AENC/switchchain Changeset - 06fad9499398 · Centrum Wiskunde & Informatica (CWI)

Changeset - 06fad9499398

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Tom Bannink - 8 years ago 2017-03-01 13:19:29
tombannink@gmail.com

Add TODO list to mathematica notebook

2 files changed with 24 insertions and 6 deletions:

cpp/showgraphs.m

cpp/switchchain.cpp

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cpp/showgraphs.m

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 (* ::Package:: *)
 Needs["ErrorBarPlots`"]
 (* ::Section:: *)
 (*TODO*)
 (* ::Text:: *)
 (*- Compute  Sum over i<j<k  of  (1-Exp[- d_i d_j / (2E)]) * (1 - Exp[-d_j d_k / (2E)]) * (1 - Exp[-d_k d_i / (2E)]) .*)
 (*   Only depends on degree sequence. Can be done with current data.*)
 (*- Do a single very long run to see if there are any weird things after many steps*)
 (*- Use different starting point for switch chain that is closer to uniform:*)
 (*   Do configuration model, starting with the vertex with highest degree and keeping track of a "forbidden list" meaning dont pair something that is not allowed*)
 (*   (a) How close is this to uniform ? At least w.r.t. the measure of #triangles*)
 (*   (b) How often does this procedure work/fail. Might still be faster to do switchings from Erdos-Gallai.*)
 (*- Improve runtime*)
 (*   (a) Don't remove/add edges from the std::vector. Simply replace them*)
 (*   (b) Better triangle counting? (I doubt it)*)
 (*   (c) Do not choose the three permutations with 1/3 probability: choose the "staying" one with a very low probability. Should still be a valid switch chain?*)
 (*- ?*)
 (* ::Section:: *)
 (*Visualize graphs*)
 gsraw=Import[NotebookDirectory[]<>"graphdata.m"];
 (* ::Subsection:: *)
 (*Plot empirical distribution of maximum degree*)
 maxDegrees=Map[{#[[1]],Max[#[[3]]]}&,gsraw];
 maxDegrees=GatherBy[maxDegrees,{#[[1,2]]&,#[[1,1]]&}];
 (* maxDegrees[[ tau index, n index, run index,  ntau or dmax ]] *)
 Histogram[maxDegrees[[1,-1,All,2]],PlotRange->{{0,2000},{0,100}},AxesLabel->{"d_max","frequency"}]
 Histogram[maxDegrees[[2,-1,All,2]],PlotRange->{{0,2000},{0,100}},AxesLabel->{"d_max","frequency"}]
 Histogram[maxDegrees[[3,-1,All,2]],PlotRange->{{0,2000},{0,100}},AxesLabel->{"d_max","frequency"}]
 averages=Map[{#[[1]],Mean[#[[2,1;;-1]]]}&,gsraw];
 (* Sort by n *)
 averages=SortBy[averages,#[[1,1]]&];
 (* Split by n,tau *)
 averagesGrouped=GatherBy[averages,{#[[1,1]]&,#[[1,2]]&}];
 (* averagesGroupes[[ n index, tau index , run index, {ntau, tri, ds} ]] *)
 averagesGrouped=Transpose[averagesGrouped];
 (* averagesGrouped[[ tau index, n index, run index ]] *)
 averagesGrouped=GatherBy[averages,{#[[1,2]]&,#[[1,1]]&}];
 (* averagesGrouped[[ tau index, n index, run index , {ntau, tri, ds} ]] *)
 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[#]]]
 }&,averagesGrouped,{2}];

cpp/switchchain.cpp

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@@ @@ -81,13 +81,13 @@ int main() { @@
     Graph g;
     std::ofstream outfile("graphdata.m");
     outfile << '{';
     bool outputComma = false;
-    for (int numVertices = 2000; numVertices <= 10000; numVertices += 1000) {
+    for (int numVertices = 4000; numVertices <= 8000; numVertices += 1000) {
         for (float tau : tauValues) {
             DegreeSequence ds(numVertices);
             powerlaw_distribution degDist(tau, 2, numVertices);
             //std::poisson_distribution<> degDist(12);
@@ @@ -115,13 +115,13 @@ int main() { @@
+                }
                 std::cout << "Starting switch Markov chain with n = "
                           << numVertices << ", tau = " << tau << ". \t"
                           << std::flush;
-                constexpr int mixingTime = 15000;
+                constexpr int mixingTime = 20000;
                 constexpr int measureTime = 10000;
                 constexpr int measureSkip =
 ; // Take a sample every 100 steps
                 constexpr int measurements =
                     (measureTime - 1) / measureSkip + 1;
                 int movesDone = 0;

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