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// Copyright (c) 2015-2019 CNRS INRIA |
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// |
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#ifndef __pinocchio_cholesky_hpp__ |
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#define __pinocchio_cholesky_hpp__ |
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#include "pinocchio/multibody/model.hpp" |
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#include "pinocchio/multibody/data.hpp" |
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namespace pinocchio |
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{ |
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namespace cholesky |
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{ |
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/// |
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/// \brief Compute the Cholesky decomposition of the joint space inertia matrix M contained in |
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/// data. |
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/// |
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/// \note The Cholesky decomposition corresponds to |
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/// \f$ M = U D U^{\top}\f$ with \f$U\f$ an upper triangular matrix with ones on its main |
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/// diagonal and \f$D\f$ a diagonal matrix. |
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/// |
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/// The result stored in data.U and data.D matrices. One can retrieve the matrice M by |
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/// performing the computation data.U * data.D * data.U.transpose() |
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/// |
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/// See https://en.wikipedia.org/wiki/Cholesky_decomposition for futher details. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// |
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/// \return A reference to the upper triangular matrix \f$U\f$. |
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/// |
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template<typename Scalar, int Options, template<typename, int> class JointCollectionTpl> |
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inline const typename DataTpl<Scalar, Options, JointCollectionTpl>::MatrixXs & decompose( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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DataTpl<Scalar, Options, JointCollectionTpl> & data); |
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/// |
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/// \brief Return the solution \f$x\f$ of \f$ M x = y \f$ using the Cholesky decomposition |
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/// stored in data given the entry \f$ y \f$. Act like solveInPlace of Eigen::LLT. |
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/// |
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/// \note This algorithm is useful to compute the forward dynamics, retriving the joint |
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/// acceleration \f$ \ddot{q} \f$ from the current joint torque \f$ \tau \f$ |
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/// \f$ |
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/// M(q) \ddot{q} + b(q, \dot{q}) = \tau \iff \ddot{q} = M(q)^{-1} (\tau - b(q, |
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/// \dot{q})) |
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/// \f$ |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[inout] y The input matrix to inverse which also contains the result \f$x\f$ of the |
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/// inversion. |
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/// |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat> |
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Mat & solve( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & y); |
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/// |
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/// \brief Performs the multiplication \f$ M v \f$ by using the sparsity pattern of the M |
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/// matrix. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[in] min The input matrix to multiply with data.M. |
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/// |
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/// \return A the result of \f$ Mv \f$. |
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/// |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat> |
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typename PINOCCHIO_EIGEN_PLAIN_TYPE(Mat) Mv( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & min); |
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/// |
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/// \brief Performs the multiplication \f$ M v \f$ by using the sparsity pattern of the M |
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/// matrix. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[in] min The input matrix to multiply with data.M. |
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/// \param[out] mout The output matrix where the result of \f$ Mv \f$ is stored. |
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/// |
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/// \return A reference of the result of \f$ Mv \f$. |
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/// |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat, |
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typename MatRes> |
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MatRes & Mv( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & min, |
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const Eigen::MatrixBase<MatRes> & mout); |
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/// |
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/// \brief Performs the multiplication \f$ M v \f$ by using the Cholesky decomposition of M |
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/// stored in data. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[inout] m The input matrix where the result of \f$ Mv \f$ is stored. |
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/// |
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/// \return A reference of the result of \f$ Mv \f$. |
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/// |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat> |
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Mat & UDUtv( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & m); |
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/// |
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/// \brief Perform the sparse multiplication \f$ Uv \f$ using the Cholesky decomposition stored |
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/// in data and acting in place. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[inout] v The input matrix to multiply with data.U and also storing the result. |
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/// |
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/// \return A reference to the result of \f$ Uv \f$ stored in v. |
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/// |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat> |
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Mat & Uv( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & v); |
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/// |
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/// \brief Perform the sparse multiplication \f$ U^{\top}v \f$ using the Cholesky decomposition |
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/// stored in data and acting in place. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[inout] v The input matrix to multiply with data.U.tranpose() and also storing the |
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/// result. |
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/// |
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/// \return A reference to the result of \f$ U^{\top}v \f$ stored in v. |
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/// |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat> |
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Mat & Utv( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & v); |
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/// |
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/// \brief Perform the pivot inversion \f$ U^{-1}v \f$ using the Cholesky decomposition stored |
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/// in data and acting in place. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[inout] v The input matrix to multiply with data.U^{-1} and also storing the result. |
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/// |
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/// \return A reference to the result of \f$ U^{-1}v \f$ stored in v. |
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/// |
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/// \remarks The result is similar to the code data.U.triangularView<Eigen::Upper> |
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/// ().solveInPlace(v). |
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/// |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat> |
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Mat & Uiv( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & v); |
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/// |
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/// \brief Perform the pivot inversion \f$ U^{-\top}v \f$ using the Cholesky decomposition |
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/// stored in data and acting in place. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[inout] v The input matrix to multiply with data.U^{-\top} and also storing the |
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/// result. |
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/// |
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/// \return A reference to the result of \f$ U^{-\top}v \f$ stored in v. |
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/// |
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/// \remarks The result is similar to the code data.U.triangularView<Eigen::Upper> |
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/// ().transpose().solveInPlace(v). |
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/// |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat> |
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Mat & Utiv( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & v); |
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/// |
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/// \brief Perform the sparse inversion \f$ M^{-1}v \f$ using the Cholesky decomposition stored |
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/// in data and acting in place. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[inout] v The input matrix to multiply with data.M^{-1} and also storing the result. |
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/// |
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/// \return A reference to the result of \f$ M^{-1}v \f$ stored in v. |
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/// |
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// TODO Clearify, it seems it is exactly the same as solve in l. 54 |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat> |
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Mat & solve( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & v); |
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/// |
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/// \brief Computes the inverse of the joint space inertia matrix M from its Cholesky |
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/// factorization. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// \param[out] Minv The output matrix where the result is stored. |
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/// |
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/// \return A reference to the result. |
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/// |
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template< |
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typename Scalar, |
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int Options, |
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template<typename, int> class JointCollectionTpl, |
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typename Mat> |
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Mat & computeMinv( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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const DataTpl<Scalar, Options, JointCollectionTpl> & data, |
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const Eigen::MatrixBase<Mat> & Minv); |
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/// |
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/// \brief Computes the inverse of the joint space inertia matrix M from its Cholesky |
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/// factorization. |
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/// The results is then directly stored in data.Minv. |
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/// |
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/// \tparam JointCollection Collection of Joint types. |
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/// |
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/// \param[in] model The model structure of the rigid body system. |
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/// \param[in] data The data structure of the rigid body system. |
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/// |
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/// \return A reference to the result data.Minv. |
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/// |
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template<typename Scalar, int Options, template<typename, int> class JointCollectionTpl> |
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const typename DataTpl<Scalar, Options, JointCollectionTpl>::RowMatrixXs & computeMinv( |
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const ModelTpl<Scalar, Options, JointCollectionTpl> & model, |
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DataTpl<Scalar, Options, JointCollectionTpl> & data) |
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{ |
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return computeMinv(model, data, data.Minv); |
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} |
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} // namespace cholesky |
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} // namespace pinocchio |
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/* --- Details -------------------------------------------------------------------- */ |
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/* --- Details -------------------------------------------------------------------- */ |
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/* --- Details -------------------------------------------------------------------- */ |
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#include "pinocchio/algorithm/cholesky.hxx" |
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#if PINOCCHIO_ENABLE_TEMPLATE_INSTANTIATION |
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#include "pinocchio/algorithm/cholesky.txx" |
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#endif // PINOCCHIO_ENABLE_TEMPLATE_INSTANTIATION |
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#endif // ifndef __pinocchio_cholesky_hpp__ |
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