(* ::Package:: *)

Needs["ErrorBarPlots`"]

(* ::Section:: *)

(*Triangle exponent*)

(* ::Text:: *)

(*Expected number of triangles is the following powerlaw*)

(* ::DisplayFormula:: *)

(*#triangles = const\[Cross]n^(T(\[Tau]))      where    T(\[Tau])=3/2 (3-\[Tau])*)

(* When importing from exponent-only-data file or property-data file *)

(* graphdata_exponent_mix32.m *)

(* graphdata_exponent_highN.m *)

(* graphdata_properties2.m *)

(* graphdata_canonical_properties.m *)

gsraw=Import[NotebookDirectory[]<>"data/graphdata_exponent_hightau.m"];

gsraw=SortBy[gsraw,#[[1,1]]&]; (* Sort by n *)

averagesGrouped=GatherBy[gsraw,{#[[1,2]]&,#[[1,1]]&}];

gsraw2=Import[NotebookDirectory[]<>"data/graphdata_canonical_properties2.m"];

gsraw2=SortBy[gsraw2,#[[1,1]]&]; (* Sort by n *)

averagesGrouped2=GatherBy[gsraw2,{#[[1,2]]&,#[[1,1]]&}];

canonicalDatapoints=Map[{#[[1,1,1]],Mean[#[[All,2]]]}&,averagesGrouped2,{2}];

(* averagesGrouped[[ tau index, n index, run index , {ntau, avgtri} ]] *)

nlabels=Map["n = "<>ToString[#]&,averagesGrouped[[1,All,1,1,1]]];

taulabels=Map["tau = "<>ToString[#]&,averagesGrouped[[All,1,1,1,2]]];

mediansErrorBars=Map[

{{#[[1,1,1]],Median[#[[All,2]]]},

ErrorBar[MedianDeviation[#[[All,2]]]]

}&,averagesGrouped,{2}];

averagesErrorBars=Map[

{{#[[1,1,1]],Mean[#[[All,2]]]},

ErrorBar[StandardDeviation[#[[All,2]]]]

}&,averagesGrouped,{2}];

ErrorListPlot[mediansErrorBars,Joined->True,PlotMarkers->Automatic,PlotRange->All,AxesLabel->{"n","median triangles"},PlotLegends->taulabels]

ListLogLogPlot[averagesErrorBars[[All,All,1]],Joined->True,PlotMarkers->Automatic,AxesLabel->{"n","\[LeftAngleBracket]triangles\[RightAngleBracket]"},PlotLegends->taulabels]

ListLogLogPlot[mediansErrorBars[[All,All,1]],Joined->True,PlotMarkers->Automatic,AxesLabel->{"n","median triangles"},PlotLegends->taulabels]

(* ::Subsection:: *)

(*Fitting the log-log-plot*)

nRange=5;;-1;

nRange=All;

averagesLoglogdata=Log[averagesErrorBars[[All,nRange,1]]];

mediansLoglogdata=Log[mediansErrorBars[[All,nRange,1]]];

averagesFits=Map[Fit[#,{1,logn},logn]&,averagesLoglogdata];

averagesFitsExtra=Map[LinearModelFit[#,logn,logn]&,averagesLoglogdata];

mediansFits=Map[Fit[#,{1,logn},logn]&,mediansLoglogdata];

mediansFitsExtra=Map[LinearModelFit[#,logn,logn]&,mediansLoglogdata];

canonicalloglogdata=Log[canonicalDatapoints[[All,nRange]]];

canonicalFitsExtra=Map[LinearModelFit[#,logn,logn]&,canonicalloglogdata];

averagesFitsExtra[[1]]["ParameterConfidenceIntervalTable"]

averagesFitsExtra[[1]]["BestFitParameters"]

averagesFitsExtra[[1]]["ParameterErrors"]

averagesFitsExtra[[1]]["ParameterConfidenceIntervals"]

plot1a=Show[ListLogLogPlot[averagesErrorBars[[All,All,1]],Joined->False,PlotMarkers->Automatic,AxesLabel->{"n","\[LeftAngleBracket]triangles\[RightAngleBracket]"},PlotLegends->taulabels],Plot[averagesFits,{logn,1,2000}]]

plot1b=Show[ListLogLogPlot[mediansErrorBars[[All,All,1]],Joined->False,PlotMarkers->Automatic,AxesLabel->{"n","median triangles"},PlotLegends->taulabels],Plot[mediansFits,{logn,1,2000}]]

Export[NotebookDirectory[]<>"plots/avgtris_n.pdf",plot1]

(* ::Subsection:: *)

(*Plot of T(\[Tau])*)

tauValues=averagesGrouped[[All,1,1,1,2]];

averagesExponents=Transpose[{tauValues,averagesFits[[All,2,1]]}];

mediansExponents=Transpose[{tauValues,mediansFits[[All,2,1]]}];

Show[ListPlot[{averagesExponents,mediansExponents},Joined->True,PlotMarkers->Automatic,AxesLabel->{"tau","exponent"},PlotRange->{{2,3},{0,1.6}}],Plot[3/2(3-tau),{tau,2,3}]]

(* ::Subsection:: *)

(*T(\[Tau]) including error bars*)

(* For visual, shift the tau values slightly left or right to distinguish the two datasets *)

tauValues=averagesGrouped[[All,1,1,1,2]];

averagesExponentsErrorBars=Map[{{#[[1]],#[[2]]["BestFitParameters"][[2]]},ErrorBar[#[[2]]["ParameterConfidenceIntervals"][[2]]-#[[2]]["BestFitParameters"][[2]]]}&,

Transpose[{tauValues-0.003,averagesFitsExtra}]];

mediansExponentsErrorBars=Map[{{#[[1]],#[[2]]["BestFitParameters"][[2]]},ErrorBar[#[[2]]["ParameterConfidenceIntervals"][[2]]-#[[2]]["BestFitParameters"][[2]]]}&,

Transpose[{tauValues+0.003,mediansFitsExtra}]];

canonicalExponentsErrorBars=Map[{{#[[1]],#[[2]]["BestFitParameters"][[2]]},ErrorBar[#[[2]]["ParameterConfidenceIntervals"][[2]]-#[[2]]["BestFitParameters"][[2]]]}&,

plot2=Show[

ErrorListPlot[{averagesExponentsErrorBars,mediansExponentsErrorBars,canonicalExponentsErrorBars},

Joined->True,PlotMarkers->Automatic,

Frame->True,FrameLabel->{"tau","triangle exponent"},

PlotRange->{{2,3},{0,1.6}},

ImageSize->300],

Plot[3/2(3-tau),{tau,2,3},PlotStyle->{Black,Dashed}]]

Export[NotebookDirectory[]<>"plots/triangle_exponent.pdf",plot2]