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Public Types | Public Member Functions | Static Public Member Functions | Public Attributes | Static Public Attributes | List of all members
JFIT::JEstimator< JLine1Z > Class Reference

Linear fit of straight line parallel to z-axis to set of hits (objects with position and time). More...

#include <JLine1ZEstimator.hh>

Inheritance diagram for JFIT::JEstimator< JLine1Z >:
JFIT::JLine1Z

Public Types

typedef double JLine1Z::* parameter_type
 

Public Member Functions

 JEstimator ()
 Default constructor.
 
template<class T >
 JEstimator (T __begin, T __end)
 Constructor.
 
template<class T >
const JEstimator< JLine1Z > & operator() (T __begin, T __end)
 Fit.
 
template<class T >
void update (T __begin, T __end, const JMatrixNZ &A)
 Update track parameters using updated co-variance matrix (e.g. matrix with one hit switched off).
 
void move (const double step, const double velocity)
 Move vertex along this line with given velocity.
 
void setZ (const double z, const double velocity)
 Set z-position of vertex.
 
double getDistanceSquared (const JVector3D &pos) const
 Get distance squared.
 
double getDistance (const JVector3D &pos) const
 Get distance.
 
double getT (const JVector3D &pos) const
 Get arrival time of Cherenkov light at given position.
 
double getZ (const JPosition3D &pos) const
 Get point of emission of Cherenkov light along muon path.
 
JVersor3D getDirection (const JVector3D &pos) const
 Get photon direction of Cherenkov light on PMT.
 
double getDot (const JAxis3D &axis) const
 Get cosine angle of impact of Cherenkov light on PMT.
 

Static Public Member Functions

static parameter_type pX ()
 
static parameter_type pY ()
 
static parameter_type pT ()
 

Public Attributes

JMATH::JMatrix3S V
 co-variance matrix of fit parameters
 
JMATH::JSVD3D svd
 

Static Public Attributes

static const int NUMBER_OF_PARAMETERS = 3
 number of parameters of fit
 
static double MINIMAL_SVD_WEIGHT = 1.0e-4
 minimal SVD weight.
 

Detailed Description

Linear fit of straight line parallel to z-axis to set of hits (objects with position and time).

\begin{center}\setlength{\unitlength}{0.7cm}\begin{picture}(8,12) \put( 1.0, 0.5){\vector(0,1){9}} \put( 1.0,10.0){\makebox(0,0){$z$}} \put( 1.0, 0.0){\makebox(0,0){muon}} \put( 1.0, 8.0){\line(1,0){6}} \put( 4.0, 8.5){\makebox(0,0)[c]{$R$}} \multiput( 1.0, 2.0)(0.5, 0.5){12}{\qbezier(0.0,0.0)(-0.1,0.35)(0.25,0.25)\qbezier(0.25,0.25)(0.6,0.15)(0.5,0.5)} \put( 4.5, 4.5){\makebox(0,0)[l]{photon}} \put( 1.0, 2.0){\circle*{0.2}} \put( 0.5, 2.0){\makebox(0,0)[r]{$(x_{0},y_{0},z_{0},t_{0})$}} \put( 1.0, 8.0){\circle*{0.2}} \put( 0.5, 8.0){\makebox(0,0)[r]{$(x_{0},y_{0},z_{j})$}} \put( 7.0, 8.0){\circle*{0.2}} \put( 7.0, 9.0){\makebox(0,0)[c]{PMT}} \put( 7.5, 8.0){\makebox(0,0)[l]{$(x_{j},y_{j},z_{j},t_{j})$}} \put( 1.1, 2.1){ \put(0.0,1.00){\vector(-1,0){0.1}} \qbezier(0.0,1.0)(0.25,1.0)(0.5,0.75) \put(0.5,0.75){\vector(1,-1){0.1}} \put(0.4,1.5){\makebox(0,0){$\theta_{c}$}} } \end{picture} \end{center}

\[ ct_j = ct_0 + (z_j - z_0) + \tan(\theta_{c}) \sqrt((x_j - x_0)^2 + (y_j - y_0)^2) \]

where:

\begin{eqnarray*} x_0 & = & \textrm{x position of track (fit parameter)} \\ y_0 & = & \textrm{y position of track (fit parameter)} \\ z_0 & = & \textrm{z position of track} \\ t_0 & = & \textrm{time of track at } z = z_0 \textrm{ (fit parameter)} \\ \\ c & = & \textrm{speed of light in vacuum} \\ \theta_{c} & = & \textrm{Cherenkov angle} \\ \end{eqnarray*}

Defining:

\begin{eqnarray*} t_j' & \equiv & ct_j / \tan(\theta_{c}) - (z_j - z_0)/\tan(\theta_{c}) \\ t_0' & \equiv & ct_0 / \tan(\theta_{c}) \\ \end{eqnarray*}

\[ \Rightarrow (t_j' - t_0')^2 = (x_j - x_0)^2 + (y_j - y_0)^2 \]

The parameters $ \{x_0, y_0, t_0\} $ are estimated in the constructor of this class based on consecutive pairs of equations by which the quadratic terms in $ x_0 $, $ y_0 $ and $ t_0 $ are eliminated.

Definition at line 89 of file JLine1ZEstimator.hh.

Member Typedef Documentation

◆ parameter_type

typedef double JLine1Z::* JFIT::JLine1Z::parameter_type
inherited

Definition at line 178 of file JLine1Z.hh.

Constructor & Destructor Documentation

◆ JEstimator() [1/2]

JFIT::JEstimator< JLine1Z >::JEstimator ( )
inline

Default constructor.

Definition at line 96 of file JLine1ZEstimator.hh.

96 :
97 JLine1Z()
98 {}
JFIT::JLine1Z::JLine1Z
JLine1Z()
Default constructor.
Definition JLine1Z.hh:39

◆ JEstimator() [2/2]

template<class T >
JFIT::JEstimator< JLine1Z >::JEstimator ( T __begin,
T __end )
inline

Constructor.

Parameters
__beginbegin of data
__endend of data

Definition at line 108 of file JLine1ZEstimator.hh.

108 :
109 JLine1Z()
110 {
111 (*this)(__begin, __end);
112 }

Member Function Documentation

◆ operator()()

template<class T >
const JEstimator< JLine1Z > & JFIT::JEstimator< JLine1Z >::operator() ( T __begin,
T __end )
inline

Fit.

The template argument T refers to an iterator of a data structure which should have the following member methods:

  • double getX(); // [m]
  • double getY(); // [m]
  • double getZ(); // [m]
  • double getT(); // [ns]
Parameters
__beginbegin of data
__endend of data
Returns
this fit

Definition at line 129 of file JLine1ZEstimator.hh.

130 {
131 using namespace std;
132 using namespace JPP;
133
134 const int N = distance(__begin, __end);
135
136 if (N >= NUMBER_OF_PARAMETERS) {
137
138 __x = 0.0;
139 __y = 0.0;
140 __z = 0.0;
141 __t = 0.0;
142
143 double t0 = 0.0;
144
145 for (T i = __begin; i != __end; ++i) {
146 __x += i->getX();
147 __y += i->getY();
148 __z += i->getZ();
149 t0 += i->getT();
150 }
151
152 const double W = 1.0/N;
153
154 __x *= W;
155 __y *= W;
156 __z *= W;
157 t0 *= W;
158
159 V.reset();
160
161 t0 *= getSpeedOfLight();
162
163 double y0 = 0.0;
164 double y1 = 0.0;
165 double y2 = 0.0;
166
167 T j = __begin;
168
169 double xi = j->getX() - getX();
170 double yi = j->getY() - getY();
171 double ti = (j->getT() * getSpeedOfLight() - t0 - j->getZ() + getZ()) / getKappaC();
172
173 for (bool done = false; !done; ) {
174
175 if ((done = (++j == __end))) {
176 j = __begin;
177 }
178
179 double xj = j->getX() - getX();
180 double yj = j->getY() - getY();
181 double tj = (j->getT() * getSpeedOfLight() - t0 - j->getZ() + getZ()) / getKappaC();
182
183 double dx = xj - xi;
184 double dy = yj - yi;
185 double dt = ti - tj; // opposite sign!
186
187 const double y = ((xj + xi) * dx +
188 (yj + yi) * dy +
189 (tj + ti) * dt);
190
191 dx *= 2;
192 dy *= 2;
193 dt *= 2;
194
195 V.a00 += dx * dx;
196 V.a01 += dx * dy;
197 V.a02 += dx * dt;
198 V.a11 += dy * dy;
199 V.a12 += dy * dt;
200 V.a22 += dt * dt;
201
202 y0 += dx * y;
203 y1 += dy * y;
204 y2 += dt * y;
205
206 xi = xj;
207 yi = yj;
208 ti = tj;
209 }
210
211 t0 *= getInverseSpeedOfLight();
212
213 V.a10 = V.a01;
214 V.a20 = V.a02;
215 V.a21 = V.a12;
216
217 svd.decompose(V);
218
219 if (fabs(svd.S.a11) < MINIMAL_SVD_WEIGHT * fabs(svd.S.a00)) {
220 THROW(JValueOutOfRange, "JEstimator<JLine1Z>::JEstimator(): singular value " << svd.S.a11 << ' ' << svd.S.a00);
221 }
222
223 V = svd.invert(MINIMAL_SVD_WEIGHT);
224
225 __x += V.a00 * y0 + V.a01 * y1 + V.a02 * y2;
226 __y += V.a10 * y0 + V.a11 * y1 + V.a12 * y2;
227 __t = V.a20 * y0 + V.a21 * y1 + V.a22 * y2;
228
229 __t *= getKappaC() * getInverseSpeedOfLight();
230 __t += t0;
231
232 } else {
233 throw JValueOutOfRange("JEstimator<JLine1Z>::JEstimator(): Not enough data points.");
234 }
235
236 return *this;
237 }
JFIT::JEstimator< JLine1Z >::NUMBER_OF_PARAMETERS
static const int NUMBER_OF_PARAMETERS
number of parameters of fit
Definition JLine1ZEstimator.hh:352
JFIT::JEstimator< JLine1Z >::MINIMAL_SVD_WEIGHT
static double MINIMAL_SVD_WEIGHT
minimal SVD weight.
Definition JLine1ZEstimator.hh:355
JFIT::JEstimator< JLine1Z >::V
JMATH::JMatrix3S V
co-variance matrix of fit parameters
Definition JLine1ZEstimator.hh:353
JFIT::JLine1Z::getZ
double getZ(const JPosition3D &pos) const
Get point of emission of Cherenkov light along muon path.
Definition JLine1Z.hh:134

◆ update()

template<class T >
void JFIT::JEstimator< JLine1Z >::update ( T __begin,
T __end,
const JMatrixNZ & A )
inline

Update track parameters using updated co-variance matrix (e.g. matrix with one hit switched off).

In this, it is assumed that the changes in x and y positions are small compared to the actual distances between the track and the hits.

The template argument T refers to an iterator of a data structure which should have the following member methods:

  • double getX(); // [m]
  • double getY(); // [m]
  • double getZ(); // [m]
  • double getT(); // [ns]
Parameters
__beginbegin of data
__endend of data
Aco-variance matrix of hits

Definition at line 257 of file JLine1ZEstimator.hh.

258 {
259 using namespace std;
260 using namespace JPP;
261
262 const int N = distance(__begin, __end);
263
264 if (N != (int) A.size()) {
265 THROW(JValueOutOfRange, "JEstimator<JLine1Z>::update(): Wrong number of points " << N << " != " << A.size());
266 }
267
268 if (N >= NUMBER_OF_PARAMETERS) {
269
270 double x1 = 0.0;
271 double y1 = 0.0;
272 double t1 = 0.0;
273
274 V.reset();
275
276 T i = __begin;
277
278 for (size_t row = 0; row != A.size(); ++row, ++i) {
279
280 const double dx = i->getX() - getX();
281 const double dy = i->getY() - getY();
282
283 const double rt = sqrt(dx*dx + dy*dy);
284
285 double xr = getKappaC() * getInverseSpeedOfLight();
286 double yr = getKappaC() * getInverseSpeedOfLight();
287 double tr = 1.0;
288
289 if (rt != 0.0) {
290 xr *= -dx / rt;
291 yr *= -dy / rt;
292 }
293
294 T j = __begin;
295
296 for (size_t col = 0; col != A.size(); ++col, ++j) {
297
298 const double dx = j->getX() - getX();
299 const double dy = j->getY() - getY();
300 const double dz = j->getZ() - getZ();
301
302 const double rt = sqrt(dx*dx + dy*dy);
303
304 double xc = getKappaC() * getInverseSpeedOfLight();
305 double yc = getKappaC() * getInverseSpeedOfLight();
306 double tc = 1.0;
307
308 if (rt != 0.0) {
309 xc *= -dx / rt;
310 yc *= -dy / rt;
311 }
312
313 const double ts = j->getT() - (dz + rt * getKappaC()) * getInverseSpeedOfLight();
314
315 const double vs = A(row,col);
316
317 x1 += xr * vs * ts;
318 y1 += yr * vs * ts;
319 t1 += tr * vs * ts;
320
321 V.a00 += xr * vs * xc;
322 V.a01 += xr * vs * yc;
323 V.a02 += xr * vs * tc;
324 V.a11 += yr * vs * yc;
325 V.a12 += yr * vs * tc;
326 V.a22 += tr * vs * tc;
327 }
328 }
329
330 V.a10 = V.a01;
331 V.a20 = V.a02;
332 V.a21 = V.a12;
333
334 svd.decompose(V);
335
336 if (fabs(svd.S.a11) < MINIMAL_SVD_WEIGHT * fabs(svd.S.a00)) {
337 THROW(JValueOutOfRange, "JEstimator<JLine1Z>::update(): singular value " << svd.S.a11 << ' ' << svd.S.a00);
338 }
339
340 V = svd.invert(MINIMAL_SVD_WEIGHT);
341
342 __x += V.a00 * x1 + V.a01 * y1 + V.a02 * t1;
343 __y += V.a10 * x1 + V.a11 * y1 + V.a12 * t1;
344 __t = V.a20 * x1 + V.a21 * y1 + V.a22 * t1;
345
346 } else {
347 THROW(JValueOutOfRange, "JEstimator<JLine1Z>::update(): Not enough data points " << N);
348 }
349 }

◆ move()

void JFIT::JLine1Z::move ( const double step,
const double velocity )
inlineinherited

Move vertex along this line with given velocity.

Parameters
stepstep
velocityvelocity

Definition at line 62 of file JLine1Z.hh.

63 {
64 __z += step;
65 __t += step / velocity;
66 }

◆ setZ()

void JFIT::JLine1Z::setZ ( const double z,
const double velocity )
inlineinherited

Set z-position of vertex.

Parameters
zz-position
velocityvelocity

Definition at line 75 of file JLine1Z.hh.

76 {
77 move(z - getZ(), velocity);
78 }
JFIT::JLine1Z::move
void move(const double step, const double velocity)
Move vertex along this line with given velocity.
Definition JLine1Z.hh:62

◆ getDistanceSquared()

double JFIT::JLine1Z::getDistanceSquared ( const JVector3D & pos) const
inlineinherited

Get distance squared.

Parameters
posposition
Returns
square of distance

Definition at line 87 of file JLine1Z.hh.

88 {
89 const double dx = pos.getX() - this->getX();
90 const double dy = pos.getY() - this->getY();
91
92 return dx*dx + dy*dy;
93 }

◆ getDistance()

double JFIT::JLine1Z::getDistance ( const JVector3D & pos) const
inlineinherited

Get distance.

Parameters
posposition
Returns
distance

Definition at line 102 of file JLine1Z.hh.

103 {
104 return sqrt(this->getDistanceSquared(pos));
105 }
JFIT::JLine1Z::getDistanceSquared
double getDistanceSquared(const JVector3D &pos) const
Get distance squared.
Definition JLine1Z.hh:87

◆ getT()

double JFIT::JLine1Z::getT ( const JVector3D & pos) const
inlineinherited

Get arrival time of Cherenkov light at given position.

Parameters
posposition [m]
Returns
time [ns]

Definition at line 114 of file JLine1Z.hh.

115 {
116 using namespace JPP;
117
118 const double dx = pos.getX() - this->getX();
119 const double dy = pos.getY() - this->getY();
120 const double dz = pos.getZ() - this->getZ();
121
122 const double R = sqrt(dx*dx + dy*dy);
123
124 return this->getT() + (dz + R * getKappaC()) * getInverseSpeedOfLight();
125 }
JFIT::JLine1Z::getT
double getT(const JVector3D &pos) const
Get arrival time of Cherenkov light at given position.
Definition JLine1Z.hh:114

◆ getZ()

double JFIT::JLine1Z::getZ ( const JPosition3D & pos) const
inlineinherited

Get point of emission of Cherenkov light along muon path.

Parameters
posposition
Returns
position along muon path

Definition at line 134 of file JLine1Z.hh.

135 {
136 using namespace JPP;
137
138 return pos.getZ() - this->getDistance(pos) / getTanThetaC();
139 }
JFIT::JLine1Z::getDistance
double getDistance(const JVector3D &pos) const
Get distance.
Definition JLine1Z.hh:102

◆ getDirection()

JVersor3D JFIT::JLine1Z::getDirection ( const JVector3D & pos) const
inlineinherited

Get photon direction of Cherenkov light on PMT.

Parameters
posPMT position
Returns
direction

Definition at line 148 of file JLine1Z.hh.

149 {
150 using namespace JPP;
151
152 double dx = pos.getX() - this->getX();
153 double dy = pos.getY() - this->getY();
154
155 const double R = sqrt(dx*dx + dy*dy);
156
157 dx *= getSinThetaC() / R;
158 dy *= getSinThetaC() / R;
159
160 const double dz = getCosThetaC();
161
162 return JVersor3D(dx,dy,dz);
163 }

◆ getDot()

double JFIT::JLine1Z::getDot ( const JAxis3D & axis) const
inlineinherited

Get cosine angle of impact of Cherenkov light on PMT.

Parameters
axisPMT axis
Returns
cosine angle of impact

Definition at line 172 of file JLine1Z.hh.

173 {
174 return getDirection(axis.getPosition()).getDot(axis.getDirection());
175 }
JFIT::JLine1Z::getDirection
JVersor3D getDirection(const JVector3D &pos) const
Get photon direction of Cherenkov light on PMT.
Definition JLine1Z.hh:148

◆ pX()

static parameter_type JFIT::JLine1Z::pX ( )
inlinestaticinherited

Definition at line 180 of file JLine1Z.hh.

180{ return &JLine1Z::__x; }

◆ pY()

static parameter_type JFIT::JLine1Z::pY ( )
inlinestaticinherited

Definition at line 181 of file JLine1Z.hh.

181{ return &JLine1Z::__y; }

◆ pT()

static parameter_type JFIT::JLine1Z::pT ( )
inlinestaticinherited

Definition at line 182 of file JLine1Z.hh.

182{ return &JLine1Z::__t; }

Member Data Documentation

◆ NUMBER_OF_PARAMETERS

const int JFIT::JEstimator< JLine1Z >::NUMBER_OF_PARAMETERS = 3
static

number of parameters of fit

Definition at line 352 of file JLine1ZEstimator.hh.

◆ V

JMATH::JMatrix3S JFIT::JEstimator< JLine1Z >::V

co-variance matrix of fit parameters

Definition at line 353 of file JLine1ZEstimator.hh.

◆ svd

JMATH::JSVD3D JFIT::JEstimator< JLine1Z >::svd

Definition at line 354 of file JLine1ZEstimator.hh.

◆ MINIMAL_SVD_WEIGHT

double JFIT::JEstimator< JLine1Z >::MINIMAL_SVD_WEIGHT = 1.0e-4
static

minimal SVD weight.

Set default minimal SVD weight.

Definition at line 355 of file JLine1ZEstimator.hh.

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