# Class Acts::EigenStepper¶

template<typename extensionlist_t = StepperExtensionList<DefaultExtension>, typename auctioneer_t = detail::VoidAuctioneer>
class EigenStepper

Runge-Kutta-Nystroem stepper based on Eigen implementation for the following ODE:

r = (x,y,z) … global position T = (Ax,Ay,Az) … momentum direction (normalized)

dr/ds = T dT/ds = q/p * (T x B)

with s being the arc length of the track, q the charge of the particle, p the momentum magnitude and B the magnetic field

Public Types

using BoundState = std::tuple<BoundTrackParameters, Jacobian, double>
using Covariance = BoundSymMatrix
using CurvilinearState = std::tuple<CurvilinearTrackParameters, Jacobian, double>
using Jacobian = BoundMatrix

Jacobian, Covariance and State defintions.

Public Functions

EigenStepper(std::shared_ptr<const MagneticFieldProvider> bField)

Constructor requires knowledge of the detector’s magnetic field.

Result<BoundState> boundState(State &state, const Surface &surface, bool transportCov = true, const FreeToBoundCorrection &freeToBoundCorrection = FreeToBoundCorrection(false)) const

Create and return the bound state at the current position.

This transports (if necessary) the covariance to the surface and creates a bound state. It does not check if the transported state is at the surface, this needs to be guaranteed by the propagator

Parameters
• state[in] State that will be presented as `BoundState`

• surface[in] The surface to which we bind the state

• transportCov[in] Flag steering covariance transport

• freeToBoundCorrection[in] Correction for non-linearity effect during transform from free to bound

Returns

A bound state:

• the parameters at the surface

• the stepwise jacobian towards it (from last bound)

• and the path length (from start - for ordering)

inline double charge(const State &state) const

Charge access.

Parameters

state – [in] The stepping state (thread-local cache)

CurvilinearState curvilinearState(State &state, bool transportCov = true) const

Create and return a curvilinear state at the current position.

This transports (if necessary) the covariance to the current position and creates a curvilinear state.

Parameters
• state[in] State that will be presented as `CurvilinearState`

• transportCov[in] Flag steering covariance transport

Returns

A curvilinear state:

• the curvilinear parameters at given position

• the stepweise jacobian towards it (from last bound)

• and the path length (from start - for ordering)

inline Vector3 direction(const State &state) const

Momentum direction accessor.

Parameters

state – [in] The stepping state (thread-local cache)

inline Result<Vector3> getField(State &state, const Vector3 &pos) const

Get the field for the stepping, it checks first if the access is still within the Cell, and updates the cell if necessary.

Parameters
• state[inout] is the propagation state associated with the track the magnetic field cell is used (and potentially updated)

• pos[in] is the field position

inline double getStepSize(const State &state, ConstrainedStep::Type stype) const

Get the step size.

Parameters
• state – [in] The stepping state (thread-local cache)

• stype – [in] The step size type to be returned

template<typename charge_t>
State makeState(std::reference_wrapper<const GeometryContext> gctx, std::reference_wrapper<const MagneticFieldContext> mctx, const SingleBoundTrackParameters<charge_t> &par, NavigationDirection ndir = NavigationDirection::Forward, double ssize = std::numeric_limits<double>::max(), double stolerance = s_onSurfaceTolerance) const
inline double momentum(const State &state) const

Absolute momentum accessor.

Parameters

state – [in] The stepping state (thread-local cache)

inline std::string outputStepSize(const State &state) const

Output the Step Size - single component.

Parameters

state – [in,out] The stepping state (thread-local cache)

inline double overstepLimit(const State&) const

Overstep limit.

inline Vector3 position(const State &state) const

Global particle position accessor.

Parameters

state – [in] The stepping state (thread-local cache)

inline void releaseStepSize(State &state) const

Release the Step size.

Parameters

state – [in,out] The stepping state (thread-local cache)

void resetState(State &state, const BoundVector &boundParams, const BoundSymMatrix &cov, const Surface &surface, const NavigationDirection navDir = NavigationDirection::Forward, const double stepSize = std::numeric_limits<double>::max()) const

Resets the state.

Parameters
• state[inout] State of the stepper

• boundParams[in] Parameters in bound parametrisation

• cov[in] Covariance matrix

• surface[in] The reference surface of the bound parameters

• stepSize[in] Step size

void setIdentityJacobian(State &state) const

Method that reset the Jacobian to the Identity for when no bound state are available.

Parameters

state[inout] State of the stepper

inline void setStepSize(State &state, double stepSize, ConstrainedStep::Type stype = ConstrainedStep::actor, bool release = true) const

Set Step size - explicitely with a double.

Parameters
• state – [in,out] The stepping state (thread-local cache)

• stepSize – [in] The step size value

• stype – [in] The step size type to be set

• release – [in] Do we release the step size?

template<typename propagator_state_t>
Result<double> step(propagator_state_t &state) const

Perform a Runge-Kutta track parameter propagation step.

Note

The state contains the desired step size. It can be negative during backwards track propagation, and since we’re using an adaptive algorithm, it can be modified by the stepper class during propagation.

Parameters

state[inout] is the propagation

inline double time(const State &state) const

Time access.

Parameters

state – [in] The stepping state (thread-local cache)

void transportCovarianceToBound(State &state, const Surface &surface, const FreeToBoundCorrection &freeToBoundCorrection = FreeToBoundCorrection(false)) const

Method for on-demand transport of the covariance to a new curvilinear frame at current position, or direction of the state.

Note

no check is done if the position is actually on the surface

Template Parameters

surface_t – the Surface type

Parameters
• state[inout] State of the stepper

• surface[in] is the surface to which the covariance is forwarded to

• freeToBoundCorrection[in] Correction for non-linearity effect during transform from free to bound

void transportCovarianceToCurvilinear(State &state) const

Method for on-demand transport of the covariance to a new curvilinear frame at current position, or direction of the state.

Parameters

state[inout] State of the stepper

void update(State &state, const FreeVector &freeParams, const BoundVector &boundParams, const Covariance &covariance, const Surface &surface) const

Method to update a stepper state to the some parameters.

Parameters
• state[inout] State object that will be updated

• freeParams[in] Free parameters that will be written into `state`

• boundParams[in] Corresponding bound parameters used to update jacToGlobal in `state`

• covariance[in] The covariance that will be written into `state`

• surface[in] The surface used to update the jacToGlobal

void update(State &state, const Vector3 &uposition, const Vector3 &udirection, double up, double time) const

Method to update momentum, direction and p.

Parameters
• state[inout] State object that will be updated

• uposition[in] the updated position

• udirection[in] the updated direction

• up[in] the updated momentum value

• time[in] the updated time value

template<typename object_intersection_t>
inline void updateStepSize(State &state, const object_intersection_t &oIntersection, bool release = true) const

Update step size.

This method intersects the provided surface and update the navigation step estimation accordingly (hence it changes the state). It also returns the status of the intersection to trigger onSurface in case the surface is reached.

Parameters
• state – [in,out] The stepping state (thread-local cache)

• oIntersection – [in] The ObjectIntersection to layer, boundary, etc

• release – [in] boolean to trigger step size release

inline Intersection3D::Status updateSurfaceStatus(State &state, const Surface &surface, const BoundaryCheck &bcheck, LoggerWrapper logger = getDummyLogger()) const

Update surface status.

It checks the status to the reference surface & updates the step size accordingly

Parameters
• state[inout] The stepping state (thread-local cache)

• surface[in] The surface provided

• bcheck[in] The boundary check for this status update

• logger[in] A `LoggerWrapper` instance

struct State

State for track parameter propagation.

It contains the stepping information and is provided thread local by the propagator

Public Functions

State() = delete
template<typename charge_t>
inline explicit State(const GeometryContext &gctx, MagneticFieldProvider::Cache fieldCacheIn, const SingleBoundTrackParameters<charge_t> &par, NavigationDirection ndir = NavigationDirection::Forward, double ssize = std::numeric_limits<double>::max(), double stolerance = s_onSurfaceTolerance)

Constructor from the initial bound track parameters.

Note

the covariance matrix is copied when needed

Template Parameters

charge_t – Type of the bound parameter charge

Parameters
• gctx[in] is the context object for the geometry

• fieldCacheIn[in] is the cache object for the magnetic field

• par[in] The track parameters at start

• ndir[in] The navigation direction w.r.t momentum

• ssize[in] is the maximum step size

• stolerance[in] is the stepping tolerance

Public Members

auctioneer_t auctioneer

Auctioneer for choosing the extension.

Vector3 B_first

Magnetic field evaulations.

Vector3 B_last
Vector3 B_middle
Covariance cov = Covariance::Zero()
bool covTransport = false

Covariance matrix (and indicator) associated with the initial error on track parameters.

FreeVector derivative = FreeVector::Zero()

The propagation derivative.

extensionlist_t extension

List of algorithmic extensions.

MagneticFieldProvider::Cache fieldCache

This caches the current magnetic field cell and stays (and interpolates) within it as long as this is valid.

See step() code for details.

std::reference_wrapper<const GeometryContext> geoContext

The geometry context.

Jacobian jacobian = Jacobian::Identity()

The full jacobian of the transport entire transport.

BoundToFreeMatrix jacToGlobal = BoundToFreeMatrix::Zero()

Jacobian from local to the global frame.

FreeMatrix jacTransport = FreeMatrix::Identity()

Pure transport jacobian part from runge kutta integration.

Vector3 k1

k_i of the RKN4 algorithm

Vector3 k2
Vector3 k3
Vector3 k4
std::array<double, 4> kQoP

k_i elements of the momenta

Navigation direction, this is needed for searching.

FreeVector pars = FreeVector::Zero()

Internal free vector parameters.

double pathAccumulated = 0.

Accummulated path length state.

double previousStepSize = 0.

Last performed step (for overstep limit calculation)

double q = 1.

The charge as the free vector can be 1/p or q/p.

struct Acts::EigenStepper::State::[anonymous] stepData

Storage of magnetic field and the sub steps during a RKN4 step.

ConstrainedStep stepSize

Adaptive step size of the runge-kutta integration.

double tolerance = s_onSurfaceTolerance

The tolerance for the stepping.