Description

Collaboration diagram for Linear algebra:

Classes
class	chrono::ChMatrix33< Real >
	Definition of a 3x3 fixed size matrix to represent 3D rotations and inertia tensors. More...

class	chrono::ChFpMatrix34< Real >
	Special MBD 3x4 matrix [Fp(q)], as in [Fp(q)] * [Fm(q)]' = [A(q)]. More...

class	chrono::ChFmMatrix34< Real >
	Special MBD 3x4 matrix [Fm(q)], as in [Fp(q)] * [Fm(q)]' = [A(q)]. More...

class	chrono::ChGlMatrix34< Real >
	Special MBD 3x4 matrix [Gl(q)], as in local angular speed conversion. More...

class	chrono::ChGwMatrix34< Real >
	Special MBD 3x4 matrix [Gw(q)], as in absolute angular speed conversion. More...

class	chrono::ChStarMatrix33< Real >
	Special MBD 3x3 "star" matrix, , representing vector cross products. More...

class	chrono::ChStarMatrix44< Real >
	Special MBD 4x4 "star" matrix, representing quaternion cross product. More...

class	chrono::ChSparsityPatternLearner
	Utility class for extracting sparsity patter from a sparse matrix. More...

Typedefs
template<typename T = double>
using	chrono::ChMatrixDynamic = Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor >
	Dense matrix with dynamic size (i.e., with size a run-time variable, unknown at compile time). More...

template<typename T , int M, int N>
using	chrono::ChMatrixNM = Eigen::Matrix< T, M, N, Eigen::RowMajor >
	Dense matrix with fixed size (known at compile time). More...

template<typename T = double>
using	chrono::ChVectorDynamic = Eigen::Matrix< T, Eigen::Dynamic, 1, Eigen::ColMajor >
	Column vector with dynamic size (i.e., with size a run-time variable, unknown at compile time). More...

template<typename T = double>
using	chrono::ChRowVectorDynamic = Eigen::Matrix< T, 1, Eigen::Dynamic, Eigen::RowMajor >
	Row vector with dynamic size (i.e., with size a run-time variable, unknown at compile time). More...

template<typename T , int N>
using	chrono::ChVectorN = Eigen::Matrix< T, N, 1 >
	Column vector with fixed size (known at compile time). More...

template<typename T , int N>
using	chrono::ChRowVectorN = Eigen::Matrix< T, 1, N, Eigen::RowMajor >
	Row vector with fixed size (known at compile time). More...

using	chrono::ChMatrixRef = Eigen::Ref< Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > >
	Reference to a dense matrix expression, with double coefficients. More...

using	chrono::ChMatrixConstRef = const Eigen::Ref< const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > > &
	Constant reference to a dense matrix expression, with double coefficients. More...

using	chrono::ChVectorRef = Eigen::Ref< Eigen::Matrix< double, Eigen::Dynamic, 1, Eigen::ColMajor > >
	Reference to a column vector expression, with double coefficients. More...

using	chrono::ChVectorConstRef = const Eigen::Ref< const Eigen::Matrix< double, Eigen::Dynamic, 1, Eigen::ColMajor > > &
	Constant reference to a column vector expression, with double coefficients. More...

using	chrono::ChRowVectorRef = Eigen::Ref< Eigen::Matrix< double, 1, Eigen::Dynamic, Eigen::RowMajor > >
	Reference to a row vector expression, with double coefficients. More...

using	chrono::ChRowVectorConstRef = const Eigen::Ref< const Eigen::Matrix< double, 1, Eigen::Dynamic, Eigen::RowMajor > > &
	Constant reference to a row vector expression, with double coefficients. More...

template<typename T = double>
using	chrono::ChArray = Eigen::Array< T, Eigen::Dynamic, 1, Eigen::ColMajor >
	General-purpose column array with dynamic size. More...

using	chrono::ChSparseMatrix = Eigen::SparseMatrix< double, Eigen::RowMajor, int >
	Sparse matrix representation. More...

template<typename T = double>
using	chrono::ChMatrix34 = Eigen::Matrix< T, 3, 4, Eigen::RowMajor >
	3x4 dense matrix (fixed-size, row-major ordering)

template<typename T = double>
using	chrono::ChMatrix43 = Eigen::Matrix< T, 4, 3, Eigen::ColMajor >
	4x3 dense matrix (fixed-size, row-major ordering)

template<typename T = double>
using	chrono::ChMatrix44 = Eigen::Matrix< T, 4, 4, Eigen::RowMajor >
	4x4 dense matrix (fixed-size, row-major ordering)

Functions
void	chrono::StreamOUTdenseMatlabFormat (ChMatrixConstRef A, ChStreamOutAscii &stream)
	Serialization of a dense matrix or vector into an ASCII stream (e.g. a file) in Matlab format.

void	chrono::PasteMatrix (ChSparseMatrix &matrTo, ChMatrixConstRef matrFrom, int insrow, int inscol, bool overwrite=true)
	Paste a given matrix into a sparse matrix at position (insrow, inscol). More...

void	chrono::StreamOUTsparseMatlabFormat (ChSparseMatrix &matr, ChStreamOutAscii &mstream)
	Serialization of a sparse matrix to an ASCI stream (e.g., a file) in Matlab sparse matrix format. More...

void	chrono::StreamOUT (ChSparseMatrix &matr, ChStreamOutAscii &stream)
	Serialization of a sparse matrix to an ASCII stream (for debugging; only the top-left 8x8 corner is printed).

template<typename Real >
ChVector< Real >	chrono::operator* (const Eigen::Transpose< Eigen::Matrix< Real, 3, 3, Eigen::RowMajor >> &A, const ChVector< Real > &v)
	Multiply a transposed 3x3 matrix with a vector.

template<typename Real >
ChVector< Real >	chrono::operator* (const Eigen::Transpose< const Eigen::Matrix< Real, 3, 3, Eigen::RowMajor >> &A, const ChVector< Real > &v)
	Multiply a transposed const 3x3 matrix with a vector.

template<class Real >
ChMatrix33< Real >	chrono::TensorProduct (const ChVector< Real > &vA, const ChVector< Real > &vB)
	Return the outer product (a 3x3 matrix) of two vectors.

template<typename T , typename U >
ChVector< T >	chrono::operator* (const ChMatrix34< T > &A, const ChQuaternion< U > &q)
	Multiply a 3x4 matrix with a quaternion and return a 3d vector.

template<typename T , typename U >
ChQuaternion< T >	chrono::operator* (const ChMatrix43< T > &A, const ChVector< U > &v)
	Multiply a 4x3 matrix with a 3d vector and return a quaternion.

template<typename T , typename U >
ChQuaternion< T >	chrono::operator* (const Eigen::Transpose< Eigen::Matrix< T, 3, 4, Eigen::RowMajor >> &A, const ChVector< U > &v)
	Multiply the transpose of a 3x4 matrix with a 3d vector and return a quaternion.

template<typename T , typename U >
ChQuaternion< T >	chrono::operator* (const ChMatrix44< T > &A, const ChQuaternion< U > &q)
	Multiply a 4x4 matrix with a quaternion and return a quaternion.

	chrono::ChMatrix33< Real >::ChMatrix33 (const ChQuaternion< Real > &q)
	Construct a 3x3 rotation matrix from the given quaternion.

	chrono::ChMatrix33< Real >::ChMatrix33 (Real val)
	Construct a diagonal matrix with the specified value on the diagonal.

	chrono::ChMatrix33< Real >::ChMatrix33 (const ChVector< Real > &v)
	Construct a diagonal matrix with the specified values on the diagonal.

	chrono::ChMatrix33< Real >::ChMatrix33 (const ChVector<> &diag, const ChVector<> &off_diag)
	Construct a symmetric 3x3 matrix with the specified vectors for the diagonal and off-digonal elements. More...

	chrono::ChMatrix33< Real >::ChMatrix33 (Real angle, const ChVector<> &axis)
	Construct a 3x3 rotation matrix from an angle and a rotation axis. More...

	chrono::ChMatrix33< Real >::ChMatrix33 (const ChVector<> &X, const ChVector<> &Y, const ChVector<> &Z)
	Construct a 3x3 matrix with the given vectors as columns. More...

ChVector< Real >	chrono::ChMatrix33< Real >::operator* (const ChVector< Real > &v) const
	Multiply this matrix by a 3d vector.

void	chrono::ChMatrix33< Real >::Set_A_quaternion (const ChQuaternion< Real > &quat)
	Fill this 3x3 matrix as a rotation matrix, given a unit quaternion.

void	chrono::ChMatrix33< Real >::Set_A_Eulero (const ChVector< Real > &angles)
	Fill this 3x3 matrix as a rotation matrix, given three Euler angles.

void	chrono::ChMatrix33< Real >::Set_A_Cardano (const ChVector< Real > &angles)
	Fill this 3x3 matrix as a rotation matrix, given three Cardano angles.

void	chrono::ChMatrix33< Real >::Set_A_Hpb (const ChVector< Real > &angles)
	Fill this 3x3 matrix as a rotation matrix, given three head, pitch, banking angles.

void	chrono::ChMatrix33< Real >::Set_A_Rxyz (const ChVector< Real > &xyz)
	Fill this 3x3 matrix as a rotation matrix, given three angles of consecutive rotations about x,y,z axis.

void	chrono::ChMatrix33< Real >::Set_A_Rodriguez (const ChVector< Real > &rod)
	Fill this 3x3 matrix as a rotation matrix, given three Rodriguez parameters.

void	chrono::ChMatrix33< Real >::Set_A_axis (const ChVector< Real > &X, const ChVector< Real > &Y, const ChVector< Real > &Z)
	Fill this 3x3 matrix as a rotation matrix, given the three versors X,Y,Z of the basis.

void	chrono::ChMatrix33< Real >::Set_A_Xdir (const ChVector< Real > &Xdir, const ChVector< Real > &Vsingular=ChVector< Real >(0, 1, 0))
	Fill this 3x3 matrix as a rotation matrix with the X axis along the provided direction. More...

ChVector< Real >	chrono::ChMatrix33< Real >::Get_A_Eulero () const
	Return the Eulero angles. More...

ChVector< Real >	chrono::ChMatrix33< Real >::Get_A_Cardano () const
	Return the Cardano angles. More...

ChVector< Real >	chrono::ChMatrix33< Real >::Get_A_Hpb () const
	Return the head-pitch-banking angles. More...

ChVector< Real >	chrono::ChMatrix33< Real >::Get_A_Rxyz () const
	Return the angles for consecutive rotations on x,y,z axes. More...

ChVector< Real >	chrono::ChMatrix33< Real >::Get_A_Rodriguez () const
	Return the Rodriguez parameters. More...

ChQuaternion< Real >	chrono::ChMatrix33< Real >::Get_A_quaternion () const
	Return the corresponding unit quaternion. More...

ChVector< Real >	chrono::ChMatrix33< Real >::Get_A_Xaxis () const
	Return the versor of X axis.

ChVector< Real >	chrono::ChMatrix33< Real >::Get_A_Yaxis () const
	Return the versor of Y axis.

ChVector< Real >	chrono::ChMatrix33< Real >::Get_A_Zaxis () const
	Return the versor of Z axis.

ChVector< Real >	chrono::ChMatrix33< Real >::GetAx () const
	Assuming this matrix is a rotation matrix, get Ax vector.

void	chrono::ChMatrix33< Real >::SelfAdjointEigenSolve (ChMatrix33< Real > &evec, ChVectorN< Real, 3 > &evals) const
	Compute eigenvectors and eigenvalues. More...

Typedef Documentation

◆ ChArray

template<typename T = double>

using chrono::ChArray = typedef Eigen::Array<T, Eigen::Dynamic, 1, Eigen::ColMajor>

General-purpose column array with dynamic size.

This class provides easy-access to coefficient-wise operations.

◆ ChMatrixConstRef

using chrono::ChMatrixConstRef = typedef const Eigen::Ref<const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> >&

Constant reference to a dense matrix expression, with double coefficients.

This allows writing non-template functions that can accept either a ChMatrixDynamic or a ChMatrixNM.

◆ ChMatrixDynamic

template<typename T = double>

using chrono::ChMatrixDynamic = typedef Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>

Dense matrix with dynamic size (i.e., with size a run-time variable, unknown at compile time).

A ChMatrixDynamic is templated by the type of its coefficients (default: double).

◆ ChMatrixNM

template<typename T , int M, int N>

using chrono::ChMatrixNM = typedef Eigen::Matrix<T, M, N, Eigen::RowMajor>

Dense matrix with fixed size (known at compile time).

A ChMatrixNM is templated by the type of its coefficients and by the matrix dimensions (number of rows and columns).

◆ ChMatrixRef

using chrono::ChMatrixRef = typedef Eigen::Ref<Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> >

Reference to a dense matrix expression, with double coefficients.

This allows writing non-template functions that can accept either a ChMatrixDynamic or a ChMatrixNM.

◆ ChRowVectorConstRef

using chrono::ChRowVectorConstRef = typedef const Eigen::Ref<const Eigen::Matrix<double, 1, Eigen::Dynamic, Eigen::RowMajor> >&

Constant reference to a row vector expression, with double coefficients.

This allows writing non-template functions that can accept either a ChRowVectorDynamic or a CVectorN.

◆ ChRowVectorDynamic

template<typename T = double>

using chrono::ChRowVectorDynamic = typedef Eigen::Matrix<T, 1, Eigen::Dynamic, Eigen::RowMajor>

Row vector with dynamic size (i.e., with size a run-time variable, unknown at compile time).

A ChRowVectorDynamic is templated by the type of its coefficients (default: double).

◆ ChRowVectorN

template<typename T , int N>

using chrono::ChRowVectorN = typedef Eigen::Matrix<T, 1, N, Eigen::RowMajor>

Row vector with fixed size (known at compile time).

A ChRowVectorN is templated by the type of its coefficients and the number of elements.

◆ ChRowVectorRef

using chrono::ChRowVectorRef = typedef Eigen::Ref<Eigen::Matrix<double, 1, Eigen::Dynamic, Eigen::RowMajor> >

Reference to a row vector expression, with double coefficients.

This allows writing non-template functions that can accept either a ChRowVectorDynamic or a CVectorN.

◆ ChSparseMatrix

using chrono::ChSparseMatrix = typedef Eigen::SparseMatrix<double, Eigen::RowMajor, int>

Sparse matrix representation.

A ChSparseMatrix is an Eigen SparseMatrix with double coefficients, row-major storage order, and int indices.

◆ ChVectorConstRef

using chrono::ChVectorConstRef = typedef const Eigen::Ref<const Eigen::Matrix<double, Eigen::Dynamic, 1, Eigen::ColMajor> >&

Constant reference to a column vector expression, with double coefficients.

This allows writing non-template functions that can accept either a ChVectorDynamic or a ChRowVectorN.

◆ ChVectorDynamic

template<typename T = double>

using chrono::ChVectorDynamic = typedef Eigen::Matrix<T, Eigen::Dynamic, 1, Eigen::ColMajor>

Column vector with dynamic size (i.e., with size a run-time variable, unknown at compile time).

A ChVectorDynamic is templated by the type of its coefficients (default: double).

◆ ChVectorN

template<typename T , int N>

using chrono::ChVectorN = typedef Eigen::Matrix<T, N, 1>

Column vector with fixed size (known at compile time).

A ChVectorN is templated by the type of its coefficients and the number of elements.

◆ ChVectorRef

using chrono::ChVectorRef = typedef Eigen::Ref<Eigen::Matrix<double, Eigen::Dynamic, 1, Eigen::ColMajor> >

Reference to a column vector expression, with double coefficients.

This allows writing non-template functions that can accept either a ChVectorDynamic or a ChVectorN.

Function Documentation

◆ ChMatrix33() [1/3]

template<typename Real>

chrono::ChMatrix33< Real >::ChMatrix33	(	const ChVector<> &	diag,
		const ChVector<> &	off_diag
	)

Construct a symmetric 3x3 matrix with the specified vectors for the diagonal and off-digonal elements.

The off-diagonal vector is assumed to contain the elements A(0,1), A(0,2), A(1,2) in this order.

◆ ChMatrix33() [2/3]

template<typename Real>

chrono::ChMatrix33< Real >::ChMatrix33	(	const ChVector<> &	X,
		const ChVector<> &	Y,
		const ChVector<> &	Z
	)

Construct a 3x3 matrix with the given vectors as columns.

If the three vectors are mutually orthogonal unit vectors, the resulting matrix is a rotation matrix.

◆ ChMatrix33() [3/3]

template<typename Real>

chrono::ChMatrix33< Real >::ChMatrix33	(	Real	angle,
		const ChVector<> &	axis
	)

Construct a 3x3 rotation matrix from an angle and a rotation axis.

Note that the axis direction must be normalized.

◆ Get_A_Cardano()

template<typename Real >

ChVector< Real > chrono::ChMatrix33< Real >::Get_A_Cardano ( ) const

inline

Return the Cardano angles.