X-Git-Url: https://git.sesse.net/?a=blobdiff_plain;f=foosrank.cpp;h=03edcb5b4c1047572a644aa4122af70e288c32f7;hb=HEAD;hp=802464d6e4d81cd8eee49d7ee6c12ddb39bb78c1;hpb=8e3849860e66edb4742b3525e1d0fa436cc188b9;p=foosball diff --git a/foosrank.cpp b/foosrank.cpp index 802464d..03edcb5 100644 --- a/foosrank.cpp +++ b/foosrank.cpp @@ -16,11 +16,6 @@ static const double int_step_size = 75.0; // rating constant (see below) static const double rating_constant = 455.0; -#if USE_LOGISTIC_DISTRIBUTION -// constant used in the logistic pdf -static const double l_const = M_PI / (2.0 * sqrt(3.0)); -#endif - using namespace std; static double prob_score_real(int k, int a, double binomial, double rd_norm); @@ -103,7 +98,7 @@ static double fac(int x) return prod; } -static void compute_opponent_rating_pdf(int k, int a, double mu2, double sigma2, double winfac, vector > &result) +static void compute_opponent_rating_pdf(int k, int a, double mu2, double sigma2, double winfac, vector > *result) { double binomial_precompute = prodai(k, a) / fac(k-1); winfac /= rating_constant; @@ -111,27 +106,31 @@ static void compute_opponent_rating_pdf(int k, int a, double mu2, double sigma2, 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); + static bool inited = false; + static fftw_plan f1, f2, b; + static complex *func1, *func2, *res; + + if (!inited) { + 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); + inited = true; + } // start off by zero for (int i = 0; i < sz*2; ++i) { @@ -149,8 +148,7 @@ static void compute_opponent_rating_pdf(int k, int a, double mu2, double sigma2, // opponent's pdf #if USE_LOGISTIC_DISTRIBUTION double z = (x1 - mu2) * invsigma2; - double ch = cosh(l_const * z); - func1[i].real() = 1.0 / (ch * ch); + func1[i].real() = sech2(0.5 * z); #else double z = (x1 - mu2) * invsq2sigma2; func1[i].real() = exp(-z*z); @@ -160,7 +158,7 @@ static void compute_opponent_rating_pdf(int k, int a, double mu2, double sigma2, func2[(i - sz/2 + sz*2)%(sz*2)].real() = prob_score_real(k, a, binomial_precompute, x2*winfac); } - result.reserve(sz*2); + result->reserve(sz*2); // convolve fftw_execute(f1); @@ -170,23 +168,23 @@ static void compute_opponent_rating_pdf(int k, int a, double mu2, double sigma2, } fftw_execute(b); - result.reserve(sz); + result->reserve(sz); for (int i = 0; i < sz; ++i) { double r1 = i*h; - result.push_back(make_pair(r1, abs(res[i]))); + result->push_back(make_pair(r1, abs(res[i]))); } } // normalize the curve so we know that A ~= 1 -static void normalize(vector > &curve) +static void normalize(vector > *curve) { double peak = 0.0; - for (vector >::const_iterator i = curve.begin(); i != curve.end(); ++i) { + for (vector >::const_iterator i = curve->begin(); i != curve->end(); ++i) { peak = max(peak, i->second); } double invpeak = 1.0 / peak; - for (vector >::iterator i = curve.begin(); i != curve.end(); ++i) { + for (vector >::iterator i = curve->begin(); i != curve->end(); ++i) { i->second *= invpeak; } } @@ -247,7 +245,7 @@ static void solve_matrix(double *A, double *x, double *B) // Give an OK starting estimate for the least squares, by numerical integration // of statistical moments. -static void estimate_musigma(vector > &curve, double &mu_result, double &sigma_result) +static void estimate_musigma(const vector > &curve, double *mu_result, double *sigma_result) { double h = (curve.back().first - curve.front().first) / (curve.size() - 1); @@ -278,8 +276,8 @@ static void estimate_musigma(vector > &curve, double &mu_re ex = (h/3.0) * ex / area; ex2 = (h/3.0) * ex2 / area; - mu_result = ex; - sigma_result = sqrt(ex2 - ex * ex); + *mu_result = ex; + *sigma_result = sqrt(ex2 - ex * ex); } // Find best fit of the data in curves to a Gaussian pdf, based on the @@ -289,7 +287,7 @@ static void estimate_musigma(vector > &curve, double &mu_re // 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. -static void least_squares(vector > &curve, double mu1, double sigma1, double &mu_result, double &sigma_result) +static void least_squares(const vector > &curve, double mu1, double sigma1, double *mu_result, double *sigma_result) { double A = 1.0; double mu = mu1; @@ -316,11 +314,11 @@ static void least_squares(vector > &curve, double mu1, doub #if USE_LOGISTIC_DISTRIBUTION // df/dA(x_i) - matA[i + 0 * curve.size()] = sech2(l_const * (x-mu)/sigma); + matA[i + 0 * curve.size()] = sech2(0.5 * (x-mu)/sigma); // df/dµ(x_i) - matA[i + 1 * curve.size()] = 2.0 * l_const * A * matA[i + 0 * curve.size()] - * tanh(l_const * (x-mu)/sigma) / sigma; + matA[i + 1 * curve.size()] = A * matA[i + 0 * curve.size()] + * tanh(0.5 * (x-mu)/sigma) / sigma; // df/dσ(x_i) matA[i + 2 * curve.size()] = @@ -346,7 +344,7 @@ static void least_squares(vector > &curve, double mu1, doub double y = curve[i].second; #if USE_LOGISTIC_DISTRIBUTION - dbeta[i] = y - A * sech2(l_const * (x-mu)/sigma); + dbeta[i] = y - A * sech2(0.5 * (x-mu)/sigma); #else dbeta[i] = y - A * exp(- (x-mu)*(x-mu)/(2.0*sigma*sigma)); #endif @@ -368,18 +366,18 @@ static void least_squares(vector > &curve, double mu1, doub break; } - mu_result = mu; - sigma_result = sigma; + *mu_result = mu; + *sigma_result = sigma; } -static void compute_new_rating(double mu1, double sigma1, double mu2, double sigma2, int score1, int score2, double &mu, double &sigma, double &probability) +void compute_new_rating(double mu1, double sigma1, double mu2, double sigma2, int score1, int score2, double *mu, double *sigma, double *probability) { vector > curve; if (score1 > score2) { - compute_opponent_rating_pdf(score1, score2, mu2, sigma2, -1.0, curve); + compute_opponent_rating_pdf(score1, score2, mu2, sigma2, -1.0, &curve); } else { - compute_opponent_rating_pdf(score2, score1, mu2, sigma2, 1.0, curve); + compute_opponent_rating_pdf(score2, score1, mu2, sigma2, 1.0, &curve); } // multiply in the gaussian @@ -389,24 +387,27 @@ static void compute_new_rating(double mu1, double sigma1, double mu2, double sig // my pdf double z = (r1 - mu1) / sigma1; #if USE_LOGISTIC_DISTRIBUTION - double ch = cosh(l_const * z); - curve[i].second /= (ch * ch); + curve[i].second *= sech2(0.5 * z); #else double gaussian = exp(-(z*z/2.0)); curve[i].second *= gaussian; #endif } - + // Compute the overall probability of the given result, by integrating // the entire resulting pdf. Note that since we're actually evaluating // a double integral, we'll need to multiply by h² instead of h. - // (TODO: Use Simpson's rule here.) { double h = (curve.back().first - curve.front().first) / (curve.size() - 1); - double sum = 0.0; - for (unsigned i = 0; i < curve.size(); ++i) { - sum += h * h * curve[i].second; + double sum = curve.front().second; + for (unsigned i = 1; i < curve.size() - 1; i += 2) { + sum += 4.0 * curve[i].second; } + for (unsigned i = 2; i < curve.size() - 1; i += 2) { + sum += 2.0 * curve[i].second; + } + sum += curve.back().second; + sum *= h * h / 3.0; // FFT convolution multiplication factor (FFTW computes unnormalized // transforms) @@ -414,32 +415,32 @@ static void compute_new_rating(double mu1, double sigma1, double mu2, double sig // pdf normalization factors #if USE_LOGISTIC_DISTRIBUTION - sum *= M_PI / (sigma1 * 4.0 * sqrt(3.0)); - sum *= M_PI / (sigma2 * 4.0 * sqrt(3.0)); + sum /= (sigma1 * 4.0); + sum /= (sigma2 * 4.0); #else sum /= (sigma1 * sqrt(2.0 * M_PI)); sum /= (sigma2 * sqrt(2.0 * M_PI)); #endif - probability = sum; + *probability = sum; } double mu_est, sigma_est; - normalize(curve); - estimate_musigma(curve, mu_est, sigma_est); + normalize(&curve); + estimate_musigma(curve, &mu_est, &sigma_est); least_squares(curve, mu_est, sigma_est, mu, 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, double &probability) +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, double *probability) { 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); + 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); + compute_opponent_rating_pdf(score2, score1, mu_t, sigma_t, 1.0, &curve); } newcurve.reserve(curve.size()); @@ -465,7 +466,7 @@ static void compute_new_double_rating(double mu1, double sigma1, double mu2, dou #if USE_LOGISTIC_DISTRIBUTION double z = (r2 - mu2) * invsigma2; - double gaussian = sech2(l_const * z); + double gaussian = sech2(0.5 * z); #else double z = (r2 - mu2) * invsq2sigma2; double gaussian = exp(-z*z); @@ -475,7 +476,7 @@ static void compute_new_double_rating(double mu1, double sigma1, double mu2, dou #if USE_LOGISTIC_DISTRIBUTION double z = (r1 - mu1) / sigma1; - double gaussian = sech2(l_const * z); + double gaussian = sech2(0.5 * z); #else double z = (r1 - mu1) / sigma1; double gaussian = exp(-(z*z/2.0)); @@ -487,13 +488,19 @@ static void compute_new_double_rating(double mu1, double sigma1, double mu2, dou // the entire resulting pdf. Note that since we're actually evaluating // a triple integral, we'll need to multiply by 4h³ (no idea where the // 4 factor comes from, probably from the 0..6000 range somehow) instead - // of h. (TODO: Use Simpson's rule here.) + // of h. { double h = (newcurve.back().first - newcurve.front().first) / (newcurve.size() - 1); - double sum = 0.0; - for (unsigned i = 0; i < newcurve.size(); ++i) { - sum += 4.0 * h * h * h * newcurve[i].second; + double sum = newcurve.front().second; + for (unsigned i = 1; i < newcurve.size() - 1; i += 2) { + sum += 4.0 * newcurve[i].second; } + for (unsigned i = 2; i < newcurve.size() - 1; i += 2) { + sum += 2.0 * newcurve[i].second; + } + sum += newcurve.back().second; + + sum *= 4.0 * h * h * h / 3.0; // FFT convolution multiplication factor (FFTW computes unnormalized // transforms) @@ -501,21 +508,21 @@ static void compute_new_double_rating(double mu1, double sigma1, double mu2, dou // pdf normalization factors #if USE_LOGISTIC_DISTRIBUTION - sum *= M_PI / (sigma1 * 4.0 * sqrt(3.0)); - sum *= M_PI / (sigma2 * 4.0 * sqrt(3.0)); - sum *= M_PI / (sigma_t * 4.0 * sqrt(3.0)); + sum /= (sigma1 * 4.0); + sum /= (sigma2 * 4.0); + sum /= (sigma_t * 4.0); #else sum /= (sigma1 * sqrt(2.0 * M_PI)); sum /= (sigma2 * sqrt(2.0 * M_PI)); sum /= (sigma_t * sqrt(2.0 * M_PI)); #endif - probability = sum; + *probability = sum; } double mu_est, sigma_est; - normalize(newcurve); - estimate_musigma(newcurve, mu_est, sigma_est); + normalize(&newcurve); + estimate_musigma(newcurve, &mu_est, &sigma_est); least_squares(newcurve, mu_est, sigma_est, mu, sigma); } @@ -540,28 +547,24 @@ int main(int argc, char **argv) int score1 = atoi(argv[9]); int score2 = atoi(argv[10]); double mu, sigma, probability; - compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, score1, score2, mu, sigma, probability); - if (score1 > score2) { - printf("%f %f %f\n", mu, sigma, probability); - } else { - printf("%f %f %f\n", mu, sigma, probability); - } + compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, score1, score2, &mu, &sigma, &probability); + printf("%f %f %f\n", mu, sigma, probability); } 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; double probability; - compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, k, i, newmu1_1, newsigma1_1, probability); - compute_new_double_rating(mu2, sigma2, mu1, sigma1, mu3, sigma3, mu4, sigma4, k, i, newmu1_2, newsigma1_2, probability); - compute_new_double_rating(mu3, sigma3, mu4, sigma4, mu1, sigma1, mu2, sigma2, i, k, newmu2_1, newsigma2_1, probability); - compute_new_double_rating(mu4, sigma4, mu3, sigma3, mu1, sigma1, mu2, sigma2, i, k, newmu2_2, newsigma2_2, probability); + compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, k, i, &newmu1_1, &newsigma1_1, &probability); + compute_new_double_rating(mu2, sigma2, mu1, sigma1, mu3, sigma3, mu4, sigma4, k, i, &newmu1_2, &newsigma1_2, &probability); + compute_new_double_rating(mu3, sigma3, mu4, sigma4, mu1, sigma1, mu2, sigma2, i, k, &newmu2_1, &newsigma2_1, &probability); + compute_new_double_rating(mu4, sigma4, mu3, sigma3, mu1, sigma1, mu2, sigma2, i, k, &newmu2_2, &newsigma2_2, &probability); printf("%u-%u,%f,%+f,%+f,%+f,%+f\n", k, i, probability, newmu1_1-mu1, newmu1_2-mu2, newmu2_1-mu3, newmu2_2-mu4); @@ -570,11 +573,10 @@ int main(int argc, char **argv) double newmu1_1, newmu1_2, newmu2_1, newmu2_2; double newsigma1_1, newsigma1_2, newsigma2_1, newsigma2_2; double probability; - compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, k, i, newmu1_1, newsigma1_1, probability); - compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, i, k, newmu1_1, newsigma1_1, probability); - compute_new_double_rating(mu2, sigma2, mu1, sigma1, mu3, sigma3, mu4, sigma4, i, k, newmu1_2, newsigma1_2, probability); - compute_new_double_rating(mu3, sigma3, mu4, sigma4, mu1, sigma1, mu2, sigma2, k, i, newmu2_1, newsigma2_1, probability); - compute_new_double_rating(mu4, sigma4, mu3, sigma3, mu1, sigma1, mu2, sigma2, k, i, newmu2_2, newsigma2_2, probability); + compute_new_double_rating(mu1, sigma1, mu2, sigma2, mu3, sigma3, mu4, sigma4, i, k, &newmu1_1, &newsigma1_1, &probability); + compute_new_double_rating(mu2, sigma2, mu1, sigma1, mu3, sigma3, mu4, sigma4, i, k, &newmu1_2, &newsigma1_2, &probability); + compute_new_double_rating(mu3, sigma3, mu4, sigma4, mu1, sigma1, mu2, sigma2, k, i, &newmu2_1, &newsigma2_1, &probability); + compute_new_double_rating(mu4, sigma4, mu3, sigma3, mu1, sigma1, mu2, sigma2, k, i, &newmu2_2, &newsigma2_2, &probability); printf("%u-%u,%f,%+f,%+f,%+f,%+f\n", i, k, probability, newmu1_1-mu1, newmu1_2-mu2, newmu2_1-mu3, newmu2_2-mu4); @@ -583,28 +585,24 @@ int main(int argc, char **argv) int score1 = atoi(argv[5]); int score2 = atoi(argv[6]); double mu, sigma, probability; - compute_new_rating(mu1, sigma1, mu2, sigma2, score1, score2, mu, sigma, probability); + compute_new_rating(mu1, sigma1, mu2, sigma2, score1, score2, &mu, &sigma, &probability); - if (score1 > score2) { - printf("%f %f %f\n", mu, sigma, probability); - } else { - printf("%f %f %f\n", mu, sigma, probability); - } + printf("%f %f %f\n", mu, sigma, probability); } else { int k = atoi(argv[5]); // assess all possible scores for (int i = 0; i < k; ++i) { double newmu1, newmu2, newsigma1, newsigma2, probability; - compute_new_rating(mu1, sigma1, mu2, sigma2, k, i, newmu1, newsigma1, probability); - compute_new_rating(mu2, sigma2, mu1, sigma1, i, k, newmu2, newsigma2, probability); + compute_new_rating(mu1, sigma1, mu2, sigma2, k, i, &newmu1, &newsigma1, &probability); + compute_new_rating(mu2, sigma2, mu1, sigma1, i, k, &newmu2, &newsigma2, &probability); printf("%u-%u,%f,%+f,%+f\n", k, i, probability, newmu1-mu1, newmu2-mu2); } for (int i = k; i --> 0; ) { double newmu1, newmu2, newsigma1, newsigma2, probability; - compute_new_rating(mu1, sigma1, mu2, sigma2, i, k, newmu1, newsigma1, probability); - compute_new_rating(mu2, sigma2, mu1, sigma1, k, i, newmu2, newsigma2, probability); + compute_new_rating(mu1, sigma1, mu2, sigma2, i, k, &newmu1, &newsigma1, &probability); + compute_new_rating(mu2, sigma2, mu1, sigma1, k, i, &newmu2, &newsigma2, &probability); printf("%u-%u,%f,%+f,%+f\n", i, k, probability, newmu1-mu1, newmu2-mu2); }