-#include <stdio.h>
-#include <math.h>
-#include <assert.h>
+#include <cstdio>
+#include <cmath>
+#include <cassert>
#include <vector>
#include <algorithm>
+#include <complex>
+#include <fftw3.h>
+
+#define USE_LOGISTIC_DISTRIBUTION 0
+
// 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;
+#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;
-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 prodai(int k, double a);
-double fac(int x);
+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);
+
+#if USE_LOGISTIC_DISTRIBUTION
+// sech²(x)
+static double sech2(double x)
+{
+ double e = exp(2.0 * x);
+ return 4.0 * e / ((e+1.0) * (e+1.0));
+}
+#endif
+#if 0
// probability of match ending k-a (k>a) when winnerR - loserR = RD
//
// +inf
// 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);
+ return prob_score_real(k, a, prodai(k, a) / fac(k-1), rd/rating_constant);
}
+#endif
+
+// 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;
-// Same, but takes in Product(a+i, i=1..k-1) and (k-1)! as an argument in
+ 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 prodai, double kfac, double rd_norm)
+static double prob_score_real(int k, int 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 * 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] (r2-r1) Gaussian[mu2, sigma2] (dr2) 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 (r1-r2) instead of (r2-r1).
-//
-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 opponent_rating_pdf(int k, double a, double r1, double mu2, double sigma2, double winfac)
+static void compute_opponent_rating_pdf(int k, int a, double mu2, double sigma2, double winfac, vector<pair<double, double> > &result)
{
- double prodai_precompute = prodai(k, a);
- double kfac_precompute = fac(k-1);
+ double binomial_precompute = prodai(k, a) / 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);
-
- 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<double> *func1, *func2, *res;
+
+ func1 = reinterpret_cast<complex<double> *>(fftw_malloc(sz*2*sizeof(complex<double>)));
+ func2 = reinterpret_cast<complex<double> *>(fftw_malloc(sz*2*sizeof(complex<double>)));
+ res = reinterpret_cast<complex<double> *>(fftw_malloc(sz*2*sizeof(complex<double>)));
+ f1 = fftw_plan_dft_1d(sz*2,
+ reinterpret_cast<fftw_complex*>(func1),
+ reinterpret_cast<fftw_complex*>(func1),
+ FFTW_FORWARD,
+ FFTW_MEASURE);
+ f2 = fftw_plan_dft_1d(sz*2,
+ reinterpret_cast<fftw_complex*>(func2),
+ reinterpret_cast<fftw_complex*>(func2),
+ FFTW_FORWARD,
+ FFTW_MEASURE);
+ b = fftw_plan_dft_1d(sz*2,
+ reinterpret_cast<fftw_complex*>(res),
+ reinterpret_cast<fftw_complex*>(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);
+
+#if USE_LOGISTIC_DISTRIBUTION
+ double invsigma2 = 1.0 / sigma2;
+#else
+ double invsq2sigma2 = 1.0 / (sqrt(2.0) * sigma2);
+#endif
+ for (int i = 0; i < sz; ++i) {
+ double x1 = 0.0 + h*i;
+
+ // 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);
+#else
+ double z = (x1 - mu2) * invsq2sigma2;
+ func1[i].real() = exp(-z*z);
+#endif
+
+ 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, (r1 - x)*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);
+
+ result.reserve(sz);
+ 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
-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.
+// solves Ax = B by Gauss-Jordan elimination, where A is an NxN matrix,
+// x is a column vector of length N and B is a row vector of length N.
// Destroys its input in the process.
-void solve3x3(double *A, double *x, double *B)
+template<int N>
+static void solve_matrix(double *A, double *x, double *B)
{
- // row 1 -= row 0 * (a1/a0)
- {
- double f = A[1] / A[0];
- A[1] = 0.0;
- A[4] -= A[3] * f;
- A[7] -= A[6] * f;
-
- B[1] -= B[0] * f;
- }
-
- // row 2 -= row 0 * (a2/a0)
- {
- double f = A[2] / A[0];
- A[2] = 0.0;
- A[5] -= A[3] * f;
- A[8] -= A[6] * f;
-
- B[2] -= B[0] * f;
- }
-
- // row 2 -= row 1 * (a5/a4)
- {
- double f = A[5] / A[4];
- A[5] = 0.0;
- A[8] -= A[7] * f;
-
- B[2] -= B[1] * f;
- }
-
- // back substitute:
-
- // row 1 -= row 2 * (a7/a8)
- {
- double f = A[7] / A[8];
- A[7] = 0.0;
-
- B[1] -= B[2] * f;
- }
-
- // row 0 -= row 2 * (a6/a8)
- {
- double f = A[6] / A[8];
- A[6] = 0.0;
+ for (int i = 0; i < N; ++i) {
+ for (int j = i+1; j < N; ++j) {
+ // row j -= row i * (a[i,j] / a[i,i])
+ double f = A[j+i*N] / A[i+i*N];
+
+ A[j+i*N] = 0.0;
+ for (int k = i+1; k < N; ++k) {
+ A[j+k*N] -= A[i+k*N] * f;
+ }
- B[0] -= B[2] * f;
+ B[j] -= B[i] * f;
+ }
}
- // row 0 -= row 1 * (a3/a4)
- {
- double f = A[3] / A[4];
- A[3] = 0.0;
-
- B[0] -= B[1] * f;
+ // back-substitute
+ for (int i = N; i --> 0; ) {
+ for (int j = i; j --> 0; ) {
+ // row j -= row i * (a[j,j] / a[j,i])
+ double f = A[i+j*N] / A[j+j*N];
+
+ // A[j+i*N] = 0.0;
+ B[j] -= B[i] * f;
+ }
}
// normalize
- x[0] = B[0] / A[0];
- x[1] = B[1] / A[4];
- x[2] = B[2] / A[8];
+ for (int i = 0; i < N; ++i) {
+ x[i] = B[i] / A[i+i*N];
+ }
}
// 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;
for (unsigned i = 0; i < curve.size(); ++i) {
double x = curve[i].first;
+#if USE_LOGISTIC_DISTRIBUTION
+ // df/dA(x_i)
+ matA[i + 0 * curve.size()] = sech2(l_const * (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;
+
+ // df/dσ(x_i)
+ matA[i + 2 * curve.size()] =
+ matA[i + 1 * curve.size()] * (x-mu)/sigma;
+#else
// df/dA(x_i)
matA[i + 0 * curve.size()] =
exp(-(x-mu)*(x-mu)/(2.0*sigma*sigma));
// df/dµ(x_i)
- matA[i + 1 * curve.size()] =
+ matA[i + 1 * curve.size()] =
A * (x-mu)/(sigma*sigma) * matA[i + 0 * curve.size()];
// df/dσ(x_i)
matA[i + 2 * curve.size()] =
matA[i + 1 * curve.size()] * (x-mu)/sigma;
+#endif
}
// find dβ
double x = curve[i].first;
double y = curve[i].second;
+#if USE_LOGISTIC_DISTRIBUTION
+ dbeta[i] = y - A * sech2(l_const * (x-mu)/sigma);
+#else
dbeta[i] = y - A * exp(- (x-mu)*(x-mu)/(2.0*sigma*sigma));
+#endif
}
// compute a and b
mat_mul_trans(matA, curve.size(), 3, dbeta, curve.size(), 1, matATdb);
// solve
- solve3x3(matATA, dlambda, matATdb);
+ solve_matrix<3>(matATA, dlambda, matATdb);
A += dlambda[0];
mu += dlambda[1];
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, double &probability)
{
vector<pair<double, double> > 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;
+
+ // my pdf
+ double z = (r1 - mu1) / sigma1;
+#if USE_LOGISTIC_DISTRIBUTION
+ double ch = cosh(l_const * z);
+ curve[i].second /= (ch * ch);
+#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.
+ // (For some reason, Simpson's rule gives markedly worse accuracy here.
+ // Probably related to h² somehow?)
+ {
+ double h = (curve.back().first - curve.front().first) / (curve.size() - 1);
+ double sum = 0.0;
+ for (unsigned i = 0; i < curve.size(); ++i) {
+ sum += curve[i].second;
}
+
+ sum *= h * h;
+
+ // FFT convolution multiplication factor (FFTW computes unnormalized
+ // transforms)
+ sum /= (curve.size() * 2);
+
+ // 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));
+#else
+ sum /= (sigma1 * sqrt(2.0 * M_PI));
+ sum /= (sigma2 * sqrt(2.0 * M_PI));
+#endif
+
+ probability = sum;
}
double 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)
+{
+ vector<pair<double, double> > 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);
+ }
+
+ newcurve.reserve(curve.size());
+
+ // 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
+#if USE_LOGISTIC_DISTRIBUTION
+ double invsigma2 = 1.0 / sigma2;
+#else
+ double invsq2sigma2 = 1.0 / (sqrt(2.0) * sigma2);
+#endif
+ for (unsigned j = 0; j < curve.size(); ++j) {
+ double r1plusr2 = curve[j].first;
+ double r2 = r1plusr2 - r1;
+
+#if USE_LOGISTIC_DISTRIBUTION
+ double z = (r2 - mu2) * invsigma2;
+ double gaussian = sech2(l_const * z);
+#else
+ double z = (r2 - mu2) * invsq2sigma2;
+ double gaussian = exp(-z*z);
+#endif
+ sum += curve[j].second * gaussian;
+ }
+
+#if USE_LOGISTIC_DISTRIBUTION
+ double z = (r1 - mu1) / sigma1;
+ double gaussian = sech2(l_const * z);
+#else
+ double z = (r1 - mu1) / sigma1;
+ double gaussian = exp(-(z*z/2.0));
+#endif
+ newcurve.push_back(make_pair(r1, gaussian * sum));
+ }
+
+ // Compute the overall probability of the given result, by integrating
+ // 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: Evaluate Simpson's rule here, although it's probably even worse
+ // than for the single case.)
+ {
+ double h = (newcurve.back().first - newcurve.front().first) / (newcurve.size() - 1);
+ double sum = 0.0;
+ for (unsigned i = 0; i < newcurve.size(); ++i) {
+ sum += newcurve[i].second;
+ }
+
+ sum *= 4.0 * h * h * h;
+
+ // FFT convolution multiplication factor (FFTW computes unnormalized
+ // transforms)
+ sum /= (newcurve.size() * 2);
+
+ // 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));
+#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;
+ }
+
+ 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, 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);
+ }
+ } 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);
+ printf("%u-%u,%f,%+f,%+f,%+f,%+f\n",
+ k, i, probability, 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;
+ 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);
+ printf("%u-%u,%f,%+f,%+f,%+f,%+f\n",
+ i, k, probability, 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;
- compute_new_rating(mu1, sigma1, mu2, sigma2, score1, score2, mu, sigma);
- printf("%f %f\n", mu, sigma);
+ double 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);
+ }
} else {
int k = atoi(argv[5]);
// assess all possible scores
for (int i = 0; i < k; ++i) {
- double newmu1, newmu2, newsigma1, newsigma2;
- compute_new_rating(mu1, sigma1, mu2, sigma2, k, i, newmu1, newsigma1);
- compute_new_rating(mu2, sigma2, mu1, sigma1, i, k, newmu2, newsigma2);
+ 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);
printf("%u-%u,%f,%+f,%+f\n",
- k, i, prob_score(k, i, mu1-mu2), newmu1-mu1, newmu2-mu2);
+ k, i, probability, newmu1-mu1, newmu2-mu2);
}
for (int i = k; i --> 0; ) {
- double newmu1, newmu2, newsigma1, newsigma2;
- compute_new_rating(mu1, sigma1, mu2, sigma2, i, k, newmu1, newsigma1);
- compute_new_rating(mu2, sigma2, mu1, sigma1, k, i, newmu2, newsigma2);
+ 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);
printf("%u-%u,%f,%+f,%+f\n",
- i, k, prob_score(k, i, mu2-mu1), newmu1-mu1, newmu2-mu2);
+ i, k, probability, newmu1-mu1, newmu2-mu2);
}
}
+
+ fp = fopen("fftw-wisdom", "wb");
+ if (fp != NULL) {
+ fftw_export_wisdom_to_file(fp);
+ fclose(fp);
+ }
}
projects / foosball / blobdiff