forked from sPHENIX-Collaboration/coresoftware
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sPHENIXTracker.cpp
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sPHENIXTracker.cpp
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#include "sPHENIXTracker.h"
#include "CylinderKalman.h"
#include "Pincushion.h"
#include "SimpleTrack3D.h"
#include "vector_math_inline.h"
#include <Eigen/Core>
#include <Eigen/Dense>
#include <Eigen/LU>
#include <algorithm>
#include <cfloat>
#include <cmath>
#include <cstddef>
#include <sys/time.h>
#include <iostream>
#include <utility>
#include <xmmintrin.h>
class HelixResolution;
using namespace std;
using namespace Eigen;
using namespace SeamStress;
class hit_triplet {
public:
hit_triplet(unsigned int h1, unsigned int h2, unsigned int h3, unsigned int t,
float c)
: hit1(h1), hit2(h2), hit3(h3), track(t), chi2(c) {}
~hit_triplet() {}
bool operator<(const hit_triplet& other) const {
return (hit1 < other.hit1) ||
((hit2 < other.hit2) && (hit1 == other.hit1)) ||
((hit3 < other.hit3) && (hit1 == other.hit1) &&
(hit2 == other.hit2));
}
bool operator==(const hit_triplet& other) const {
return ((hit1 == other.hit1) && (hit2 == other.hit2) &&
(hit3 == other.hit3));
}
unsigned int hit1, hit2, hit3, track;
float chi2;
};
class hitTriplet {
public:
hitTriplet(unsigned int h1, unsigned int h2, unsigned int h3, unsigned int t,
float c)
: hit1(h1), hit2(h2), hit3(h3), track(t), chi2(c) {}
~hitTriplet() {}
bool operator<(const hitTriplet& other) const {
return (hit1 < other.hit1) ||
((hit2 < other.hit2) && (hit1 == other.hit1)) ||
((hit3 < other.hit3) && (hit1 == other.hit1) &&
(hit2 == other.hit2));
}
bool operator==(const hitTriplet& other) const {
return ((hit1 == other.hit1) && (hit2 == other.hit2) &&
(hit3 == other.hit3));
}
unsigned int hit1, hit2, hit3, track;
float chi2;
};
void sPHENIXTracker::tripletRejection(vector<SimpleTrack3D>& input,
vector<SimpleTrack3D>& /*output*/,
vector<bool>& usetrack,
vector<float>& next_best_chi2) {
vector<hitTriplet> trips;
for (unsigned int i = 0; i < input.size(); ++i) {
for (unsigned int h1 = 0; h1 < input[i].hits.size(); ++h1) {
for (unsigned int h2 = (h1 + 1); h2 < input[i].hits.size(); ++h2) {
for (unsigned int h3 = (h2 + 1); h3 < input[i].hits.size(); ++h3) {
if (cut_on_dca == false) {
trips.push_back(hitTriplet(
input[i].hits[h1].get_id(), input[i].hits[h2].get_id(),
input[i].hits[h3].get_id(), i, track_states[i].chi2));
}
}
}
}
}
if (trips.size() == 0) {
return;
}
sort(trips.begin(), trips.end());
unsigned int pos = 0;
// unsigned int cur_h1 = trips[pos].hit1;
// unsigned int cur_h2 = trips[pos].hit2;
while (pos < trips.size()) {
unsigned int next_pos = pos + 1;
if (next_pos >= trips.size()) {
break;
}
while (trips[pos] == trips[next_pos]) {
next_pos += 1;
if (next_pos >= trips.size()) {
break;
}
}
if ((next_pos - pos) > 1) {
float best_chi2 = trips[pos].chi2;
float next_chi2 = trips[pos + 1].chi2;
unsigned int best_pos = pos;
for (unsigned int i = (pos + 1); i < next_pos; ++i) {
if (input[trips[i].track].hits.size() <
input[trips[best_pos].track].hits.size()) {
continue;
} else if ((input[trips[i].track].hits.size() >
input[trips[best_pos].track].hits.size()) ||
(input[trips[i].track].hits.back().get_layer() >
input[trips[best_pos].track].hits.back().get_layer())) {
next_chi2 = best_chi2;
best_chi2 = trips[i].chi2;
best_pos = i;
continue;
}
if ((trips[i].chi2 < best_chi2) ||
(usetrack[trips[best_pos].track] == false)) {
next_chi2 = best_chi2;
best_chi2 = trips[i].chi2;
best_pos = i;
} else if (trips[i].chi2 < next_chi2) {
next_chi2 = trips[i].chi2;
}
}
for (unsigned int i = pos; i < next_pos; ++i) {
if (i != best_pos) {
usetrack[trips[i].track] = false;
} else {
next_best_chi2[trips[i].track] = next_chi2;
}
}
}
pos = next_pos;
// cur_h1 = trips[pos].hit1;
// cur_h2 = trips[pos].hit2;
}
}
sPHENIXTracker::sPHENIXTracker(unsigned int n_phi, unsigned int n_d,
unsigned int n_k, unsigned int n_dzdl,
unsigned int n_z0,
HelixResolution& min_resolution,
HelixResolution& max_resolution,
HelixRange& range, vector<float>& material,
vector<float>& radius, float Bfield)
: HelixHough(n_phi, n_d, n_k, n_dzdl, n_z0, min_resolution, max_resolution,
range),
fast_chi2_cut_par0(12.),
fast_chi2_cut_par1(0.),
fast_chi2_cut_max(FLT_MAX),
chi2_cut(3.),
chi2_removal_cut(1.),
n_removal_hits(0),
seeding(false),
verbosity(0),
cut_on_dca(false),
dca_cut(0.01),
vertex_x(0.),
vertex_y(0.),
vertex_z(0.),
required_layers(0),
reject_ghosts(false),
nfits(0),
findtracksiter(0),
prev_max_k(0.),
prev_max_dzdl(0.),
prev_p_inv(0.),
seed_layer(0),
ca_chi2_cut(2.0),
cosang_cut(0.985) {
vector<float> detector_material;
for (unsigned int i = 0; i < radius.size(); ++i) {
detector_radii.push_back(radius[i]);
}
for (unsigned int i = 0; i < material.size(); ++i) {
detector_scatter.push_back(1.41421356237309515 * 0.0136 *
sqrt(3. * material[i]));
detector_material.push_back(3. * material[i]);
}
detector_B_field = Bfield;
integrated_scatter.assign(detector_scatter.size(), 0.);
float total_scatter_2 = 0.;
for (unsigned int l = 0; l < detector_scatter.size(); ++l) {
total_scatter_2 += detector_scatter[l] * detector_scatter[l];
integrated_scatter[l] = sqrt(total_scatter_2);
}
kalman =
new CylinderKalman(detector_radii, detector_material, detector_B_field);
vector<SimpleHit3D> one_layer;
layer_sorted.assign(n_layers, one_layer);
for (unsigned int i = 0; i < 4; ++i) {
layer_sorted_1[i].assign(n_layers, one_layer);
}
temp_comb.assign(n_layers, 0);
}
sPHENIXTracker::sPHENIXTracker(vector<vector<unsigned int> >& zoom_profile,
unsigned int minzoom, HelixRange& range,
vector<float>& material, vector<float>& radius,
float Bfield, bool parallel,
unsigned int num_threads)
: HelixHough(zoom_profile, minzoom, range),
fast_chi2_cut_par0(12.),
fast_chi2_cut_par1(0.),
fast_chi2_cut_max(FLT_MAX),
chi2_cut(3.),
chi2_removal_cut(1.),
n_removal_hits(0),
seeding(false),
verbosity(0),
cut_on_dca(false),
dca_cut(0.01),
vertex_x(0.),
vertex_y(0.),
vertex_z(0.),
required_layers(0),
reject_ghosts(false),
nfits(0),
findtracksiter(0),
prev_max_k(0.),
prev_max_dzdl(0.),
prev_p_inv(0.),
seed_layer(0),
nthreads(num_threads),
vssp(NULL),
pins(NULL),
is_parallel(parallel),
is_thread(false),
ca_chi2_cut(2.0),
cosang_cut(0.985) {
vector<float> detector_material;
for (unsigned int i = 0; i < radius.size(); ++i) {
detector_radii.push_back(radius[i]);
}
for (unsigned int i = 0; i < material.size(); ++i) {
detector_scatter.push_back(1.41421356237309515 * 0.0136 *
sqrt(3. * material[i]));
detector_material.push_back(3. * material[i]);
}
detector_B_field = Bfield;
integrated_scatter.assign(detector_scatter.size(), 0.);
float total_scatter_2 = 0.;
for (unsigned int l = 0; l < detector_scatter.size(); ++l) {
total_scatter_2 += detector_scatter[l] * detector_scatter[l];
integrated_scatter[l] = sqrt(total_scatter_2);
}
kalman =
new CylinderKalman(detector_radii, detector_material, detector_B_field);
vector<SimpleHit3D> one_layer;
layer_sorted.assign(n_layers, one_layer);
for (unsigned int i = 0; i < 4; ++i) {
layer_sorted_1[i].assign(n_layers, one_layer);
}
temp_comb.assign(n_layers, 0);
if (is_parallel == true) {
Seamstress::init_vector(num_threads, vss);
vssp = new vector<Seamstress*>();
for (unsigned int i = 0; i < vss.size(); i++) {
vssp->push_back(&(vss[i]));
}
pins = new Pincushion<sPHENIXTracker>(this, vssp);
vector<vector<unsigned int> > zoom_profile_new;
for (unsigned int i = 1; i < zoom_profile.size(); ++i) {
zoom_profile_new.push_back(zoom_profile[i]);
}
for (unsigned int i = 0; i < nthreads; ++i) {
thread_trackers.push_back(new sPHENIXTracker(zoom_profile, minzoom, range,
material, radius, Bfield));
thread_trackers.back()->setThread();
thread_trackers.back()->setStartZoom(1);
thread_tracks.push_back(vector<SimpleTrack3D>());
thread_ranges.push_back(HelixRange());
thread_hits.push_back(vector<SimpleHit3D>());
split_output_hits.push_back(new vector<vector<SimpleHit3D> >());
split_ranges.push_back(new vector<HelixRange>());
split_input_hits.push_back(vector<SimpleHit3D>());
}
}
}
sPHENIXTracker::~sPHENIXTracker() {
if (kalman != NULL) delete kalman;
for (unsigned int i = 0; i < vss.size(); i++) {
vss[i].stop();
}
for (unsigned int i = 0; i < thread_trackers.size(); ++i) {
delete thread_trackers[i];
delete split_output_hits[i];
delete split_ranges[i];
}
if (pins != NULL) delete pins;
if (vssp != NULL) delete vssp;
}
float sPHENIXTracker::kappaToPt(float kappa) {
return detector_B_field / 333.6 / kappa;
}
float sPHENIXTracker::ptToKappa(float pt) {
return detector_B_field / 333.6 / pt;
}
// hel should be +- 1
// static void xyTangent(SimpleHit3D& hit1, SimpleHit3D& hit2, float kappa,
// float hel, float& ux_out, float& uy_out, float& ux_in,
// float& uy_in) {
// float x = hit2.get_x() - hit1.get_x();
// float y = hit2.get_y() - hit1.get_y();
// float D = sqrt(x * x + y * y);
// float ak = 0.5 * kappa * D;
// float D_inv = 1. / D;
// float hk = sqrt(1. - ak * ak);
// float kcx = (ak * x + hel * hk * y) * D_inv;
// float kcy = (ak * y - hel * hk * x) * D_inv;
// float ktx = -(kappa * y - kcy);
// float kty = kappa * x - kcx;
// float norm = 1. / sqrt(ktx * ktx + kty * kty);
// ux_out = ktx * norm;
// uy_out = kty * norm;
// ktx = kcy;
// kty = -kcx;
// norm = 1. / sqrt(ktx * ktx + kty * kty);
// ux_in = ktx * norm;
// uy_in = kty * norm;
// }
// hel should be +- 1
// static float cosScatter(SimpleHit3D& hit1, SimpleHit3D& hit2, SimpleHit3D& hit3,
// float kappa, float hel) {
// float ux_in = 0.;
// float uy_in = 0.;
// float ux_out = 0.;
// float uy_out = 0.;
// float temp1 = 0.;
// float temp2 = 0.;
// xyTangent(hit1, hit2, kappa, hel, ux_in, uy_in, temp1, temp2);
// xyTangent(hit2, hit3, kappa, hel, temp1, temp2, ux_out, uy_out);
// return ux_in * ux_out + uy_in * uy_out;
// }
// static float dzdsSimple(SimpleHit3D& hit1, SimpleHit3D& hit2, float k) {
// float x = hit2.get_x() - hit1.get_x();
// float y = hit2.get_y() - hit1.get_y();
// float D = sqrt(x * x + y * y);
// float s = 0.;
// float temp1 = k * D * 0.5;
// temp1 *= temp1;
// float temp2 = D * 0.5;
// s += 2. * temp2;
// temp2 *= temp1;
// s += temp2 / 3.;
// temp2 *= temp1;
// s += (3. / 20.) * temp2;
// temp2 *= temp1;
// s += (5. / 56.) * temp2;
// return (hit2.get_z() - hit1.get_z()) / s;
// }
float sPHENIXTracker::dcaToVertexXY(SimpleTrack3D& track, float vx, float vy) {
float d_out = 0.;
// find point at the dca to 0
float x0 = track.d * cos(track.phi);
float y0 = track.d * sin(track.phi);
// change variables so x0,y0 -> 0,0
float phi2 =
atan2((1. + track.kappa * track.d) * sin(track.phi) - track.kappa * y0,
(1. + track.kappa * track.d) * cos(track.phi) - track.kappa * x0);
// translate so that (0,0) -> (x0 - vx , y0 - vy)
float cosphi = cos(phi2);
float sinphi = sin(phi2);
float tx = cosphi + track.kappa * (x0 - vx);
float ty = sinphi + track.kappa * (y0 - vy);
float dk = sqrt(tx * tx + ty * ty) - 1.;
if (track.kappa == 0.) {
d_out = (x0 - vx) * cosphi + (y0 - vy) * sinphi;
} else {
d_out = dk / track.kappa;
}
return fabs(d_out);
}
void sPHENIXTracker::finalize(vector<SimpleTrack3D>& input,
vector<SimpleTrack3D>& output) {
if (is_thread == true) {
for (unsigned int i = 0; i < input.size(); ++i) {
output.push_back(input[i]);
}
return;
}
unsigned int nt = input.size();
vector<bool> usetrack;
usetrack.assign(input.size(), true);
vector<float> next_best_chi2;
next_best_chi2.assign(input.size(), 99999.);
if (reject_ghosts == true) {
tripletRejection(input, output, usetrack, next_best_chi2);
}
vector<HelixKalmanState> states_new;
for (unsigned int i = 0; i < nt; ++i) {
if (usetrack[i] == true) {
if (!(track_states[i].chi2 == track_states[i].chi2)) {
continue;
}
output.push_back(input[i]);
output.back().index = (output.size() - 1);
states_new.push_back(track_states[i]);
isolation_variable.push_back(next_best_chi2[i]);
}
}
track_states = states_new;
if (smooth_back == true) {
for (unsigned int i = 0; i < output.size(); ++i) {
HelixKalmanState state = track_states[i];
track_states[i].C *= 3.;
track_states[i].chi2 = 0.;
track_states[i].x_int = 0.;
track_states[i].y_int = 0.;
track_states[i].z_int = 0.;
// track_states[i].position = output[i].hits.size();
track_states[i].position = 0;
for (int h = (output[i].hits.size() - 1); h >= 0; --h) {
SimpleHit3D hit = output[i].hits[h];
float err_scale = 1.;
int layer = hit.get_layer();
if ((layer >= 0) && (layer < (int)(hit_error_scale.size()))) {
err_scale = hit_error_scale[layer];
}
err_scale *=
3.0; // fudge factor, like needed due to non-gaussian errors
// \todo location of a rescale fudge factor
kalman->addHit(hit, track_states[i]);
track_states[i].position = h;
}
// track_states[i].C = state.C;
track_states[i].chi2 = state.chi2;
track_states[i].C *= 2. / 3.;
output[i].phi = track_states[i].phi;
output[i].d = track_states[i].d;
output[i].kappa = track_states[i].kappa;
output[i].z0 = track_states[i].z0;
output[i].dzdl = track_states[i].dzdl;
}
}
if (verbosity > 0) {
cout << "# fits = " << nfits << endl;
cout << "findTracks called " << findtracksiter << " times" << endl;
cout << "CAtime = " << CAtime << endl;
cout << "KALime = " << KALtime << endl;
}
}
void sPHENIXTracker::findTracks(vector<SimpleHit3D>& hits,
vector<SimpleTrack3D>& tracks,
const HelixRange& range) {
findtracksiter += 1;
findTracksBySegments(hits, tracks, range);
}
bool sPHENIXTracker::breakRecursion(const vector<SimpleHit3D>& hits,
const HelixRange& /*range*/) {
if (seeding == true) {
return false;
}
unsigned int layer_mask[4] = {0, 0, 0, 0};
for (unsigned int i = 0; i < hits.size(); ++i) {
if (hits[i].get_layer() < 32) {
layer_mask[0] = layer_mask[0] | (1 << hits[i].get_layer());
} else if (hits[i].get_layer() < 64) {
layer_mask[1] = layer_mask[1] | (1 << (hits[i].get_layer() - 32));
} else if (hits[i].get_layer() < 96) {
layer_mask[2] = layer_mask[2] | (1 << (hits[i].get_layer() - 64));
} else if (hits[i].get_layer() < 128) {
layer_mask[3] = layer_mask[3] | (1 << (hits[i].get_layer() - 96));
}
}
unsigned int nlayers =
__builtin_popcount(layer_mask[0]) + __builtin_popcount(layer_mask[1]) +
__builtin_popcount(layer_mask[2]) + __builtin_popcount(layer_mask[3]);
return (nlayers < required_layers);
}
float sPHENIXTracker::phiError(SimpleHit3D& hit, float /*min_k*/, float max_k,
float min_d, float max_d, float /*min_z0*/,
float /*max_z0*/, float /*min_dzdl*/, float max_dzdl,
bool pairvoting) {
float Bfield_inv = 1. / detector_B_field;
float p_inv = 0.;
if ((prev_max_k == max_k) && (prev_max_dzdl == max_dzdl)) {
p_inv = prev_p_inv;
} else {
prev_max_k = max_k;
prev_max_dzdl = max_dzdl;
prev_p_inv = 3.33333333333333314e+02 * max_k * Bfield_inv *
sqrt(1. - max_dzdl * max_dzdl);
p_inv = prev_p_inv;
}
float total_scatter_2 = 0.;
for (int i = seed_layer + 1; i <= (hit.get_layer()); ++i) {
float this_scatter = detector_scatter[i - 1] *
(detector_radii[i] - detector_radii[i - 1]) /
detector_radii[i];
total_scatter_2 += this_scatter * this_scatter;
}
float angle = p_inv * sqrt(total_scatter_2) * 1.0;
float dsize = 0.5 * (max_d - min_d);
float angle_from_d = dsize / detector_radii[hit.get_layer()];
float returnval = 0.;
if (pairvoting == false) {
if (angle_from_d > angle) {
returnval = 0.;
} else {
returnval = (angle - angle_from_d);
}
} else {
returnval = angle;
}
return returnval;
}
float sPHENIXTracker::dzdlError(SimpleHit3D& hit, float /*min_k*/, float max_k,
float /*min_d*/, float /*max_d*/, float min_z0,
float max_z0, float /*min_dzdl*/, float max_dzdl,
bool pairvoting) {
float Bfield_inv = 1. / detector_B_field;
float p_inv = 0.;
if ((prev_max_k == max_k) && (prev_max_dzdl == max_dzdl)) {
p_inv = prev_p_inv;
} else {
prev_max_k = max_k;
prev_max_dzdl = max_dzdl;
prev_p_inv = 3.33333333333333314e+02 * max_k * Bfield_inv *
sqrt(1. - max_dzdl * max_dzdl);
p_inv = prev_p_inv;
}
float total_scatter_2 = 0.;
for (int i = seed_layer + 1; i <= (hit.get_layer()); ++i) {
float this_scatter = detector_scatter[i - 1] *
(detector_radii[i] - detector_radii[i - 1]) /
detector_radii[i];
total_scatter_2 += this_scatter * this_scatter;
}
float angle = p_inv * sqrt(total_scatter_2) * 1.0;
float z0size = 0.5 * (max_z0 - min_z0);
float angle_from_z0 = z0size / detector_radii[hit.get_layer()];
float returnval = 0.;
if (pairvoting == false) {
if (angle_from_z0 > angle) {
returnval = 0.;
} else {
returnval = (angle - angle_from_z0);
}
} else {
returnval = angle;
}
return returnval;
}
void sPHENIXTracker::setRangeFromSeed(HelixRange& range, SimpleTrack3D& seed) {
HelixKalmanState* state = &(seed_states[seed.index]);
float dphi = 2. * sqrt(state->C(0, 0));
float dd = 2. * sqrt(state->C(1, 1));
float dk = 2. * state->C(2, 2);
float dz0 = 2. * sqrt(state->C(3, 3));
float ddzdl = 2. * sqrt(state->C(4, 4));
range.min_phi = seed.phi - dphi;
range.max_phi = seed.phi + dphi;
if (range.min_phi < 0.) {
range.min_phi = 0.;
}
if (range.max_phi > 2. * M_PI) {
range.max_phi = 2. * M_PI;
}
range.min_d = seed.d - dd;
range.max_d = seed.d + dd;
range.min_k = seed.kappa - dk;
range.max_k = seed.kappa + dk;
if (range.min_k < 0.) {
range.min_k = 0.;
}
range.min_k = range.min_k * range.min_k;
range.max_k = range.max_k * range.max_k;
range.min_dzdl = seed.dzdl - ddzdl;
range.max_dzdl = seed.dzdl + ddzdl;
range.min_z0 = seed.z0 - dz0;
range.max_z0 = seed.z0 + dz0;
}
float sPHENIXTracker::fitTrack(SimpleTrack3D& track) {
vector<float> chi2_hit;
return sPHENIXTracker::fitTrack(track, chi2_hit);
}
float sPHENIXTracker::fitTrack(SimpleTrack3D& track, vector<float>& chi2_hit) {
chi2_hit.clear();
vector<float> xyres;
vector<float> xyres_inv;
vector<float> zres;
vector<float> zres_inv;
for (unsigned int i = 0; i < track.hits.size(); i++) {
/// \todo fudge factor location
xyres.push_back(sqrt((0.5*sqrt(12.)*sqrt(track.hits[i].get_size(0,0))) * (0.5*sqrt(12.)*sqrt(track.hits[i].get_size(0,0))) +
(0.5*sqrt(12.)*sqrt(track.hits[i].get_size(1,1))) * (0.5*sqrt(12.)*sqrt(track.hits[i].get_size(1,1)))));
xyres_inv.push_back(1. / xyres.back());
zres.push_back((0.5*sqrt(12.)*sqrt(track.hits[i].get_size(2,2))));
zres_inv.push_back(1. / zres.back());
}
chi2_hit.resize(track.hits.size(), 0.);
MatrixXf y = MatrixXf::Zero(track.hits.size(), 1);
for (unsigned int i = 0; i < track.hits.size(); i++) {
y(i, 0) = (pow(track.hits[i].get_x(), 2) + pow(track.hits[i].get_y(), 2));
y(i, 0) *= xyres_inv[i];
}
MatrixXf X = MatrixXf::Zero(track.hits.size(), 3);
for (unsigned int i = 0; i < track.hits.size(); i++) {
X(i, 0) = track.hits[i].get_x();
X(i, 1) = track.hits[i].get_y();
X(i, 2) = -1.;
X(i, 0) *= xyres_inv[i];
X(i, 1) *= xyres_inv[i];
X(i, 2) *= xyres_inv[i];
}
MatrixXf Xt = X.transpose();
MatrixXf prod = Xt * X;
MatrixXf Xty = Xt * y;
MatrixXf beta = prod.ldlt().solve(Xty);
float cx = beta(0, 0) * 0.5;
float cy = beta(1, 0) * 0.5;
float r = sqrt(cx * cx + cy * cy - beta(2, 0));
float phi = atan2(cy, cx);
float d = sqrt(cx * cx + cy * cy) - r;
float k = 1. / r;
MatrixXf diff = y - (X * beta);
MatrixXf chi2 = (diff.transpose()) * diff;
float dx = d * cos(phi);
float dy = d * sin(phi);
MatrixXf y2 = MatrixXf::Zero(track.hits.size(), 1);
for (unsigned int i = 0; i < track.hits.size(); i++) {
y2(i, 0) = track.hits[i].get_z();
y2(i, 0) *= zres_inv[i];
}
MatrixXf X2 = MatrixXf::Zero(track.hits.size(), 2);
for (unsigned int i = 0; i < track.hits.size(); i++) {
float D = sqrt(pow(dx - track.hits[i].get_x(), 2) + pow(dy - track.hits[i].get_y(), 2));
float s = 0.0;
if (0.5 * k * D > 0.1) {
float v = 0.5 * k * D;
if (v >= 0.999999) {
v = 0.999999;
}
s = 2. * asin(v) / k;
} else {
float temp1 = k * D * 0.5;
temp1 *= temp1;
float temp2 = D * 0.5;
s += 2. * temp2;
temp2 *= temp1;
s += temp2 / 3.;
temp2 *= temp1;
s += (3. / 20.) * temp2;
temp2 *= temp1;
s += (5. / 56.) * temp2;
}
X2(i, 0) = s;
X2(i, 1) = 1.0;
X2(i, 0) *= zres_inv[i];
X2(i, 1) *= zres_inv[i];
}
MatrixXf Xt2 = X2.transpose();
MatrixXf prod2 = Xt2 * X2;
MatrixXf Xty2 = Xt2 * y2;
MatrixXf beta2 = prod2.ldlt().solve(Xty2);
MatrixXf diff2 = y2 - (X2 * beta2);
MatrixXf chi2_z = (diff2.transpose()) * diff2;
float z0 = beta2(1, 0);
float dzdl = beta2(0, 0) / sqrt(1. + beta2(0, 0) * beta2(0, 0));
track.phi = phi;
track.d = d;
track.kappa = k;
track.dzdl = dzdl;
track.z0 = z0;
if (track.kappa != 0.) {
r = 1. / track.kappa;
} else {
r = 1.0e10;
}
cx = (track.d + r) * cos(track.phi);
cy = (track.d + r) * sin(track.phi);
float chi2_tot = 0.;
for (unsigned int h = 0; h < track.hits.size(); h++) {
float dx1 = track.hits[h].get_x() - cx;
float dy1 = track.hits[h].get_y() - cy;
float dx2 = track.hits[h].get_x() + cx;
float dy2 = track.hits[h].get_y() + cy;
float xydiff1 = sqrt(dx1 * dx1 + dy1 * dy1) - r;
float xydiff2 = sqrt(dx2 * dx2 + dy2 * dy2) - r;
float xydiff = xydiff2;
if (fabs(xydiff1) < fabs(xydiff2)) {
xydiff = xydiff1;
}
float ls_xy = xyres[h];
chi2_hit[h] = 0.;
chi2_hit[h] += xydiff * xydiff / (ls_xy * ls_xy);
chi2_hit[h] += diff2(h, 0) * diff2(h, 0);
chi2_tot += chi2_hit[h];
}
unsigned int deg_of_freedom = 2 * track.hits.size() - 5;
return (chi2_tot) / ((float)(deg_of_freedom));
}
void sPHENIXTracker::calculateKappaTangents(
float* x1_a, float* y1_a, float* z1_a, float* x2_a, float* y2_a,
float* z2_a, float* x3_a, float* y3_a, float* z3_a, float* dx1_a,
float* dy1_a, float* dz1_a, float* dx2_a, float* dy2_a, float* dz2_a,
float* dx3_a, float* dy3_a, float* dz3_a, float* kappa_a, float* dkappa_a,
float* ux_mid_a, float* uy_mid_a, float* ux_end_a, float* uy_end_a,
float* dzdl_1_a, float* dzdl_2_a, float* ddzdl_1_a, float* ddzdl_2_a) {
static const __m128 two = {2., 2., 2., 2.};
__m128 x1 = _mm_load_ps(x1_a);
__m128 x2 = _mm_load_ps(x2_a);
__m128 x3 = _mm_load_ps(x3_a);
__m128 y1 = _mm_load_ps(y1_a);
__m128 y2 = _mm_load_ps(y2_a);
__m128 y3 = _mm_load_ps(y3_a);
__m128 z1 = _mm_load_ps(z1_a);
__m128 z2 = _mm_load_ps(z2_a);
__m128 z3 = _mm_load_ps(z3_a);
__m128 dx1 = _mm_load_ps(dx1_a);
__m128 dx2 = _mm_load_ps(dx2_a);
__m128 dx3 = _mm_load_ps(dx3_a);
__m128 dy1 = _mm_load_ps(dy1_a);
__m128 dy2 = _mm_load_ps(dy2_a);
__m128 dy3 = _mm_load_ps(dy3_a);
__m128 dz1 = _mm_load_ps(dz1_a);
__m128 dz2 = _mm_load_ps(dz2_a);
__m128 dz3 = _mm_load_ps(dz3_a);
__m128 D12 = _mm_sub_ps(x2, x1);
D12 = _mm_mul_ps(D12, D12);
__m128 tmp1 = _mm_sub_ps(y2, y1);
tmp1 = _mm_mul_ps(tmp1, tmp1);
D12 = _mm_add_ps(D12, tmp1);
D12 = _vec_sqrt_ps(D12);
__m128 D23 = _mm_sub_ps(x3, x2);
D23 = _mm_mul_ps(D23, D23);
tmp1 = _mm_sub_ps(y3, y2);
tmp1 = _mm_mul_ps(tmp1, tmp1);
D23 = _mm_add_ps(D23, tmp1);
D23 = _vec_sqrt_ps(D23);
__m128 D31 = _mm_sub_ps(x1, x3);
D31 = _mm_mul_ps(D31, D31);
tmp1 = _mm_sub_ps(y1, y3);
tmp1 = _mm_mul_ps(tmp1, tmp1);
D31 = _mm_add_ps(D31, tmp1);
D31 = _vec_sqrt_ps(D31);
__m128 k = _mm_mul_ps(D12, D23);
k = _mm_mul_ps(k, D31);
k = _vec_rec_ps(k);
tmp1 = (D12 + D23 + D31) * (D23 + D31 - D12) * (D12 + D31 - D23) *
(D12 + D23 - D31);
tmp1 = _vec_sqrt_ps(tmp1);
k *= tmp1;
__m128 tmp2 = _mm_cmpgt_ps(tmp1, zero);
tmp1 = _mm_and_ps(tmp2, k);
tmp2 = _mm_andnot_ps(tmp2, zero);
k = _mm_xor_ps(tmp1, tmp2);
_mm_store_ps(kappa_a, k);
__m128 k_inv = _vec_rec_ps(k);
__m128 D12_inv = _vec_rec_ps(D12);
__m128 D23_inv = _vec_rec_ps(D23);
__m128 D31_inv = _vec_rec_ps(D31);
__m128 dr1 = dx1 * dx1 + dy1 * dy1;
dr1 = _vec_sqrt_ps(dr1);
__m128 dr2 = dx2 * dx2 + dy2 * dy2;
dr2 = _vec_sqrt_ps(dr2);
__m128 dr3 = dx3 * dx3 + dy3 * dy3;
dr3 = _vec_sqrt_ps(dr3);
__m128 dk1 = (dr1 + dr2) * D12_inv * D12_inv;
__m128 dk2 = (dr2 + dr3) * D23_inv * D23_inv;
__m128 dk = dk1 + dk2;
_mm_store_ps(dkappa_a, dk);
__m128 ux12 = (x2 - x1) * D12_inv;
__m128 uy12 = (y2 - y1) * D12_inv;
__m128 ux23 = (x3 - x2) * D23_inv;
__m128 uy23 = (y3 - y2) * D23_inv;
__m128 ux13 = (x3 - x1) * D31_inv;
__m128 uy13 = (y3 - y1) * D31_inv;
__m128 cosalpha = ux12 * ux13 + uy12 * uy13;
__m128 sinalpha = ux13 * uy12 - ux12 * uy13;
__m128 ux_mid = ux23 * cosalpha - uy23 * sinalpha;
__m128 uy_mid = ux23 * sinalpha + uy23 * cosalpha;
_mm_store_ps(ux_mid_a, ux_mid);
_mm_store_ps(uy_mid_a, uy_mid);
__m128 ux_end = ux23 * cosalpha + uy23 * sinalpha;
__m128 uy_end = uy23 * cosalpha - ux23 * sinalpha;
_mm_store_ps(ux_end_a, ux_end);
_mm_store_ps(uy_end_a, uy_end);
// asin(x) = 2*atan( x/( 1 + sqrt( 1 - x*x ) ) )
__m128 v = one - sinalpha * sinalpha;
v = _vec_sqrt_ps(v);
v += one;
v = _vec_rec_ps(v);
v *= sinalpha;
__m128 s2 = _vec_atan_ps(v);
s2 *= two;
s2 *= k_inv;
tmp1 = _mm_cmpgt_ps(k, zero);
tmp2 = _mm_and_ps(tmp1, s2);
tmp1 = _mm_andnot_ps(tmp1, D23);
s2 = _mm_xor_ps(tmp1, tmp2);
// dz/dl = (dz/ds)/sqrt(1 + (dz/ds)^2)
// = dz/sqrt(s^2 + dz^2)
__m128 del_z_2 = z3 - z2;
__m128 dzdl_2 = s2 * s2 + del_z_2 * del_z_2;
dzdl_2 = _vec_rsqrt_ps(dzdl_2);
dzdl_2 *= del_z_2;
__m128 ddzdl_2 = (dz2 + dz3) * D23_inv;
_mm_store_ps(dzdl_2_a, dzdl_2);
_mm_store_ps(ddzdl_2_a, ddzdl_2);
sinalpha = ux13 * uy23 - ux23 * uy13;
v = one - sinalpha * sinalpha;
v = _vec_sqrt_ps(v);
v += one;
v = _vec_rec_ps(v);
v *= sinalpha;
__m128 s1 = _vec_atan_ps(v);
s1 *= two;
s1 *= k_inv;
tmp1 = _mm_cmpgt_ps(k, zero);
tmp2 = _mm_and_ps(tmp1, s1);
tmp1 = _mm_andnot_ps(tmp1, D12);
s1 = _mm_xor_ps(tmp1, tmp2);
__m128 del_z_1 = z2 - z1;
__m128 dzdl_1 = s1 * s1 + del_z_1 * del_z_1;
dzdl_1 = _vec_rsqrt_ps(dzdl_1);
dzdl_1 *= del_z_1;
__m128 ddzdl_1 = (dz1 + dz2) * D12_inv;
_mm_store_ps(dzdl_1_a, dzdl_1);
_mm_store_ps(ddzdl_1_a, ddzdl_1);
}
void sPHENIXTracker::calculateKappaTangents(
float* x1_a, float* y1_a, float* z1_a, float* x2_a, float* y2_a,
float* z2_a, float* x3_a, float* y3_a, float* z3_a, float* dx1_a,
float* dy1_a, float* dz1_a, float* dx2_a, float* dy2_a, float* dz2_a,
float* dx3_a, float* dy3_a, float* dz3_a, float* kappa_a, float* dkappa_a,
float* ux_mid_a, float* uy_mid_a, float* ux_end_a, float* uy_end_a,
float* dzdl_1_a, float* dzdl_2_a, float* ddzdl_1_a, float* ddzdl_2_a,
float sinang_cut, float cosang_diff_inv, float* cur_kappa_a,
float* cur_dkappa_a, float* cur_ux_a, float* cur_uy_a, float* cur_chi2_a,
float* chi2_a) {
static const __m128 two = {2., 2., 2., 2.};
__m128 x1 = _mm_load_ps(x1_a);
__m128 x2 = _mm_load_ps(x2_a);
__m128 x3 = _mm_load_ps(x3_a);
__m128 y1 = _mm_load_ps(y1_a);
__m128 y2 = _mm_load_ps(y2_a);
__m128 y3 = _mm_load_ps(y3_a);
__m128 z1 = _mm_load_ps(z1_a);
__m128 z2 = _mm_load_ps(z2_a);
__m128 z3 = _mm_load_ps(z3_a);
__m128 dx1 = _mm_load_ps(dx1_a);
__m128 dx2 = _mm_load_ps(dx2_a);
__m128 dx3 = _mm_load_ps(dx3_a);
__m128 dy1 = _mm_load_ps(dy1_a);
__m128 dy2 = _mm_load_ps(dy2_a);
__m128 dy3 = _mm_load_ps(dy3_a);
__m128 dz1 = _mm_load_ps(dz1_a);
__m128 dz2 = _mm_load_ps(dz2_a);
__m128 dz3 = _mm_load_ps(dz3_a);
__m128 D12 = _mm_sub_ps(x2, x1);
D12 = _mm_mul_ps(D12, D12);
__m128 tmp1 = _mm_sub_ps(y2, y1);
tmp1 = _mm_mul_ps(tmp1, tmp1);
D12 = _mm_add_ps(D12, tmp1);
D12 = _vec_sqrt_ps(D12);
__m128 D23 = _mm_sub_ps(x3, x2);
D23 = _mm_mul_ps(D23, D23);
tmp1 = _mm_sub_ps(y3, y2);
tmp1 = _mm_mul_ps(tmp1, tmp1);
D23 = _mm_add_ps(D23, tmp1);
D23 = _vec_sqrt_ps(D23);
__m128 D31 = _mm_sub_ps(x1, x3);
D31 = _mm_mul_ps(D31, D31);
tmp1 = _mm_sub_ps(y1, y3);
tmp1 = _mm_mul_ps(tmp1, tmp1);
D31 = _mm_add_ps(D31, tmp1);
D31 = _vec_sqrt_ps(D31);