[list, PlotRange -> All],
      
 Plot[fun, {x, 0, 125}, PlotRange -> All, PlotStyle -> Red],
      
 PlotRange -> All]


      enter image description here



      Then you can simply run through the list and separate it into two lists based on whether the value is above or below the mean fit:



      upperLine = {};
      
lowerLine = {};
      
Do[
      
 If[list[[x]] > fun,
      
   AppendTo[upperLine, {x, list[[x]]}],
      
   AppendTo[lowerLine, {x, list[[x]]}]];
      
 , {x, 1, Length[list]}]


      The upperLine and lowerLine data sets then look like:



      {ListLinePlot[upperLine], ListLinePlot[lowerLine]}


      enter image description here



      Repeat the process on the lowerLine data to separate the sequences further.






      share|improve this answer











      $endgroup$


















        1












        $begingroup$

        You could for instance fit a mean polynomial function through the data:



        fun = NonlinearModelFit[list, a x^2 + b x + c , {a, b, c}, x] //Normal



        -48.3941 + 6.86017 x + 0.0161064 x^2




        This will separarate the upper line from the lower line that you can see in the plot:



        Show[
        
 ListLinePlot[list, PlotRange -> All],
        
 Plot[fun, {x, 0, 125}, PlotRange -> All, PlotStyle -> Red],
        
 PlotRange -> All]


        enter image description here



        Then you can simply run through the list and separate it into two lists based on whether the value is above or below the mean fit:



        upperLine = {};
        
lowerLine = {};
        
Do[
        
 If[list[[x]] > fun,
        
   AppendTo[upperLine, {x, list[[x]]}],
        
   AppendTo[lowerLine, {x, list[[x]]}]];
        
 , {x, 1, Length[list]}]


        The upperLine and lowerLine data sets then look like:



        {ListLinePlot[upperLine], ListLinePlot[lowerLine]}


        enter image description here



        Repeat the process on the lowerLine data to separate the sequences further.






        share|improve this answer











        $endgroup$
















          1












          1








          1





          $begingroup$

          You could for instance fit a mean polynomial function through the data:



          fun = NonlinearModelFit[list, a x^2 + b x + c , {a, b, c}, x] //Normal



          -48.3941 + 6.86017 x + 0.0161064 x^2




          This will separarate the upper line from the lower line that you can see in the plot:



          Show[
          
 ListLinePlot[list, PlotRange -> All],
          
 Plot[fun, {x, 0, 125}, PlotRange -> All, PlotStyle -> Red],
          
 PlotRange -> All]


          enter image description here



          Then you can simply run through the list and separate it into two lists based on whether the value is above or below the mean fit:



          upperLine = {};
          
lowerLine = {};
          
Do[
          
 If[list[[x]] > fun,
          
   AppendTo[upperLine, {x, list[[x]]}],
          
   AppendTo[lowerLine, {x, list[[x]]}]];
          
 , {x, 1, Length[list]}]


          The upperLine and lowerLine data sets then look like:



          {ListLinePlot[upperLine], ListLinePlot[lowerLine]}


          enter image description here



          Repeat the process on the lowerLine data to separate the sequences further.






          share|improve this answer











          $endgroup$



          You could for instance fit a mean polynomial function through the data:



          fun = NonlinearModelFit[list, a x^2 + b x + c , {a, b, c}, x] //Normal



          -48.3941 + 6.86017 x + 0.0161064 x^2




          This will separarate the upper line from the lower line that you can see in the plot:



          Show[
          
 ListLinePlot[list, PlotRange -> All],
          
 Plot[fun, {x, 0, 125}, PlotRange -> All, PlotStyle -> Red],
          
 PlotRange -> All]


          enter image description here



          Then you can simply run through the list and separate it into two lists based on whether the value is above or below the mean fit:



          upperLine = {};
          
lowerLine = {};
          
Do[
          
 If[list[[x]] > fun,
          
   AppendTo[upperLine, {x, list[[x]]}],
          
   AppendTo[lowerLine, {x, list[[x]]}]];
          
 , {x, 1, Length[list]}]


          The upperLine and lowerLine data sets then look like:



          {ListLinePlot[upperLine], ListLinePlot[lowerLine]}


          enter image description here



          Repeat the process on the lowerLine data to separate the sequences further.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 5 hours ago

























          answered 5 hours ago









          KagaratschKagaratsch

          4,87531348




          4,87531348























              2












              $begingroup$

              list = {2, 3, 5, 11, 7, 23, 13, 29, 41, 17, 53, 37, 83, 43, 89, 19, 
              
   113, 131, 67, 47, 73, 31, 79, 173, 179, 61, 191, 97, 233, 239, 251,
              
    127, 139, 281, 71, 293, 101, 103, 107, 163, 59, 359, 193, 199, 
              
   137, 419, 431, 443, 151, 491, 509, 181, 109, 277, 593, 149, 307, 
              
   641, 653, 659, 683, 719, 241, 743, 373, 761, 257, 157, 263, 809, 
              
   271, 409, 283, 433, 911, 311, 313, 953, 487, 331, 499, 1013, 1019, 
              
   1031, 347, 1049, 211, 269, 367, 1103, 577, 167, 397, 1223, 1229, 
              
   619, 1289, 223, 673, 229, 461, 467, 1409, 709, 1439, 1451, 727, 
              
   739, 1481, 1499, 503, 1511, 1559, 1583, 1601, 401, 557, 337, 853, 
              
   1733, 349, 883, 197};
              

              
upper = FindPeaks[list];
              

              
lower = {1, -1} # & /@ FindPeaks[-list];
              

              
ListLinePlot[{list, lower, upper},
              
 PlotStyle -> {LightGray, Blue, Red}]


              enter image description here






              share|improve this answer









              $endgroup$


















                2












                $begingroup$

                list = {2, 3, 5, 11, 7, 23, 13, 29, 41, 17, 53, 37, 83, 43, 89, 19, 
                
   113, 131, 67, 47, 73, 31, 79, 173, 179, 61, 191, 97, 233, 239, 251,
                
    127, 139, 281, 71, 293, 101, 103, 107, 163, 59, 359, 193, 199, 
                
   137, 419, 431, 443, 151, 491, 509, 181, 109, 277, 593, 149, 307, 
                
   641, 653, 659, 683, 719, 241, 743, 373, 761, 257, 157, 263, 809, 
                
   271, 409, 283, 433, 911, 311, 313, 953, 487, 331, 499, 1013, 1019, 
                
   1031, 347, 1049, 211, 269, 367, 1103, 577, 167, 397, 1223, 1229, 
                
   619, 1289, 223, 673, 229, 461, 467, 1409, 709, 1439, 1451, 727, 
                
   739, 1481, 1499, 503, 1511, 1559, 1583, 1601, 401, 557, 337, 853, 
                
   1733, 349, 883, 197};
                

                
upper = FindPeaks[list];
                

                
lower = {1, -1} # & /@ FindPeaks[-list];
                

                
ListLinePlot[{list, lower, upper},
                
 PlotStyle -> {LightGray, Blue, Red}]


                enter image description here






                share|improve this answer









                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  list = {2, 3, 5, 11, 7, 23, 13, 29, 41, 17, 53, 37, 83, 43, 89, 19, 
                  
   113, 131, 67, 47, 73, 31, 79, 173, 179, 61, 191, 97, 233, 239, 251,
                  
    127, 139, 281, 71, 293, 101, 103, 107, 163, 59, 359, 193, 199, 
                  
   137, 419, 431, 443, 151, 491, 509, 181, 109, 277, 593, 149, 307, 
                  
   641, 653, 659, 683, 719, 241, 743, 373, 761, 257, 157, 263, 809, 
                  
   271, 409, 283, 433, 911, 311, 313, 953, 487, 331, 499, 1013, 1019, 
                  
   1031, 347, 1049, 211, 269, 367, 1103, 577, 167, 397, 1223, 1229, 
                  
   619, 1289, 223, 673, 229, 461, 467, 1409, 709, 1439, 1451, 727, 
                  
   739, 1481, 1499, 503, 1511, 1559, 1583, 1601, 401, 557, 337, 853, 
                  
   1733, 349, 883, 197};
                  

                  
upper = FindPeaks[list];
                  

                  
lower = {1, -1} # & /@ FindPeaks[-list];
                  

                  
ListLinePlot[{list, lower, upper},
                  
 PlotStyle -> {LightGray, Blue, Red}]


                  enter image description here






                  share|improve this answer









                  $endgroup$



                  list = {2, 3, 5, 11, 7, 23, 13, 29, 41, 17, 53, 37, 83, 43, 89, 19, 
                  
   113, 131, 67, 47, 73, 31, 79, 173, 179, 61, 191, 97, 233, 239, 251,
                  
    127, 139, 281, 71, 293, 101, 103, 107, 163, 59, 359, 193, 199, 
                  
   137, 419, 431, 443, 151, 491, 509, 181, 109, 277, 593, 149, 307, 
                  
   641, 653, 659, 683, 719, 241, 743, 373, 761, 257, 157, 263, 809, 
                  
   271, 409, 283, 433, 911, 311, 313, 953, 487, 331, 499, 1013, 1019, 
                  
   1031, 347, 1049, 211, 269, 367, 1103, 577, 167, 397, 1223, 1229, 
                  
   619, 1289, 223, 673, 229, 461, 467, 1409, 709, 1439, 1451, 727, 
                  
   739, 1481, 1499, 503, 1511, 1559, 1583, 1601, 401, 557, 337, 853, 
                  
   1733, 349, 883, 197};
                  

                  
upper = FindPeaks[list];
                  

                  
lower = {1, -1} # & /@ FindPeaks[-list];
                  

                  
ListLinePlot[{list, lower, upper},
                  
 PlotStyle -> {LightGray, Blue, Red}]


                  enter image description here







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 1 hour ago









                  Bob HanlonBob Hanlon

                  61.9k33598




                  61.9k33598






























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