{{n,avgECM},ErrorBar[sdECM]}

}

]

allErrorBars=Map[getErrorBars,gdata,{2}];

Map[ErrorListPlot[Transpose[#],

ImageSize->500,

Frame->True,

PlotMarkers->Automatic

]&,allErrorBars[[{1,6,11}]]]

(* ::Subsection:: *)

(*Fitting the log-log-plot*)

nRange=All;

(* Weight: 1/err^2 *)

(* Weight: N/Total[(xs-Mean[xs])^2] *)

getWeight[xs_]:=1/(Log[Mean[xs]]-Log[Mean[xs]-Sqrt[Total[(xs-Mean[xs])^2]/Length[xs]]])^2;

(* Several runs for fixed tau but different n *)

getFitData[runs_,index_]:=Map[{Log[#[[1,1]]],Log[Mean[#[[index]]]],getWeight[#[[index]]]}&,runs];

uniformFitData=Map[getFitData[#,2]&,gdata[[All,nRange]]];

ECMFitData=Map[getFitData[#,3]&,gdata[[All,nRange]]];

uniformFits=Map[LinearModelFit[#[[All,{1,2}]],logn,logn(*,Weights\[Rule]#[[All,3]]*)]&,uniformFitData];

ECMFits=    Map[LinearModelFit[#[[All,{1,2}]],logn,logn(*,Weights\[Rule]#[[All,3]]*)]&,ECMFitData];

(*

uniformloglog=Log[dataPointsUniform[[All,nRange]]];

ECMloglog=Log[dataPointsECM[[All,nRange]]];

uniformFits=Map[LinearModelFit[#,logn,logn]&,uniformloglog];

ECMFits=Map[LinearModelFit[#,logn,logn]&,ECMloglog];

*)

uniformFuncs=Map[#[logn]&,uniformFits];

ECMFuncs=Map[#[logn]&,ECMFits];

uniformFits[[1]]["ParameterTable"] (* Get `Standard Error' by "ParameterErrors" *)

uniformFits[[1]]["ParameterConfidenceIntervalTable"] (* Get confidence by "ParameterConfidenceIntervals *)

(* estimate +- standard error *)

uniformFits[[1]]["BestFitParameters"]-uniformFits[[1]]["ParameterErrors"]

uniformFits[[1]]["BestFitParameters"]+uniformFits[[1]]["ParameterErrors"]

tauChoices={1,4,6,8,11};

taulabels=Map["\[Tau] = "<>ToString[NumberForm[#[[1,1,2]],{3,2}]]&,gdata[[tauChoices]]];

repeatColors[n_,k_]:=Table[ColorData[97][Mod[i,k,1]],{i,1,n}]

plot1=Show[ListLogLogPlot[Evaluate[dataPointsUniform[[tauChoices]]~Join~dataPointsECM[[tauChoices]]],

Frame->True,

FrameTicks->{{Table[{10^k,Superscript[10,k]},{k,0,6}],Automatic},{{1000,2000,5000,10000},Automatic}},

FrameLabel->{"n","triangles"},

ImageSize->250,

PlotMarkers->Automatic,

PlotLegends->taulabels,

PlotStyle->repeatColors[10,5]

],

Plot[Evaluate[uniformFuncs[[tauChoices]]],{logn,1,20000}],

Plot[Evaluate[ECMFuncs[[tauChoices]]],{logn,1,20000}]

]

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

(* ::Subsection:: *)

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

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

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

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

averagesLoglogdata=Map[{Log[#[[1,1,1]]],Log[Mean[#[[All,2]]]]}&,averagesGrouped[[All,nRange]],{2}];

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

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

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

Transpose[{avgTauValues-0.000,averagesFitsExtra}]];

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

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

uniformExponents=Map[{{#[[1]],#[[2]]["BestFitParameters"][[2]]},ErrorBar[#[[2]]["ParameterConfidenceIntervals"][[2]]-#[[2]]["BestFitParameters"][[2]]]}&, Transpose[{tauValues+0.000,uniformFits}]];

ECMExponents    =Map[{{#[[1]],#[[2]]["BestFitParameters"][[2]]},ErrorBar[#[[2]]["ParameterConfidenceIntervals"][[2]]-#[[2]]["BestFitParameters"][[2]]]}&, Transpose[{tauValues+0.000,ECMFits}]];

Needs["MaTeX`"]

plot2=Show[

ErrorListPlot[{ECMExponents,uniformExponents,averagesExponentsErrorBars},

Joined->True,PlotMarkers->Automatic,

PlotLegends->Placed[{"ECM","canonical","average"},{Left,Bottom}],

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

ImageSize->300],

Plot[3/2(3-tau),{tau,2,3},PlotStyle->{Black,Dashed},PlotLegends->Placed[LineLegend[{MaTeX["\\frac{3}{2}(3-\\tau)"]},LegendMarkerSize->20],{Left,Bottom}]]]

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