-#include <stdio.h>
-#include <math.h>
-#include <assert.h>
+#include <cstdio>
+#include <cmath>
+#include <cassert>
#include <vector>
#include <algorithm>
using namespace std;
-double prob_score(int k, double a, double rd);
-double prob_score_real(int k, double a, double binomial, double rd_norm);
-double prodai(int k, double a);
-double fac(int x);
+static double prob_score(int k, int a, double rd);
+static double prob_score_real(int k, int a, double binomial, double rd_norm);
+static double prodai(int k, int a);
+static double fac(int x);
// probability of match ending k-a (k>a) when winnerR - loserR = RD
// Glicko/Bradley-Terry assumption that a player rated 400 points over
// his/her opponent will win with a probability of 10/11 =~ 0.90909.
//
-double prob_score(int k, double a, double rd)
+static double prob_score(int k, int a, double rd)
{
return prob_score_real(k, a, prodai(k, a) / fac(k-1), rd/rating_constant);
}
+// computes x^a, probably more efficiently than pow(x, a) (but requires that a
+// is n unsigned integer)
+static double intpow(double x, unsigned a)
+{
+ double result = 1.0;
+
+ while (a > 0) {
+ if (a & 1) {
+ result *= x;
+ }
+ a >>= 1;
+ x *= x;
+ }
+
+ return result;
+}
+
// 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 binomial, double rd_norm)
+static double prob_score_real(int k, int a, double binomial, double rd_norm)
{
- double nom = binomial * pow(2.0, rd_norm * a);
- double denom = pow(1.0 + pow(2.0, rd_norm), k+a);
+ double nom = binomial * intpow(pow(2.0, rd_norm), a);
+ double denom = intpow(1.0 + pow(2.0, rd_norm), k+a);
return nom/denom;
}
// Calculates Product(a+i, i=1..k-1) (see above).
-double prodai(int k, double a)
+static double prodai(int k, int a)
{
double prod = 1.0;
for (int i = 1; i < k; ++i)
return prod;
}
-double fac(int x)
+static double fac(int x)
{
double prod = 1.0;
for (int i = 2; i <= x; ++i)
return prod;
}
-//
-// Computes the integral
-//
-// +inf
-// /
-// |
-// | ProbScore[a] (r1-r2) Gaussian[mu2, sigma2] (r2) dr2
-// |
-// /
-// -inf
-//
-// For practical reasons, -inf and +inf are replaced by 0 and 3000, which
-// is reasonable in the this context.
-//
-// The Gaussian is not normalized.
-//
-// 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 (r2-r1) instead of (r1-r2).
-//
-class ProbScoreEvaluator {
-private:
- int k;
- double a;
- double binomial_precompute, r1, mu2, sigma2, winfac;
-
-public:
- 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, binomial_precompute, (r1 - x)*winfac);
- double z = (x - mu2)/sigma2;
- double gaussian = exp(-(z*z/2.0));
- return probscore * gaussian;
- }
-};
-
-void convolve(int size)
-{
-}
-
-void compute_opponent_rating_pdf(int k, double a, double mu2, double sigma2, double winfac, vector<pair<double, double> > &result)
+static void compute_opponent_rating_pdf(int k, int a, double mu2, double sigma2, double winfac, vector<pair<double, double> > &result)
{
double binomial_precompute = prodai(k, a) / fac(k-1);
winfac /= rating_constant;
}
// normalize the curve so we know that A ~= 1
-void normalize(vector<pair<double, double> > &curve)
+
static void normalize(vector<pair<double, double> > &curve)
{
double peak = 0.0;
for (vector<pair<double, double> >::const_iterator i = curve.begin(); i != curve.end(); ++i) {
}
}
-// computes matA * matB
-void mat_mul(double *matA, unsigned ah, unsigned aw,
- double *matB, unsigned bh, unsigned bw,
- double *result)
-{
- assert(aw == bh);
- for (unsigned y = 0; y < bw; ++y) {
- for (unsigned x = 0; x < ah; ++x) {
- double sum = 0.0;
- for (unsigned c = 0; c < aw; ++c) {
- sum += matA[c*ah + x] * matB[y*bh + c];
- }
- result[y*bw + x] = sum;
- }
- }
-}
-
// computes matA^T * matB
-void mat_mul_trans(double *matA, unsigned ah, unsigned aw,
- double *matB, unsigned bh, unsigned bw,
- double *result)
+static void mat_mul_trans(double *matA, unsigned ah, unsigned aw,
+ double *matB, unsigned bh, unsigned bw,
+ double *result)
{
assert(ah == bh);
for (unsigned y = 0; y < bw; ++y) {
}
}
-void print3x3(double *M)
-{
- printf("%f %f %f\n", M[0], M[3], M[6]);
- printf("%f %f %f\n", M[1], M[4], M[7]);
- printf("%f %f %f\n", M[2], M[5], M[8]);
-}
-
-void print3x1(double *M)
-{
- printf("%f\n", M[0]);
- printf("%f\n", M[1]);
- printf("%f\n", M[2]);
-}
-
// solves Ax = B by Gauss-Jordan elimination, where A is a 3x3 matrix,
// x is a column vector of length 3 and B is a row vector of length 3.
// Destroys its input in the process.
-void solve3x3(double *A, double *x, double *B)
+static void solve3x3(double *A, double *x, double *B)
{
// row 1 -= row 0 * (a1/a0)
{
// Give an OK starting estimate for the least squares, by numerical integration
// of statistical moments.
-void estimate_musigma(vector<pair<double, double> > &curve, double &mu_result, double &sigma_result)
+
static void estimate_musigma(vector<pair<double, double> > &curve, double &mu_result, double &sigma_result)
{
double h = (curve.back().first - curve.front().first) / (curve.size() - 1);
// Note that the algorithm blows up quite hard if the initial estimate is
// not good enough. Use estimate_musigma to get a reasonable starting
// estimate.
-void least_squares(vector<pair<double, double> > &curve, double mu1, double sigma1, double &mu_result, double &sigma_result)
+
static void least_squares(vector<pair<double, double> > &curve, double mu1, double sigma1, double &mu_result, double &sigma_result)
{
double A = 1.0;
double mu = mu1;
sigma_result = sigma;
}
-void compute_new_rating(double mu1, double sigma1, double mu2, double sigma2, int score1, int score2, double &mu, double &sigma)
+static void compute_new_rating(double mu1, double sigma1, double mu2, double sigma2, int score1, int score2, double &mu, double &sigma)
{
vector<pair<double, double> > curve;
least_squares(curve, mu_est, sigma_est, mu, sigma);
}
-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)
+static 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, newcurve;
double mu_t = mu3 + mu4;
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