Tests/IntegrationTests/PropagationTests.hpp

0001 // This file is part of the ACTS project.
0002 //
0003 // Copyright (C) 2016 CERN for the benefit of the ACTS project
0004 //
0005 // This Source Code Form is subject to the terms of the Mozilla Public
0006 // License, v. 2.0. If a copy of the MPL was not distributed with this
0007 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
0008
0009 #pragma once
0010
0011 #include "Acts/Definitions/Direction.hpp"
0012 #include "Acts/Definitions/Units.hpp"
0013 #include "Acts/EventData/TrackParameters.hpp"
0014 #include "Acts/Geometry/CuboidVolumeBuilder.hpp"
0015 #include "Acts/Geometry/GeometryContext.hpp"
0016 #include "Acts/Geometry/TrackingGeometry.hpp"
0017 #include "Acts/Geometry/TrackingGeometryBuilder.hpp"
0018 #include "Acts/MagneticField/MagneticFieldContext.hpp"
0019 #include "Acts/Material/HomogeneousVolumeMaterial.hpp"
0020 #include "Acts/Material/Interactions.hpp"
0021 #include "Acts/Material/Material.hpp"
0022 #include "Acts/Surfaces/CylinderSurface.hpp"
0023 #include "Acts/Surfaces/DiscSurface.hpp"
0024 #include "Acts/Surfaces/PlaneSurface.hpp"
0025 #include "Acts/Surfaces/RectangleBounds.hpp"
0026 #include "Acts/Surfaces/StrawSurface.hpp"
0027 #include "Acts/Tests/CommonHelpers/FloatComparisons.hpp"
0028 #include "Acts/Tests/CommonHelpers/PredefinedMaterials.hpp"
0029 #include "Acts/Utilities/Logger.hpp"
0030 #include "Acts/Utilities/MathHelpers.hpp"
0031 #include "Acts/Utilities/UnitVectors.hpp"
0032 #include "Acts/Utilities/detail/periodic.hpp"
0033
0034 #include <utility>
0035
0036 inline std::shared_ptr<const Acts::TrackingGeometry> createDenseBlock(
0037     const Acts::GeometryContext& geoCtx) {
0038   using namespace Acts;
0039   using namespace UnitLiterals;
0040
0041   CuboidVolumeBuilder::VolumeConfig vConf;
0042   vConf.position = {0., 0., 0.};
0043   vConf.length = {4_m, 4_m, 4_m};
0044   vConf.volumeMaterial =
0045       std::make_shared<const HomogeneousVolumeMaterial>(Test::makeBeryllium());
0046   CuboidVolumeBuilder::Config conf;
0047   conf.volumeCfg.push_back(vConf);
0048   conf.position = {0., 0., 0.};
0049   conf.length = {4_m, 4_m, 4_m};
0050   CuboidVolumeBuilder cvb(conf);
0051   TrackingGeometryBuilder::Config tgbCfg;
0052   tgbCfg.trackingVolumeBuilders.push_back(
0053       [=](const auto& context, const auto& inner, const auto&) {
0054         return cvb.trackingVolume(context, inner, nullptr);
0055       });
0056
0057   return TrackingGeometryBuilder(tgbCfg).trackingGeometry(geoCtx);
0058 }
0059
0060 inline std::tuple<std::shared_ptr<const Acts::TrackingGeometry>,
0061                   std::vector<const Acts::Surface*>>
0062 createDenseTelescope(const Acts::GeometryContext& geoCtx,
0063                      Acts::Material material, double thickness) {
0064   using namespace Acts;
0065   using namespace UnitLiterals;
0066
0067   CuboidVolumeBuilder::Config conf;
0068   conf.position = {0., 0., 0.};
0069   conf.length = {4_m, 2_m, 2_m};
0070
0071   {
0072     CuboidVolumeBuilder::VolumeConfig start;
0073     start.position = {-1_m, 0, 0};
0074     start.length = {1_m, 1_m, 1_m};
0075     start.name = "start";
0076
0077     conf.volumeCfg.push_back(start);
0078   }
0079
0080   if (thickness < 1_m) {
0081     CuboidVolumeBuilder::VolumeConfig gap;
0082     gap.position = {-0.25 * (1_m + thickness), 0, 0};
0083     gap.length = {0.5 * (1_m - thickness), 1_m, 1_m};
0084     gap.name = "gap1";
0085
0086     conf.volumeCfg.push_back(gap);
0087   }
0088
0089   {
0090     CuboidVolumeBuilder::VolumeConfig dense;
0091     dense.position = {0, 0, 0};
0092     dense.length = {thickness, 1_m, 1_m};
0093     dense.volumeMaterial =
0094         std::make_shared<const HomogeneousVolumeMaterial>(material);
0095     dense.name = "dense";
0096
0097     conf.volumeCfg.push_back(dense);
0098   }
0099
0100   if (thickness < 1_m) {
0101     CuboidVolumeBuilder::VolumeConfig gap;
0102     gap.position = {0.25 * (1_m + thickness), 0, 0};
0103     gap.length = {0.5 * (1_m - thickness), 1_m, 1_m};
0104     gap.name = "gap2";
0105
0106     conf.volumeCfg.push_back(gap);
0107   }
0108
0109   {
0110     CuboidVolumeBuilder::SurfaceConfig surface;
0111     surface.position = {1.5_m, 0, 0};
0112     surface.rotation =
0113         Eigen::AngleAxisd(std::numbers::pi / 2, Eigen::Vector3d::UnitY())
0114             .matrix();
0115     surface.rBounds = std::make_shared<RectangleBounds>(1_m, 1_m);
0116
0117     CuboidVolumeBuilder::LayerConfig layer;
0118     layer.surfaceCfg.push_back(surface);
0119
0120     CuboidVolumeBuilder::VolumeConfig end;
0121     end.position = {1_m, 0, 0};
0122     end.length = {1_m, 1_m, 1_m};
0123     end.layerCfg.push_back(layer);
0124     end.name = "end";
0125
0126     conf.volumeCfg.push_back(end);
0127   }
0128
0129   CuboidVolumeBuilder cvb(conf);
0130
0131   TrackingGeometryBuilder::Config tgbCfg;
0132   tgbCfg.trackingVolumeBuilders.push_back(
0133       [=](const auto& context, const auto& inner, const auto&) {
0134         return cvb.trackingVolume(context, inner, nullptr);
0135       });
0136   auto detector = TrackingGeometryBuilder(tgbCfg).trackingGeometry(geoCtx);
0137
0138   std::vector<const Surface*> surfaces;
0139   detector->visitSurfaces(
0140       [&](const Surface* surface) { surfaces.push_back(surface); });
0141
0142   return {std::move(detector), std::move(surfaces)};
0143 }
0144
0145 // parameter construction helpers
0146
0147 /// Construct (initial) curvilinear parameters.
0148 inline Acts::BoundTrackParameters makeParametersCurvilinear(double phi,
0149                                                             double theta,
0150                                                             double absMom,
0151                                                             double charge) {
0152   using namespace Acts;
0153   using namespace UnitLiterals;
0154
0155   Vector4 pos4 = Vector4::Zero();
0156   auto particleHypothesis = ParticleHypothesis::pionLike(std::abs(charge));
0157   return BoundTrackParameters::createCurvilinear(
0158       pos4, phi, theta, particleHypothesis.qOverP(absMom, charge), std::nullopt,
0159       particleHypothesis);
0160 }
0161
0162 /// Construct (initial) curvilinear parameters with covariance.
0163 inline Acts::BoundTrackParameters makeParametersCurvilinearWithCovariance(
0164     double phi, double theta, double absMom, double charge) {
0165   using namespace Acts;
0166   using namespace UnitLiterals;
0167
0168   BoundVector stddev = BoundVector::Zero();
0169   // TODO use momentum-dependent resolutions
0170   stddev[eBoundLoc0] = 15_um;
0171   stddev[eBoundLoc1] = 80_um;
0172   stddev[eBoundTime] = 20_ps;
0173   stddev[eBoundPhi] = 20_mrad;
0174   stddev[eBoundTheta] = 30_mrad;
0175   stddev[eBoundQOverP] = 1_e / 10_GeV;
0176   BoundSquareMatrix corr = BoundSquareMatrix::Identity();
0177   corr(eBoundLoc0, eBoundLoc1) = corr(eBoundLoc1, eBoundLoc0) = 0.125;
0178   corr(eBoundLoc0, eBoundPhi) = corr(eBoundPhi, eBoundLoc0) = 0.25;
0179   corr(eBoundLoc1, eBoundTheta) = corr(eBoundTheta, eBoundLoc1) = -0.25;
0180   corr(eBoundTime, eBoundQOverP) = corr(eBoundQOverP, eBoundTime) = 0.125;
0181   corr(eBoundPhi, eBoundTheta) = corr(eBoundTheta, eBoundPhi) = -0.25;
0182   corr(eBoundPhi, eBoundQOverP) = corr(eBoundPhi, eBoundQOverP) = -0.125;
0183   corr(eBoundTheta, eBoundQOverP) = corr(eBoundTheta, eBoundQOverP) = 0.5;
0184   BoundSquareMatrix cov = stddev.asDiagonal() * corr * stddev.asDiagonal();
0185
0186   Vector4 pos4 = Vector4::Zero();
0187   auto particleHypothesis = ParticleHypothesis::pionLike(std::abs(charge));
0188   return BoundTrackParameters::createCurvilinear(
0189       pos4, phi, theta, particleHypothesis.qOverP(absMom, charge), cov,
0190       particleHypothesis);
0191 }
0192
0193 /// Construct (initial) neutral curvilinear parameters.
0194 inline Acts::BoundTrackParameters makeParametersCurvilinearNeutral(
0195     double phi, double theta, double absMom) {
0196   using namespace Acts;
0197   using namespace UnitLiterals;
0198
0199   Vector4 pos4 = Vector4::Zero();
0200   return BoundTrackParameters::createCurvilinear(
0201       pos4, phi, theta, 1 / absMom, std::nullopt, ParticleHypothesis::pion0());
0202 }
0203
0204 // helpers to compare track parameters
0205
0206 /// Check that two parameters object are consistent within the tolerances.
0207 ///
0208 /// \warning Does not check that they are defined on the same surface.
0209 inline void checkParametersConsistency(const Acts::BoundTrackParameters& cmp,
0210                                        const Acts::BoundTrackParameters& ref,
0211                                        const Acts::GeometryContext& geoCtx,
0212                                        double epsPos, double epsDir,
0213                                        double epsMom) {
0214   using namespace Acts;
0215
0216   // check stored parameters
0217   CHECK_CLOSE_ABS(cmp.template get<eBoundLoc0>(),
0218                   ref.template get<eBoundLoc0>(), epsPos);
0219   CHECK_CLOSE_ABS(cmp.template get<eBoundLoc1>(),
0220                   ref.template get<eBoundLoc1>(), epsPos);
0221   CHECK_CLOSE_ABS(cmp.template get<eBoundTime>(),
0222                   ref.template get<eBoundTime>(), epsPos);
0223   // check phi equivalence with circularity
0224   CHECK_SMALL(detail::radian_sym(cmp.template get<eBoundPhi>() -
0225                                  ref.template get<eBoundPhi>()),
0226               epsDir);
0227   CHECK_CLOSE_ABS(cmp.template get<eBoundTheta>(),
0228                   ref.template get<eBoundTheta>(), epsDir);
0229   CHECK_CLOSE_ABS(cmp.template get<eBoundQOverP>(),
0230                   ref.template get<eBoundQOverP>(), epsMom);
0231   // check derived parameters
0232   CHECK_CLOSE_ABS(cmp.position(geoCtx), ref.position(geoCtx), epsPos);
0233   CHECK_CLOSE_ABS(cmp.time(), ref.time(), epsPos);
0234   CHECK_CLOSE_ABS(cmp.direction(), ref.direction(), epsDir);
0235   CHECK_CLOSE_ABS(cmp.absoluteMomentum(), ref.absoluteMomentum(), epsMom);
0236   // charge should be identical not just similar
0237   BOOST_CHECK_EQUAL(cmp.charge(), ref.charge());
0238 }
0239
0240 /// Check that two parameters covariances are consistent within the tolerances.
0241 ///
0242 /// \warning Does not check that the parameters value itself are consistent.
0243 inline void checkCovarianceConsistency(const Acts::BoundTrackParameters& cmp,
0244                                        const Acts::BoundTrackParameters& ref,
0245                                        double relativeTolerance) {
0246   // either both or none have covariance set
0247   if (cmp.covariance().has_value()) {
0248     // comparison parameters have covariance but the reference does not
0249     BOOST_CHECK(ref.covariance().has_value());
0250   }
0251   if (ref.covariance().has_value()) {
0252     // reference parameters have covariance but the comparison does not
0253     BOOST_CHECK(cmp.covariance().has_value());
0254   }
0255   if (cmp.covariance().has_value() && ref.covariance().has_value()) {
0256     CHECK_CLOSE_COVARIANCE(cmp.covariance().value(), ref.covariance().value(),
0257                            relativeTolerance);
0258   }
0259 }
0260
0261 // helpers to construct target surfaces from track states
0262
0263 /// Construct the transformation from the curvilinear to the global coordinates.
0264 inline Acts::Transform3 createCurvilinearTransform(
0265     const Acts::BoundTrackParameters& params,
0266     const Acts::GeometryContext& geoCtx) {
0267   using namespace Acts;
0268
0269   Vector3 unitW = params.direction();
0270   auto [unitU, unitV] = createCurvilinearUnitVectors(unitW);
0271
0272   RotationMatrix3 rotation = RotationMatrix3::Zero();
0273   rotation.col(0) = unitU;
0274   rotation.col(1) = unitV;
0275   rotation.col(2) = unitW;
0276   Translation3 offset(params.position(geoCtx));
0277   Transform3 toGlobal = offset * rotation;
0278
0279   return toGlobal;
0280 }
0281
0282 /// Construct a z-cylinder centered at zero with the track on its surface.
0283 struct ZCylinderSurfaceBuilder {
0284   std::shared_ptr<Acts::CylinderSurface> operator()(
0285       const Acts::BoundTrackParameters& params,
0286       const Acts::GeometryContext& geoCtx) {
0287     using namespace Acts;
0288
0289     auto radius = params.position(geoCtx).template head<2>().norm();
0290     auto halfz = std::numeric_limits<double>::max();
0291     return Surface::makeShared<CylinderSurface>(Transform3::Identity(), radius,
0292                                                 halfz);
0293   }
0294 };
0295
0296 /// Construct a disc at track position with plane normal along track tangent.
0297 struct DiscSurfaceBuilder {
0298   std::shared_ptr<Acts::DiscSurface> operator()(
0299       const Acts::BoundTrackParameters& params,
0300       const Acts::GeometryContext& geoCtx) {
0301     using namespace Acts;
0302     using namespace UnitLiterals;
0303
0304     auto cl = createCurvilinearTransform(params, geoCtx);
0305     // shift the origin of the plane so the local particle position does not
0306     // sit directly at the rho=0,phi=undefined singularity
0307     // TODO this is a hack do avoid issues with the numerical covariance
0308     //      transport that does not work well at rho=0,
0309     Vector3 localOffset = Vector3::Zero();
0310     localOffset[ePos0] = 1_cm;
0311     localOffset[ePos1] = -1_cm;
0312     Vector3 globalOriginDelta = cl.linear() * localOffset;
0313     cl.pretranslate(globalOriginDelta);
0314
0315     return Surface::makeShared<DiscSurface>(cl);
0316   }
0317 };
0318
0319 /// Construct a plane at track position with plane normal along track tangent.
0320 struct PlaneSurfaceBuilder {
0321   std::shared_ptr<Acts::PlaneSurface> operator()(
0322       const Acts::BoundTrackParameters& params,
0323       const Acts::GeometryContext& geoCtx) {
0324     using namespace Acts;
0325
0326     return Surface::makeShared<PlaneSurface>(
0327         createCurvilinearTransform(params, geoCtx));
0328   }
0329 };
0330
0331 /// Construct a z-straw at the track position.
0332 struct ZStrawSurfaceBuilder {
0333   std::shared_ptr<Acts::StrawSurface> operator()(
0334       const Acts::BoundTrackParameters& params,
0335       const Acts::GeometryContext& geoCtx) {
0336     using namespace Acts;
0337
0338     return Surface::makeShared<StrawSurface>(
0339         Transform3(Translation3(params.position(geoCtx))));
0340   }
0341 };
0342
0343 // helper functions to run the propagation with additional checks
0344
0345 /// Propagate the initial parameters for the given pathlength in space.
0346 ///
0347 /// Use a negative path length to indicate backward propagation.
0348 template <typename propagator_t,
0349           typename options_t = typename propagator_t::template Options<>>
0350 inline std::pair<Acts::BoundTrackParameters, double> transportFreely(
0351     const propagator_t& propagator, const Acts::GeometryContext& geoCtx,
0352     const Acts::MagneticFieldContext& magCtx,
0353     const Acts::BoundTrackParameters& initialParams, double pathLength) {
0354   using namespace Acts;
0355   using namespace UnitLiterals;
0356
0357   // setup propagation options
0358   options_t options(geoCtx, magCtx);
0359   options.direction = Direction::fromScalar(pathLength);
0360   options.pathLimit = pathLength;
0361   options.surfaceTolerance = 1_nm;
0362   options.stepping.stepTolerance = 1_nm;
0363
0364   auto result = propagator.propagate(initialParams, options);
0365   BOOST_CHECK(result.ok());
0366   BOOST_CHECK(result.value().endParameters);
0367
0368   return {*result.value().endParameters, result.value().pathLength};
0369 }
0370
0371 /// Propagate the initial parameters to the target surface.
0372 template <typename propagator_t,
0373           typename options_t = typename propagator_t::template Options<>>
0374 inline std::pair<Acts::BoundTrackParameters, double> transportToSurface(
0375     const propagator_t& propagator, const Acts::GeometryContext& geoCtx,
0376     const Acts::MagneticFieldContext& magCtx,
0377     const Acts::BoundTrackParameters& initialParams,
0378     const Acts::Surface& targetSurface, double pathLimit) {
0379   using namespace Acts;
0380   using namespace UnitLiterals;
0381
0382   // setup propagation options
0383   options_t options(geoCtx, magCtx);
0384   options.direction = Direction::Forward();
0385   options.pathLimit = pathLimit;
0386   options.surfaceTolerance = 1_nm;
0387   options.stepping.stepTolerance = 1_nm;
0388
0389   auto result = propagator.propagate(initialParams, targetSurface, options);
0390   BOOST_CHECK(result.ok());
0391   BOOST_CHECK(result.value().endParameters);
0392
0393   return {*result.value().endParameters, result.value().pathLength};
0394 }
0395
0396 // self-consistency tests for a single propagator
0397
0398 /// Propagate the initial parameters the given path length along its
0399 /// trajectory and then propagate the final parameters back. Verify that the
0400 /// propagated parameters match the initial ones.
0401 template <typename propagator_t,
0402           typename options_t = typename propagator_t::template Options<>>
0403 inline void runForwardBackwardTest(
0404     const propagator_t& propagator, const Acts::GeometryContext& geoCtx,
0405     const Acts::MagneticFieldContext& magCtx,
0406     const Acts::BoundTrackParameters& initialParams, double pathLength,
0407     double epsPos, double epsDir, double epsMom) {
0408   // propagate parameters Acts::Direction::Forward()
0409   auto [fwdParams, fwdPathLength] = transportFreely<propagator_t, options_t>(
0410       propagator, geoCtx, magCtx, initialParams, pathLength);
0411   CHECK_CLOSE_ABS(fwdPathLength, pathLength, epsPos);
0412   // propagate propagated parameters back again
0413   auto [bwdParams, bwdPathLength] = transportFreely<propagator_t, options_t>(
0414       propagator, geoCtx, magCtx, fwdParams, -pathLength);
0415   CHECK_CLOSE_ABS(bwdPathLength, -pathLength, epsPos);
0416   // check that initial and back-propagated parameters match
0417   checkParametersConsistency(initialParams, bwdParams, geoCtx, epsPos, epsDir,
0418                              epsMom);
0419 }
0420
0421 /// Propagate the initial parameters once for the given path length and
0422 /// use the propagated parameters to define a target surface. Propagate the
0423 /// initial parameters again to the target surface. Verify that the surface has
0424 /// been found and the parameters are consistent.
0425 template <typename propagator_t, typename surface_builder_t,
0426           typename options_t = typename propagator_t::template Options<>>
0427 inline void runToSurfaceTest(const propagator_t& propagator,
0428                              const Acts::GeometryContext& geoCtx,
0429                              const Acts::MagneticFieldContext& magCtx,
0430                              const Acts::BoundTrackParameters& initialParams,
0431                              double pathLength,
0432                              surface_builder_t&& buildTargetSurface,
0433                              double epsPos, double epsDir, double epsMom) {
0434   // free propagation for the given path length
0435   auto [freeParams, freePathLength] = transportFreely<propagator_t, options_t>(
0436       propagator, geoCtx, magCtx, initialParams, pathLength);
0437   CHECK_CLOSE_ABS(freePathLength, pathLength, epsPos);
0438   // build a target surface at the propagated position
0439   auto surface = buildTargetSurface(freeParams, geoCtx);
0440   BOOST_CHECK(surface);
0441
0442   // bound propagation onto the target surface
0443   // increase path length limit to ensure the surface can be reached
0444   auto [surfParams, surfPathLength] =
0445       transportToSurface<propagator_t, options_t>(propagator, geoCtx, magCtx,
0446                                                   initialParams, *surface,
0447                                                   1.5 * pathLength);
0448   CHECK_CLOSE_ABS(surfPathLength, pathLength, epsPos);
0449
0450   // check that the to-surface propagation matches the defining free parameters
0451   CHECK_CLOSE_ABS(surfParams.position(geoCtx), freeParams.position(geoCtx),
0452                   epsPos);
0453   CHECK_CLOSE_ABS(surfParams.time(), freeParams.time(), epsPos);
0454   CHECK_CLOSE_ABS(surfParams.direction(), freeParams.direction(), epsDir);
0455   CHECK_CLOSE_ABS(surfParams.absoluteMomentum(), freeParams.absoluteMomentum(),
0456                   epsMom);
0457   CHECK_CLOSE_ABS(surfPathLength, freePathLength, epsPos);
0458 }
0459
0460 // consistency tests between two propagators
0461
0462 /// Propagate the initial parameters along their trajectory for the given path
0463 /// length using two different propagators and verify consistent output.
0464 template <typename cmp_propagator_t, typename ref_propagator_t>
0465 inline void runForwardComparisonTest(
0466     const cmp_propagator_t& cmpPropagator,
0467     const ref_propagator_t& refPropagator, const Acts::GeometryContext& geoCtx,
0468     const Acts::MagneticFieldContext& magCtx,
0469     const Acts::BoundTrackParameters& initialParams, double pathLength,
0470     double epsPos, double epsDir, double epsMom, double tolCov) {
0471   // propagate twice using the two different propagators
0472   auto [cmpParams, cmpPath] = transportFreely<cmp_propagator_t>(
0473       cmpPropagator, geoCtx, magCtx, initialParams, pathLength);
0474   auto [refParams, refPath] = transportFreely<ref_propagator_t>(
0475       refPropagator, geoCtx, magCtx, initialParams, pathLength);
0476   // check parameter comparison
0477   checkParametersConsistency(cmpParams, refParams, geoCtx, epsPos, epsDir,
0478                              epsMom);
0479   checkCovarianceConsistency(cmpParams, refParams, tolCov);
0480   CHECK_CLOSE_ABS(cmpPath, pathLength, epsPos);
0481   CHECK_CLOSE_ABS(refPath, pathLength, epsPos);
0482   CHECK_CLOSE_ABS(cmpPath, refPath, epsPos);
0483 }
0484
0485 /// Propagate the initial parameters along their trajectory for the given path
0486 /// length using the reference propagator. Use the propagated track parameters
0487 /// to define a target plane. Propagate the initial parameters using two
0488 /// different propagators and verify consistent output.
0489 template <typename cmp_propagator_t, typename ref_propagator_t,
0490           typename surface_builder_t>
0491 inline void runToSurfaceComparisonTest(
0492     const cmp_propagator_t& cmpPropagator,
0493     const ref_propagator_t& refPropagator, const Acts::GeometryContext& geoCtx,
0494     const Acts::MagneticFieldContext& magCtx,
0495     const Acts::BoundTrackParameters& initialParams, double pathLength,
0496     surface_builder_t&& buildTargetSurface, double epsPos, double epsDir,
0497     double epsMom, double tolCov) {
0498   // free propagation with the reference propagator for the given path length
0499   auto [freeParams, freePathLength] = transportFreely<ref_propagator_t>(
0500       refPropagator, geoCtx, magCtx, initialParams, pathLength);
0501   CHECK_CLOSE_ABS(freePathLength, pathLength, epsPos);
0502
0503   // build a target surface at the propagated position
0504   auto surface = buildTargetSurface(freeParams, geoCtx);
0505   BOOST_CHECK(surface);
0506
0507   // propagate twice to the surface using the two different propagators
0508   // increase path length limit to ensure the surface can be reached
0509   auto [cmpParams, cmpPath] = transportToSurface<cmp_propagator_t>(
0510       cmpPropagator, geoCtx, magCtx, initialParams, *surface, 1.5 * pathLength);
0511   auto [refParams, refPath] = transportToSurface<ref_propagator_t>(
0512       refPropagator, geoCtx, magCtx, initialParams, *surface, 1.5 * pathLength);
0513   // check parameter comparison
0514   checkParametersConsistency(cmpParams, refParams, geoCtx, epsPos, epsDir,
0515                              epsMom);
0516   checkCovarianceConsistency(cmpParams, refParams, tolCov);
0517   CHECK_CLOSE_ABS(cmpPath, pathLength, epsPos);
0518   CHECK_CLOSE_ABS(refPath, pathLength, epsPos);
0519   CHECK_CLOSE_ABS(cmpPath, refPath, epsPos);
0520 }
0521
0522 template <typename propagator_t>
0523 inline void runDenseForwardTest(
0524     const propagator_t& propagator, const Acts::GeometryContext& geoCtx,
0525     const Acts::MagneticFieldContext& magCtx, double p, double q,
0526     const Acts::Surface& targetSurface, const Acts::Material& material,
0527     double thickness, const Acts::Logger& logger = Acts::getDummyLogger()) {
0528   using namespace Acts;
0529   using namespace UnitLiterals;
0530
0531   const auto particleHypothesis = ParticleHypothesis::muon();
0532   const float mass = particleHypothesis.mass();
0533   const float absQ = std::abs(q);
0534   const double initialQOverP = particleHypothesis.qOverP(p, q);
0535   const auto initialParams = BoundTrackParameters::createCurvilinear(
0536       Vector4(-1.5_m, 0, 0, 0), Vector3::UnitX(), initialQOverP,
0537       BoundVector::Constant(1e-16).asDiagonal(), particleHypothesis);
0538
0539   typename propagator_t::template Options<> options(geoCtx, magCtx);
0540   options.maxSteps = 10000;
0541   options.stepping.maxStepSize = 100_mm;
0542   options.stepping.dense.meanEnergyLoss = true;
0543   options.stepping.dense.momentumCutOff = 1_MeV;
0544
0545   const auto result =
0546       propagator.propagate(initialParams, targetSurface, options);
0547
0548   BOOST_CHECK(result.ok());
0549   CHECK_CLOSE_REL(3_m, result->pathLength, 1e-6);
0550   BOOST_CHECK(result->endParameters);
0551
0552   BoundTrackParameters endParams = result->endParameters.value();
0553
0554   BOOST_CHECK(endParams.covariance());
0555   CHECK_CLOSE_ABS(initialParams.position(geoCtx) + Acts::Vector3(3_m, 0, 0),
0556                   endParams.position(geoCtx), 1e-6);
0557   CHECK_CLOSE_ABS(initialParams.direction(), endParams.direction(), 1e-6);
0558
0559   const auto& cov = endParams.covariance().value();
0560
0561   const double endQOverP = endParams.qOverP();
0562   const double endP = endParams.absoluteMomentum();
0563   const double endEloss =
0564       Acts::fastHypot(p, mass) - Acts::fastHypot(endP, mass);
0565   const double endErrX = std::sqrt(cov(eBoundLoc0, eBoundLoc0));
0566   const double endErrY = std::sqrt(cov(eBoundLoc1, eBoundLoc1));
0567   const double endErrQOverP = std::sqrt(cov(eBoundQOverP, eBoundQOverP));
0568   const double endErrP =
0569       (absQ / std::pow(endParams.qOverP(), 2)) * endErrQOverP;
0570   const double endErrE = (p / Acts::fastHypot(p, mass)) * endErrP;
0571   const double endErrTheta = std::sqrt(cov(eBoundTheta, eBoundTheta));
0572   const double endErrPhi = std::sqrt(cov(eBoundPhi, eBoundPhi));
0573
0574   ACTS_VERBOSE("input q/p = " << initialQOverP);
0575   ACTS_VERBOSE("input p = " << p);
0576   ACTS_VERBOSE("output q/p = " << endQOverP);
0577   ACTS_VERBOSE("output p = " << endP);
0578   ACTS_VERBOSE("output t = " << endParams.time());
0579   ACTS_VERBOSE("output eloss = " << endEloss);
0580   ACTS_VERBOSE("output err x = " << endErrX);
0581   ACTS_VERBOSE("output err y = " << endErrY);
0582   ACTS_VERBOSE("output err q/p = " << endErrQOverP);
0583   ACTS_VERBOSE("output err p = " << endErrP);
0584   ACTS_VERBOSE("output err E = " << endErrE);
0585   ACTS_VERBOSE("output err theta = " << endErrTheta);
0586   ACTS_VERBOSE("output err phi = " << endErrPhi);
0587
0588   BOOST_CHECK_CLOSE(endErrX, endErrY, 1e-6);
0589   BOOST_CHECK_CLOSE(endErrTheta, endErrPhi, 1e-6);
0590
0591   const float elossInitial = computeEnergyLossMean(
0592       MaterialSlab(material, thickness), particleHypothesis.absolutePdg(), mass,
0593       initialQOverP, absQ);
0594   const float elossFinal = computeEnergyLossMean(
0595       MaterialSlab(material, thickness), particleHypothesis.absolutePdg(), mass,
0596       endQOverP, absQ);
0597
0598   ACTS_VERBOSE("ref eloss initial = " << elossInitial);
0599   ACTS_VERBOSE("ref eloss final = " << elossFinal);
0600
0601   // energy loss will be smaller than elossInitial because of the increasing
0602   // radiation losses
0603   BOOST_CHECK_LT(endEloss, elossInitial);
0604   BOOST_CHECK_GT(endEloss, elossFinal);
0605
0606   const float theta0Initial = computeMultipleScatteringTheta0(
0607       MaterialSlab(material, thickness), particleHypothesis.absolutePdg(), mass,
0608       initialQOverP, absQ);
0609   const float theta0Final = computeMultipleScatteringTheta0(
0610       MaterialSlab(material, thickness), particleHypothesis.absolutePdg(), mass,
0611       endQOverP, absQ);
0612
0613   ACTS_VERBOSE("ref theta0 initial = " << theta0Initial);
0614   ACTS_VERBOSE("ref theta0 final = " << theta0Final);
0615
0616   // angle errors will be larger than theta0Initial because of the energy loss
0617   BOOST_CHECK_GE(endErrTheta, theta0Initial);
0618   BOOST_CHECK_LT(endErrTheta, theta0Final);
0619   CHECK_CLOSE_REL(endErrTheta, 0.5 * (theta0Initial + theta0Final), 0.1);
0620
0621   // estimates the positional uncertainty after crossing the material
0622   // block by integrating the angle variance over substeps
0623   const auto estimateVarX = [&](double qOverP, std::size_t substeps) {
0624     double previousTheta0 = 0;
0625     double varAngle = 0;
0626     double varPosition = 0;
0627     double covAnglePosition = 0;
0628
0629     const auto step = [&](double substep, double theta0) {
0630       double deltaVarTheta = square(theta0) - square(previousTheta0);
0631       double deltaVarPos = varAngle * square(substep) +
0632                            2 * covAnglePosition * substep +
0633                            deltaVarTheta * (square(substep) / 3);
0634       double deltaCovAnglePosition =
0635           varAngle * substep + deltaVarTheta * substep / 2;
0636       previousTheta0 = theta0;
0637       varAngle += deltaVarTheta;
0638       varPosition += deltaVarPos;
0639       covAnglePosition += deltaCovAnglePosition;
0640     };
0641
0642     // step through the material block
0643     for (std::size_t i = 0; i < substeps; ++i) {
0644       const float theta0 = computeMultipleScatteringTheta0(
0645           MaterialSlab(material, (i + 1) * thickness / substeps),
0646           particleHypothesis.absolutePdg(), mass, qOverP, absQ);
0647       step(thickness / substeps, theta0);
0648     }
0649
0650     // step to the target surface
0651     step(1_m, previousTheta0);
0652
0653     return varPosition;
0654   };
0655
0656   // as a lower bound for sigma_x we use the initial theta0
0657   const double lowerBoundVarX = estimateVarX(initialQOverP, 10);
0658   // as an upper bound for sigma_x we use the final theta0
0659   const double upperBoundVarX = estimateVarX(endQOverP, 10);
0660
0661   const double lowerBoundSigmaX = std::sqrt(lowerBoundVarX);
0662   const double upperBoundSigmaX = std::sqrt(upperBoundVarX);
0663
0664   ACTS_VERBOSE("ref lower bound sigma x = " << lowerBoundSigmaX);
0665   ACTS_VERBOSE("ref upper bound sigma x = " << upperBoundSigmaX);
0666
0667   BOOST_CHECK_GT(endErrX, lowerBoundSigmaX);
0668   BOOST_CHECK_LT(endErrX, upperBoundSigmaX);
0669   CHECK_CLOSE_REL(endErrX, 0.5 * (lowerBoundSigmaX + upperBoundSigmaX), 0.2);
0670
0671   const float qOverPSigma = computeEnergyLossLandauSigmaQOverP(
0672       MaterialSlab(material, thickness), mass, initialQOverP, absQ);
0673
0674   ACTS_VERBOSE("ref sigma q/p = " << qOverPSigma);
0675
0676   CHECK_CLOSE_REL(endErrQOverP, qOverPSigma, 1e-4);
0677 }