path: root/tempering_analysis.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     29108,        698]
NotebookOptionsPosition[     27171,        661]
NotebookOutlinePosition[     27505,        676]
CellTagsIndexPosition[     27462,        673]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{"getData", "[", "dir_", "]"}], ":=", 
  RowBox[{"Dataset", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"With", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{
         RowBox[{"data", "=", 
          RowBox[{"Import", "[", "#", "]"}]}], ",", 
         RowBox[{"metadata", "=", 
          RowBox[{"ToExpression", "/@", 
           RowBox[{"Rest", "[", 
            RowBox[{"StringSplit", "[", 
             RowBox[{
              RowBox[{"FileBaseName", "[", "#", "]"}], ",", "\"\<_\>\""}], 
             "]"}], "]"}]}]}]}], "}"}], ",", 
       RowBox[{"<|", 
        RowBox[{
         RowBox[{"\"\<n\>\"", "\[Rule]", 
          RowBox[{"metadata", "[", 
           RowBox[{"[", "1", "]"}], "]"}]}], ",", 
         RowBox[{"\"\<\[Beta]0\>\"", "\[Rule]", 
          RowBox[{"metadata", "[", 
           RowBox[{"[", "2", "]"}], "]"}]}], ",", 
         RowBox[{"\"\<\[Beta]f\>\"", "\[Rule]", 
          RowBox[{"metadata", "[", 
           RowBox[{"[", "3", "]"}], "]"}]}], ",", 
         RowBox[{"\"\<n\[Beta]\>\"", "\[Rule]", 
          RowBox[{"metadata", "[", 
           RowBox[{"[", "4", "]"}], "]"}]}], ",", 
         RowBox[{"\"\<As\>\"", "\[Rule]", 
          RowBox[{
           RowBox[{"Rest", "[", "data", "]"}], "/", 
           RowBox[{"First", "[", 
            RowBox[{"First", "[", "data", "]"}], "]"}]}]}]}], "|>"}]}], "]"}],
      "&"}], "/@", 
    RowBox[{"FileNames", "[", 
     RowBox[{"FileNameJoin", "[", 
      RowBox[{"{", 
       RowBox[{"dir", ",", "\"\<probs_*.dat\>\""}], "}"}], "]"}], "]"}]}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.778948155736003*^9, 3.778948220094614*^9}, {
  3.778948251774682*^9, 3.778948445776267*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"6ca216e4-4a7b-4e5f-a718-f4e70c77d6a2"],

Cell[BoxData[
 RowBox[{
  RowBox[{"d", "=", 
   RowBox[{"getData", "[", "\"\<~/doc/research/hadamard/code/\>\"", "]"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.778948447393362*^9, 3.778948476191824*^9}, {
  3.7795618755287123`*^9, 3.779561880399358*^9}},
 CellLabel->"In[15]:=",ExpressionUUID->"3b7ef50e-b362-4da3-b734-818bb17a7c2f"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"c", "[", 
    RowBox[{"\[Beta]i_", ",", "\[Beta]j_"}], "]"}], "[", "A_", "]"}], ":=", 
  RowBox[{"2", 
   FractionBox[
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox["\[Beta]i", "2"], "+", 
      SuperscriptBox["\[Beta]j", "2"]}], ")"}], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"\[Beta]i", "-", "\[Beta]j"}], ")"}], "2"]], 
   SuperscriptBox[
    RowBox[{"InverseErfc", "[", "A", "]"}], "2"]}]}]], "Input",
 CellChangeTimes->{{3.7789451133983593`*^9, 3.778945185413146*^9}, {
  3.778945446992125*^9, 3.778945447478743*^9}},
 CellLabel->"In[3]:=",ExpressionUUID->"f756d73a-4921-45d7-acd1-44fe21438a02"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Ts", "[", "dat_", "]"}], ":=", 
  RowBox[{"Range", "[", 
   RowBox[{
    RowBox[{"dat", "[", "\"\<\[Beta]0\>\"", "]"}], ",", 
    RowBox[{"dat", "[", "\"\<\[Beta]f\>\"", "]"}], ",", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       RowBox[{"dat", "[", "\"\<\[Beta]f\>\"", "]"}], "-", 
       RowBox[{"dat", "[", "\"\<\[Beta]0\>\"", "]"}]}], ")"}], "/", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"dat", "[", "\"\<n\[Beta]\>\"", "]"}], "-", "1"}], ")"}]}]}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.778948523412203*^9, 3.778948610089134*^9}, {
  3.7789486512266293`*^9, 3.778948654153482*^9}},
 CellLabel->"In[4]:=",ExpressionUUID->"c91e85b2-f90e-40d7-bf19-7a03fd9499bb"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Cstmp", "[", "dat_", "]"}], ":=", 
  RowBox[{"With", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"ts", "=", 
      RowBox[{"Ts", "[", "dat", "]"}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"{", 
         RowBox[{"#", ",", 
          RowBox[{"#", "+", 
           RowBox[{"ts", "[", 
            RowBox[{"[", "2", "]"}], "]"}], "-", 
           RowBox[{"ts", "[", 
            RowBox[{"[", "1", "]"}], "]"}]}]}], "}"}], "&"}], "/@", "ts"}], 
      ",", 
      RowBox[{"Last", "/@", 
       RowBox[{"dat", "[", "\"\<As\>\"", "]"}]}]}], "}"}]}], "]"}]}]], "Input",\

 CellChangeTimes->{{3.7789537137281647`*^9, 3.7789537203664207`*^9}},
 CellLabel->"In[5]:=",ExpressionUUID->"1b068f0a-fa61-487d-893c-5b00f279e758"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Cs", "[", "dat_", "]"}], ":=", 
  RowBox[{"With", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"ts", "=", 
      RowBox[{"Ts", "[", "dat", "]"}]}], "}"}], ",", 
    RowBox[{"MapThread", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Mean", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"#1", "[", 
             RowBox[{"[", "1", "]"}], "]"}], ",", 
            RowBox[{"#1", "[", 
             RowBox[{"[", "2", "]"}], "]"}]}], "}"}], "]"}], ",", 
         RowBox[{
          RowBox[{"c", "[", 
           RowBox[{
            RowBox[{"#1", "[", 
             RowBox[{"[", "1", "]"}], "]"}], ",", 
            RowBox[{"#1", "[", 
             RowBox[{"[", "2", "]"}], "]"}]}], "]"}], "[", "#2", "]"}]}], 
        "}"}], "&"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"{", 
           RowBox[{"#", ",", 
            RowBox[{"#", "+", 
             RowBox[{"ts", "[", 
              RowBox[{"[", "2", "]"}], "]"}], "-", 
             RowBox[{"ts", "[", 
              RowBox[{"[", "1", "]"}], "]"}]}]}], "}"}], "&"}], "/@", 
         RowBox[{"Most", "[", "ts", "]"}]}], ",", 
        RowBox[{"Last", "/@", 
         RowBox[{"dat", "[", "\"\<As\>\"", "]"}]}]}], "}"}]}], "]"}]}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.7789479000625353`*^9, 3.7789480157738333`*^9}, {
  3.778948503834503*^9, 3.778948518745183*^9}, {3.778948666921554*^9, 
  3.778948688346896*^9}, {3.7789536224795513`*^9, 3.778953623110043*^9}, {
  3.778953673879937*^9, 3.778953685238799*^9}, {3.778953742582839*^9, 
  3.778953745606895*^9}},
 CellLabel->"In[6]:=",ExpressionUUID->"83b164e2-d1bf-4be5-bf92-d3645cb950ca"],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[CapitalDelta]Ss", "[", "dat_", "]"}], ":=", 
  RowBox[{"With", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"ts", "=", 
       RowBox[{"1", "/", 
        RowBox[{"Ts", "[", "dat", "]"}]}]}], ",", 
      RowBox[{"cs", "=", 
       RowBox[{"Cs", "[", "dat", "]"}]}]}], "}"}], ",", 
    RowBox[{
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"Mean", "[", 
         RowBox[{"1", "/", "#1"}], "]"}], ",", 
        FractionBox[
         RowBox[{"#2", 
          RowBox[{"(", 
           RowBox[{
            RowBox[{"#1", "[", 
             RowBox[{"[", "1", "]"}], "]"}], "-", 
            RowBox[{"#1", "[", 
             RowBox[{"[", "2", "]"}], "]"}]}], ")"}]}], 
         RowBox[{"Mean", "[", "#1", "]"}]]}], "}"}], "&"}], "@@@", 
     RowBox[{"Thread", "[", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"Rest", "@", 
         RowBox[{"Rest", "[", 
          RowBox[{"FoldList", "[", 
           RowBox[{
            RowBox[{
             RowBox[{"{", 
              RowBox[{
               RowBox[{"#1", "[", 
                RowBox[{"[", "2", "]"}], "]"}], ",", "#2"}], "}"}], "&"}], 
            ",", 
            RowBox[{"{", 
             RowBox[{"0", ",", "0"}], "}"}], ",", "ts"}], "]"}], "]"}]}], ",", 
        RowBox[{
         RowBox[{"Cs", "[", "dat", "]"}], "[", 
         RowBox[{"[", 
          RowBox[{"All", ",", "2"}], "]"}], "]"}]}], "}"}], "]"}]}]}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.779561994673626*^9, 3.7795620342479887`*^9}, {
  3.779700498628436*^9, 3.779700513292344*^9}, {3.7797005747090063`*^9, 
  3.779700575188902*^9}, {3.779700627710291*^9, 3.7797006535654173`*^9}, {
  3.779700716133662*^9, 3.7797008200306168`*^9}, {3.779700857824486*^9, 
  3.7797008584386597`*^9}, {3.7797008994884863`*^9, 3.779700901055118*^9}, {
  3.779700939144706*^9, 3.779700939215414*^9}},
 CellLabel->"In[7]:=",ExpressionUUID->"cfeba3ce-dc48-40c8-b8b8-f34cf59a253d"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Ss", "[", "dat_", "]"}], ":=", 
  RowBox[{"With", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"ss", "=", 
      RowBox[{"\[CapitalDelta]Ss", "[", "dat", "]"}]}], "}"}], ",", 
    RowBox[{"Thread", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"ss", "[", 
        RowBox[{"[", 
         RowBox[{"All", ",", "1"}], "]"}], "]"}], ",", 
       RowBox[{"Accumulate", "[", 
        RowBox[{"ss", "[", 
         RowBox[{"[", 
          RowBox[{"All", ",", "2"}], "]"}], "]"}], "]"}]}], "}"}], "]"}]}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.779700960584425*^9, 3.7797010023114433`*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"a1830ef0-911d-442d-b5d2-b62c202fce89"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ListPlot", "[", 
  RowBox[{
   RowBox[{"d", "[", 
    RowBox[{
     RowBox[{"Select", "[", 
      RowBox[{
       RowBox[{"#n\[Beta]", "\[Equal]", "64"}], "&"}], "]"}], ",", 
     RowBox[{
      RowBox[{"With", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"L", "=", 
          SuperscriptBox["#n", "2"]}], "}"}], ",", 
        RowBox[{
         RowBox[{
          RowBox[{"{", 
           RowBox[{"#1", ",", 
            RowBox[{"#2", "/", "L"}]}], "}"}], "&"}], "@@@", 
         RowBox[{"Ss", "[", "#", "]"}]}]}], "]"}], "&"}]}], "]"}], ",", 
   RowBox[{"Joined", "\[Rule]", "True"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input",
 CellChangeTimes->CompressedData["
1:eJwdxVkogwEAB/A5krlTJtLYis2WI02KUZMkVxkxtQcWGqYpV59cL2SON0tR
yssaNiXKPvHg2DLTjBqtkCixpmwefA9zfP/v4dePp9LKO0NZLBaXhsuF9tZj
gU9mSxpXYm/tHYEPAk2jeNMh1uErBzWPnUob54TedMRPxoS6vxhvf7OleKzD
dY83iKcHrJ7de8avTuoFawQHXiy1L3xiSdhY6im9ecbCw1X75izMefoWYLZ8
kcCVkt5RrP/9FZ7R83fdItyToijFZHtDGW6g8mvw2k4V89e5dh1HiTRGXNKY
t4sVg6o9vBzQWbAjfJrElLvPitXcCWY9GenCCS2GaxyRUxFipf/x1DMf6t/T
cVuoPQMXFHUP46Xg8ghutsQ5cJrRw3wz5y7xC32yy7rYMqx5nKLis32yZ9IQ
xLlbYnYC/luNwReNRdGF9PyXe+apFRMPJw5wM7E2IHH66eUt1S78NjR5i7s+
ZHf4H8z/9Bs=
  "],
 CellLabel->"In[24]:=",ExpressionUUID->"73943d9b-70f3-4562-ab84-3881106d7e0c"],

Cell[BoxData[
 GraphicsBox[{{}, {{{}, {}, 
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], LineBox[CompressedData["
1:eJw1yX8s1HEcx/ETF83k5yHhHOe4H+gPrl/q+/4uZiyUa/0Y0oysbjL6pd3W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       "]]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], LineBox[CompressedData["
1:eJw1yX8s1HEcx/E7ThzLb+dHPzgO5/w4LX8ws+/bRmGtH7ejov7x41r0Q4XR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       "]]}, 
     {RGBColor[0.560181, 0.691569, 0.194885], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], LineBox[CompressedData["
1:eJw1yQ0s1HEcx3EPM0+JRLg4d8cd5zhjlZrW/6th5rHSNbPGJuqOPGx1pZKx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       "]]}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.560181, 0.691569, 0.194885], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.560181, 0.691569, 0.194885], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, {}, {}, {}, {}, {}, {}, {}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.560181, 0.691569, 0.194885], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, {}, {}, {}, {}, {}, {}, {}}}, {{}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0.052083333333333336`, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImageSize->{983., Automatic},
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0.052083333333333336`, 15.875}, {0, 0.6609294624557724}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.778946374557211*^9, 3.7789464676677723`*^9, 3.778946508497999*^9, 
   3.778946604369417*^9, {3.7789466690966673`*^9, 3.778946701500992*^9}, {
   3.778946731994258*^9, 3.778946749349575*^9}, 3.7789467962636337`*^9, 
   3.778946833931172*^9, 3.778947082771483*^9, {3.778947327915792*^9, 
   3.778947345892826*^9}, 3.778948029994212*^9, 3.7789481053151817`*^9, {
   3.778948692166095*^9, 3.7789487038141737`*^9}, 3.778953585064103*^9, 
   3.778953624385591*^9, 3.778953682031535*^9, 3.778953746826598*^9, {
   3.77956194067076*^9, 3.779561968768979*^9}, 3.779624858106914*^9, {
   3.779624924084155*^9, 3.779624933643355*^9}, {3.779625037660088*^9, 
   3.779625061656746*^9}, 3.779699807199407*^9, {3.779700827690935*^9, 
   3.7797008596365232`*^9}, 3.7797009048423357`*^9, 3.779700941258234*^9, {
   3.779701005894755*^9, 3.779701033694045*^9}, 3.78008725076254*^9, 
   3.780087374491346*^9, 3.780087426664627*^9, {3.780087476814011*^9, 
   3.7800874839642763`*^9}},
 CellLabel->"Out[24]=",ExpressionUUID->"2a29681a-d1fe-4e5f-9729-68c4489a550c"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ListPlot", "[", 
  RowBox[{
   RowBox[{"d", "[", 
    RowBox[{
     RowBox[{"Select", "[", 
      RowBox[{
       RowBox[{"#n", "\[Equal]", "20"}], "&"}], "]"}], ",", 
     RowBox[{
      RowBox[{"With", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"L", "=", 
          SuperscriptBox["#n", "2"]}], "}"}], ",", 
        RowBox[{
         RowBox[{
          RowBox[{"{", 
           RowBox[{"#1", ",", 
            RowBox[{"#2", "/", "L"}]}], "}"}], "&"}], "@@@", 
         RowBox[{"Cs", "[", "#", "]"}]}]}], "]"}], "&"}]}], "]"}], ",", 
   RowBox[{"Joined", "\[Rule]", "True"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.779700477940461*^9, 3.77970048742832*^9}, {
  3.780087268580113*^9, 3.7800872686230392`*^9}, {3.780087382286021*^9, 
  3.780087398738736*^9}, {3.7800877026590443`*^9, 3.780087726448501*^9}},
 CellLabel->"In[28]:=",ExpressionUUID->"60949ea9-18bb-4b5b-868e-6a12e7d013f6"],

Cell[BoxData[
 GraphicsBox[{{}, {{{}, {}, 
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], LineBox[CompressedData["
1:eJw11HtM01cUB/AKoqwBZBQYrVQohUJ59gFlZo7fUYnoJjiRanAoOhyyhMIS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       "]]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], LineBox[CompressedData["
1:eJw90Q0slHEcB/ATksmSq+Q4584d55yTVpHTnl8X0yytNOta4rALa05UitmN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       "]]}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, {}, {}, {}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, {}, {}, {}}}, {{}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 19.9}, {0, 2.666747640711386}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.7797004888467417`*^9, {3.780087263365243*^9, 3.780087269048139*^9}, {
   3.780087378630178*^9, 3.780087399174458*^9}, {3.780087705097999*^9, 
   3.780087726696293*^9}},
 CellLabel->"Out[28]=",ExpressionUUID->"1c27332b-7aa0-4f6c-9d7f-d912fe119acd"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"a", "=", 
   RowBox[{
   "Import", "[", 
    "\"\<~/doc/research/hadamard/code/energies_24_0.200000_20.000000_100.dat\>\
\"", "]"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.779699855009756*^9, 3.779699866112481*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"bb64ee8f-2ab2-44da-86d3-071e144df4ac"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ListPlot", "[", "a", "]"}]], "Input",
 CellChangeTimes->{{3.7796998674408073`*^9, 3.779699868848329*^9}},
 CellLabel->"In[9]:=",ExpressionUUID->"27200d6e-a8c7-4ded-bf66-0ba360a8d0c7"],

Cell[BoxData[
 GraphicsBox[{{}, {{
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], PointBox[{{1., 1.*^7}, {1., 1.*^7}}]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6], PointBox[CompressedData["
1:eJw1y38w13cAx/FvrUkWKm7JaX5m5Ed+fP1qystX+NIX3y9fvnw1oqVrd8vO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       "]]}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, {}, {}, {}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, 
     {RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.009166666666666668],
       AbsoluteThickness[1.6]}, {}, {}, {}}}, {{}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0., -4.400895677366526*^9},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0., 100.}, {-5.689886659390474*^9, -4.468737307999365*^9}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{3.7796998691208344`*^9},
 CellLabel->"Out[9]=",ExpressionUUID->"161e209e-ab11-4d64-99a1-d2cc4b5ffda5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"16", "/", "64"}], "//", "N"}]], "Input",
 CellChangeTimes->{{3.7796999517774973`*^9, 3.779699965625023*^9}},
 CellLabel->"In[12]:=",ExpressionUUID->"85d1832b-b409-4be7-b8d2-26df59eff8fb"],

Cell[BoxData["0.25`"], "Output",
 CellChangeTimes->{{3.779699954939776*^9, 3.779699966125688*^9}},
 CellLabel->"Out[12]=",ExpressionUUID->"5dbe4cc3-7c89-4c96-870e-625a9bf27876"]
}, Open  ]]
},
WindowSize->{1277, 1076},
WindowMargins->{{Automatic, 2}, {Automatic, 2}},
FrontEndVersion->"12.0 for Linux x86 (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 1782, 46, 124, "Input",ExpressionUUID->"6ca216e4-4a7b-4e5f-a718-f4e70c77d6a2"],
Cell[2343, 68, 337, 7, 31, "Input",ExpressionUUID->"3b7ef50e-b362-4da3-b734-818bb17a7c2f"],
Cell[2683, 77, 668, 18, 59, "Input",ExpressionUUID->"f756d73a-4921-45d7-acd1-44fe21438a02"],
Cell[3354, 97, 722, 18, 31, "Input",ExpressionUUID->"c91e85b2-f90e-40d7-bf19-7a03fd9499bb"],
Cell[4079, 117, 804, 24, 31, "Input",ExpressionUUID->"1b068f0a-fa61-487d-893c-5b00f279e758"],
Cell[4886, 143, 1753, 48, 55, "Input",ExpressionUUID->"83b164e2-d1bf-4be5-bf92-d3645cb950ca"],
Cell[6642, 193, 1968, 53, 83, "Input",ExpressionUUID->"cfeba3ce-dc48-40c8-b8b8-f34cf59a253d"],
Cell[8613, 248, 712, 20, 31, "Input",ExpressionUUID->"a1830ef0-911d-442d-b5d2-b62c202fce89"],
Cell[CellGroupData[{
Cell[9350, 272, 1317, 33, 39, "Input",ExpressionUUID->"73943d9b-70f3-4562-ab84-3881106d7e0c"],
Cell[10670, 307, 6446, 123, 630, "Output",ExpressionUUID->"2a29681a-d1fe-4e5f-9729-68c4489a550c"]
}, Open  ]],
Cell[CellGroupData[{
Cell[17153, 435, 979, 25, 39, "Input",ExpressionUUID->"60949ea9-18bb-4b5b-868e-6a12e7d013f6"],
Cell[18135, 462, 4725, 95, 244, "Output",ExpressionUUID->"1c27332b-7aa0-4f6c-9d7f-d912fe119acd"]
}, Open  ]],
Cell[22875, 560, 330, 8, 31, "Input",ExpressionUUID->"bb64ee8f-2ab2-44da-86d3-071e144df4ac"],
Cell[CellGroupData[{
Cell[23230, 572, 207, 3, 31, "Input",ExpressionUUID->"27200d6e-a8c7-4ded-bf66-0ba360a8d0c7"],
Cell[23440, 577, 3276, 68, 214, "Output",ExpressionUUID->"161e209e-ab11-4d64-99a1-d2cc4b5ffda5"]
}, Open  ]],
Cell[CellGroupData[{
Cell[26753, 650, 222, 4, 31, "Input",ExpressionUUID->"85d1832b-b409-4be7-b8d2-26df59eff8fb"],
Cell[26978, 656, 177, 2, 35, "Output",ExpressionUUID->"5dbe4cc3-7c89-4c96-870e-625a9bf27876"]
}, Open  ]]
}
]
*)