Converting from “matrix” data into “coordinate” data












2












$begingroup$


Say I have data which looks like data1 - this is "matrix" like data (is there a better descriptor?). The data looks like a matrix, and at each point in the matrix, it has a value. I can plot these in ListContourPlot and the like. e.g. 



datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];



(* matrix like data *) 



data1 = N[ Table[PDF[datafunction, {x, y}] /. {x -> xinsert, y -> yinsert}, {xinsert, -4, 4, 1}, {yinsert, -2, 2, 1}]];

ListContourPlot[data1]


enter image description here
However, I can also create the same effect by making "coordinate" like data, where the data is a list of coordinates. 



(* coordinate like data *) 



data2 = RandomVariate[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], 1000];

ListPlot[data2]


enter image description here
How would I convert data1 into data2? How do I convert matrix-like into coordinate-like?



I need to do some PCA analysis, I require the data to be in the form of individual points.






list-manipulation data-structures







share|improve this question











$endgroup$








  • 1




    $begingroup$
    How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
    $endgroup$
    – Sjoerd C. de Vries
    10 hours ago
















2












$begingroup$


Say I have data which looks like data1 - this is "matrix" like data (is there a better descriptor?). The data looks like a matrix, and at each point in the matrix, it has a value. I can plot these in ListContourPlot and the like. e.g. 



datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];



(* matrix like data *) 



data1 = N[ Table[PDF[datafunction, {x, y}] /. {x -> xinsert, y -> yinsert}, {xinsert, -4, 4, 1}, {yinsert, -2, 2, 1}]];

ListContourPlot[data1]


enter image description here
However, I can also create the same effect by making "coordinate" like data, where the data is a list of coordinates. 



(* coordinate like data *) 



data2 = RandomVariate[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], 1000];

ListPlot[data2]


enter image description here
How would I convert data1 into data2? How do I convert matrix-like into coordinate-like?



I need to do some PCA analysis, I require the data to be in the form of individual points.






list-manipulation data-structures







share|improve this question











$endgroup$








  • 1




    $begingroup$
    How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
    $endgroup$
    – Sjoerd C. de Vries
    10 hours ago














2












2








2





$begingroup$


Say I have data which looks like data1 - this is "matrix" like data (is there a better descriptor?). The data looks like a matrix, and at each point in the matrix, it has a value. I can plot these in ListContourPlot and the like. e.g. 



datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];



(* matrix like data *) 



data1 = N[ Table[PDF[datafunction, {x, y}] /. {x -> xinsert, y -> yinsert}, {xinsert, -4, 4, 1}, {yinsert, -2, 2, 1}]];

ListContourPlot[data1]


enter image description here
However, I can also create the same effect by making "coordinate" like data, where the data is a list of coordinates. 



(* coordinate like data *) 



data2 = RandomVariate[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], 1000];

ListPlot[data2]


enter image description here
How would I convert data1 into data2? How do I convert matrix-like into coordinate-like?



I need to do some PCA analysis, I require the data to be in the form of individual points.






list-manipulation data-structures







share|improve this question











$endgroup$




Say I have data which looks like data1 - this is "matrix" like data (is there a better descriptor?). The data looks like a matrix, and at each point in the matrix, it has a value. I can plot these in ListContourPlot and the like. e.g. 



datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];



(* matrix like data *) 



data1 = N[ Table[PDF[datafunction, {x, y}] /. {x -> xinsert, y -> yinsert}, {xinsert, -4, 4, 1}, {yinsert, -2, 2, 1}]];

ListContourPlot[data1]


enter image description here
However, I can also create the same effect by making "coordinate" like data, where the data is a list of coordinates. 



(* coordinate like data *) 



data2 = RandomVariate[MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}], 1000];

ListPlot[data2]


enter image description here
How would I convert data1 into data2? How do I convert matrix-like into coordinate-like?



I need to do some PCA analysis, I require the data to be in the form of individual points.






list-manipulation data-structures




list-manipulation data-structures






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 9 hours ago







Tomi

















asked 11 hours ago









TomiTomi

974514




974514








  • 1




    $begingroup$
    How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
    $endgroup$
    – Sjoerd C. de Vries
    10 hours ago














  • 1




    $begingroup$
    How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
    $endgroup$
    – Sjoerd C. de Vries
    10 hours ago








1




1




$begingroup$
How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
$endgroup$
– Sjoerd C. de Vries
10 hours ago




$begingroup$
How do you think one could infer the individual counts from a total count? Once we have totaled data and thrown away the parts there is no way to reconstruct them. The mapping between sums and their constituents is not bijective.
$endgroup$
– Sjoerd C. de Vries
10 hours ago










2 Answers
2






active

oldest

votes


















4












$begingroup$

The reshaping can be done in several ways. Below is given one using SparseArray.



First generating the data (simpler than in the question):



datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];



data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];



MatrixForm[data1]


Make index-to-value associations corresponding to the ranges used to make data1:



aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];

aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];


Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.



arules = Most[ArrayRules[SparseArray[data1]]];

data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]


Plot (note the axes ticks):



ListContourPlot[data2]


enter image description here






share|improve this answer









$endgroup$





















    2












    $begingroup$

    An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:



    xrange = {-4, 4};
    
yrange = {-2, 2};
    
sa = SparseArray[data1];
    
nzp = sa["NonzeroPositions"];
    
nzv = sa["NonzeroValues"];
    
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
    
     Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
    

    
data2b == data2 (* from Anton's answer *)



    True







    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












      $begingroup$

      The reshaping can be done in several ways. Below is given one using SparseArray.



      First generating the data (simpler than in the question):



      datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
      

      
data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];
      

      
MatrixForm[data1]


      Make index-to-value associations corresponding to the ranges used to make data1:



      aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];
      
aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];


      Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.



      arules = Most[ArrayRules[SparseArray[data1]]];
      
data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]


      Plot (note the axes ticks):



      ListContourPlot[data2]


      enter image description here






      share|improve this answer









      $endgroup$


















        4












        $begingroup$

        The reshaping can be done in several ways. Below is given one using SparseArray.



        First generating the data (simpler than in the question):



        datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
        

        
data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];
        

        
MatrixForm[data1]


        Make index-to-value associations corresponding to the ranges used to make data1:



        aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];
        
aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];


        Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.



        arules = Most[ArrayRules[SparseArray[data1]]];
        
data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]


        Plot (note the axes ticks):



        ListContourPlot[data2]


        enter image description here






        share|improve this answer









        $endgroup$
















          4












          4








          4





          $begingroup$

          The reshaping can be done in several ways. Below is given one using SparseArray.



          First generating the data (simpler than in the question):



          datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
          

          
data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];
          

          
MatrixForm[data1]


          Make index-to-value associations corresponding to the ranges used to make data1:



          aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];
          
aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];


          Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.



          arules = Most[ArrayRules[SparseArray[data1]]];
          
data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]


          Plot (note the axes ticks):



          ListContourPlot[data2]


          enter image description here






          share|improve this answer









          $endgroup$



          The reshaping can be done in several ways. Below is given one using SparseArray.



          First generating the data (simpler than in the question):



          datafunction = MultinormalDistribution[{0, 0}, {{2, 1/2}, {1/2, 1}}];
          

          
data1 = N[Table[PDF[datafunction][{x, y}], {x, -4, 4, 1}, {y, -2, 2, 1}]];
          

          
MatrixForm[data1]


          Make index-to-value associations corresponding to the ranges used to make data1:



          aX = AssociationThread[Range[Length[#]], #] &@Range[-4, 4, 1];
          
aY = AssociationThread[Range[Length[#]], #] &@Range[-2, 2, 1];


          Convert to a sparse array, take the corresponding rules, and map the {x,y} indexes to the actual x's and y's.



          arules = Most[ArrayRules[SparseArray[data1]]];
          
data2 = Map[{aX[#[[1, 1]]], aY[#[[1, 2]]], #[[2]]} &, arules]


          Plot (note the axes ticks):



          ListContourPlot[data2]


          enter image description here







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 8 hours ago









          Anton AntonovAnton Antonov

          24k167114




          24k167114























              2












              $begingroup$

              An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:



              xrange = {-4, 4};
              
yrange = {-2, 2};
              
sa = SparseArray[data1];
              
nzp = sa["NonzeroPositions"];
              
nzv = sa["NonzeroValues"];
              
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
              
     Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
              

              
data2b == data2 (* from Anton's answer *)



              True







              share|improve this answer









              $endgroup$


















                2












                $begingroup$

                An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:



                xrange = {-4, 4};
                
yrange = {-2, 2};
                
sa = SparseArray[data1];
                
nzp = sa["NonzeroPositions"];
                
nzv = sa["NonzeroValues"];
                
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
                
     Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
                

                
data2b == data2 (* from Anton's answer *)



                True







                share|improve this answer









                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:



                  xrange = {-4, 4};
                  
yrange = {-2, 2};
                  
sa = SparseArray[data1];
                  
nzp = sa["NonzeroPositions"];
                  
nzv = sa["NonzeroValues"];
                  
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
                  
     Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
                  

                  
data2b == data2 (* from Anton's answer *)



                  True







                  share|improve this answer









                  $endgroup$



                  An alternative approach based on Rescaleing the "NonzeroPositions" of SparseArray[data1]:



                  xrange = {-4, 4};
                  
yrange = {-2, 2};
                  
sa = SparseArray[data1];
                  
nzp = sa["NonzeroPositions"];
                  
nzv = sa["NonzeroValues"];
                  
data2b = Join[Transpose[Rescale[#, MinMax@#, #2] & @@@
                  
     Thread[ {Transpose@nzp, {xrange, yrange}}]], List /@ nzv, 2];
                  

                  
data2b == data2 (* from Anton's answer *)



                  True








                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 1 hour ago









                  kglrkglr

                  188k10203421




                  188k10203421






























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