Cholesky decompositions. More...

Functions
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>
Mat &	computeMinv (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< Mat > &Minv)
	Computes the inverse of the joint space inertia matrix M from its Cholesky factorization.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl>
const DataTpl< Scalar, Options, JointCollectionTpl >::RowMatrixXs &	computeMinv (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, DataTpl< Scalar, Options, JointCollectionTpl > &data)
	Computes the inverse of the joint space inertia matrix M from its Cholesky factorization. The results is then directly stored in data.Minv.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl>
const DataTpl< Scalar, Options, JointCollectionTpl >::MatrixXs &	decompose (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, DataTpl< Scalar, Options, JointCollectionTpl > &data)
	Compute the Cholesky decomposition of the joint space inertia matrix M contained in data.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>
Mat	Mv (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< Mat > &min)
	Performs the multiplication by using the sparsity pattern of the M matrix.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat, typename MatRes>
MatRes &	Mv (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< Mat > &min, const Eigen::MatrixBase< MatRes > &mout)
	Performs the multiplication by using the sparsity pattern of the M matrix.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>
Mat &	solve (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< Mat > &y)
	Return the solution of using the Cholesky decomposition stored in data given the entry . Act like solveInPlace of Eigen::LLT.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>
Mat &	UDUtv (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< Mat > &m)
	Performs the multiplication by using the Cholesky decomposition of M stored in data.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>
Mat &	Uiv (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< Mat > &v)
	Perform the pivot inversion $U^{-1}v$ using the Cholesky decomposition stored in data and acting in place.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>
Mat &	Utiv (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< Mat > &v)
	Perform the pivot inversion $U^{-\top}v$ using the Cholesky decomposition stored in data and acting in place.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>
Mat &	Utv (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< Mat > &v)
	Perform the sparse multiplication $U^{\top}v$ using the Cholesky decomposition stored in data and acting in place.
template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>
Mat &	Uv (const ModelTpl< Scalar, Options, JointCollectionTpl > &model, const DataTpl< Scalar, Options, JointCollectionTpl > &data, const Eigen::MatrixBase< Mat > &v)
	Perform the sparse multiplication using the Cholesky decomposition stored in data and acting in place.

Detailed Description

Cholesky decompositions.

Function Documentation

◆ computeMinv() [1/2]

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>

Mat & computeMinv	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		const DataTpl< Scalar, Options, JointCollectionTpl > &	data,
		const Eigen::MatrixBase< Mat > &	Minv )

Computes the inverse of the joint space inertia matrix M from its Cholesky factorization.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[out]	Minv	The output matrix where the result is stored.

Returns: A reference to the result.

◆ computeMinv() [2/2]

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl>

const DataTpl< Scalar, Options, JointCollectionTpl >::RowMatrixXs & computeMinv	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		DataTpl< Scalar, Options, JointCollectionTpl > &	data )

Computes the inverse of the joint space inertia matrix M from its Cholesky factorization. The results is then directly stored in data.Minv.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.

Returns: A reference to the result data.Minv.

Definition at line 293 of file cholesky.hpp.

◆ decompose()

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl>

const DataTpl< Scalar, Options, JointCollectionTpl >::MatrixXs & decompose	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		DataTpl< Scalar, Options, JointCollectionTpl > &	data )

inline

Compute the Cholesky decomposition of the joint space inertia matrix M contained in data.

Note: The Cholesky decomposition corresponds to $M = U D U^{\top}$ with an upper triangular matrix with ones on its main diagonal and a diagonal matrix.

The result stored in data.U and data.D matrices. One can retrieve the matrice M by performing the computation data.U * data.D * data.U.transpose()

See https://en.wikipedia.org/wiki/Cholesky_decomposition for futher details.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.

Returns: A reference to the upper triangular matrix .

◆ Mv() [1/2]

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>

Mat Mv	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		const DataTpl< Scalar, Options, JointCollectionTpl > &	data,
		const Eigen::MatrixBase< Mat > &	min )

Performs the multiplication $ M v $ by using the sparsity pattern of the M matrix.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[in]	min	The input matrix to multiply with data.M.

Returns: A the result of .

◆ Mv() [2/2]

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat, typename MatRes>

MatRes & Mv	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		const DataTpl< Scalar, Options, JointCollectionTpl > &	data,
		const Eigen::MatrixBase< Mat > &	min,
		const Eigen::MatrixBase< MatRes > &	mout )

Performs the multiplication $ M v $ by using the sparsity pattern of the M matrix.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[in]	min	The input matrix to multiply with data.M.
[out]	mout	The output matrix where the result of is stored.

Returns: A reference of the result of .

◆ solve()

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>

Mat & solve	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		const DataTpl< Scalar, Options, JointCollectionTpl > &	data,
		const Eigen::MatrixBase< Mat > &	y )

Return the solution $x$ of $ M x = y $ using the Cholesky decomposition stored in data given the entry $ y $ . Act like solveInPlace of Eigen::LLT.

Perform the sparse inversion $M^{-1}v$ using the Cholesky decomposition stored in data and acting in place.

Note: This algorithm is useful to compute the forward dynamics, retriving the joint acceleration $\ddot{q}$ from the current joint torque $\tau$ $M(q) \ddot{q} + b(q, \dot{q}) = \tau \iff \ddot{q} = M(q)^{-1} (\tau - b(q, \dot{q}))$

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[in,out]	y	The input matrix to inverse which also contains the result of the inversion.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[in,out]	v	The input matrix to multiply with data.M^{-1} and also storing the result.

Returns: A reference to the result of $M^{-1}v$ stored in v.

◆ UDUtv()

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>

Mat & UDUtv	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		const DataTpl< Scalar, Options, JointCollectionTpl > &	data,
		const Eigen::MatrixBase< Mat > &	m )

Performs the multiplication $ M v $ by using the Cholesky decomposition of M stored in data.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[in,out]	m	The input matrix where the result of is stored.

Returns: A reference of the result of .

◆ Uiv()

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>

Mat & Uiv	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		const DataTpl< Scalar, Options, JointCollectionTpl > &	data,
		const Eigen::MatrixBase< Mat > &	v )

Perform the pivot inversion $U^{-1}v$ using the Cholesky decomposition stored in data and acting in place.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[in,out]	v	The input matrix to multiply with data.U^{-1} and also storing the result.

Returns: A reference to the result of $U^{-1}v$ stored in v.

Remarks: The result is similar to the code data.U.triangularView<Eigen::Upper> ().solveInPlace(v).

◆ Utiv()

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>

Mat & Utiv	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		const DataTpl< Scalar, Options, JointCollectionTpl > &	data,
		const Eigen::MatrixBase< Mat > &	v )

Perform the pivot inversion $U^{-\top}v$ using the Cholesky decomposition stored in data and acting in place.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[in,out]	v	The input matrix to multiply with data.U^{-\top} and also storing the result.

Returns: A reference to the result of $U^{-\top}v$ stored in v.

Remarks: The result is similar to the code data.U.triangularView<Eigen::Upper> ().transpose().solveInPlace(v).

◆ Utv()

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>

Mat & Utv	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		const DataTpl< Scalar, Options, JointCollectionTpl > &	data,
		const Eigen::MatrixBase< Mat > &	v )

Perform the sparse multiplication $U^{\top}v$ using the Cholesky decomposition stored in data and acting in place.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[in,out]	v	The input matrix to multiply with data.U.tranpose() and also storing the result.

Returns: A reference to the result of $U^{\top}v$ stored in v.

◆ Uv()

template<typename Scalar, int Options, template< typename, int > class JointCollectionTpl, typename Mat>

Mat & Uv	(	const ModelTpl< Scalar, Options, JointCollectionTpl > &	model,
		const DataTpl< Scalar, Options, JointCollectionTpl > &	data,
		const Eigen::MatrixBase< Mat > &	v )

Perform the sparse multiplication $ Uv $ using the Cholesky decomposition stored in data and acting in place.

Template Parameters

JointCollection Collection of Joint types.

Parameters

[in]	model	The model structure of the rigid body system.
[in]	data	The data structure of the rigid body system.
[in,out]	v	The input matrix to multiply with data.U and also storing the result.

Returns: A reference to the result of stored in v.

Functions

Detailed Description

Function Documentation

◆ computeMinv() [1/2]

◆ computeMinv() [2/2]

◆ decompose()

◆ Mv() [1/2]

◆ Mv() [2/2]

◆ solve()

◆ UDUtv()

◆ Uiv()

◆ Utiv()

◆ Utv()

◆ Uv()