Composed trajectories: geometric constraint added (to kinematic)

git-svn-id: http://svnsrv.desy.de/public/GeneralBrokenLines/trunk@148 281f6f2b-e318-4fd1-8bce-1a4ba7aab212

cpp/CMakeLists.txt

@@ -6,8 +6,8 @@ PROJECT(GBL)
 
 # project version
 SET( ${PROJECT_NAME}_VERSION_MAJOR 2 )
-SET( ${PROJECT_NAME}_VERSION_MINOR 1 )
-SET( ${PROJECT_NAME}_VERSION_PATCH 6 )
+SET( ${PROJECT_NAME}_VERSION_MINOR 2 )
+SET( ${PROJECT_NAME}_VERSION_PATCH 0 )
 
 # make life easier and simply use the ilcsoft default settings
 # load default ilcsoft settings (install prefix, build type, rpath, etc.)

cpp/examples/exampleUtil.cpp

@@ -361,7 +361,7 @@ GblDetectorLayer::GblDetectorLayer(const std::string aName,
 GblDetectorLayer::~GblDetectorLayer() {
 }
 
-/// Print GblSiliconlayer.
+/// Print GblDetectorLayer.
 void GblDetectorLayer::print() const {
 	IOFormat CleanFmt(4, 0, ", ", "\n", "[", "]");
 	std::cout << " Layer " << name << " " << layer << " : " << measDim << "D, "
@@ -391,14 +391,27 @@ Eigen::Vector2d GblDetectorLayer::getPrecision() const {
 	return precision;
 }
 
+/// Get center.
+Eigen::Vector3d GblDetectorLayer::getCenter() const {
+	return center;
+}
+
 /// Get directions of measurement system.
 /**
  * Matrix from row vectors (transformation from global to measurement system)
  */
-const Eigen::Matrix3d& GblDetectorLayer::getMeasSystemDirs() const {
+Eigen::Matrix3d GblDetectorLayer::getMeasSystemDirs() const {
 	return global2meas;;
 }
 
+/// Get directions of alignment system.
+/**
+ * Matrix from row vectors (transformation from global to alignment system)
+ */
+Eigen::Matrix3d GblDetectorLayer::getAlignSystemDirs() const {
+	return global2align;;
+}
+
 /// Intersect with helix.
 /**
  * \param [in]  hlx  helix
@@ -413,7 +426,7 @@ GblHelixPrediction GblDetectorLayer::intersectWithHelix(
  * \param[in] position   position (of prediction or measurement)
  * \param[in] direction  track direction
  */
-const Matrix<double, 3, 6> GblDetectorLayer::getRigidBodyDerGlobal(
+Matrix<double, 3, 6> GblDetectorLayer::getRigidBodyDerGlobal(
 		Eigen::Vector3d& position, Eigen::Vector3d& direction) const {
 // lever arms (for rotations)
 	Vector3d dist = position;
@@ -435,14 +448,20 @@ const Matrix<double, 3, 6> GblDetectorLayer::getRigidBodyDerGlobal(
 	return global2meas * drdm * dmdg;
 }
 
-/// Get rigid body derivatives in local (alignment) frame (with N=(0,0,1)).
+/// Get rigid body derivatives in local (alignment) frame (rotated in measurement plane).
 /**
- * Normal to measurement plane has to be (0,0,1) in local frame.
+ * The orthogonal alignment frame differs from measurement frame only by rotations
+ * around normal to measurement plane.
+ *
+ * Equivalent to:
+ * \code
+ * getRigidBodyDerGlobal(position, direction) * getTrafoLocalToGlobal(center, global2align)
+ * \endcode
  *
  * \param[in] position   position (of prediction or measurement)
  * \param[in] direction  track direction
  */
-const Matrix<double, 2, 6> GblDetectorLayer::getRigidBodyDerLocal(
+Matrix<double, 2, 6> GblDetectorLayer::getRigidBodyDerLocal(
 		Eigen::Vector3d& position, Eigen::Vector3d& direction) const {
 	// track direction in local system
 	Vector3d tLoc = global2align * direction;
@@ -458,7 +477,47 @@ const Matrix<double, 2, 6> GblDetectorLayer::getRigidBodyDerLocal(
 	Matrix<double, 2, 6> drldg;
 	drldg << 1.0, 0.0, -uSlope, vPos * uSlope, -uPos * uSlope, vPos, 0.0, 1.0, -vSlope, vPos
 			* vSlope, -uPos * vSlope, -uPos;
-	return drldg;
+	// local (alignment) to measurement system
+	Matrix3d local2meas = global2meas * global2align.transpose();
+	return local2meas.block<2, 2>(0, 0) * drldg;
+}
+
+/// Get transformation for rigid body derivatives from global to local (alignment) system.
+/**
+ * local = rotation * (global-offset)
+ *
+ * \param[in] offset    offset of alignment system
+ * \param[in] rotation  rotation of alignment system
+ */
+Matrix<double, 6, 6> GblDetectorLayer::getTrafoGlobalToLocal(
+		Eigen::Vector3d& offset, Eigen::Matrix3d& rotation) const {
+	// transformation global to local
+	Matrix<double, 6, 6> glo2loc = Matrix<double, 6, 6>::Zero();
+	Matrix3d leverArms;
+	leverArms << 0., offset[2], -offset[1], -offset[2], 0., offset[0], offset[1], -offset[0], 0.;
+	glo2loc.block<3, 3>(0, 0) = rotation;
+	glo2loc.block<3, 3>(0, 3) = -rotation * leverArms;
+	glo2loc.block<3, 3>(3, 3) = rotation;
+	return glo2loc;
+}
+
+/// Get transformation for rigid body derivatives from local (alignment) to global system.
+/**
+ * local = rotation * (global-offset)
+ *
+ * \param[in] offset    offset of alignment system
+ * \param[in] rotation  rotation of alignment system
+ */
+Matrix<double, 6, 6> GblDetectorLayer::getTrafoLocalToGlobal(
+		Eigen::Vector3d& offset, Eigen::Matrix3d& rotation) const {
+	// transformation local to global
+	Matrix<double, 6, 6> loc2glo = Matrix<double, 6, 6>::Zero();
+	Matrix3d leverArms;
+	leverArms << 0., offset[2], -offset[1], -offset[2], 0., offset[0], offset[1], -offset[0], 0.;
+	loc2glo.block<3, 3>(0, 0) = rotation.transpose();
+	loc2glo.block<3, 3>(0, 3) = leverArms * rotation.transpose();
+	loc2glo.block<3, 3>(3, 3) = rotation.transpose();
+	return loc2glo;
 }
 
 }

cpp/examples/exampleUtil.h

@@ -116,12 +116,18 @@ public:
 	double getRadiationLength() const;
 	Eigen::Vector2d getResolution() const;
 	Eigen::Vector2d getPrecision() const;
-	const Eigen::Matrix3d& getMeasSystemDirs() const;
+	Eigen::Vector3d getCenter() const;
+	Eigen::Matrix3d getMeasSystemDirs() const;
+	Eigen::Matrix3d getAlignSystemDirs() const;
 	GblHelixPrediction intersectWithHelix(GblSimpleHelix hlx) const;
-	const Eigen::Matrix<double, 3, 6> getRigidBodyDerGlobal(
-			Eigen::Vector3d& position, Eigen::Vector3d& direction) const;
-	const Eigen::Matrix<double, 2, 6> getRigidBodyDerLocal(
-			Eigen::Vector3d& position, Eigen::Vector3d& direction) const;
+	Eigen::Matrix<double, 3, 6> getRigidBodyDerGlobal(Eigen::Vector3d& position,
+			Eigen::Vector3d& direction) const;
+	Eigen::Matrix<double, 2, 6> getRigidBodyDerLocal(Eigen::Vector3d& position,
+			Eigen::Vector3d& direction) const;
+	Eigen::Matrix<double, 6, 6> getTrafoGlobalToLocal(Eigen::Vector3d& offset,
+			Eigen::Matrix3d& rotation) const;
+	Eigen::Matrix<double, 6, 6> getTrafoLocalToGlobal(Eigen::Vector3d& offset,
+			Eigen::Matrix3d& rotation) const;
 
 private:
 	std::string name; ///< name

cpp/include/GblTrajectory.h

@@ -165,7 +165,8 @@ private:
 	std::vector<unsigned int> numPoints; ///< Number of points on (sub)trajectory
 	unsigned int numTrajectories; ///< Number of trajectories (in composed trajectory)
 	unsigned int numOffsets; ///< Number of (points with) offsets on trajectory
-	unsigned int numInnerTrans; ///< Number of inner transformations to external parameters
+	unsigned int numInnerTransformations; ///< Number of inner transformations to external parameters
+	unsigned int numInnerTransOffsets; ///< Number of (points with) offsets affected by inner transformations to external parameters
 	unsigned int numCurvature; ///< Number of curvature parameters (0 or 1) or external parameters
 	unsigned int numParameters; ///< Number of fit parameters
 	unsigned int numLocals; ///< Total number of (additional) local parameters
@@ -181,11 +182,13 @@ private:
 	std::vector<unsigned int> measDataIndex; ///< mapping points to data blocks from measurements
 	std::vector<unsigned int> scatDataIndex; ///< mapping points to data blocks from scatterers
 	Eigen::MatrixXd externalSeed; ///< Precision (inverse covariance matrix) of external seed
-	std::vector<Eigen::MatrixXd> innerTransformations; ///< Transformations at innermost points of
-	// composed trajectory (from common external parameters)
-	Eigen::MatrixXd externalDerivatives; // Derivatives for external measurements of composed trajectory
-	Eigen::VectorXd externalMeasurements; // Residuals for external measurements of composed trajectory
-	Eigen::VectorXd externalPrecisions; // Precisions for external measurements of composed trajectory
+	// composed trajectory
+	std::vector<Eigen::MatrixXd> innerTransformations; ///< Transformations at innermost points of composed trajectory (from common external parameters)
+	std::vector<Eigen::MatrixXd> innerTransDer; ///< Derivatives at innermost points of composed trajectory
+	std::vector<std::array<unsigned int, 5> > innerTransLab; ///< Labels at innermost points of composed trajectory
+	Eigen::MatrixXd externalDerivatives; ///< Derivatives for external measurements of composed trajectory
+	Eigen::VectorXd externalMeasurements; ///< Residuals for external measurements of composed trajectory
+	Eigen::VectorXd externalPrecisions; ///< Precisions for external measurements of composed trajectory
 	// linear equation system
 	VVector theVector; ///< Vector of linear equation system
 	BorderedBandMatrix theMatrix; ///< (Bordered band) matrix of linear equation system
@@ -212,9 +215,9 @@ template<typename Seed>
 GblTrajectory::GblTrajectory(const std::vector<GblPoint> &aPointList,
 		unsigned int aLabel, const Eigen::MatrixBase<Seed>& aSeed,
 		bool flagCurv, bool flagU1dir, bool flagU2dir) :
-		numAllPoints(aPointList.size()), numPoints(), numOffsets(0), numInnerTrans(
-				0), numCurvature(flagCurv ? 1 : 0), numParameters(0), numLocals(
-				0), numMeasurements(0), externalPoint(aLabel), skippedMeasLabel(
+		numAllPoints(aPointList.size()), numPoints(), numOffsets(0), numInnerTransformations(
+				0), numInnerTransOffsets(0), numCurvature(flagCurv ? 1 : 0), numParameters(
+				0), numLocals(0), numMeasurements(0), externalPoint(aLabel), skippedMeasLabel(
 				0), maxNumGlobals(0), theDimension(0), thePoints(), theData(), measDataIndex(), scatDataIndex(), externalSeed(
 				aSeed), innerTransformations(), externalDerivatives(), externalMeasurements(), externalPrecisions() {
 
@@ -235,7 +238,7 @@ GblTrajectory::GblTrajectory(
 		const Eigen::MatrixBase<Derivatives>& extDerivatives,
 		const Eigen::MatrixBase<Measurements>& extMeasurements,
 		const Eigen::MatrixBase<Precision>& extPrecisions) :
-		numAllPoints(), numPoints(), numOffsets(0), numInnerTrans(
+		numAllPoints(), numPoints(), numOffsets(0), numInnerTransformations(
 				aPointsAndTransList.size()), numParameters(0), numLocals(0), numMeasurements(
 				0), externalPoint(0), skippedMeasLabel(0), maxNumGlobals(0), theDimension(
 				0), thePoints(), theData(), measDataIndex(), scatDataIndex(), externalSeed(), innerTransformations() {
@@ -264,7 +267,12 @@ GblTrajectory::GblTrajectory(
 	}
 	theDimension.push_back(0);
 	theDimension.push_back(1);
-	numCurvature = innerTransformations[0].cols();
+	// kinematic (2) or geometric (1) constraint
+	numInnerTransOffsets = innerTransformations[0].rows() == 5 ? 2 : 1;
+	numCurvature =
+			innerTransformations[0].rows() == 5 ?
+					innerTransformations[0].cols() :
+					innerTransformations[0].cols() + numInnerTransformations;
 	construct(); // construct (composed) trajectory
 }
 
@@ -275,7 +283,7 @@ GblTrajectory::GblTrajectory(
 		const Eigen::MatrixBase<Derivatives>& extDerivatives,
 		const Eigen::MatrixBase<Measurements>& extMeasurements,
 		const Eigen::MatrixBase<Precision>& extPrecisions) :
-		numAllPoints(), numPoints(), numOffsets(0), numInnerTrans(
+		numAllPoints(), numPoints(), numOffsets(0), numInnerTransformations(
 				aPointsAndTransList.size()), numParameters(0), numLocals(0), numMeasurements(
 				0), externalPoint(0), skippedMeasLabel(0), maxNumGlobals(0), theDimension(
 				0), thePoints(), theData(), measDataIndex(), scatDataIndex(), externalSeed(), innerTransformations() {
@@ -295,7 +303,12 @@ GblTrajectory::GblTrajectory(
 	}
 	theDimension.push_back(0);
 	theDimension.push_back(1);
-	numCurvature = innerTransformations[0].cols();
+	// kinematic (2) or geometric (1) constraint
+	numInnerTransOffsets = innerTransformations[0].rows() == 5 ? 2 : 1;
+	numCurvature =
+			innerTransformations[0].rows() == 5 ?
+					innerTransformations[0].cols() :
+					innerTransformations[0].cols() + numInnerTransformations;
 	construct(); // construct (composed) trajectory
 }
 

cpp/src/GblTrajectory.cpp

@@ -72,6 +72,8 @@
  *  some external parameters (like those describing a decay)
  *  and transformations at the first points from the external
  *  to the local track parameters.
+ *  The external parameters can describe the full kinematics (all track parameters)
+ *  or only the geometry (position parameters at common vertex).
  *
  *  The conventions for the coordinate systems follow:
  *  Derivation of Jacobians for the propagation of covariance
@@ -160,10 +162,10 @@ namespace gbl {
  */
 GblTrajectory::GblTrajectory(const std::vector<GblPoint> &aPointList,
 		bool flagCurv, bool flagU1dir, bool flagU2dir) :
-		numAllPoints(aPointList.size()), numPoints(), numOffsets(0), numInnerTrans(
-				0), numCurvature(flagCurv ? 1 : 0), numParameters(0), numLocals(
-				0), numMeasurements(0), externalPoint(0), skippedMeasLabel(0), maxNumGlobals(
-				0), theDimension(0), thePoints(), theData(), measDataIndex(), scatDataIndex(), externalSeed(), innerTransformations(), externalDerivatives(), externalMeasurements(), externalPrecisions() {
+		numAllPoints(aPointList.size()), numPoints(), numOffsets(0), numInnerTransformations(
+				0), numInnerTransOffsets(0), numCurvature(flagCurv ? 1 : 0), numParameters(
+				0), numLocals(0), numMeasurements(0), externalPoint(0), skippedMeasLabel(
+				0), maxNumGlobals(0), theDimension(0), thePoints(), theData(), measDataIndex(), scatDataIndex(), externalSeed(), innerTransformations(), externalDerivatives(), externalMeasurements(), externalPrecisions() {
 
 	if (flagU1dir)
 		theDimension.push_back(0);
@@ -182,7 +184,7 @@ GblTrajectory::GblTrajectory(const std::vector<GblPoint> &aPointList,
  */
 GblTrajectory::GblTrajectory(
 		const std::vector<std::pair<std::vector<GblPoint>, Eigen::MatrixXd> >& aPointsAndTransList) :
-		numAllPoints(), numPoints(), numOffsets(0), numInnerTrans(
+		numAllPoints(), numPoints(), numOffsets(0), numInnerTransformations(
 				aPointsAndTransList.size()), numParameters(0), numLocals(0), numMeasurements(
 				0), externalPoint(0), skippedMeasLabel(0), maxNumGlobals(0), theDimension(
 				0), thePoints(), theData(), measDataIndex(), scatDataIndex(), externalSeed(), innerTransformations(), externalDerivatives(), externalMeasurements(), externalPrecisions() {
@@ -195,7 +197,12 @@ GblTrajectory::GblTrajectory(
 	}
 	theDimension.push_back(0);
 	theDimension.push_back(1);
-	numCurvature = innerTransformations[0].cols();
+	// kinematic (2) or geometric (1) constraint
+	numInnerTransOffsets = innerTransformations[0].rows() == 5 ? 2 : 1;
+	numCurvature =
+			innerTransformations[0].rows() == 5 ?
+					innerTransformations[0].cols() :
+					innerTransformations[0].cols() + numInnerTransformations;
 	construct(); // construct (composed) trajectory
 }
 
@@ -216,7 +223,7 @@ GblTrajectory::GblTrajectory(const std::vector<GblPoint> &aPointList,
 		unsigned int aLabel, const TMatrixDSym &aSeed, bool flagCurv,
 		bool flagU1dir, bool flagU2dir) :
 numAllPoints(aPointList.size()), numPoints(), numOffsets(0),
-numInnerTrans(0), numCurvature(flagCurv ? 1 : 0), numParameters(0),
+numInnerTransformations(0), numInnerTransOffsets(0), numCurvature(flagCurv ? 1 : 0), numParameters(0),
 numLocals(0), numMeasurements(0), externalPoint(aLabel), skippedMeasLabel(0),
 maxNumGlobals(0), theDimension(0), thePoints(), theData(), measDataIndex(),
 scatDataIndex(), externalSeed(), innerTransformations(), externalDerivatives(),
@@ -246,7 +253,7 @@ externalMeasurements(), externalPrecisions() {
  * \param [in] aPointsAndTransList List containing pairs with list of points and transformation (at inner (first) point)
  */
 GblTrajectory::GblTrajectory(const std::vector<std::pair<std::vector<GblPoint>, TMatrixD> > &aPointsAndTransList) :
-numAllPoints(), numPoints(), numOffsets(0), numInnerTrans(aPointsAndTransList.size()),
+numAllPoints(), numPoints(), numOffsets(0), numInnerTransformations(aPointsAndTransList.size()),
 numParameters(0), numLocals(0), numMeasurements(0), externalPoint(0),
 skippedMeasLabel(0), maxNumGlobals(0), theDimension(0), thePoints(), theData(),
 measDataIndex(), scatDataIndex(), externalSeed(), innerTransformations(),
@@ -269,8 +276,13 @@ externalDerivatives(), externalMeasurements(), externalPrecisions() {
 	}
 	theDimension.push_back(0);
 	theDimension.push_back(1);
-	numCurvature = innerTransformations[0].cols();
-	construct(); // construct (composed) trajectory
+	// kinematic (2) or geometric (1) constraint
+	numInnerTransOffsets = innerTransformations[0].rows() == 5 ? 2 : 1;
+	numCurvature =
+	innerTransformations[0].rows() == 5 ?
+	innerTransformations[0].cols() :
+	innerTransformations[0].cols() + numInnerTransformations;
+	construct();// construct (composed) trajectory
 }
 
 /// Create new composed trajectory from list of points and transformations with (independent) external measurements.
@@ -284,7 +296,7 @@ externalDerivatives(), externalMeasurements(), externalPrecisions() {
 GblTrajectory::GblTrajectory(const std::vector<std::pair<std::vector<GblPoint>, TMatrixD> > &aPointsAndTransList,
 		const TMatrixD &extDerivatives, const TVectorD &extMeasurements,
 		const TVectorD &extPrecisions) :
-numAllPoints(), numPoints(), numOffsets(0), numInnerTrans(aPointsAndTransList.size()),
+numAllPoints(), numPoints(), numOffsets(0), numInnerTransformations(aPointsAndTransList.size()),
 numParameters(0), numLocals(0), numMeasurements(0), externalPoint(0),
 skippedMeasLabel(0), maxNumGlobals(0), theDimension(0), thePoints(), theData(),
 measDataIndex(), scatDataIndex(), externalSeed(), innerTransformations(),
@@ -320,8 +332,13 @@ externalDerivatives(), externalMeasurements(), externalPrecisions() {
 	}
 	theDimension.push_back(0);
 	theDimension.push_back(1);
-	numCurvature = innerTransformations[0].cols();
-	construct(); // construct (composed) trajectory
+	// kinematic (2) or geometric (1) constraint
+	numInnerTransOffsets = innerTransformations[0].rows() == 5 ? 2 : 1;
+	numCurvature =
+	innerTransformations[0].rows() == 5 ?
+	innerTransformations[0].cols() :
+	innerTransformations[0].cols() + numInnerTransformations;
+	construct();// construct (composed) trajectory
 }
 
 /// Create new composed trajectory from list of points and transformations with (correlated) external measurements.
@@ -335,7 +352,7 @@ externalDerivatives(), externalMeasurements(), externalPrecisions() {
 GblTrajectory::GblTrajectory(const std::vector<std::pair<std::vector<GblPoint>, TMatrixD> > &aPointsAndTransList,
 		const TMatrixD &extDerivatives, const TVectorD &extMeasurements,
 		const TMatrixDSym &extPrecisions) :
-numAllPoints(), numPoints(), numOffsets(0), numInnerTrans(aPointsAndTransList.size()),
+numAllPoints(), numPoints(), numOffsets(0), numInnerTransformations(aPointsAndTransList.size()),
 numParameters(0), numLocals(0), numMeasurements(0), externalPoint(0),
 skippedMeasLabel(0), maxNumGlobals(0), theDimension(0), thePoints(), theData(),
 measDataIndex(), scatDataIndex(), externalSeed(), innerTransformations() {
@@ -377,8 +394,13 @@ measDataIndex(), scatDataIndex(), externalSeed(), innerTransformations() {
 	}
 	theDimension.push_back(0);
 	theDimension.push_back(1);
-	numCurvature = innerTransformations[0].cols();
-	construct(); // construct (composed) trajectory
+	// kinematic (2) or geometric (1) constraint
+	numInnerTransOffsets = innerTransformations[0].rows() == 5 ? 2 : 1;
+	numCurvature =
+	innerTransformations[0].rows() == 5 ?
+	innerTransformations[0].cols() :
+	innerTransformations[0].cols() + numInnerTransformations;
+	construct();// construct (composed) trajectory
 }
 #endif
 
@@ -429,12 +451,17 @@ void GblTrajectory::construct() {
 		std::cout << " GblTrajectory construction failed: " << e.what()
 				<< std::endl;
 		return;
+	} catch (int i) {
+		std::cout << " GblTrajectory construction failed with exception " << i
+				<< std::endl;
+		return;
 	}
 
 	constructOK = true;
 	// number of fit parameters
-	numParameters = (numOffsets - 2 * numInnerTrans) * theDimension.size()
-			+ numCurvature + numLocals;
+	numParameters =
+			(numOffsets - numInnerTransOffsets * numInnerTransformations)
+					* theDimension.size() + numCurvature + numLocals;
 }
 
 /// Define offsets from list of points.
@@ -504,7 +531,7 @@ void GblTrajectory::calcJacobians() {
 /// Get jacobian for transformation from fit to track parameters at point.
 /**
  * Jacobian broken lines (q/p,..,u_i,u_i+1..) to track (q/p,u',u) parameters
- * including additional local parameters.
+ * including additional local parameters (and transformation from external parameters).
  * \param [in] aSignedLabel (Signed) label of point for external seed
  * (<0: in front, >0: after point, slope changes at scatterer!)
  * \return List of fit parameters with non zero derivatives and
@@ -516,14 +543,7 @@ std::pair<std::vector<unsigned int>, MatrixXd> GblTrajectory::getJacobian(
 	unsigned int nDim = theDimension.size();
 	unsigned int nCurv = numCurvature;
 	unsigned int nLocals = numLocals;
-	unsigned int nBorder = nCurv + nLocals;
-	unsigned int nParBRL = nBorder + 2 * nDim;
-	unsigned int nParLoc = nLocals + 5;
-	std::vector<unsigned int> anIndex;
-	anIndex.reserve(nParBRL);
-	MatrixXd aJacobian(nParLoc, nParBRL);
-	aJacobian.setZero();
-
+	// find trajectory, position in trajectory
 	unsigned int aLabel = abs(aSignedLabel);
 	unsigned int firstLabel = 1;
 	unsigned int lastLabel = 0;
@@ -552,11 +572,31 @@ std::pair<std::vector<unsigned int>, MatrixXd> GblTrajectory::getJacobian(
 			nJacobian = 1;
 		}
 	}
+
 	const GblPoint aPoint = thePoints[aTrajectory][aLabel - firstLabel];
 	std::array<unsigned int, 5> labDer;
 	Matrix5d matDer;
 	getFitToLocalJacobian(labDer, matDer, aPoint, 5, nJacobian);
 
+	unsigned int nBand = 0; // number of parameters from band part
+	if (numInnerTransformations > 0) {
+		unsigned int lastExt = innerTransLab[aTrajectory][2
+				* numInnerTransOffsets]; // last label for external parameters
+		for (unsigned int i = 0; i < 5; ++i)
+			if (labDer[i] > lastExt)
+				nBand++;
+	} else {
+		nBand = 2 * nDim;
+	}
+
+	unsigned int nBorder = nCurv + nLocals;
+	unsigned int nParBRL = nBorder + nBand;
+	unsigned int nParLoc = nLocals + 5;
+	std::vector<unsigned int> anIndex;
+	anIndex.reserve(nParBRL);
+	MatrixXd aJacobian(nParLoc, nParBRL);
+	aJacobian.setZero();
+
 	// from local parameters
 	for (unsigned int i = 0; i < nLocals; ++i) {
 		aJacobian(i + 5, i) = 1.0;
@@ -564,13 +604,41 @@ std::pair<std::vector<unsigned int>, MatrixXd> GblTrajectory::getJacobian(
 	}
 	// from trajectory parameters
 	unsigned int iCol = nLocals;
-	for (unsigned int i = 0; i < 5; ++i) {
-		if (labDer[i] > 0) {
-			anIndex.push_back(labDer[i]);
-			for (unsigned int j = 0; j < 5; ++j) {
-				aJacobian(j, iCol) = matDer(j, i);
+	// composed trajectory ?
+	if (numInnerTransformations > 0) {
+		// transformation external to (simple) broken line (fit) parameters
+		unsigned int nSimple = nCurv + nBand;
+		MatrixXd aTrans(5, nSimple);
+		aTrans.setZero();
+		// external part, curvature
+		aTrans.block(0, 0, 1, nCurv) = innerTransDer[aTrajectory].block(0, 0, 1,
+				nCurv);
+		for (unsigned int i = 0; i < nCurv; ++i)
+			anIndex.push_back(++iCol);
+		if (nBand < 4) {
+			// external part, offsets (nBand=0: 2, nBand=2: 1)
+			unsigned int iRow = 1 + 2 * numInnerTransOffsets + nBand - 4; // start row (1: 1st, 3: 2nd offset)
+			aTrans.block(1, 0, 4 - nBand, nCurv) =
+					innerTransDer[aTrajectory].block(iRow, 0, 4 - nBand, nCurv);
+		}
+		// (remaining) band part
+		for (unsigned int i = 5 - nBand; i < 5; ++i) {
+			aTrans(i, iCol++) = 1.;
+			anIndex.push_back(
+					labDer[i]
+							- numInnerTransOffsets * nDim * (aTrajectory + 1)); // adjust label
+		}
+		aJacobian.block(0, nLocals, 5, nSimple) = matDer * aTrans;
+	} else {
+		// simple trajectory
+		for (unsigned int i = 0; i < 5; ++i) {
+			if (labDer[i] > 0) {
+				anIndex.push_back(labDer[i]);
+				for (unsigned int j = 0; j < 5; ++j) {
+					aJacobian(j, iCol) = matDer(j, i);
+				}
+				++iCol;
 			}
-			++iCol;
 		}
 	}
 	return std::make_pair(anIndex, aJacobian);
@@ -1005,6 +1073,7 @@ void GblTrajectory::buildLinearEquationSystem() {
 		if (itData->getLabel() == skippedMeasLabel
 				&& itData->getType() == InternalMeasurement)
 			continue;
+
 		itData->getLocalData(aValue, aWeight, numLocal, indLocal, derLocal);
 		for (unsigned int j = 0; j < numLocal; ++j) {
 			theVector(indLocal[j] - 1) += derLocal[j] * aWeight * aValue;
@@ -1016,6 +1085,10 @@ void GblTrajectory::buildLinearEquationSystem() {
 /// Prepare fit for simple or composed trajectory
 /**
  * Generate data (blocks) from measurements, kinks, external seed and measurements.
+ *
+ * \exception 10 : inner transformation matrix with invalid number of rows (valid are 5=kinematic or 2=geometric constraint)
+ * \exception 11 : inner transformation matrix with to few columns (must be >= number of rows)
+ * \exception 12 : inner transformation matrices with varying sizes
  */
 void GblTrajectory::prepare() {
 	unsigned int nDim = theDimension.size();
@@ -1026,23 +1099,57 @@ void GblTrajectory::prepare() {
 	measDataIndex.resize(numAllPoints + 3); // include external seed and measurements
 	scatDataIndex.resize(numAllPoints + 1);
 	unsigned int nData = 0;
-	std::vector<MatrixXd> innerTransDer;
-	std::vector<std::array<unsigned int, 5> > innerTransLab;
 	// composed trajectory ?
-	if (numInnerTrans > 0) {
-		//std::cout << "composed trajectory" << std::endl;
+	if (numInnerTransformations > 0) {
+		unsigned int nInnerTransRows = innerTransformations[0].rows();
+		unsigned int nInnerTransCols = innerTransformations[0].cols();
+		// std::cout << "composed trajectory, inner transformation (" << nInnerTransRows << "," << nInnerTransCols << ")" << std::endl;
+		// check size
+		if (nInnerTransRows != 5 and nInnerTransRows != 2) {
+			std::cout
+					<< " GblTrajectory::prepare composed trajectory with bad inner transformation matrix("
+					<< nInnerTransRows << "," << nInnerTransCols
+					<< "): invalid number of rows" << std::endl;
+			throw 10;
+		}
+		if (nInnerTransRows > nInnerTransCols) {
+			std::cout
+					<< " GblTrajectory::prepare composed trajectory with bad inner transformation matrix("
+					<< nInnerTransRows << "," << nInnerTransCols
+					<< "): too few columns" << std::endl;
+			throw 11;
+		}
 		for (unsigned int iTraj = 0; iTraj < numTrajectories; ++iTraj) {
+			// check size
+			if (nInnerTransRows != innerTransformations[iTraj].rows()
+					or nInnerTransCols != innerTransformations[iTraj].cols()) {
+				std::cout
+						<< " GblTrajectory::prepare composed trajectory with bad inner transformation matrix["
+						<< iTraj << "]: different size as [0]" << std::endl;
+				throw 12;
+			}
 			// innermost point
 			GblPoint* innerPoint = &thePoints[iTraj].front();
 			// transformation fit to local track parameters
 			std::array<unsigned int, 5> firstLabels;
-			Matrix5d matFitToLocal, matLocalToFit;
+			Matrix5d matFitToLocal;
 			getFitToLocalJacobian(firstLabels, matFitToLocal, *innerPoint, 5);
-			// transformation local track to fit parameters
-			matLocalToFit = matFitToLocal.inverse();
-			// transformation external to fit parameters at inner (first) point
-			innerTransDer.emplace_back(
-					matLocalToFit * innerTransformations[iTraj]);
+			if (nInnerTransRows == 5) {
+				// (full) kinematic constraint
+				// transformation local track to fit parameters
+				Matrix5d matLocalToFit = matFitToLocal.inverse();
+				// transformation external to fit parameters at inner (first) point
+				innerTransDer.emplace_back(
+						matLocalToFit * innerTransformations[iTraj]);
+			} else {
+				// geometric constraint (including individual curvature correction per trajectory)
+				MatrixXd matInnerToFit(5, numCurvature);
+				matInnerToFit.setZero();
+				matInnerToFit(0, nInnerTransCols + iTraj) = 1.; // curvature correction for 'iTraj'
+				matInnerToFit.block(1, 0, 2, nInnerTransCols) =
+						innerTransformations[iTraj]; // geometric derivatives
+				innerTransDer.emplace_back(matInnerToFit);
+			}
 			innerTransLab.push_back(firstLabels);
 		}
 	}
@@ -1083,22 +1190,24 @@ void GblTrajectory::prepare() {
 								* matDer.block<2, 5>(3, 0);
 					}
 
-					if (numInnerTrans > 0) {
+					if (numInnerTransformations > 0) {
 						// transform for external parameters
 						proDer.resize(measDim, Eigen::NoChange);
 						proDer.setZero();
 						// match parameters
 						unsigned int ifirst = 0;
+						unsigned int ilast = 2 * numInnerTransOffsets;
 						unsigned int ilabel = 0;
 						unsigned int numRelated = 0;
 						while (ilabel < 5) {
 							if (labDer[ilabel] > 0) {
 								while (innerTransLab[iTraj][ifirst]
-										!= labDer[ilabel] and ifirst < 5) {
+										!= labDer[ilabel] and ifirst <= ilast) {
 									++ifirst;
 								}