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PESA::T2TrackBSLLPoly Class Reference

Class that knows details of LogLikelihood approximation with a polynomial. More...

#include <T2TrackBSLLPoly.h>

Collaboration diagram for PESA::T2TrackBSLLPoly:

Public Member Functions

 T2TrackBSLLPoly (double beam_size)
void update (double z0, double d0, double phi0, double d0_var, std::vector< double > &coeff)
 Update polynomial coefficients with track data.

Private Attributes

double m_beam_size {}

Detailed Description

Class that knows details of LogLikelihood approximation with a polynomial.

Few particular things that this class handles:

  • calculation of the index of monomial (polynomial term) in the monitored array and the resulting histogram bin, the index is determined by the combination of powers of the variables.
  • calculation of the coefficients of the polynomial from track parameters.

The approximation of the LL function looks like (factorized):

LL = - (d_0 + B_x*sin(phi) - B_y*cos(phi) + t_x*z_0*sin(phi)

  • t_y*z_0*cos(phi))**2/(2*Sigma) * (1-S_prime/Sigma + (S_prime/Sigma)**2)

(ln(Sigma) + S_prime/Sigma - (S_prime/Sigma)**2/2)/2 var_b = beam_size**2 Sigma = var_d0 + var_b S_prime = omega_x*sin(phi)**2 + omega_y*cos(phi)**2

The variables here are (B_x, B_y, t_x, t_y, omega_x, omega_y), the rest are either track parameters or constants. beam_size is a constant which should be close to actual transverse beam size (typically 0.01 mm). In the expanded representation the polynomial terms have these possible combinations of powers of omega:

omega_x**2, omega_y**2, omega_x*omega_y, omega_x, omega_y, 1

with total of 6 variants and they don't depend on other variables. Four other variables can appear in the polynomial terms in these combinations:

  • squared, by itself, without any of other three variables (4)
  • product with one other variable (4*3/2)
  • by itself (4)
  • zero power of any variable (1)

Together with 6 omega combinations this gives (4+4*3/2+4+1)*6 = 90 monomials.

In addition to the 90 coefficients we also store other information in the monitored variables:

  • number of tracks
  • number of tracks multiplied by beam_size

Definition at line 58 of file T2TrackBSLLPoly.h.

Constructor & Destructor Documentation

◆ T2TrackBSLLPoly()

PESA::T2TrackBSLLPoly::T2TrackBSLLPoly ( double beam_size)
inlineexplicit

Definition at line 61 of file T2TrackBSLLPoly.h.

61: m_beam_size(beam_size) {}

Member Function Documentation

◆ update()

void T2TrackBSLLPoly::update ( double z0,
double d0,
double phi0,
double d0_var,
std::vector< double > & coeff )

Update polynomial coefficients with track data.

If vector is empty it is resized to have nbins() size, otherwise it has to be at least nbins() elements in size.

Definition at line 18 of file T2TrackBSLLPoly.cxx.

19{
20 if (coeff.empty()) {
21 coeff.resize(nbins, 0.);
22 }
23
24 double cos_phi = std::cos(phi);
25 double sin_phi = std::sin(phi);
26 double var_b = m_beam_size*m_beam_size;
27 double var_bd = var_d0 + var_b;
28 double pow_cos_phi[7]{};
29 double pow_sin_phi[7]{};
30 double pow_var_bd[4]{};
31 for (size_t i=2; i<7; ++i) {
32 pow_cos_phi[i] = std::pow(cos_phi, i);
33 pow_sin_phi[i] = std::pow(sin_phi, i);
34 }
35 for (size_t i=2; i<4; ++i) {
36 pow_var_bd[i] = std::pow(var_bd, i);
37 }
38 double pow2_d0 = std::pow(d0, 2);
39 double pow2_z0 = std::pow(z0, 2);
40
41 // z0 and its square
42 coeff[g_size*g_size2] += z0;
43 coeff[g_size*g_size2+1] += pow2_z0;
44
45 // store number of tracks and beam_size*n_tracks in last two bins
46 coeff[g_size*g_size2+2] += 1;
47 coeff[g_size*g_size2+3] += m_beam_size;
48
49 coeff[idx<0, 0, 0, 0, 0, 0>()] += -pow2_d0/(2*var_bd);
50 coeff[idx<0, 0, 0, 0, 0, 1>()] += pow_cos_phi[2]*pow2_d0/(2*pow_var_bd[2]);
51 coeff[idx<0, 0, 0, 0, 0, 2>()] += -pow_cos_phi[4]*pow2_d0/(2*pow_var_bd[3]);
52 coeff[idx<0, 0, 0, 0, 1, 0>()] += pow2_d0*pow_sin_phi[2]/(2*pow_var_bd[2]);
53 coeff[idx<0, 0, 0, 0, 1, 1>()] += -pow_cos_phi[2]*pow2_d0*pow_sin_phi[2]/pow_var_bd[3];
54 coeff[idx<0, 0, 0, 0, 2, 0>()] += -pow2_d0*pow_sin_phi[4]/(2*pow_var_bd[3]);
55 coeff[idx<0, 0, 0, 1, 0, 0>()] += cos_phi*d0*z0/var_bd;
56 coeff[idx<0, 0, 0, 1, 0, 1>()] += -pow_cos_phi[3]*d0*z0/pow_var_bd[2];
57 coeff[idx<0, 0, 0, 1, 0, 2>()] += pow_cos_phi[5]*d0*z0/pow_var_bd[3];
58 coeff[idx<0, 0, 0, 1, 1, 0>()] += -cos_phi*d0*pow_sin_phi[2]*z0/pow_var_bd[2];
59 coeff[idx<0, 0, 0, 1, 1, 1>()] += 2*pow_cos_phi[3]*d0*pow_sin_phi[2]*z0/pow_var_bd[3];
60 coeff[idx<0, 0, 0, 1, 2, 0>()] += cos_phi*d0*pow_sin_phi[4]*z0/pow_var_bd[3];
61 coeff[idx<0, 0, 0, 2, 0, 0>()] += -pow_cos_phi[2]*pow2_z0/(2*var_bd);
62 coeff[idx<0, 0, 0, 2, 0, 1>()] += pow_cos_phi[4]*pow2_z0/(2*pow_var_bd[2]);
63 coeff[idx<0, 0, 0, 2, 0, 2>()] += -pow_cos_phi[6]*pow2_z0/(2*pow_var_bd[3]);
64 coeff[idx<0, 0, 0, 2, 1, 0>()] += pow_cos_phi[2]*pow_sin_phi[2]*pow2_z0/(2*pow_var_bd[2]);
65 coeff[idx<0, 0, 0, 2, 1, 1>()] += -pow_cos_phi[4]*pow_sin_phi[2]*pow2_z0/pow_var_bd[3];
66 coeff[idx<0, 0, 0, 2, 2, 0>()] += -pow_cos_phi[2]*pow_sin_phi[4]*pow2_z0/(2*pow_var_bd[3]);
67 coeff[idx<0, 0, 1, 0, 0, 0>()] += -d0*sin_phi*z0/var_bd;
68 coeff[idx<0, 0, 1, 0, 0, 1>()] += pow_cos_phi[2]*d0*sin_phi*z0/pow_var_bd[2];
69 coeff[idx<0, 0, 1, 0, 0, 2>()] += -pow_cos_phi[4]*d0*sin_phi*z0/pow_var_bd[3];
70 coeff[idx<0, 0, 1, 0, 1, 0>()] += d0*pow_sin_phi[3]*z0/pow_var_bd[2];
71 coeff[idx<0, 0, 1, 0, 1, 1>()] += -2*pow_cos_phi[2]*d0*pow_sin_phi[3]*z0/pow_var_bd[3];
72 coeff[idx<0, 0, 1, 0, 2, 0>()] += -d0*pow_sin_phi[5]*z0/pow_var_bd[3];
73 coeff[idx<0, 0, 1, 1, 0, 0>()] += cos_phi*sin_phi*pow2_z0/var_bd;
74 coeff[idx<0, 0, 1, 1, 0, 1>()] += -pow_cos_phi[3]*sin_phi*pow2_z0/pow_var_bd[2];
75 coeff[idx<0, 0, 1, 1, 0, 2>()] += pow_cos_phi[5]*sin_phi*pow2_z0/pow_var_bd[3];
76 coeff[idx<0, 0, 1, 1, 1, 0>()] += -cos_phi*pow_sin_phi[3]*pow2_z0/pow_var_bd[2];
77 coeff[idx<0, 0, 1, 1, 1, 1>()] += 2*pow_cos_phi[3]*pow_sin_phi[3]*pow2_z0/pow_var_bd[3];
78 coeff[idx<0, 0, 1, 1, 2, 0>()] += cos_phi*pow_sin_phi[5]*pow2_z0/pow_var_bd[3];
79 coeff[idx<0, 0, 2, 0, 0, 0>()] += -pow_sin_phi[2]*pow2_z0/(2*var_bd);
80 coeff[idx<0, 0, 2, 0, 0, 1>()] += pow_cos_phi[2]*pow_sin_phi[2]*pow2_z0/(2*pow_var_bd[2]);
81 coeff[idx<0, 0, 2, 0, 0, 2>()] += -pow_cos_phi[4]*pow_sin_phi[2]*pow2_z0/(2*pow_var_bd[3]);
82 coeff[idx<0, 0, 2, 0, 1, 0>()] += pow_sin_phi[4]*pow2_z0/(2*pow_var_bd[2]);
83 coeff[idx<0, 0, 2, 0, 1, 1>()] += -pow_cos_phi[2]*pow_sin_phi[4]*pow2_z0/pow_var_bd[3];
84 coeff[idx<0, 0, 2, 0, 2, 0>()] += -pow_sin_phi[6]*pow2_z0/(2*pow_var_bd[3]);
85 coeff[idx<0, 1, 0, 0, 0, 0>()] += cos_phi*d0/var_bd;
86 coeff[idx<0, 1, 0, 0, 0, 1>()] += -pow_cos_phi[3]*d0/pow_var_bd[2];
87 coeff[idx<0, 1, 0, 0, 0, 2>()] += pow_cos_phi[5]*d0/pow_var_bd[3];
88 coeff[idx<0, 1, 0, 0, 1, 0>()] += -cos_phi*d0*pow_sin_phi[2]/pow_var_bd[2];
89 coeff[idx<0, 1, 0, 0, 1, 1>()] += 2*pow_cos_phi[3]*d0*pow_sin_phi[2]/pow_var_bd[3];
90 coeff[idx<0, 1, 0, 0, 2, 0>()] += cos_phi*d0*pow_sin_phi[4]/pow_var_bd[3];
91 coeff[idx<0, 1, 0, 1, 0, 0>()] += -pow_cos_phi[2]*z0/var_bd;
92 coeff[idx<0, 1, 0, 1, 0, 1>()] += pow_cos_phi[4]*z0/pow_var_bd[2];
93 coeff[idx<0, 1, 0, 1, 0, 2>()] += -pow_cos_phi[6]*z0/pow_var_bd[3];
94 coeff[idx<0, 1, 0, 1, 1, 0>()] += pow_cos_phi[2]*pow_sin_phi[2]*z0/pow_var_bd[2];
95 coeff[idx<0, 1, 0, 1, 1, 1>()] += -2*pow_cos_phi[4]*pow_sin_phi[2]*z0/pow_var_bd[3];
96 coeff[idx<0, 1, 0, 1, 2, 0>()] += -pow_cos_phi[2]*pow_sin_phi[4]*z0/pow_var_bd[3];
97 coeff[idx<0, 1, 1, 0, 0, 0>()] += cos_phi*sin_phi*z0/var_bd;
98 coeff[idx<0, 1, 1, 0, 0, 1>()] += -pow_cos_phi[3]*sin_phi*z0/pow_var_bd[2];
99 coeff[idx<0, 1, 1, 0, 0, 2>()] += pow_cos_phi[5]*sin_phi*z0/pow_var_bd[3];
100 coeff[idx<0, 1, 1, 0, 1, 0>()] += -cos_phi*pow_sin_phi[3]*z0/pow_var_bd[2];
101 coeff[idx<0, 1, 1, 0, 1, 1>()] += 2*pow_cos_phi[3]*pow_sin_phi[3]*z0/pow_var_bd[3];
102 coeff[idx<0, 1, 1, 0, 2, 0>()] += cos_phi*pow_sin_phi[5]*z0/pow_var_bd[3];
103 coeff[idx<0, 2, 0, 0, 0, 0>()] += -pow_cos_phi[2]/(2*var_bd);
104 coeff[idx<0, 2, 0, 0, 0, 1>()] += pow_cos_phi[4]/(2*pow_var_bd[2]);
105 coeff[idx<0, 2, 0, 0, 0, 2>()] += -pow_cos_phi[6]/(2*pow_var_bd[3]);
106 coeff[idx<0, 2, 0, 0, 1, 0>()] += pow_cos_phi[2]*pow_sin_phi[2]/(2*pow_var_bd[2]);
107 coeff[idx<0, 2, 0, 0, 1, 1>()] += -pow_cos_phi[4]*pow_sin_phi[2]/pow_var_bd[3];
108 coeff[idx<0, 2, 0, 0, 2, 0>()] += -pow_cos_phi[2]*pow_sin_phi[4]/(2*pow_var_bd[3]);
109 coeff[idx<1, 0, 0, 0, 0, 0>()] += -d0*sin_phi/var_bd;
110 coeff[idx<1, 0, 0, 0, 0, 1>()] += pow_cos_phi[2]*d0*sin_phi/pow_var_bd[2];
111 coeff[idx<1, 0, 0, 0, 0, 2>()] += -pow_cos_phi[4]*d0*sin_phi/pow_var_bd[3];
112 coeff[idx<1, 0, 0, 0, 1, 0>()] += d0*pow_sin_phi[3]/pow_var_bd[2];
113 coeff[idx<1, 0, 0, 0, 1, 1>()] += -2*pow_cos_phi[2]*d0*pow_sin_phi[3]/pow_var_bd[3];
114 coeff[idx<1, 0, 0, 0, 2, 0>()] += -d0*pow_sin_phi[5]/pow_var_bd[3];
115 coeff[idx<1, 0, 0, 1, 0, 0>()] += cos_phi*sin_phi*z0/var_bd;
116 coeff[idx<1, 0, 0, 1, 0, 1>()] += -pow_cos_phi[3]*sin_phi*z0/pow_var_bd[2];
117 coeff[idx<1, 0, 0, 1, 0, 2>()] += pow_cos_phi[5]*sin_phi*z0/pow_var_bd[3];
118 coeff[idx<1, 0, 0, 1, 1, 0>()] += -cos_phi*pow_sin_phi[3]*z0/pow_var_bd[2];
119 coeff[idx<1, 0, 0, 1, 1, 1>()] += 2*pow_cos_phi[3]*pow_sin_phi[3]*z0/pow_var_bd[3];
120 coeff[idx<1, 0, 0, 1, 2, 0>()] += cos_phi*pow_sin_phi[5]*z0/pow_var_bd[3];
121 coeff[idx<1, 0, 1, 0, 0, 0>()] += -pow_sin_phi[2]*z0/var_bd;
122 coeff[idx<1, 0, 1, 0, 0, 1>()] += pow_cos_phi[2]*pow_sin_phi[2]*z0/pow_var_bd[2];
123 coeff[idx<1, 0, 1, 0, 0, 2>()] += -pow_cos_phi[4]*pow_sin_phi[2]*z0/pow_var_bd[3];
124 coeff[idx<1, 0, 1, 0, 1, 0>()] += pow_sin_phi[4]*z0/pow_var_bd[2];
125 coeff[idx<1, 0, 1, 0, 1, 1>()] += -2*pow_cos_phi[2]*pow_sin_phi[4]*z0/pow_var_bd[3];
126 coeff[idx<1, 0, 1, 0, 2, 0>()] += -pow_sin_phi[6]*z0/pow_var_bd[3];
127 coeff[idx<1, 1, 0, 0, 0, 0>()] += cos_phi*sin_phi/var_bd;
128 coeff[idx<1, 1, 0, 0, 0, 1>()] += -pow_cos_phi[3]*sin_phi/pow_var_bd[2];
129 coeff[idx<1, 1, 0, 0, 0, 2>()] += pow_cos_phi[5]*sin_phi/pow_var_bd[3];
130 coeff[idx<1, 1, 0, 0, 1, 0>()] += -cos_phi*pow_sin_phi[3]/pow_var_bd[2];
131 coeff[idx<1, 1, 0, 0, 1, 1>()] += 2*pow_cos_phi[3]*pow_sin_phi[3]/pow_var_bd[3];
132 coeff[idx<1, 1, 0, 0, 2, 0>()] += cos_phi*pow_sin_phi[5]/pow_var_bd[3];
133 coeff[idx<2, 0, 0, 0, 0, 0>()] += -pow_sin_phi[2]/(2*var_bd);
134 coeff[idx<2, 0, 0, 0, 0, 1>()] += pow_cos_phi[2]*pow_sin_phi[2]/(2*pow_var_bd[2]);
135 coeff[idx<2, 0, 0, 0, 0, 2>()] += -pow_cos_phi[4]*pow_sin_phi[2]/(2*pow_var_bd[3]);
136 coeff[idx<2, 0, 0, 0, 1, 0>()] += pow_sin_phi[4]/(2*pow_var_bd[2]);
137 coeff[idx<2, 0, 0, 0, 1, 1>()] += -pow_cos_phi[2]*pow_sin_phi[4]/pow_var_bd[3];
138 coeff[idx<2, 0, 0, 0, 2, 0>()] += -pow_sin_phi[6]/(2*pow_var_bd[3]);
139 coeff[idx<0, 0, 0, 0, 0, 0>() +90] += -std::log(var_bd)/2;
140 coeff[idx<0, 0, 0, 0, 0, 1>() +90] += -pow_cos_phi[2]/(2*var_bd);
141 coeff[idx<0, 0, 0, 0, 0, 2>() +90] += pow_cos_phi[4]/(4*pow_var_bd[2]);
142 coeff[idx<0, 0, 0, 0, 1, 0>() +90] += -pow_sin_phi[2]/(2*var_bd);
143 coeff[idx<0, 0, 0, 0, 1, 1>() +90] += pow_cos_phi[2]*pow_sin_phi[2]/(2*pow_var_bd[2]);
144 coeff[idx<0, 0, 0, 0, 2, 0>() +90] += pow_sin_phi[4]/(4*pow_var_bd[2]);
145}
phi
Scalar phi() const
phi method
Definition AmgMatrixBasePlugin.h:67
PESA::g_size
constexpr unsigned g_size
Definition idx.h:60
PESA::nbins
constexpr unsigned nbins
Definition idx.h:73
PESA::idx
consteval int idx()
Definition idx.h:85
PESA::g_size2
constexpr unsigned g_size2
Definition idx.h:71

Member Data Documentation

◆ m_beam_size

double PESA::T2TrackBSLLPoly::m_beam_size {}
private

Definition at line 74 of file T2TrackBSLLPoly.h.

74{};
The documentation for this class was generated from the following files:
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