Invert the sign in the inner integral, as it's then expressible as a convolution.

[foosball] / foosrank.cpp

diff --git a/foosrank.cpp b/foosrank.cpp
index fc968cd647b86baa5591205f6bd2b47d9507544c..13e9a7914b93539b653a01d55ecdb5acb6019ba8 100644 (file)
--- a/foosrank.cpp
+++ b/foosrank.cpp
@@ -6,8 +6,8 @@
 #include <algorithm>
 
 // step sizes
-static const double int_step_size = 50.0;
-static const double pdf_step_size = 10.0;
+static const double int_step_size = 75.0;
+static const double pdf_step_size = 15.0;
 
 // rating constant (see below)
 static const double rating_constant = 455.0;
@@ -92,7 +92,7 @@ double fac(int x)
 //   +inf
 //    /
 //    |
-//    | ProbScore[a] (r2-r1) Gaussian[mu2, sigma2] (dr2) dr2
+//    | ProbScore[a] (r1-r2) Gaussian[mu2, sigma2] (dr2) dr2
 //    |
 //   /
 // -inf
@@ -116,7 +116,7 @@ public:
                : k(k), a(a), binomial_precompute(binomial_precompute), r1(r1), mu2(mu2), sigma2(sigma2), winfac(winfac) {}
        inline double operator() (double x) const
        {
-               double probscore = prob_score_real(k, a, binomial_precompute, (x - r1)*winfac);
+               double probscore = prob_score_real(k, a, binomial_precompute, (r1 - x)*winfac);
                double z = (x - mu2)/sigma2;
                double gaussian = exp(-(z*z/2.0));
                return probscore * gaussian;
@@ -128,7 +128,7 @@ double opponent_rating_pdf(int k, double a, double r1, double mu2, double sigma2
        double binomial_precompute = prodai(k, a) / fac(k-1);
        winfac /= rating_constant;
 
-       return simpson_integrate(ProbScoreEvaluator(k, a, binomial_precompute, r1, mu2, sigma2, winfac), 0.0, 3000.0, int_step_size);
+       return simpson_integrate(ProbScoreEvaluator(k, a, binomial_precompute, r1, mu2, sigma2, winfac), 0.0, 6000.0, int_step_size);
 }
 
 // normalize the curve so we know that A ~= 1
@@ -377,13 +377,57 @@ void compute_new_rating(double mu1, double sigma1, double mu2, double sigma2, in
                for (double r1 = 0.0; r1 < 3000.0; r1 += pdf_step_size) {
                        double z = (r1 - mu1) / sigma1;
                        double gaussian = exp(-(z*z/2.0));
-                       curve.push_back(make_pair(r1, gaussian * opponent_rating_pdf(score1, score2, r1, mu2, sigma2, 1.0)));
+                       curve.push_back(make_pair(r1, gaussian * opponent_rating_pdf(score1, score2, r1, mu2, sigma2, -1.0)));
                }
        } else {
                for (double r1 = 0.0; r1 < 3000.0; r1 += pdf_step_size) {
                        double z = (r1 - mu1) / sigma1;
                        double gaussian = exp(-(z*z/2.0));
-                       curve.push_back(make_pair(r1, gaussian * opponent_rating_pdf(score2, score1, r1, mu2, sigma2, -1.0)));
+                       curve.push_back(make_pair(r1, gaussian * opponent_rating_pdf(score2, score1, r1, mu2, sigma2, 1.0)));
+               }
+       }
+
+       double mu_est, sigma_est;
+       normalize(curve);
+       estimate_musigma(curve, mu_est, sigma_est);
+       least_squares(curve, mu_est, sigma_est, mu, sigma);
+}
+
+// int(normpdf[mu2, sigma2](t2) * ..., t2=0..3000);
+class OuterIntegralEvaluator {
+private:
+       double theta1, mu2, sigma2, mu_t, sigma_t;
+       int score1, score2;
+       double winfac;
+
+public:
+       OuterIntegralEvaluator(double theta1, double mu2, double sigma2, double mu3, double sigma3, double mu4, double sigma4, int score1, int score2, double winfac)
+               : theta1(theta1), mu2(mu2), sigma2(sigma2), mu_t(mu3 + mu4), sigma_t(sqrt(sigma3*sigma3 + sigma4*sigma4)), score1(score1), score2(score2), winfac(winfac) {}
+
+       double operator() (double theta2) const
+       {
+               double z = (theta2 - mu2) / sigma2;
+               double gaussian = exp(-(z*z/2.0));
+               double r1 = theta1 + theta2;
+               return gaussian * opponent_rating_pdf(score1, score2, r1, mu_t, sigma_t, winfac);
+       }
+};
+
+void compute_new_double_rating(double mu1, double sigma1, double mu2, double sigma2, double mu3, double sigma3, double mu4, double sigma4, int score1, int score2, double &mu, double &sigma)
+{
+       vector<pair<double, double> > curve;
+
+       if (score1 > score2) {
+               for (double r1 = 0.0; r1 < 3000.0; r1 += pdf_step_size) {
+                       double z = (r1 - mu1) / sigma1;
+                       double gaussian = exp(-(z*z/2.0));
+                       curve.push_back(make_pair(r1, gaussian * simpson_integrate(OuterIntegralEvaluator(r1,mu2,sigma2,mu3,sigma3,mu4,sigma4,score1,score2,-0.5), 0.0, 3000.0, int_step_size)));
+               }
+       } else {
+               for (double r1 = 0.0; r1 < 3000.0; r1 += pdf_step_size) {
+                       double z = (r1 - mu1) / sigma1;
+                       double gaussian = exp(-(z*z/2.0));
+                       curve.push_back(make_pair(r1, gaussian * simpson_integrate(OuterIntegralEvaluator(r1,mu2,sigma2,mu3,sigma3,mu4,sigma4,score2,score1,0.5), 0.0, 3000.0, int_step_size)));
                }
        }
 
@@ -400,7 +444,17 @@ int main(int argc, char **argv)
        double mu2 = atof(argv[3]);
        double sigma2 = atof(argv[4]);
 
-       if (argc > 6) {
+       if (argc > 8) {
+               double mu3 = atof(argv[5]);
+               double sigma3 = atof(argv[6]);
+               double mu4 = atof(argv[7]);
+               double sigma4 = atof(argv[8]);
+               int score1 = atoi(argv[9]);
+               int score2 = atoi(argv[10]);
+               double mu, sigma;
+               compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, score1, score2, mu, sigma);
+               printf("%f %f\n", mu, sigma);
+       } else if (argc > 6) {
                int score1 = atoi(argv[5]);
                int score2 = atoi(argv[6]);
                double mu, sigma;