Use covariance matrix under Monte Carlo simulation, to draw better strengths.

[wloh] / mcwordfeud.cpp

diff --git a/mcwordfeud.cpp b/mcwordfeud.cpp
index ce9dc5fd482058895b2577817d1282d51e955e6f..28a2a44c83cd19deb2bd51704d5c1dd0016ef805 100644 (file)
--- a/mcwordfeud.cpp
+++ b/mcwordfeud.cpp
@@ -7,10 +7,13 @@
 #include <vector>
 #include <string>
 #include <algorithm>
+#include <Eigen/Cholesky>
+#include <Eigen/Dense>
 
 #include "ziggurat.hpp"
 
 using namespace std;
+using namespace Eigen;
 
 #define MAX_PLAYERS 16
 
@@ -86,8 +89,7 @@ int main(int argc, char **argv)
 
        vector<string> players;
        map<string, int> player_map;
-       float ratings[MAX_PLAYERS];
-       float ratings_stddev[MAX_PLAYERS];
+       Matrix<float, Dynamic, 1, 0, MAX_PLAYERS, 1> ratings(num_players);
        bool has_scores[MAX_PLAYERS][MAX_PLAYERS];
        for (int pl1 = 0; pl1 < num_players; ++pl1) {
                for (int pl2 = 0; pl2 < num_players; ++pl2) {
@@ -98,8 +100,8 @@ int main(int argc, char **argv)
        int scores[MAX_PLAYERS][MAX_PLAYERS];
        for (int i = 0; i < num_players; ++i) {
                char buf[256];
-               float rating, rating_stddev;
-               int ret = scanf("%s %f %f", buf, &rating, &rating_stddev);
+               float rating;
+               int ret = scanf("%s %f", buf, &rating);
                if (ret < 1) {
                        fprintf(stderr, "Couldn't read player %d\n", i);
                        exit(1);
@@ -107,15 +109,25 @@ int main(int argc, char **argv)
                if (ret < 2) {
                        rating = 1500.0f;
                }
-               if (ret < 3) {
-                       rating_stddev = 0.0f;
-               }
 
                players.push_back(buf);
                player_map[buf] = i;
-               ratings[i] = rating;
-               ratings_stddev[i] = rating_stddev;
+               ratings(i) = rating;
+       }
+
+       Matrix<float, Dynamic, Dynamic, 0, MAX_PLAYERS, MAX_PLAYERS> ratings_cov(num_players, num_players);
+       for (int i = 0; i < num_players; ++i) {
+               for (int j = 0; j < num_players; ++j) {
+                       float f;
+                       if (scanf("%f", &f) != 1) {
+                               fprintf(stderr, "Couldn't read covariance matrix element (%d,%d)\n", i, j);
+                               exit(1);
+                       }
+                       ratings_cov(i, j) = f;
+               }
        }
+       Matrix<float, Dynamic, Dynamic, 0, MAX_PLAYERS, MAX_PLAYERS> ratings_cholesky =
+               ratings_cov.llt().matrixLLT();
 
        for ( ;; ) {
                char pl1[256], pl2[256];
@@ -149,10 +161,11 @@ int main(int argc, char **argv)
 
        for (int i = 0; i < trials; ++i) {
                // draw true strength for all players
-               float drawn_ratings[MAX_PLAYERS];
+               Matrix<float, Dynamic, 1, 0, MAX_PLAYERS, 1> drawn_normals(num_players);
                for (int p = 0; p < num_players; ++p) {
-                       drawn_ratings[p] = draw_gaussian(ratings[p], ratings_stddev[p]);
+                       drawn_normals(p) = draw_gaussian(0.0f, 1.0f);
                }
+               Matrix<float, Dynamic, 1, 0, MAX_PLAYERS, 1> drawn_ratings = ratings_cholesky * drawn_normals + ratings;
 
                // draw the missing matches
                for (int pl1 = 0; pl1 < num_players; ++pl1) {
@@ -161,7 +174,7 @@ int main(int argc, char **argv)
                                        continue;
                                }
 
-                               float mu = drawn_ratings[pl1] - drawn_ratings[pl2];
+                               float mu = drawn_ratings(pl1) - drawn_ratings(pl2);
                                
                                int score = lrintf(draw_gaussian(mu, match_stddev));
                                scores[pl1][pl2] = score;