#include <vector>
#include <algorithm>
-// integration step size
-static const double step_size = 10.0;
+// step sizes
+static const double int_step_size = 50.0;
+static const double pdf_step_size = 10.0;
// rating constant (see below)
static const double rating_constant = 455.0;
// Set the last parameter to 1.0 if player 1 won, or -1.0 if player 2 won.
// In the latter case, ProbScore will be given (r1-r2) instead of (r2-r1).
//
+static inline double evaluate_int_point(double a, double prodai_precompute, double r1, double mu2, double sigma2, double winfac, double x);
+
double opponent_rating_pdf(double a, double r1, double mu2, double sigma2, double winfac)
{
- double sum = 0.0;
double prodai_precompute = prodai(a);
winfac /= rating_constant;
- for (double r2 = 0.0; r2 < 3000.0; r2 += step_size) {
- double x = r2 + step_size*0.5;
- double probscore = prob_score_real(a, prodai_precompute, (r1 - x)*winfac);
- double z = (x - mu2)/sigma2;
- double gaussian = exp(-(z*z/2.0));
- sum += step_size * probscore * gaussian;
+
+ int n = int(3000.0 / int_step_size + 0.5);
+ double h = 3000.0 / double(n);
+ double sum = evaluate_int_point(a, prodai_precompute, r1, mu2, sigma2, winfac, 0.0);
+
+ for (int i = 1; i < n; i += 2) {
+ sum += 4.0 * evaluate_int_point(a, prodai_precompute, r1, mu2, sigma2, winfac, i * h);
+ }
+ for (int i = 2; i < n; i += 2) {
+ sum += 2.0 * evaluate_int_point(a, prodai_precompute, r1, mu2, sigma2, winfac, i * h);
}
- return sum;
+ sum += evaluate_int_point(a, prodai_precompute, r1, mu2, sigma2, winfac, 3000.0);
+
+ return (h/3.0) * sum;
+}
+
+static inline double evaluate_int_point(double a, double prodai_precompute, double r1, double mu2, double sigma2, double winfac, double x)
+{
+ double probscore = prob_score_real(a, prodai_precompute, (r1 - x)*winfac);
+ double z = (x - mu2)/sigma2;
+ double gaussian = exp(-(z*z/2.0));
+ return probscore * gaussian;
}
// normalize the curve so we know that A ~= 1
vector<pair<double, double> > curve;
if (score1 == 10) {
- for (double r1 = 0.0; r1 < 3000.0; r1 += step_size) {
+ 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, r1, mu2, sigma2, 1.0)));
}
} else {
- for (double r1 = 0.0; r1 < 3000.0; r1 += step_size) {
+ 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, r1, mu2, sigma2, -1.0)));