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307 lines
19 KiB
307 lines
19 KiB
/**
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* @file funcs.hh
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* @author Christoph Langenbruch, Renata Kopecna
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* @date 2009-03-18
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*
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*/
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#ifndef FUNCS_H
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#define FUNCS_H
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#include <complex>
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#include <TRandom3.h>
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#include <Math/Boost.h>
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#include <Math/Vector4D.h>
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#include <Math/Vector3D.h>
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#include <TMatrixDSym.h>
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#include <TMatrixD.h>
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#include <Math/SpecFuncMathCore.h>
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#include <Math/SpecFuncMathMore.h>
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namespace fcnc { //Forward declaration, fully defined in options.hh
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class options;
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class event;
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}
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namespace fcnc {
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typedef ROOT::Math::PxPyPzEVector LorentzVector;
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typedef ROOT::Math::Boost LorentzBoost;
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typedef ROOT::Math::DisplacementVector3D<ROOT::Math::Cartesian3D<double> > Vector3;
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TMatrixDSym get_bsz_invcov();
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TMatrixDSym get_bsz_cov();
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TMatrixD get_bsz_mu_invcov();
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double eff_paper(const double& q2, const double& ctl, const double& ctk, const double& phi);
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double get_sliding_error(double xmeas, double xth, double eup, double edown);
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double crystalball(double m, double mean, double sigma, double alpha, double n);
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double twotailedcrystalball(double m, double mean, double sigma, double alpha1, double alpha2, double n1, double n2);
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//blinding
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double evaluate_unblind_uniform(double valueSeenByAnalist, const char* blindingString, double scale);
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double evaluate_unblind_uniform_angle(double valueSeenByAnalist, const char* blindingString, double scale);
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double sqr(double x);
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//basic trigonometric functions
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double costheta2(double costheta);
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double cos2theta(double costheta);
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double sintheta2(double costheta);
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double sintheta_abs(double costheta);
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double sin2theta(double costheta);
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double chebyshev(double x, int n);
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void chebyshev(double x, int n, std::vector<double>& results);
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void chebyshev_to_poly(const std::vector<double>& chebychev, std::vector<double>& poly);
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void correct_poly(const std::vector<double>& poly, std::vector<double>& correct, double min, double max);
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double legendre(double x, int n);
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void legendre(double x, int n, std::vector<double>& results);
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void orthonormal_legendre(double x, int n, std::vector<double>& results);
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void legendre_to_poly(const std::vector<double>& legendre, std::vector<double>& poly);
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///calculates the associated legendre polynomial for l,m order
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double assoc_legendre(unsigned int l, unsigned int m, double x);
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///calculates the real part of the spherical harmonics for l, m
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double spherical_harmonic_re(unsigned int l, unsigned int m, double theta, double phi);
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///calculates the imaginary part of the spherical harmonics for l, m
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double spherical_harmonic_im(unsigned int l, unsigned int m, double theta, double phi);
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///function calculates the angles in the transversity base using the momenta of the final state particles
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void calculate_transversity_angles(const LorentzVector& mu_minus,
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const LorentzVector& mu_plus,
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const LorentzVector& k_minus,
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const LorentzVector& k_plus,
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double & cos_theta, double & angle_phi, double & cos_psi);
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///this function calculates the convolution sin(angle) from 0 to pi
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double convoluted_sin(double angle, double sigma);
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double convoluted_cos_sin(double angle, double sigma);
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double convoluted_cos(double angle, double sigma);//not used
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double convoluted_cos_2(double angle, double sigma);//not used
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double convoluted_sin_2(double angle, double sigma);//used by s wave
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double convoluted_2_sin(double angle, double sigma);//used by s wave
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double convoluted_2_cos(double angle, double sigma);//not used
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double convoluted_cos_2_sin(double angle, double sigma);
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double convoluted_2_sin_sin(double angle, double sigma);
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double convoluted_sin_3(double angle, double sigma);
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//this integrates the above expressions (vonvolution before has been from 0 to pi
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double int_convoluted_sin(double angle, double sigma);
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double int_convoluted_cos_sin(double angle, double sigma);
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double int_convoluted_cos_2_sin(double angle, double sigma);
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double int_convoluted_2_sin_sin(double angle, double sigma);
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double int_convoluted_sin_3(double angle, double sigma);
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double int_convoluted_sin_2(double angle, double sigma);//used by s wave
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double int_convoluted_2_sin(double angle, double sigma);//used by s wave
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//convolutions for phi. this is easier due to the wraparound at +-pi -> convolution from -int to inf
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double inf_convoluted_sin(double angle, double sigma);
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double inf_convoluted_cos(double angle, double sigma);
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double inf_convoluted_cos_2(double angle, double sigma);
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double inf_convoluted_sin_2(double angle, double sigma);
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double inf_convoluted_2_sin(double angle, double sigma);
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//integral of above
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double int_inf_convoluted_const(double angle, double sigma);
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double int_inf_convoluted_sin(double angle, double sigma);
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double int_inf_convoluted_cos(double angle, double sigma);
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double int_inf_convoluted_cos_2(double angle, double sigma);
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double int_inf_convoluted_sin_2(double angle, double sigma);
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double int_inf_convoluted_2_sin(double angle, double sigma);
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//integrals from -inf to inf over the convolution from 0 to pi with acceptance
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double int_convoluted_sin_cos_n(int n, double sigma);
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double int_convoluted_sin_3_cos_n(int n, double sigma);
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double int_convoluted_cos_2_sin_cos_n(int n, double sigma);
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double int_convoluted_2_sin_sin_cos_n(int n, double sigma);
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double int_convoluted_cos_sin_cos_n(int n, double sigma);
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double int_convoluted_sin_2_cos_n(int n, double sigma);
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//integrals from 0 to pi over the convolution from -inf to inf with acceptance
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double int_inf_convoluted_const_x_n(int n, double sigma);
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double int_inf_convoluted_cos_2_x_n(int n, double sigma);
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double int_inf_convoluted_sin_2_x_n(int n, double sigma);
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double int_inf_convoluted_sin_x_n(int n, double sigma);
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double int_inf_convoluted_2_sin_x_n(int n, double sigma);
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double int_inf_convoluted_cos_x_n(int n, double sigma);
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///function gives the result of exp(-ct/tau)*sin(delta_m*ct) and exp(-ct/tau)*cos(delta_m*ct) convoluted with a gaussian with width sigma
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void convoluted_exp_sincos(double ct, double sigma, double tau, double deltam, double& one, double& two);
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///function gives the norm of the expression exp(-ct/tau)*sin(delta_m*ct) and exp(-ct/tau)*cos(delta_m*ct) convoluted with a gaussian with width sigma
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void norm_convoluted_exp_sincos(double tau, double deltam, double& one, double& two);
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///function calculates exp(-ct/tau) convoluted with a gaussian with width sigma
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double convoluted_exp(double ct, double sigma_ct, double S);
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///function calculates exp(-ct/tau) depending on the parameters normalized or not
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double expdecay(double t, double tau, bool normalized);
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///function calculates 1/(sqrt(2*pi)*exp(-(x-mean)^2/(2*sigma^2)))
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double gauss(double x, double sigma, double mean);
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///function calculates a normed gaussian between the values min and max used in the mass pdfs
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double normed_gauss(double x, double sigma, double mean, double min, double max);
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///integrate gauss from a to b
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double linear(double x, double min, double max, double slope);
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///very important helper function, the error function with complex argument. This is probably one of the performance bottlenecks. Probably much faster with a lookup table and interpolation
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double threshold(double x, double thr, double n);
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double int_threshold(double a, double b, double thr, double n);
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//see arxiv 1207.4004
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/*
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std::complex<double> bw_kstar_amp(double mkpi_squared, double gammakstar, double mkstar);
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std::complex<double> bw_kstarzero_amp(double mkpisquared, double gk_re, double gk_im, double gammak, double mk, double gammakstarzero, double mkstarzero);
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double bw_kstar_amp_squared(double mkpisquared, double gammakstar, double mkstar);
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std::complex<double> bw_kstar_amp_kstarzero_amp_bar(double mkpisquared, double gammakstar, double mkstar, double gk_re, double gk_im, double gammak, double mk, double gammakstarzero, double mkstarzero);
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double bw_kstarzero_amp_squared(double mkpisquared, double gk_re, double gk_im, double gammak, double mk, double gammakstarzero, double mkstarzero);
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*/
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double daughtermom(double m, double m1, double m2);
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std::complex<double> mkpi_simple_bw_kstar_amp(double mkpi, double qsquared, double gammakstar, double mkstar);
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double mkpi_simple_bw_kstar_amp_squared(double mkpi, double qsquared, double gammakstar, double mkstar);
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double gsl_mkpi_simple_bw_kstar_amp_squared(double x, void* par);
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double int_mkpi_simple_bw_kstar_amp_squared(const double& mkpia, const double& mkpib, const double& qsquared, const double& gammakstar, const double& mkstar);
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std::complex<double> mkpi_simple_kstarzero_amp(double mkpi, double qsquared, double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero);
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double mkpi_simple_kstarzero_amp_squared(double mkpi, double qsquared, double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero);
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double gsl_mkpi_simple_kstarzero_amp_squared(double x, void* par);
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double int_mkpi_simple_kstarzero_amp_squared(const double& mkpia, const double& mkpib, const double& qsquared, const double& f800mag, const double& f800phase, const double& gammaf800, const double& mf800, const double& gammakstarzero, const double& mkstarzero);
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std::complex<double> mkpi_simple_bw_kstar_amp_kstarzero_amp_bar(double mkpi, double qsquared,
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double gammakstar, double mkstar, double asphase,
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double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero);
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std::complex<double> mkpi_simple_bw_kstar_amp_bar_kstarzero_amp(double mkpi, double qsquared,
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double gammakstar, double mkstar, double asphase,
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double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero);
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std::complex<double> int_mkpi_simple_bw_kstar_amp_kstarzero_amp_bar(const double& mkpia, const double& mkpib, const double& qsquared,
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const double& gammakstar, const double& mkstar, const double& asphase,
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const double& f800mag, const double& f800phase, const double& gammaf800, const double& mf800, const double& gammakstarzero, const double& mkstarzero);
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std::complex<double> int_mkpi_simple_bw_kstar_amp_bar_kstarzero_amp(const double& mkpia, const double& mkpib, const double& qsquared,
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const double& gammakstar, const double& mkstar, const double& asphase,
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const double& f800mag, const double& f800phase, const double& gammaf800, const double& mf800, const double& gammakstarzero, const double& mkstarzero);
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double gsl_mkpi_simple_re_bw_kstar_amp_kstarzero_amp_bar(double x, void* par);
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double gsl_mkpi_simple_im_bw_kstar_amp_kstarzero_amp_bar(double x, void* par);
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double gsl_mkpi_simple_re_bw_kstar_amp_bar_kstarzero_amp(double x, void* par);
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double gsl_mkpi_simple_im_bw_kstar_amp_bar_kstarzero_amp(double x, void* par);
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std::complex<double> mkpi_bw_kstar_amp(double mkpi, double qsquared, double gammakstar, double mkstar, double R);
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std::complex<double> mkpi_kstarzero_lass_amp(double mkpi, double qsquared, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> mkpi_bw_kstar_amp_kstarzero_lass_amp_bar(double mkpi, double qsquared, double gammakstar, double mkstar, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> mkpi_bw_kstar_amp_bar_kstarzero_lass_amp(double mkpi, double qsquared, double gammakstar, double mkstar, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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double mkpi_bw_kstar_amp_squared(double mkpi, double qsquared, double gammakstar, double mkstar, double R);
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double mkpi_kstarzero_lass_amp_squared(double mkpi, double qsquared, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> mkpi_kstarzero_isobar_amp(double mkpi, double qsquared, double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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double mkpi_kstarzero_isobar_amp_squared(double mkpi, double qsquared, double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> mkpi_bw_kstar_amp_kstarzero_isobar_amp_bar(double mkpi, double qsquared,
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double gammakstar, double mkstar, double asphase,
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double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> mkpi_bw_kstar_amp_bar_kstarzero_isobar_amp(double mkpi, double qsquared,
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double gammakstar, double mkstar, double asphase,
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double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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double gsl_mkpi_kstarzero_isobar_amp_squared(double x, void* par);
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double gsl_mkpi_re_bw_kstar_amp_kstarzero_isobar_amp_bar(double x, void* par);
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double gsl_mkpi_im_bw_kstar_amp_kstarzero_isobar_amp_bar(double x, void* par);
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double gsl_mkpi_re_bw_kstar_amp_bar_kstarzero_isobar_amp(double x, void* par);
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double gsl_mkpi_im_bw_kstar_amp_bar_kstarzero_isobar_amp(double x, void* par);
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double gsl_mkpi_bw_kstar_amp_squared(double x, void* par);
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double gsl_mkpi_kstarzero_lass_amp_squared(double x, void* par);
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double gsl_mkpi_re_bw_kstar_amp_kstarzero_lass_amp_bar(double x, void* par);
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double gsl_mkpi_im_bw_kstar_amp_kstarzero_lass_amp_bar(double x, void* par);
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double gsl_mkpi_re_bw_kstar_amp_bar_kstarzero_lass_amp(double x, void* par);
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double gsl_mkpi_im_bw_kstar_amp_bar_kstarzero_lass_amp(double x, void* par);
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double int_mkpi_bw_kstar_amp_squared(double mkpia, double mkpib, double qsquared, double gammakstar, double mkstar, double R);
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double int_mkpi_bw_kstar_amp_squared(double qsquared, double gammakstar, double mkstar, double R);
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double int_mkpi_kstarzero_lass_amp_squared(double mkpia, double mkpib, double qsquared, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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double int_mkpi_kstarzero_lass_amp_squared(double qsquared, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> int_mkpi_bw_kstar_amp_kstarzero_lass_amp_bar(double mkpia, double mkpib, double qsquared, double gammakstar, double mkstar, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> int_mkpi_bw_kstar_amp_bar_kstarzero_lass_amp(double mkpia, double mkpib, double qsquared, double gammakstar, double mkstar, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> int_mkpi_bw_kstar_amp_kstarzero_lass_amp_bar(double qsquared, double gammakstar, double mkstar, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> int_mkpi_bw_kstar_amp_bar_kstarzero_lass_amp(double qsquared, double gammakstar, double mkstar, double asphase, double a, double r, double gammakstarzero, double mkstarzero, double R);
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double int_mkpi_kstarzero_isobar_amp_squared(double mkpia, double mkpib, double qsquared, double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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double int_mkpi_kstarzero_isobar_amp_squared(double qsquared, double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> int_mkpi_bw_kstar_amp_kstarzero_isobar_amp_bar(double mkpia, double mkpib, double qsquared,
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double gammakstar, double mkstar, double asphase,
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double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> int_mkpi_bw_kstar_amp_bar_kstarzero_isobar_amp(double mkpia, double mkpib, double qsquared,
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double gammakstar, double mkstar, double asphase,
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double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> int_mkpi_bw_kstar_amp_kstarzero_isobar_amp_bar(double qsquared,
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double gammakstar, double mkstar, double asphase,
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double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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std::complex<double> int_mkpi_bw_kstar_amp_bar_kstarzero_isobar_amp(double qsquared,
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double gammakstar, double mkstar, double asphase,
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double f800mag, double f800phase, double gammaf800, double mf800, double gammakstarzero, double mkstarzero, double R);
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double rndgauss(TRandom3* rnd, double mean, double width, double min, double max);
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double rndgauss(TRandom3* rnd, double mean, double widthlo, double widthhi, double min, double max);
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void moments_to_observables(TRandom3* rnd,
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std::vector<double> mom,
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std::vector<double> momcov,
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double fsext,
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double dfsext,
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std::vector<double>& obs,
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std::vector<double>& obscov,
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bool usefsext = true
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);
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template<class T> struct NumberGreaterThan
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{
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bool operator()(const T a, const T b) const
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{ return std::abs(a) > std::abs(b); }
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};
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template<typename iterator> typename iterator::value_type add_numbers(iterator begin, iterator end){
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typedef typename iterator::value_type T;
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if (end == begin) return 0.;
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std::make_heap(begin, end, NumberGreaterThan<T>());
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for (; begin + 1 < end; ) {
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T x = *begin;
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std::pop_heap(begin, end--, NumberGreaterThan<T>());
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do {
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x += *begin;
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std::pop_heap(begin, end--, NumberGreaterThan<T>());
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} while (std::abs(*begin) >= std::abs(x) && begin < end);
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*end++ = x;
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std::push_heap(begin, end, NumberGreaterThan<T>());
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}
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return *begin;
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};
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std::vector<UInt_t>GetNOutOfM(UInt_t N, UInt_t M, Int_t Seed, bool DoubleCounts, bool PoissonFluctuate);
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template<typename iterator> typename iterator::value_type add_numbers(iterator begin, iterator end);
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int throw_multivariate_normal(const unsigned int ndim, const unsigned int ntoys, const std::vector<double>& xi, const std::vector<double>& cov, std::vector<std::vector<double> >& results);
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int get_mean_cov(const std::vector<std::vector<double> >& meas, std::vector<double>& mean, std::vector<double>& cov);
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void sis_to_pis(TRandom3* rnd,
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std::vector<double> sis,
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std::vector<double> sicorrs,
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std::vector<double>& pis,
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std::vector<double>& picorrs);
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std::complex<double> cErrF(const std::complex<double>& x);
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///implementation 2 of the complex error function
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std::complex<double> cErrF_2(const std::complex<double>& x);
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std::complex<double> ErrF_2(const std::complex<double>& x);
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///implementation 3 of the complex error function
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std::complex<double> cErrF_3(const std::complex<double>& x);
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///the faddeeva function function
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std::complex<double> Faddeeva_2 (const std::complex<double>& z);
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///used by cErrF, does the actual calculations
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std::complex<double> wErrF(const std::complex<double>& arg);
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///This is another version of the complex error function, used in the newer cdf code
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std::complex<double> nwwerf(const std::complex<double> z);
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}
|
|
|
|
#endif
|