(* ::Package:: *)

Needs["ErrorBarPlots`"]


(* ::Section:: *)
(*Data import*)


gsraw=Import[NotebookDirectory[]<>"data/graphdata_timeevol.m"];
(* gsraw=SortBy[gsraw,{#[[1,1]]&,#[[1,2]]&}]; (* Sort by n and then by tau. The {} forces a *stable* sort because otherwise Mathematica sorts also on triangle count and other things. *) *)


gdata=GatherBy[gsraw,{#[[1,2]]&,#[[1,1]]&}];
(* Data format: *)
(* gdata[[ tau index, n index, run index , datatype index ]] *)
(* datatype index:
1: {n,tau}
2: #triangles time sequence
3: degree sequence
*)
nlabels=Map["n = "<>ToString[#]&,gdata[[1,All,1,1,1]]];
taulabels=Map["tau = "<>ToString[#]&,gdata[[All,1,1,1,2]]];


(* Get the runs that have the same degree sequence *)
gdata2=GatherBy[gsraw,{#[[1,2]]&,#[[1,1]]&,#[[3]]&}];
(* gdata[[ tau index, n index, ds run index, MC run index , datatype index ]] *)


(* ::Section:: *)
(*Triangle creation frequencies*)


(* ::Subsection:: *)
(*Plot triangle count over "time" in Markov chain instances*)


numPlots=20;
selectedData=gdata[[1,1]][[-numPlots;;-1]];
measureSkip=1;
minCount=Min[Map[Min[#[[2]]]&,selectedData]];
maxCount=Max[Map[Max[#[[2]]]&,selectedData]];
maxTime=Max[Map[Length[#[[2]]]&,selectedData]];
(* maxTime=30000; *)
skipPts=Max[1,Round[maxTime/500]]; (* Plotting every point is slow. Plot only once per `skipPts` timesteps *)
coarseData=Map[#[[2,1;;maxTime;;skipPts]]&,selectedData];
labels=Map["{n,tau} = "<>ToString[#[[1]]]&,selectedData];
ListPlot[coarseData,Joined->True,PlotRange->{0*minCount,maxCount},DataRange->{0,measureSkip*maxTime},PlotLegends->labels]
(* Map[ListPlot[#,Joined->True,PlotRange\[Rule]{minCount,maxCount},DataRange\[Rule]{0,maxTime}]&,coarseData] *)


differences=Map[Differences[#[[2,25000;;-1]]]&,gdata2,{4}];
differences=Map[Flatten,differences,{3}];


(* For each (n,tau) take 2 degree sequences *)
histograms1=Map[Histogram[#[[{2,1}]],{-25.5,25.5,1},{"Log","Probability"},ImageSize->280]&,differences,{2}];


(* For each (n,tau) take the average over all degree sequences *)
histograms2=Map[Histogram[Flatten[#],{-3.5,3.5,1},"Probability",PlotRange->{0,1},LabelingFunction->(Placed[NumberForm[#,{2,3}],Above]&),ImageSize->280]&,differences,{2}];


TableForm[histograms2,TableHeadings->{taulabels,nlabels}]


{h1,h2,h3}={
Show[histograms1[[2]],PlotLabel->"n=1000, \[Tau]=2.2"],
Show[histograms1[[5]],PlotLabel->"n=1000, \[Tau]=2.5"],
Show[histograms1[[8]],PlotLabel->"n=1000, \[Tau]=2.8"]};
{h1zoomed,h2zoomed,h3zoomed}={
Show[histograms2[[2]],PlotLabel->"n=1000, \[Tau]=2.2"],
Show[histograms2[[5]],PlotLabel->"n=1000, \[Tau]=2.5"],
Show[histograms2[[8]],PlotLabel->"n=1000, \[Tau]=2.8"]};
hcol=GraphicsGrid[Transpose[{{h1,h2,h3},{h1zoomed,h2zoomed,h3zoomed}}]]


Export[NotebookDirectory[]<>"plots/triangle_creation_frequencies_log.pdf",hcol]