exampleComposedKin.cpp

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/*
 * exampleCdc.cpp
 *
 *  Created on: 23 Mar 2023
 *      Author: kleinwrt
 */
 
#include <time.h>
#include "exampleUtilCdc.h"
#include "GblTrajectory.h"
 
using namespace gbl;
using namespace Eigen;
 
 
void exampleComposedKin() {
 
        // detector setup, ~ Belle-II CDC
        const unsigned int nSuper = 9; // number of super layers
        double nLayer[nSuper] = { 8, 6, 6, 6, 6, 6, 6, 6, 6 }; // number of layers per super layer
        double rInner[nSuper] = { 16.80, 25.70, 36.52, 47.69, 58.41, 69.53, 80.25,
                        91.37, 102.00 }; // inner radius of super layer
        double rOuter[nSuper] = { 23.80, 34.80, 45.57, 56.69, 67.41, 78.53, 89.25,
                        100.37, 111.14 }; // outer radius of super layer
        double stereo[nSuper] = { 0., 0.068, 0., -0.060, 0., 0.064, 0., -0.072, 0. }; // stereo angle of super layer
        double zStart[nSuper] = { -35.9, -51.4, -57.5, -59.6, -61.8, -63.9, -66.0,
                        -68.2, -70.2 }; // -Z end of wires per super layer
        double zEnd[nSuper] = { 67.9, 98.6, 132.9, 144.7, 146.8, 148.9, 151.0,
                        153.2, 155.3 }; // +Z end of wires per super layer
 
        unsigned int nTry = 1000; //: number of tries
        std::cout << " GblComposedKin $Id$ " << nTry << ", " << nSuper << std::endl;
        srand(4711);
        clock_t startTime = clock();
 
        const double bfac = 0.0045;  // B*c for 1.5 T
 
        double beamPos[] = { 0., 0., 0. };
        double beamSize[] = { 0.005, 0.005, 0.3 };
        const bool useBeamSpot = true;
 
        MilleBinary mille; // for producing MillePede-II binary file
 
        double Chi2Sum = 0.;
        int NdfSum = 0;
        double LostSum = 0.;
        int numFit = 0;
        unsigned int iEvent = 0;
 
        // event loop
        for (unsigned int iTry = 0; iTry < nTry; ++iTry) {
                unsigned int nTrack;
                std::vector<std::array<double, 6>> allGenPar; // collect parameters for generation of tracks
 
                // inline generation of track pair
                iEvent++;
                nTrack = 2;
                // helix parameter for track generation
                const double qbyp = 0.2; // 5 GeV
                const double genDca = beamSize[0] * unrm(); // normal
                const double genZ0 = beamSize[2] * unrm(); // normal
                const double genPhi0 = M_PI * (2. * unif() - 1.); // uniform, [-30..30] deg
                const double genDzds = 2. * unif() - 1.; // uniform, lambda ~ [-45..45] deg
                const double genCurv = bfac * qbyp * sqrt(1. + genDzds * genDzds);
 
                std::cout << " gen(inline)  " << iEvent << ": " << genCurv << " "
                                << genPhi0 << " " << genDca << " " << genDzds << " " << genZ0
                                << std::endl;
                std::array<double, 6> par = { genCurv, genPhi0, genDca, genDzds, genZ0,
                                1. };
                allGenPar.push_back(par);
                // back to back track
                std::array<double, 6> par2 = { -genCurv, genPhi0 + M_PI, -genDca,
                                -genDzds, genZ0, -1. };
                allGenPar.push_back(par2);
 
                std::vector<std::vector<GblPoint>> listsOfPoints;
                std::vector<Matrix<double, 5, 8>> listOfTrafos;
                for (unsigned int iTrack = 0; iTrack < nTrack; ++iTrack) {
                        //
                        // generate hits: (virtual) wires as detector layers at constant radii
                        //
                        std::array<double, 6> genPar = allGenPar[iTrack];
                        double curv(genPar[0]), phi0(genPar[1]), dca(genPar[2]), dzds(
                                        genPar[3]), z0(genPar[4]);
                        // local constant (Bfield) helix
                        GblSimpleHelix hlx = GblSimpleHelix(curv, phi0, dca, dzds, z0);
 
                        std::vector<GblDetectorLayer> layers;
 
                        // beam spot (required as first (and common) point for composed trajectory)
                        double sArc = hlx.getArcLengthXY(beamPos[0], beamPos[1]);
                        // add virtual layer
                        layers.push_back(
                                        CreateImpactPar("impact", 0, beamPos[0], beamPos[1],
                                                        beamPos[2], phi0 + sArc * curv, dzds, beamSize[0],
                                                        beamSize[1], beamSize[2]));
 
                        unsigned int cLayer = 0;
                        for (unsigned int iSuper = 0; iSuper < nSuper; ++iSuper) {
                                double radius = rInner[iSuper];
                                double step = (rOuter[iSuper] - radius) / (nLayer[iSuper] - 1);
 
                                for (unsigned int iLayer = 0; iLayer < nLayer[iSuper];
                                                ++iLayer) {
                                        // check for |dca| < radius
                                        if (fabs(dca) < radius) {
                                                // arc length to layer
                                                double sArc = hlx.getArcLengthR(radius);
                                                if (sArc == 0.)
                                                        goto theEnd;
                                                // phi of position at layer
                                                double phiPos = hlx.getPhi(radius);
                                                // (virtual) wire position
                                                double xPos(cos(phiPos) * radius), yPos(
                                                                sin(phiPos) * radius), zPos(z0 + sArc * dzds);
                                                // add virtual wire
                                                if (zPos > zStart[iSuper] and zPos < zEnd[iSuper])
                                                        layers.push_back(
                                                                        CreateWireCdc("wire", ++cLayer, xPos, yPos,
                                                                                        zPos, phi0 + sArc * curv, dzds,
                                                                                        stereo[iSuper], 0.015));
                                        }
                                        // next layer
                                        radius += step;
                                }
                        }
                        theEnd:
 
                        //
                        // create GBL trajectory (list of GBL points)
                        //
                        // seed (with true parameters)
                        std::array<double, 6> seedPar = allGenPar[iTrack];
                        // transformations to common POSITION parameters (at vertex) of composed trajectory at first point
                        Matrix<double, 5, 8> innerTrafo = Matrix<double, 5, 8>::Zero();
                        if (allGenPar[iTrack][5] < 0.) {
                                // outer track
                                innerTrafo(0, 5) = -1.; // q/p
                                innerTrafo(1, 6) = 1.; // u'
                                innerTrafo(2, 7) = -1.; // v'
                                innerTrafo(3, 3) = -1.; // u
                                innerTrafo(4, 4) = 1.; // v
                        } else {
                                // leading track
                                innerTrafo(0, 0) = 1.; // q/p
                                innerTrafo(1, 1) = 1.; // u'
                                innerTrafo(2, 2) = 1.; // v'
                                innerTrafo(3, 3) = 1.; // u
                                innerTrafo(4, 4) = 1.; // v
                        }
                        listOfTrafos.push_back(innerTrafo);
                        // optionally distort seed
                        //seedPar[0] *= 0.99;
                        //seedPar[1] += 0.01;
                        double seedCurv(seedPar[0]), seedPhi0(seedPar[1]), seedDca(
                                        seedPar[2]), seedDzds(seedPar[3]), seedZ0(seedPar[4]);
                        GblSimpleHelix seed = GblSimpleHelix(seedCurv, seedPhi0, seedDca,
                                        seedDzds, seedZ0);
                        // (previous) arc-length
                        double sOld = 0.;
                        const double cosLambdaSeed = 1. / sqrt(1. + (seedDzds * seedDzds));
                        // for multiple scattering (not (yet) implemented)
                        const double qbyp = seedCurv / bfac * cosLambdaSeed;
                        // list of points on trajectory
                        std::vector<GblPoint> listOfPoints;
                        for (unsigned int iLayer = 0; iLayer < layers.size(); ++iLayer) {
                                GblDetectorLayer& layer = layers[iLayer];
                                unsigned int lid = layer.getLayerID(); // layer ID (0 = vertex)
                                // std::cout << " hit " << lid << " " << hits[iLayer].transpose() << std::endl;
                                // prediction from seeding helix
                                GblHelixPrediction pred = layer.intersectWithHelix(seed);
                                double sArc = pred.getArcLength();      // arc-length
                                Vector2d measPrediction = pred.getMeasPred(); // measurement prediction
                                Vector2d measPrecision = layer.getPrecision(); // measurement precision
                                // residuals
                                Vector2d res = measPrediction; // (virtual) wire positioned at measurement
                                // smear u according to resolution
                                Vector2d sigma = layer.getResolution();
                                if (lid > 0) // wire layer?
                                        res[0] += sigma[0] * unrm();
                                else
                                        std::cout << " impact par " << res[0] << " " << res[1]
                                                        << " " << seedCurv << " " << seedPhi0 << " "
                                                        << seedDca << " " << seedDzds << " " << seedZ0
                                                        << " " << sArc << " " << layers.size() << std::endl;
                                // transformation global system to local (curvilinear) (u,v) (matrix from row vectors)
                                Matrix<double, 2, 3> transG2l = pred.getCurvilinearDirs();
                                // transformation measurement system to global system
                                Matrix3d transM2g = layer.getMeasSystemDirs().inverse();
                                // projection matrix (measurement plane to local (u,v))
                                Matrix2d proM2l = transG2l * transM2g.block<3, 2>(0, 0); // skip measurement normal
                                // projection matrix (local (u,v) to measurement plane)
                                Matrix2d proL2m = proM2l.inverse();
                                // propagation
                                Matrix5d jacPointToPoint = gblSimpleJacobian(
                                                (sArc - sOld) / cosLambdaSeed, cosLambdaSeed, bfac);
                                sOld = sArc;
                                // point with (independent) measurements (in measurement system)
                                GblPoint point(jacPointToPoint);
                                if (lid > 0 or (iTrack == 0 and useBeamSpot)) // vertex only for first track (large correlations!)
                                        point.addMeasurement(proL2m, res, measPrecision);
                                // global labels and parameters for rigid body alignment
                                std::vector<int> labGlobal(6);
                                Vector3d pos = pred.getPosition();
                                Vector3d dir = pred.getDirection();
                                /* Layer alignment in local (measurement) system
                                 for (int p = 0; p < 6; p++)
                                 labGlobal[p] = (iLayer + 1) * 10 + p + 1;
                                 Matrix<double, 2, 6> derGlobal = layer.getRigidBodyDerLocal(pos,
                                 dir);
                                 */
                                // Chamber alignment in global system
                                unsigned int layerID = layer.getLayerID();
                                for (int p = 0; p < 6; p++)
                                        labGlobal[p] = layerID * 1000 + p + 1;  // layer alignment
                                Matrix<double, 2, 6> derGlobal = layer.getRigidBodyDerGlobal(
                                                pos, dir).block<2, 6>(0, 0);
                                point.addGlobals(labGlobal, derGlobal);
                                // add scatterer to point
                                double radlen = layer.getRadiationLength()
                                                / fabs(pred.getCosIncidence());
                                double errMs = gblMultipleScatteringError(qbyp, radlen);// simple model
                                if (errMs > 0.) {
                                        Vector2d scat(0., 0.);
                                        Vector2d scatPrec(1. / (errMs * errMs),
                                                        1. / (errMs * errMs)); // scattering precision matrix is diagonal in curvilinear system
                                        point.addScatterer(scat, scatPrec);
                                }
                                // add point to trajectory
                                listOfPoints.push_back(point);
                        }
                        listsOfPoints.push_back(listOfPoints);
                }
 
                // require 2 decent trajectories for composed trajectory
                unsigned int nAccepted = 0;
                for (unsigned int iTrack = 0; iTrack < nTrack; ++iTrack)
                        // sufficient length?
                        if (listsOfPoints[iTrack].size() >= 10)
                                nAccepted++;
                if (nAccepted != 2)
                        continue;
 
                // prepare composed trajectory
                std::vector<std::pair<std::vector<GblPoint>, MatrixXd> > aPointsAndTransList;
                for (unsigned int iTrack = 0; iTrack < nTrack; ++iTrack) {
                        aPointsAndTransList.push_back(
                                        make_pair(listsOfPoints[iTrack], listOfTrafos[iTrack]));
                }
                //
                // fit composed GBL trajectory
                //
 
                // create trajectory
                GblTrajectory traj(aPointsAndTransList);
                // fit trajectory
                double Chi2;
                int Ndf;
                double lostWeight;
                unsigned int ierr = traj.fit(Chi2, Ndf, lostWeight);
                std::cout << " Fit " << iTry << ": " << Chi2 << ", " << Ndf << ", "
                                << lostWeight << std::endl;
                traj.printTrajectory();
                // successfully fitted?
                if (!ierr) {
                        // write to MP binary file
                        traj.milleOut(mille);
                        // update statistics
                        Chi2Sum += Chi2;
                        NdfSum += Ndf;
                        LostSum += lostWeight;
                        numFit++;
                }
 
        }
 
        clock_t endTime = clock();
        double diff = endTime - startTime;
        double cps = CLOCKS_PER_SEC;
        std::cout << " Time elapsed " << diff / cps << " s" << std::endl;
        std::cout << " Chi2/Ndf = " << Chi2Sum / NdfSum << std::endl;
        std::cout << " Tracks fitted " << numFit << std::endl;
        if (LostSum > 0.)
                std::cout << " Weight lost   " << LostSum << std::endl;
}