Algebra types

Detailed Description

These are the default vector/matrix types that should be used throughout the codebase.

They all use the common ACTS scalar type but support variable size either at compile- or runtime.

Eigen does not have a distinct type for symmetric matrices. A typedef for fixed-size matrices is still defined to simplify definition (one template size vs two template size for generic matrices) and to clarify semantic meaning in interfaces. It also ensures that the matrix is square. However, the user is responsible for ensuring that the values are symmetric.

Without a distinct type for symmetric matrices, there is no way to provide any conditions e.g. square size, for the dynamic-sized case. Consequently, no dynamic-sized symmetric matrix type is defined. Use the Acts::ActsDynamicMatrix instead.

Typedefs
using	Acts::ActsDynamicMatrix = Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>
	Dynamic-sized matrix type.
using	Acts::ActsDynamicVector = Eigen::Matrix<double, Eigen::Dynamic, 1>
	Dynamic-sized vector type.
template<unsigned int kRows, unsigned int kCols>
using	Acts::ActsMatrix = Eigen::Matrix<double, kRows, kCols>
	Fixed-size matrix type for NxM matrices.
template<unsigned int kSize>
using	Acts::ActsSquareMatrix = Eigen::Matrix<double, kSize, kSize>
	Fixed-size square matrix type for NxN matrices.
template<unsigned int kSize>
using	Acts::ActsVector = Eigen::Matrix<double, kSize, 1>
	Fixed-size vector type for N-dimensional vectors.
using	Acts::AngleAxis3 = Eigen::AngleAxis<double>
	Rotation defined by an angle around a rotation axis in 3D.
using	Acts::RotationMatrix2 = SquareMatrix2
	2D rotation matrix
using	Acts::RotationMatrix3 = SquareMatrix3
	3D rotation matrix
using	Acts::SquareMatrix2 = ActsSquareMatrix<2>
	2x2 square matrix type, typically used for 2D coordinate covariance
using	Acts::SquareMatrix3 = ActsSquareMatrix<3>
	3x3 square matrix type, typically used for 3D coordinate covariance
using	Acts::SquareMatrix4 = ActsSquareMatrix<4>
	4x4 square matrix type, typically used for 4D coordinate covariance
using	Acts::Transform2 = Eigen::Transform<double, 2, Eigen::AffineCompact>
	2D affine transformation stored as a compact 2x3 matrix
using	Acts::Transform3 = Eigen::Transform<double, 3, Eigen::Affine>
	3D affine transformation stored as a 4x4 matrix
using	Acts::Translation2 = Eigen::Translation<double, 2>
	2D translation transformation
using	Acts::Translation3 = Eigen::Translation<double, 3>
	3D translation transformation
using	Acts::Vector2 = ActsVector<2>
	2-dimensional vector type for 2D coordinates
using	Acts::Vector3 = ActsVector<3>
	3-dimensional vector type for e.g. spatial coordinates and momenta
using	Acts::Vector4 = ActsVector<4>
	4-dimensional vector type for space-time coordinates

Variables
constexpr double	Acts::s_transformEquivalentTolerance = 1e-9
	Tolerance for transform equivalence checks.

Typedef Documentation

ActsDynamicMatrix

using Acts::ActsDynamicMatrix = Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>

Dynamic-sized matrix type.

ActsDynamicVector

using Acts::ActsDynamicVector = Eigen::Matrix<double, Eigen::Dynamic, 1>

Dynamic-sized vector type.

ActsMatrix

template<unsigned int kRows, unsigned int kCols>

using Acts::ActsMatrix = Eigen::Matrix<double, kRows, kCols>

Fixed-size matrix type for NxM matrices.

Template Parameters

kRows	Number of rows
kCols	Number of columns

ActsSquareMatrix

template<unsigned int kSize>

using Acts::ActsSquareMatrix = Eigen::Matrix<double, kSize, kSize>

Fixed-size square matrix type for NxN matrices.

Template Parameters

kSize

The dimension of the square matrix

ActsVector

template<unsigned int kSize>

using Acts::ActsVector = Eigen::Matrix<double, kSize, 1>

Fixed-size vector type for N-dimensional vectors.

Template Parameters

kSize

The dimension of the vector

AngleAxis3

using Acts::AngleAxis3 = Eigen::AngleAxis<double>

Rotation defined by an angle around a rotation axis in 3D.

RotationMatrix2

using Acts::RotationMatrix2 = SquareMatrix2

2D rotation matrix

RotationMatrix3

using Acts::RotationMatrix3 = SquareMatrix3

3D rotation matrix

SquareMatrix2

using Acts::SquareMatrix2 = ActsSquareMatrix<2>

2x2 square matrix type, typically used for 2D coordinate covariance

SquareMatrix3

using Acts::SquareMatrix3 = ActsSquareMatrix<3>

3x3 square matrix type, typically used for 3D coordinate covariance

SquareMatrix4

using Acts::SquareMatrix4 = ActsSquareMatrix<4>

4x4 square matrix type, typically used for 4D coordinate covariance

Transform2

using Acts::Transform2 = Eigen::Transform<double, 2, Eigen::AffineCompact>

2D affine transformation stored as a compact 2x3 matrix

Transform3

using Acts::Transform3 = Eigen::Transform<double, 3, Eigen::Affine>

3D affine transformation stored as a 4x4 matrix

Translation2

using Acts::Translation2 = Eigen::Translation<double, 2>

2D translation transformation

Translation3

using Acts::Translation3 = Eigen::Translation<double, 3>

3D translation transformation

Vector2

using Acts::Vector2 = ActsVector<2>

2-dimensional vector type for 2D coordinates

Vector3

using Acts::Vector3 = ActsVector<3>

3-dimensional vector type for e.g. spatial coordinates and momenta

Vector4

using Acts::Vector4 = ActsVector<4>

4-dimensional vector type for space-time coordinates

Variable Documentation

s_transformEquivalentTolerance

double Acts::s_transformEquivalentTolerance = 1e-9

constexpr

Tolerance for transform equivalence checks.