X-Git-Url: https://git.sesse.net/?a=blobdiff_plain;f=foosrank.cpp;h=cc660764762885eacd62abf9362e7b7cca54e3c3;hb=b74e01d91de149544b5a01ddcbd20c90abaa9b42;hp=f16618297c2cd3abdce54e141dca95b039a4bb74;hpb=0a47f6b013ac235066c0cdef2364bb51e897a042;p=foosball diff --git a/foosrank.cpp b/foosrank.cpp index f166182..cc66076 100644 --- a/foosrank.cpp +++ b/foosrank.cpp @@ -5,9 +5,11 @@ #include #include +#include +#include + // 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; // rating constant (see below) static const double rating_constant = 455.0; @@ -15,10 +17,11 @@ static const double rating_constant = 455.0; 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); + // probability of match ending k-a (k>a) when winnerR - loserR = RD // // +inf @@ -37,16 +40,16 @@ 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; } @@ -73,7 +76,7 @@ double fac(int x) // +inf // / // | -// | ProbScore[a] (r2-r1) Gaussian[mu2, sigma2] (dr2) dr2 +// | ProbScore[a] (r1-r2) Gaussian[mu2, sigma2] (r2) dr2 // | // / // -inf @@ -84,37 +87,87 @@ double fac(int x) // 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 (r1-r2) instead of (r2-r1). +// In the latter case, ProbScore will be given (r2-r1) instead of (r1-r2). // -static inline double evaluate_int_point(int k, double a, double prodai_precompute, double kfac_precompute, double r1, double mu2, double sigma2, double winfac, double x); +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; + } +}; -double opponent_rating_pdf(int k, double a, double r1, double mu2, double sigma2, double winfac) +void convolve(int size) { - double prodai_precompute = prodai(k, a); - double kfac_precompute = fac(k-1); - winfac /= rating_constant; +} - int n = int(3000.0 / int_step_size + 0.5); - double h = 3000.0 / double(n); - double sum = evaluate_int_point(k, a, prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac, 0.0); +void compute_opponent_rating_pdf(int k, double a, double mu2, double sigma2, double winfac, vector > &result) +{ + double binomial_precompute = prodai(k, a) / fac(k-1); + winfac /= rating_constant; - for (int i = 1; i < n; i += 2) { - sum += 4.0 * evaluate_int_point(k, a, prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac, i * h); + int sz = (6000.0 - 0.0) / int_step_size; + double h = (6000.0 - 0.0) / sz; + + fftw_plan f1, f2, b; + complex *func1, *func2, *res; + + func1 = reinterpret_cast *>(fftw_malloc(sz*2*sizeof(complex))); + func2 = reinterpret_cast *>(fftw_malloc(sz*2*sizeof(complex))); + res = reinterpret_cast *>(fftw_malloc(sz*2*sizeof(complex))); + f1 = fftw_plan_dft_1d(sz*2, + reinterpret_cast(func1), + reinterpret_cast(func1), + FFTW_FORWARD, + FFTW_MEASURE); + f2 = fftw_plan_dft_1d(sz*2, + reinterpret_cast(func2), + reinterpret_cast(func2), + FFTW_FORWARD, + FFTW_MEASURE); + b = fftw_plan_dft_1d(sz*2, + reinterpret_cast(res), + reinterpret_cast(res), + FFTW_BACKWARD, + FFTW_MEASURE); + + // start off by zero + for (int i = 0; i < sz*2; ++i) { + func1[i].real() = func1[i].imag() = func2[i].real() = func2[i].imag() = 0.0; } - for (int i = 2; i < n; i += 2) { - sum += 2.0 * evaluate_int_point(k, a, prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac, i * h); + + for (int i = 0; i < sz; ++i) { + double x1 = 0.0 + h*i; + double z = (x1 - mu2)/sigma2; + func1[i].real() = exp(-(z*z/2.0)); + + double x2 = -3000.0 + h*i; + func2[(i - sz/2 + sz*2)%(sz*2)].real() = prob_score_real(k, a, binomial_precompute, x2*winfac); } - sum += evaluate_int_point(k, a, prodai_precompute, kfac_precompute, r1, mu2, sigma2, winfac, 3000.0); - return (h/3.0) * sum; -} + result.reserve(sz*2); -static inline double evaluate_int_point(int k, double a, double prodai_precompute, double kfac_precompute, double r1, double mu2, double sigma2, double winfac, double x) -{ - double probscore = prob_score_real(k, a, prodai_precompute, kfac_precompute, (x - r1)*winfac); - double z = (x - mu2)/sigma2; - double gaussian = exp(-(z*z/2.0)); - return probscore * gaussian; + // convolve + fftw_execute(f1); + fftw_execute(f2); + for (int i = 0; i < sz*2; ++i) { + res[i] = func1[i] * func2[i]; + } + fftw_execute(b); + for (int i = 0; i < sz; ++i) { + double r1 = i*h; + result.push_back(make_pair(r1, abs(res[i]))); + } } // normalize the curve so we know that A ~= 1 @@ -360,17 +413,17 @@ void compute_new_rating(double mu1, double sigma1, double mu2, double sigma2, in vector > 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 * opponent_rating_pdf(score1, score2, r1, mu2, sigma2, 1.0))); - } + compute_opponent_rating_pdf(score1, score2, mu2, sigma2, -1.0, curve); } 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))); - } + compute_opponent_rating_pdf(score2, score1, mu2, sigma2, 1.0, curve); + } + + // multiply in the gaussian + for (unsigned i = 0; i < curve.size(); ++i) { + double r1 = curve[i].first; + double z = (r1 - mu1) / sigma1; + double gaussian = exp(-(z*z/2.0)); + curve[i].second *= gaussian; } double mu_est, sigma_est; @@ -379,14 +432,103 @@ void compute_new_rating(double mu1, double sigma1, double mu2, double sigma2, in 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) +{ + vector > curve, newcurve; + double mu_t = mu3 + mu4; + double sigma_t = sqrt(sigma3*sigma3 + sigma4*sigma4); + + if (score1 > score2) { + compute_opponent_rating_pdf(score1, score2, mu_t, sigma_t, -1.0, curve); + } else { + compute_opponent_rating_pdf(score2, score1, mu_t, sigma_t, 1.0, curve); + } + + // iterate over r1 + double h = 3000.0 / curve.size(); + for (unsigned i = 0; i < curve.size(); ++i) { + double sum = 0.0; + + // could be anything, but this is a nice start + //double r1 = curve[i].first; + double r1 = i * h; + + // iterate over r2 + for (unsigned j = 0; j < curve.size(); ++j) { + double r1plusr2 = curve[j].first; + double r2 = r1plusr2 - r1; + + double z = (r2 - mu2) / sigma2; + double gaussian = exp(-(z*z/2.0)); + sum += curve[j].second * gaussian; + } + + double z = (r1 - mu1) / sigma1; + double gaussian = exp(-(z*z/2.0)); + newcurve.push_back(make_pair(r1, gaussian * sum)); + } + + + double mu_est, sigma_est; + normalize(newcurve); + estimate_musigma(newcurve, mu_est, sigma_est); + least_squares(newcurve, mu_est, sigma_est, mu, sigma); +} + int main(int argc, char **argv) { + FILE *fp = fopen("fftw-wisdom", "rb"); + if (fp != NULL) { + fftw_import_wisdom_from_file(fp); + fclose(fp); + } + double mu1 = atof(argv[1]); double sigma1 = atof(argv[2]); double mu2 = atof(argv[3]); double sigma2 = atof(argv[4]); - if (argc > 6) { + if (argc > 10) { + 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 > 8) { + double mu3 = atof(argv[5]); + double sigma3 = atof(argv[6]); + double mu4 = atof(argv[7]); + double sigma4 = atof(argv[8]); + int k = atoi(argv[9]); + + // assess all possible scores + for (int i = 0; i < k; ++i) { + double newmu1_1, newmu1_2, newmu2_1, newmu2_2; + double newsigma1_1, newsigma1_2, newsigma2_1, newsigma2_2; + compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, k, i, newmu1_1, newsigma1_1); + compute_new_double_rating(mu2, sigma2, mu1, sigma1, mu3, sigma3, mu4, sigma4, k, i, newmu1_2, newsigma1_2); + compute_new_double_rating(mu3, sigma3, mu4, sigma4, mu1, sigma1, mu2, sigma2, i, k, newmu2_1, newsigma2_1); + compute_new_double_rating(mu4, sigma4, mu3, sigma3, mu1, sigma1, mu2, sigma2, i, k, newmu2_2, newsigma2_2); + printf("%u-%u,%f,%+f,%+f,%+f,%+f\n", + k, i, prob_score(k, i, mu3+mu4-(mu1+mu2)), newmu1_1-mu1, newmu1_2-mu2, + newmu2_1-mu3, newmu2_2-mu4); + } + for (int i = k; i --> 0; ) { + double newmu1_1, newmu1_2, newmu2_1, newmu2_2; + double newsigma1_1, newsigma1_2, newsigma2_1, newsigma2_2; + compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, i, k, newmu1_1, newsigma1_1); + compute_new_double_rating(mu2, sigma2, mu1, sigma1, mu3, sigma3, mu4, sigma4, i, k, newmu1_2, newsigma1_2); + compute_new_double_rating(mu3, sigma3, mu4, sigma4, mu1, sigma1, mu2, sigma2, k, i, newmu2_1, newsigma2_1); + compute_new_double_rating(mu4, sigma4, mu3, sigma3, mu1, sigma1, mu2, sigma2, k, i, newmu2_2, newsigma2_2); + printf("%u-%u,%f,%+f,%+f,%+f,%+f\n", + i, k, prob_score(k, i, mu1+mu2-(mu3+mu4)), newmu1_1-mu1, newmu1_2-mu2, + newmu2_1-mu3, newmu2_2-mu4); + } + } else if (argc > 6) { int score1 = atoi(argv[5]); int score2 = atoi(argv[6]); double mu, sigma; @@ -411,5 +553,11 @@ int main(int argc, char **argv) i, k, prob_score(k, i, mu1-mu2), newmu1-mu1, newmu2-mu2); } } + + fp = fopen("fftw-wisdom", "wb"); + if (fp != NULL) { + fftw_export_wisdom_to_file(fp); + fclose(fp); + } }