From dcda30d3618c2bbda271223809572a624dfbeeff 2017-06-11 15:07:19
From: Tom Bannink <tombannink@gmail.com>
Date: 2017-06-11 15:07:19
Subject: [PATCH] Update spectrum computation

---

diff --git a/cpp/switchchain_spectrum.cpp b/cpp/switchchain_spectrum.cpp
index e9d8603be10a778cd2facf9c113bf48b65a899dd..65dd3fb144ba2f158149bec11fc4388542bc36ec 100644
--- a/cpp/switchchain_spectrum.cpp
+++ b/cpp/switchchain_spectrum.cpp
@@ -13,38 +13,66 @@
 #include <vector>
 
 int main(int argc, char* argv[]) {
-    // Generate a random degree sequence
-    std::mt19937 rng(std::random_device{}());
+    // Simulation parameters
+    const int numVerticesMin = 100;
+    const int numVerticesMax = 500;
+    const int numVerticesStep = 100;
 
-    // Goal:
-    // Degrees follow a power-law distribution with some parameter tau
-    // Expect:  #tri = const * n^{ something }
-    // The goal is to find the 'something' by finding the number of triangles
-    // for different values of n and tau
     float tauValues[] = {2.1f, 2.2f, 2.3f, 2.4f, 2.5f, 2.6f, 2.7f, 2.8f, 2.9f};
 
-    Graph g;
+    const int totalDegreeSamples = 5;
 
-    std::ofstream outfile;
+    auto getMixingTime = [](int n, float tau) {
+        return int(30.0f * (50.0f - 30.0f * (tau - 2.0f)) * n);
+    };
+    constexpr int measurements = 50;
+    constexpr int measureSkip = 200; // Take a sample every ... steps
 
+    // Output file
+    std::ofstream outfile;
     if (argc >= 2)
         outfile.open(argv[1]);
-    else   
+    else
         outfile.open("graphdata_spectrum.m");
-
     if (!outfile.is_open()) {
         std::cout << "ERROR: Could not open output file.\n";
         return 1;
     }
 
+    // Output Mathematica-style comment to indicate file contents
+    outfile << "(*\n";
+    outfile << "n from " << numVerticesMin << " to " << numVerticesMax
+            << " step " << numVerticesStep << std::endl;
+    outfile << "tauValues: " << tauValues << std::endl;
+    outfile << "degreeSamples: " << totalDegreeSamples << std::endl;
+    outfile << "mixingTime: 30 * (50 - 30 (tau - 2)) n\n";
+    outfile << "data:\n";
+    outfile << "1: {n,tau}\n";
+    outfile << "2: triangleSeq\n";
+    outfile << "3: edges\n";
+    outfile << "4: start adj spectrum\n";
+    outfile << "5: start laplacian spectrum\n";
+    outfile << "6: end adj spectrum\n";
+    outfile << "7: end laplacian spectrum\n";
+    outfile << "*)" << std::endl;
+
+    // Mathematica does not accept things of the form 1.23e-5
+    // (instead it would write that as 1.23*^-5)
+    // so simply use normal notation up to 6 decimals
+    outfile << std::fixed;
+
     outfile << '{';
     bool outputComma = false;
 
-    for (int numVertices = 500; numVertices <= 500; numVertices += 1000) {
+    std::mt19937 rng(std::random_device{}());
+    Graph g;
+    for (int numVertices = numVerticesMin; numVertices <= numVerticesMax;
+         numVertices += numVerticesStep) {
         for (float tau : tauValues) {
             // For a single n,tau take samples over several instances of
             // the degree distribution.
-            for (int degreeSample = 0; degreeSample < 5; ++degreeSample) {
+            for (int degreeSample = 0; degreeSample < totalDegreeSamples;
+                 ++degreeSample) {
                 DegreeSequence ds;
                 generatePowerlawGraph(numVertices, tau, g, ds, rng);
 
@@ -57,14 +85,7 @@ int main(int argc, char* argv[]) {
                 std::cout << "Running n = " << numVertices << ", tau = " << tau
                           << ". \t" << std::flush;
 
-                //int mixingTime = (32.0f - 26.0f*(tau - 2.0f)) * numVertices; //40000;
-                //constexpr int measurements = 50;
-                //constexpr int measureSkip =
-                //    200; // Take a sample every ... steps
-                int mixingTime = 0;
-                constexpr int measurements = 50000;
-                constexpr int measureSkip = 1;
-
+                int mixingTime = getMixingTime(numVertices,tau);;
 
                 int movesTotal = 0;
                 int movesSuccess = 0;
@@ -93,7 +114,8 @@ int main(int argc, char* argv[]) {
                           << "% successrate). " << std::flush;
                 // std::cout << std::endl;
 
-                GraphSpectrum gs(g);
+                GraphSpectrum gs_start(g);
+                GraphSpectrum gs_end(chain.g);
 
                 if (outputComma)
                     outfile << ',' << '\n';
@@ -103,8 +125,10 @@ int main(int argc, char* argv[]) {
                 outfile << '{' << '{' << numVertices << ',' << tau << '}';
                 outfile << ',' << triangles;
                 outfile << ',' << g.edgeCount();
-                outfile << ',' << gs.computeAdjacencySpectrum();
-                outfile << ',' << gs.computeLaplacianSpectrum();
+                outfile << ',' << gs_start.computeAdjacencySpectrum();
+                outfile << ',' << gs_start.computeLaplacianSpectrum();
+                outfile << ',' << gs_end.computeAdjacencySpectrum();
+                outfile << ',' << gs_end.computeLaplacianSpectrum();
                 outfile << '}' << std::flush;
 
                 std::cout << std::endl;