// 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);
// 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);
#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()] =
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
// 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;
// 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));
#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);
#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));
// 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));