Implement new TrackState EDM used in KF

This MR adds a new track state EDM called MultiTrajectory. It acts as a track state collection, which internally stores all track state components in arrays. Each track state is then an index tuple, pointing to the components in the backing storage. Each track state has a previous index. Iterating back from a track state over these previous indices until you reach the beginning of the trajectory gives you a consistent set of track state. In the case of the regular KF, this is always a simple sequence, but it can be used to have forking trajectories, that can then be traced back individually.

Additionally, the index structure allows reusing storage between track state. If you have a track state with one set of predicted parameters, for instance, it will allow you to clone a track state, only resetting some components, and reusing shared ones (this bit isn't actually implemented yet).

Measurements are stored in an overallocated way, meaning there is always storage for the maximum measurement dimension.

MultiTrajectory can be queried for a track state representation at given index. This will return a TrackStateProxy. Track state proxies have getters for all components, and where possible, will return mutable (or immutable in case of a const proxy) references (sometimes implemented as Eigen map types). This means you can write things like

auto trackstate = trajectory.getTrackState(4);
trackstate.filtered() = (A * B + C).inverse()

and the result will end up in the backing storage of MultiTrajectory. Methods for the calibrated measurement are implemented as both returning the actual overallocated backing storage matrix, as well as an effective matrix. The latter are in fact dynamic views into the static matrices, and thus should be avoided in any kind of context where performance is relevant.

The new EDM is used in the updated gain matrix updator and smoother. Here, the measurement visitor (see !598 (merged)), to dispatch a statically sized calculation based on the runtime measurement value that is stored in the trajectory.

This MR requires !598 (merged) and !596 (merged) to be merged first (i.e. includes their changes)

Closes #564 (closed) Closes #550 (closed)

Core/include/Acts/Fitter/GainMatrixUpdator.hpp

@@ -11,6 +11,7 @@
 #include <memory>
 #include <variant>
 #include "Acts/EventData/Measurement.hpp"
+#include "Acts/EventData/MeasurementHelpers.hpp"
 #include "Acts/EventData/MultiTrajectory.hpp"
 #include "Acts/EventData/TrackParameters.hpp"
 #include "Acts/Fitter/detail/VoidKalmanComponents.hpp"
@@ -70,43 +71,39 @@ class GainMatrixUpdator {
     auto filtered = trackState.filtered();
     auto filtered_covariance = trackState.filteredCovariance();
 
-    // For, we use the dynamically sized views we obtain from the track state
-    // proxy. THIS IS SLOW!
-    // @TODO: Use switch to dispatch to fixed size call path or use fixed size
-    // math without dispatch
-
-    const auto calibrated = trackState.effectiveCalibrated();
-    const auto calibrated_covariance =
-        trackState.effectiveCalibratedCovariance();
-
-    const auto H = trackState.effectiveProjector();
-
-    // SLOW SLOW SLOW
-    ActsMatrixXd K =
-        predicted_covariance * H.transpose() *
-        (H * predicted_covariance * H.transpose() + calibrated_covariance)
-            .inverse();
-
-    filtered = predicted + K * (calibrated - H * predicted);
-    filtered_covariance =
-        (ActsSymMatrixD<
-             MultiTrajectory<SourceLink>::ParametersSize>::Identity() -
-         K * H) *
-        predicted_covariance;
-
-    // calculate filtered residual
-    // SLOW SLOW SLOW
-    ActsVectorXd residual(trackState.calibratedSize());
-    residual = (calibrated - H * filtered);
-
-    // SLOW SLOW SLOW
-    ActsMatrixXd meas_unity(trackState.calibratedSize(),
-                            trackState.calibratedSize());
-    meas_unity.setIdentity();
-
-    trackState.chi2() =
-        (residual.transpose() *
-         ((meas_unity - H * K) * calibrated_covariance).inverse() * residual);
+    visit_measurement(
+        trackState.calibrated(), trackState.calibratedCovariance(),
+        trackState.calibratedSize(),
+        [&](const auto calibrated, const auto calibrated_covariance) {
+          constexpr size_t measdim = decltype(calibrated)::RowsAtCompileTime;
+          using cov_t = ActsSymMatrixD<measdim>;
+          using par_t = ActsVectorD<measdim>;
+
+          const ActsMatrixD<measdim, BoundParsDim> H =
+              trackState.projector()
+                  .template topLeftCorner<measdim, BoundParsDim>();
+
+          const ActsMatrixD<BoundParsDim, measdim> K =
+              predicted_covariance * H.transpose() *
+              (H * predicted_covariance * H.transpose() + calibrated_covariance)
+                  .inverse();
+
+          filtered = predicted + K * (calibrated - H * predicted);
+          filtered_covariance =
+              (ActsSymMatrixD<
+                   MultiTrajectory<SourceLink>::ParametersSize>::Identity() -
+               K * H) *
+              predicted_covariance;
+
+          // calculate filtered residual
+          par_t residual(trackState.calibratedSize());
+          residual = (calibrated - H * filtered);
+
+          trackState.chi2() =
+              (residual.transpose() *
+               ((cov_t::Identity() - H * K) * calibrated_covariance).inverse() *
+               residual);
+        });
 
     // always succeed, no outlier logic yet
     return true;