Changeset - efc6996e97a2
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Tom Bannink - 8 years ago 2017-03-13 17:28:41
tom.bannink@cwi.nl
Add adaptive mixing time
2 files changed with 49 insertions and 22 deletions:
cpp/switchchain.cpp
12
15
showgraphs.m
37
7
0 comments (0 inline, 0 general)
cpp/switchchain.cpp
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@@ -36,21 +36,17 @@ class SwitchChain {
 
    }
 

			




	
	
	
		
 
    bool doMove() {

			




	
	
	
		
 
        Edge e1, e2;

			




	
	
	
		
 
        int e1index, e2index;

			




	
	
	
		
 
        int timeout = 0;

			




	
	
	
		
 
        // Keep regenerating while conflicting edges

			




	
	
	
		
 
        do {

			




	
	
	
		
 
            e1index = edgeDistribution(mt);

			




	
	
	
		
 
            e2index = edgeDistribution(mt);

			




	
	
	
		
 
            e1 = g.getEdge(e1index);

			




	
	
	
		
 
            e2 = g.getEdge(e2index);

			




	
	
	
		
 
            ++timeout;

			




	
	
	
		
 
            if (timeout % 100 == 0) {

			




	
	
	
		
 
            if (++timeout % 100 == 0) {

			




	
	
	
		
 
                std::cerr << "Warning: sampled " << timeout

			




	
	
	
		
 
                          << " random edges but they keep conflicting.\n";

			




	
	
	
		
 
            }

			




	
	
	
		
 
        } while (edgeConflicts(e1, e2));

			




	
	
	
		
 
        } while (edgeConflicts(g.getEdge(e1index), g.getEdge(e2index)));

			




	
	
	
		
 

			




	
	
	
		
 
        // Consider one of the three possible permutations

			




	
	
	
		
 
        // 1) e1.u - e1.v and e2.u - e2.v (original)

			




	
	
		
 
@@ -117,12 +113,10 @@ int main() {

			




	
	
	
		
 
                std::cout << "Running n = " << numVertices << ", tau = " << tau

			




	
	
	
		
 
                          << ". \t" << std::flush;

			




	
	
	
		
 

			




	
	
	
		
 
                constexpr int mixingTime = 40000;

			




	
	
	
		
 
                constexpr int measureTime = 20000;

			




	
	
	
		
 
                int mixingTime = (32.0f - 26.0f*(tau - 2.0f)) * numVertices; //40000;

			




	
	
	
		
 
                constexpr int measurements = 50;

			




	
	
	
		
 
                constexpr int measureSkip =

			




	
	
	
		
 
                    200; // Take a sample every ... steps

			




	
	
	
		
 
                constexpr int measurements =

			




	
	
	
		
 
                    (measureTime - 1) / measureSkip + 1;

			




	
	
	
		
 
                int movesDone = 0;

			




	
	
	
		
 

			




	
	
	
		
 
                int triangles[measurements];

			




	
	
		
 
@@ -131,15 +125,18 @@ int main() {

			




	
	
	
		
 
                    if (chain.doMove())

			




	
	
	
		
 
                        ++movesDone;

			




	
	
	
		
 
                }

			




	
	
	
		
 
                for (int i = 0; i < measureTime; ++i) {

			




	
	
	
		
 
                for (int i = 0; i < measurements; ++i) {

			




	
	
	
		
 
                    for (int j = 0; j < measureSkip; ++j)

			




	
	
	
		
 
                        if (chain.doMove())

			




	
	
	
		
 
                            ++movesDone;

			




	
	
	
		
 
                    if (i % measureSkip == 0)

			




	
	
	
		
 
                        triangles[i / measureSkip] = chain.g.countTriangles();

			




	
	
	
		
 
                    triangles[i] = chain.g.countTriangles();

			




	
	
	
		
 
                }

			




	
	
	
		
 

			




	
	
	
		
 
                std::cout << movesDone << '/' << mixingTime + measureTime

			




	
	
	
		
 
                          << " moves succeeded." << std::endl;

			




	
	
	
		
 
                std::cout << movesDone << '/' << mixingTime + measurements * measureSkip

			




	
	
	
		
 
                          << " moves succeeded ("

			




	
	
	
		
 
                          << 100.0f * float(movesDone) /

			




	
	
	
		
 
                                 float(mixingTime + measurements * measureSkip)

			




	
	
	
		
 
                          << "%)." << std::endl;

			




	
	
	
		
 

			




	
	
	
		
 
                if (outputComma)

			




	
	
	
		
 
                    outfile << ',';

			




        

    


    
    

    

        

                

                    showgraphs.m
                

                

                  
                      
                        

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@@ -64,7 +64,7 @@ Grid[Partition[gs,10],Frame->All]

			




	
	
	
		
 
(*Data import and data merge*)

			




	
	
	
		
 

			




	
	
	
		
 

			




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

			




	
	
	
		
 
gsraw=Import[NotebookDirectory[]<>"data/graphdata2.m"];

			




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

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
		
 
@@ -109,7 +109,7 @@ 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[[2,4,1;;100]]];

			




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

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
Show[ListPlot[avgAndProp,AxesOrigin->{0,0},AxesLabel->{"degree-sequence-property","<#triangles>"},AspectRatio->1],Plot[x,{x,1,1000}]]

			




	
	
		
 
@@ -120,17 +120,47 @@ Show[ListPlot[avgAndProp,AxesOrigin->{0,0},AxesLabel->{"degree-sequence-property

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
numPlots=20;

			




	
	
	
		
 
selectedData=gsraw[[-numPlots;;-1]];

			




	
	
	
		
 
selectedData=gdata[[5,-1]][[-numPlots;;-1]];

			




	
	
	
		
 
minCount=Min[Map[Min[#[[2]]]&,selectedData]];

			




	
	
	
		
 
maxCount=Max[Map[Max[#[[2]]]&,selectedData]];

			




	
	
	
		
 
maxTime=Max[Map[Length[#[[2]]]&,selectedData]];

			




	
	
	
		
 
skipPts=Max[1,Round[maxTime/100]]; (* Plotting every point is slow. Plot only once per `skipPts` timesteps *)

			




	
	
	
		
 
coarseData=Map[#[[2,1;;-1;;skipPts]]&,selectedData];

			




	
	
	
		
 
labels=Map["{n,tau} = "<>ToString[#[[1]]]&,selectedData];

			




	
	
	
		
 
ListPlot[coarseData,Joined->True,PlotRange->{minCount,maxCount},DataRange->{0,maxTime},PlotLegends->labels]

			




	
	
	
		
 
ListPlot[coarseData,Joined->True,PlotRange->{minCount,maxCount},DataRange->{0,200*maxTime},PlotLegends->labels]

			




	
	
	
		
 
(* Map[ListPlot[#,Joined->True,PlotRange\[Rule]{minCount,maxCount},DataRange\[Rule]{0,maxTime}]&,coarseData] *)

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
(* ::Subsection:: *)

			




	
	
	
		
 
(*Compute 'mixing time'*)

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
(* Compute average of last part and check when the value drops below that for the first time *)

			




	
	
	
		
 
getMixingTime[values_]:=Module[{avg},

			




	
	
	
		
 
    (* average over the last 20 percent *)

			




	
	
	
		
 
    avg=Mean[values[[-Round[Length[values]/5];;-1]]];

			




	
	
	
		
 
    FirstPosition[values,_?(#<=avg&)][[1]]

			




	
	
	
		
 
]

			




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

			




	
	
	
		
 
mixingTimes=Map[{#[[1,1]],(1/#[[1,1]])200 * getMixingTime[#[[2]]]}&,gdata,{3}];

			




	
	
	
		
 
mixingTimesBars=Map[

			




	
	
	
		
 
    {{#[[1,1]],Mean[#[[All,2]]]},ErrorBar[StandardDeviation[#[[All,2]]]/Sqrt[Length[#]]]}&

			




	
	
	
		
 
,mixingTimes,{2}];

			




	
	
	
		
 
ErrorListPlot[mixingTimesBars,Joined->True,PlotMarkers->Automatic,AxesLabel->{"n","~~mixing time divided by n"},PlotLegends->taulabels]

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
(* For n fixed, look at function of tau *)

			




	
	
	
		
 
mixingTimes=Map[{#[[1,2]],(1/#[[1,1]])200 * getMixingTime[#[[2]]]}&,gdata,{3}];

			




	
	
	
		
 
mixingTimesBars=Map[

			




	
	
	
		
 
    {{#[[1,1]],Mean[#[[All,2]]]},ErrorBar[StandardDeviation[#[[All,2]]]]}&

			




	
	
	
		
 
,mixingTimes[[All,-1]],{1}];

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
Show[

			




	
	
	
		
 
ErrorListPlot[mixingTimesBars,Joined->True,PlotMarkers->Automatic,AxesLabel->{"tau","~~mixing time divided by n, for n = 1000"},PlotRange->{{2,3},{0,30}}]

			




	
	
	
		
 
,Plot[(32-26(tau-2)),{tau,2,3}]]

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
(* ::Subsection:: *)

			




	
	
	
		
 
(*Plot average #triangles vs n*)

			




	
	
	
		
 

			




	
	
		
 
@@ -143,11 +173,11 @@ nlabels=Map["n = "<>ToString[#]&,averagesGrouped[[1,All,1,1,1]]];

			




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

			




	
	
	
		
 
averagesErrorBars=Map[

			




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

			




	
	
	
		
 
ErrorBar[StandardDeviation[#[[All,2]]]/Sqrt[Length[#]]]

			




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

			




	
	
	
		
 
}&,averagesGrouped,{2}];

			




	
	
	
		
 

			




	
	
	
		
 

			




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

			




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

			




	
	
	
		
 

			




	
	
	
		
 

			




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

			




	
	
		
 
@@ -166,7 +196,7 @@ Show[ListLogLogPlot[averagesErrorBars[[All,All,1]],PlotMarkers->Automatic,AxesLa

			




	
	
	
		
 

			




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

			




	
	
	
		
 
exponents=Transpose[{tauValues,fits[[All,2,1]]}];

			




	
	
	
		
 
Show[ListPlot[exponents,Joined->True,PlotMarkers->Automatic,AxesLabel->{"tau","triangle-law-exponent"}],Plot[3/2(3-tau),{tau,2,3}]]

			




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

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
(* ::Subsection:: *)

			




        

    



    


    



    



      

      





    
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