(* ::Package:: *)

Needs["ErrorBarPlots`"]

(* ::Section:: *)

(*Data import*)

gsraw=Import[NotebookDirectory[]<>"data/graphdata_dsp.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: avgtris

3: dsp

*)

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

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

(* ::Section:: *)

(*Plot triangle counts vs dsp*)

(* ::Subsection:: *)

(*Compute dsp from ds*)

getProperty[ds1_]:=Module[{ds,n=Length[ds1],tmp=ConstantArray[0,{Length[ds1],Length[ds1]}]},

ds=N[ds1/Sqrt[N[Total[ds1]]]]; (* scale degrees by 1/Sqrt[total] *)

(* The next table contains unneeded entries, but its faster to have a square table for the sum *)

tmp=Table[1.-Exp[-ds[[i]]ds[[j]]],{i,1,n},{j,1,n}];

Sum[tmp[[i,j]]*tmp[[j,k]]*tmp[[i,k]],{i,3,n},{j,2,i-1},{k,1,j-1}] (* somehow i>j>k is about 60x faster than doing i<j<k !!! *)

(* This sparser table is slower

tmp=Table[1.-Exp[-ds[[i]]ds[[j]]],{i,1,n-1},{j,i+1,n}];

(* tmp[[a,b]] is now with  ds[[a]]*ds[[a+b]] *)

Sum[tmp[[i,j-i]]*tmp[[j,k-j]]*tmp[[i,k-i]],{i,1,n-2},{j,i+1,n-1},{k,j+1,n}]

*)

];

(* gdata[[ tau index, n index, run index , {ntau, #tris, ds} ]] *)

avgAndProp=ParallelMap[{getProperty[#[[3]]],Mean[#[[2,1;;-1]]]}&,gdata[[2,2,1;;100]]];

(* ::Subsection:: *)

(*Plot #trianges vs some degree-sequence-property*)

allPlots=Map[Show[

ListPlot[#[[All,{2,3}]],

AxesOrigin->{0,0},

Frame->True,FrameLabel->{"degree-sequence-property","average number of triangles"},

AspectRatio->Automatic,

ImageSize->Automatic,

PlotLabel->"n = "<>ToString[#[[1,1,1]]]<>" , \[Tau] = "<>ToString[#[[1,1,2]]],

PlotStyle->Black

],Plot[x,{x,1,10000}]]

&,gdata,{2}]

plotgrid=GraphicsRow[{GraphicsColumn[allPlots[[{1,2},1]]],allPlots[[3,1]]},Spacings->0,ImageSize->600]

Export[NotebookDirectory[]<>"plots/dsp_correlations.pdf",plotgrid]