using namespace std;
double prob_score(int k, double a, double rd);
-double prob_score_real(int k, double a, double prodai, double kfac, double rd_norm);
+double prob_score_real(int k, double a, double binomial, double rd_norm);
double prodai(int k, double a);
double fac(int x);
//
double prob_score(int k, double a, double rd)
{
- return prob_score_real(k, a, prodai(k, a), fac(k-1), rd/rating_constant);
+ return prob_score_real(k, a, prodai(k, a) / fac(k-1), rd/rating_constant);
}
-// Same, but takes in Product(a+i, i=1..k-1) and (k-1)! as an argument in
+// Same, but takes in binomial(a+k-1, k-1) as an argument in
// addition to a. Faster if you already have that precomputed, and assumes rd
// is already divided by 455.
-double prob_score_real(int k, double a, double prodai, double kfac, double rd_norm)
+double prob_score_real(int k, double a, double binomial, double rd_norm)
{
- double nom = prodai * pow(2.0, rd_norm * a);
- double denom = kfac * pow(1.0 + pow(2.0, rd_norm), k+a);
+ double nom = binomial * pow(2.0, rd_norm * a);
+ double denom = pow(1.0 + pow(2.0, rd_norm), k+a);
return nom/denom;
}
private:
int k;
double a;
- double prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac;
+ double binomial_precompute, r1, mu2, sigma2, winfac;
public:
- ProbScoreEvaluator(int k, double a, double prodai_precompute, double kfac_precompute, double r1, double mu2, double sigma2, double winfac)
- : k(k), a(a), prodai_precompute(prodai_precompute), kfac_precompute(kfac_precompute), r1(r1), mu2(mu2), sigma2(sigma2), winfac(winfac) {}
+ ProbScoreEvaluator(int k, double a, double binomial_precompute, double r1, double mu2, double sigma2, double winfac)
+ : 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, prodai_precompute, kfac_precompute, (x - r1)*winfac);
+ double probscore = prob_score_real(k, a, binomial_precompute, (x - r1)*winfac);
double z = (x - mu2)/sigma2;
double gaussian = exp(-(z*z/2.0));
return probscore * gaussian;
double opponent_rating_pdf(int k, double a, double r1, double mu2, double sigma2, double winfac)
{
- double prodai_precompute = prodai(k, a);
- double kfac_precompute = fac(k-1);
+ double binomial_precompute = prodai(k, a) / fac(k-1);
winfac /= rating_constant;
- return simpson_integrate(ProbScoreEvaluator(k, a, prodai_precompute, kfac_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, 3000.0, int_step_size);
}
// normalize the curve so we know that A ~= 1