How to plot graphs from multi-variable list by filtering results

Question

Having 100,000 points stored for 6 variables in a list. Following filters are to be applied to the variables: m1>0, 10^(-6) < m1 < 10^(-1)

sine of delta and deltap has to be taken. This will reduce all the values between [-1,1]. thetas have to be between 0-90 degrees. So corresponding radian limits and take their sine as well. We will get values from [0,1].

Once done with filtered results, I need to plot any two variables of the resultant list against any other variables, so 6C2=15 cases possible. For instance, m1 vs sin(delta) or sin(theta12) vs sin(theta23). So how do I go about manipulating "result" to get the desired plots?

Do[dm12 = RandomReal[{Sqrt[7.03*10^-5], Sqrt[8.09*10^-5]}];
 dm13 = RandomReal[{Sqrt[2.407*10^-3], Sqrt[2.643*10^-3]}];
   sp12 = RandomReal[{Sqrt[0.271], Sqrt[0.345]}];
 sp23 = RandomReal[{Sqrt[0.385], Sqrt[0.635]}];
 sp13 = RandomReal[{Sqrt[0.01934], Sqrt[0.02392]}];
 Assuming[{m1 \[Element] Reals, \[Delta] \[Element] Reals, 
   s12 \[Element] Reals, s23 \[Element] Reals, 
   s13 \[Element] Reals, \[Delta]p \[Element] Reals}, 
  data[i] = 
   FindRoot[{Sqrt[dm12^2 + m1^2] s12 s13 sp12 sp13 + 
       Sqrt[dm13^2 + m1^2] s13 sp13 Cos[\[Delta] - \[Delta]p] + 
       m1 ((-1 + s12^2)^2)^(1/4) ((-1 + s13^2)^2)^(
        1/4) ((-1 + sp12^2)^2)^(1/4) ((-1 + sp13^2)^2)^(1/4)
         Cos[1/2 (Arg[1 - s12^2] + Arg[1 - s13^2] - Arg[1 - sp12^2] - 
            Arg[1 - sp13^2])] == 
      0, -Sqrt[dm13^2 + m1^2] s13 sp13 Sin[\[Delta] - \[Delta]p] - 
       m1 ((-1 + s12^2)^2)^(1/4) ((-1 + s13^2)^2)^(
        1/4) ((-1 + sp12^2)^2)^(1/4) ((-1 + sp13^2)^2)^(1/4)
         Sin[1/2 (Arg[1 - s12^2] + Arg[1 - s13^2] - Arg[1 - sp12^2] - 
            Arg[1 - sp13^2])] == 
      0, -m1 ((-1 + s12^2)^2)^(1/4)
         s13 s23 sp12 sp23 Cos[\[Delta]p + 1/2 Arg[1 - s12^2]] - 
       m1 s12 ((-1 + s23^2)^2)^(1/4)
         sp12 sp23 Cos[1/2 Arg[1 - s23^2]] - 
       Sqrt[dm12^2 + m1^2] ((-1 + s12^2)^2)^(1/4) ((-1 + s23^2)^2)^(
        1/4) ((-1 + sp12^2)^2)^(1/4)
         sp23 Cos[
         1/2 (Arg[1 - s12^2] + Arg[1 - s23^2] - Arg[1 - sp12^2])] + 
       Sqrt[dm12^2 + m1^2] s12 s13 s23 ((-1 + sp12^2)^2)^(1/4)
         sp23 Cos[\[Delta]p - 1/2 Arg[1 - sp12^2]] + 
       Sqrt[dm13^2 + m1^2] ((-1 + s13^2)^2)^(1/4)
         s23 ((-1 + sp13^2)^2)^(1/4) ((-1 + sp23^2)^2)^(1/4)
         Cos[1/2 (Arg[1 - s13^2] - Arg[1 - sp13^2] - 
            Arg[1 - sp23^2])] + 
       Sqrt[dm12^2 + m1^2] s12 s13 s23 sp12 sp13 ((-1 + sp23^2)^2)^(
        1/4) Cos[\[Delta] - \[Delta]p + 1/2 Arg[1 - sp23^2]] - 
       Sqrt[dm12^2 + m1^2] ((-1 + s12^2)^2)^(1/4) ((-1 + s23^2)^2)^(
        1/4) sp12 sp13 ((-1 + sp23^2)^2)^(1/4)
         Cos[1/2 (2 \[Delta] - Arg[1 - s12^2] - Arg[1 - s23^2] + 
            Arg[1 - sp23^2])] + 
       m1 ((-1 + s12^2)^2)^(1/4) s13 s23 ((-1 + sp12^2)^2)^(1/4)
         sp13 ((-1 + sp23^2)^2)^(1/4)
         Cos[1/2 (2 \[Delta] - 2 \[Delta]p - Arg[1 - s12^2] + 
            Arg[1 - sp12^2] + Arg[1 - sp23^2])] + 
       m1 s12 ((-1 + s23^2)^2)^(1/4) ((-1 + sp12^2)^2)^(1/4)
         sp13 ((-1 + sp23^2)^2)^(1/4)
         Cos[1/2 (2 \[Delta] - Arg[1 - s23^2] + Arg[1 - sp12^2] + 
            Arg[1 - sp23^2])]
      == 0, 
     m1 ((-1 + s12^2)^2)^(1/4)
         s13 s23 sp12 sp23 Sin[\[Delta]p + 1/2 Arg[1 - s12^2]] + 
       m1 s12 ((-1 + s23^2)^2)^(1/4)
         sp12 sp23 Sin[1/2 Arg[1 - s23^2]] + 
       Sqrt[dm12^2 + m1^2] ((-1 + s12^2)^2)^(1/4) ((-1 + s23^2)^2)^(
        1/4) ((-1 + sp12^2)^2)^(1/4)
         sp23 Sin[
         1/2 (Arg[1 - s12^2] + Arg[1 - s23^2] - Arg[1 - sp12^2])] - 
       Sqrt[dm12^2 + m1^2] s12 s13 s23 ((-1 + sp12^2)^2)^(1/4)
         sp23 Sin[\[Delta]p - 1/2 Arg[1 - sp12^2]] - 
       Sqrt[dm13^2 + m1^2] ((-1 + s13^2)^2)^(1/4)
         s23 ((-1 + sp13^2)^2)^(1/4) ((-1 + sp23^2)^2)^(1/4)
         Sin[1/2 (Arg[1 - s13^2] - Arg[1 - sp13^2] - 
            Arg[1 - sp23^2])] + 
       Sqrt[dm12^2 + m1^2] s12 s13 s23 sp12 sp13 ((-1 + sp23^2)^2)^(
        1/4) Sin[\[Delta] - \[Delta]p + 1/2 Arg[1 - sp23^2]] - 
       Sqrt[dm12^2 + m1^2] ((-1 + s12^2)^2)^(1/4) ((-1 + s23^2)^2)^(
        1/4) sp12 sp13 ((-1 + sp23^2)^2)^(1/4)
         Sin[1/2 (2 \[Delta] - Arg[1 - s12^2] - Arg[1 - s23^2] + 
            Arg[1 - sp23^2])] + 
       m1 ((-1 + s12^2)^2)^(1/4) s13 s23 ((-1 + sp12^2)^2)^(1/4)
         sp13 ((-1 + sp23^2)^2)^(1/4)
         Sin[1/2 (2 \[Delta] - 2 \[Delta]p - Arg[1 - s12^2] + 
            Arg[1 - sp12^2] + Arg[1 - sp23^2])] + 
       m1 s12 ((-1 + s23^2)^2)^(1/4) ((-1 + sp12^2)^2)^(1/4)
         sp13 ((-1 + sp23^2)^2)^(1/4)
         Sin[1/2 (2 \[Delta] - Arg[1 - s23^2] + Arg[1 - sp12^2] + 
            Arg[1 - sp23^2])] == 0, 
     m1 ((-1 + s12^2)^2)^(1/4) s13 ((-1 + s23^2)^2)^(1/4)
         sp12 sp23 Sin[
         1/2 (2 \[Delta]p + Arg[1 - s12^2] + Arg[1 - s23^2])] - 
       Sqrt[dm12^2 + m1^2] ((-1 + s12^2)^2)^(1/4)
         s23 ((-1 + sp12^2)^2)^(1/4)
         sp23 Sin[1/2 (Arg[1 - s12^2] - Arg[1 - sp12^2])] - 
       Sqrt[dm12^2 + m1^2] s12 s13 ((-1 + s23^2)^2)^(
        1/4) ((-1 + sp12^2)^2)^(1/4)
         sp23 Sin[\[Delta]p + 1/2 Arg[1 - s23^2] - 
          1/2 Arg[1 - sp12^2]] - 
       Sqrt[dm13^2 + m1^2] ((-1 + s13^2)^2)^(1/4) ((-1 + s23^2)^2)^(
        1/4) ((-1 + sp13^2)^2)^(1/4) ((-1 + sp23^2)^2)^(1/4)
         Sin[1/2 (Arg[1 - s13^2] + Arg[1 - s23^2] - Arg[1 - sp13^2] - 
            Arg[1 - sp23^2])] + 
       Sqrt[dm12^2 + m1^2] ((-1 + s12^2)^2)^(1/4)
         s23 sp12 sp13 ((-1 + sp23^2)^2)^(1/4)
         Sin[\[Delta] - 1/2 Arg[1 - s12^2] + 1/2 Arg[1 - sp23^2]] + 
       Sqrt[dm12^2 + m1^2] s12 s13 ((-1 + s23^2)^2)^(1/4)
         sp12 sp13 ((-1 + sp23^2)^2)^(1/4)
         Sin[\[Delta] - \[Delta]p - 1/2 Arg[1 - s23^2] + 
          1/2 Arg[1 - sp23^2]] - 
       m1 s12 s23 ((-1 + sp12^2)^2)^(1/4) sp13 ((-1 + sp23^2)^2)^(1/4)
         Sin[1/2 (2 \[Delta] + Arg[1 - sp12^2] + Arg[1 - sp23^2])] + 
       m1 ((-1 + s12^2)^2)^(1/4) s13 ((-1 + s23^2)^2)^(
        1/4) ((-1 + sp12^2)^2)^(1/4) sp13 ((-1 + sp23^2)^2)^(1/4)
         Sin[1/2 (2 \[Delta] - 2 \[Delta]p - Arg[1 - s12^2] - 
            Arg[1 - s23^2] + Arg[1 - sp12^2] + Arg[1 - sp23^2])] == 0,
      m1 s12 s23 sp12 sp23 - 
       m1 ((-1 + s12^2)^2)^(1/4) s13 ((-1 + s23^2)^2)^(1/4)
         sp12 sp23 Cos[
         1/2 (2 \[Delta]p + Arg[1 - s12^2] + Arg[1 - s23^2])] + 
       Sqrt[dm12^2 + m1^2] ((-1 + s12^2)^2)^(1/4)
         s23 ((-1 + sp12^2)^2)^(1/4)
         sp23 Cos[1/2 (Arg[1 - s12^2] - Arg[1 - sp12^2])] + 
       Sqrt[dm12^2 + m1^2] s12 s13 ((-1 + s23^2)^2)^(
        1/4) ((-1 + sp12^2)^2)^(1/4)
         sp23 Cos[\[Delta]p + 1/2 Arg[1 - s23^2] - 
          1/2 Arg[1 - sp12^2]] + 
       Sqrt[dm13^2 + m1^2] ((-1 + s13^2)^2)^(1/4) ((-1 + s23^2)^2)^(
        1/4) ((-1 + sp13^2)^2)^(1/4) ((-1 + sp23^2)^2)^(1/4)
         Cos[1/2 (Arg[1 - s13^2] + Arg[1 - s23^2] - Arg[1 - sp13^2] - 
            Arg[1 - sp23^2])] + 
       Sqrt[dm12^2 + m1^2] ((-1 + s12^2)^2)^(1/4)
         s23 sp12 sp13 ((-1 + sp23^2)^2)^(1/4)
         Cos[\[Delta] - 1/2 Arg[1 - s12^2] + 1/2 Arg[1 - sp23^2]] + 
       Sqrt[dm12^2 + m1^2] s12 s13 ((-1 + s23^2)^2)^(1/4)
         sp12 sp13 ((-1 + sp23^2)^2)^(1/4)
         Cos[\[Delta] - \[Delta]p - 1/2 Arg[1 - s23^2] + 
          1/2 Arg[1 - sp23^2]] - 
       m1 s12 s23 ((-1 + sp12^2)^2)^(1/4) sp13 ((-1 + sp23^2)^2)^(1/4)
         Cos[1/2 (2 \[Delta] + Arg[1 - sp12^2] + Arg[1 - sp23^2])] + 
       m1 ((-1 + s12^2)^2)^(1/4) s13 ((-1 + s23^2)^2)^(
        1/4) ((-1 + sp12^2)^2)^(1/4) sp13 ((-1 + sp23^2)^2)^(1/4)
         Cos[1/2 (2 \[Delta] - 2 \[Delta]p - Arg[1 - s12^2] - 
            Arg[1 - s23^2] + Arg[1 - sp12^2] + Arg[1 - sp23^2])] == 
      0}, {\[Delta], \[Pi]/6}, {m1, 0.001}, {s12, 0.2}, {s23, 
     0.6}, {s13, 0.2}, {\[Delta]p, \[Pi]/3}]], {i, 0, 100000, 1}]
results = data /@ Range[100000]

kglr · Accepted Answer · 2018-03-20 20:06:26Z

0

This deals with the plotting part of the question.

results = RandomReal[100, {50, 6}]; 
labels = {"m1", "delta", "deltap", "theta12", "theta23", "theta13"};
plots = ListPlot[results[[All, #]], Frame -> True, 
     FrameLabel -> {labels[[#[[1]]]], labels[[#[[2]]]]}] & /@ Subsets[Range[6], {2}];
Grid[Partition[plots, 5], Dividers -> All]

A better alternative may be

Needs["StatisticalPlots`"]
PairwiseScatterPlot[results, DataTicks -> True, DataLabels -> labels]

** is there a way to plot one column versus the sine of another column?**

It is easy to modify first approach above:

plots2 = ListPlot[Transpose[{results[[All, #[[1]]]], Sin[results[[All, #[[1]]]]]}],
 Frame -> True, FrameLabel -> {labels[[#[[1]]]], "sin(" <> labels[[#[[2]]]] <> ")"}] & /@ 
  Subsets[Range[6], {2}];
Grid[Partition[plots2, 5], Dividers -> All]

TODO: Modify PairwiseScatterPlot to show Sin[y] on the vertical axes.

edited Mar 20, 2018 at 20:06

answered Feb 15, 2018 at 21:27

kglr

395k18 gold badges479 silver badges902 bronze badges

$\begingroup$ Thank you! I have specific labels in place of Column 1/2/3/4/5/6. I'm unable to label them pairwise. As in the labels need to be "m1, delta, deltap, theta12, theta23, theta13". So that I obtain corresponding graphs for the gridwise plot. I was able to get the same for Scatterplot. Also, is there a way to plot one column versus the sine of another column?(This is totally optional). $\endgroup$
– Eshan Bhargava
Mar 20, 2018 at 4:37
$\begingroup$ Thank you very much! I didn't get a notification update, so just saw this. Simplifies my work a lot! :) $\endgroup$
– Eshan Bhargava
Apr 5, 2018 at 11:25
$\begingroup$ @EshanBhargava, my pleasure. Thank you for the accept. $\endgroup$
– kglr
Apr 5, 2018 at 11:29

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