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 , 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. More...

template<typename Scalar , int Options, template< typename, int > class JointCollectionTpl, typename Mat >
	PINOCCHIO_EIGEN_PLAIN_TYPE (Mat) Mv(const ModelTpl< Scalar
	Performs the multiplication 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 of using the Cholesky decomposition stored in data given the entry . 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 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 using the Cholesky decomposition stored in data and acting in place. More...

Variables
JointCollectionTpl const DataTpl< Scalar, Options, JointCollectionTpl > &	data

JointCollectionTpl const DataTpl< Scalar, Options, JointCollectionTpl > const Eigen::MatrixBase< Mat > &	min

JointCollectionTpl &	model

	Options

Detailed Description

Cholesky decompositions.

Function Documentation

◆ computeMinv() [1/2]

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

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]

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

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 223 of file cholesky.hpp.

◆ decompose()

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

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 .

◆ Mv()

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

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 is stored.

Returns: A reference of the result of .

◆ PINOCCHIO_EIGEN_PLAIN_TYPE()

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

pinocchio::cholesky::PINOCCHIO_EIGEN_PLAIN_TYPE ( Mat ) const

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 .

◆ solve()

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

Mat & pinocchio::cholesky::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& 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 is stored.

Returns: A reference of the result of .

◆ Uiv()

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

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()

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

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^{-} 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& 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()

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

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 stored in v.

Variable Documentation

◆ data

JointCollectionTpl const DataTpl<Scalar,Options,JointCollectionTpl>& pinocchio::cholesky::data

Definition at line 71 of file cholesky.hpp.

◆ min

JointCollectionTpl const DataTpl<Scalar,Options,JointCollectionTpl> const Eigen::MatrixBase<Mat>& pinocchio::cholesky::min

Definition at line 71 of file cholesky.hpp.

◆ model

JointCollectionTpl& pinocchio::cholesky::model

Definition at line 71 of file cholesky.hpp.

◆ Options

pinocchio::cholesky::Options

Definition at line 71 of file cholesky.hpp.

Functions

Variables

Detailed Description

Function Documentation

◆ computeMinv() [1/2]

◆ computeMinv() [2/2]

◆ decompose()

◆ Mv()

◆ PINOCCHIO_EIGEN_PLAIN_TYPE()

◆ solve()

◆ UDUtv()

◆ Uiv()

◆ Utiv()

◆ Utv()

◆ Uv()

Variable Documentation

◆ data

◆ min

◆ model

◆ Options