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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

Detailed Description

Cholesky decompositions.

Function Documentation

◆ computeMinv() [1/2]

Mat& pinocchio::cholesky::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]

const DataTpl<Scalar, Options, JointCollectionTpl>::RowMatrixXs& pinocchio::cholesky::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()

const DataTpl<Scalar, Options, JointCollectionTpl>::MatrixXs& pinocchio::cholesky::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 \(U\) an upper triangular matrix with ones on its main diagonal and \(D\) 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 \(U\).

◆ Mv() [1/2]

Mat pinocchio::cholesky::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 \( Mv \).

◆ Mv() [2/2]

MatRes& pinocchio::cholesky::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 \( Mv \) is stored.

Returns: A reference of the result of \( Mv \).

◆ solve()

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 \(x\) 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()

Mat& pinocchio::cholesky::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 \( Mv \) is stored.

Returns: A reference of the result of \( Mv \).

◆ Uiv()

Mat& pinocchio::cholesky::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()

Mat& pinocchio::cholesky::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()

Mat& pinocchio::cholesky::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()

Mat& pinocchio::cholesky::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 \( Uv \) 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()