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// Copyright (c) 2024 INRIA |
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#ifndef __pinocchio_math_tridiagonal_matrix_hpp__ |
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#define __pinocchio_math_tridiagonal_matrix_hpp__ |
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#include "pinocchio/fwd.hpp" |
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#include <Eigen/Dense> |
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namespace pinocchio |
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{ |
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template<typename Scalar, int Options = 0> |
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struct TridiagonalSymmetricMatrixTpl; |
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template<typename _Scalar, int _Options> |
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struct traits<TridiagonalSymmetricMatrixTpl<_Scalar, _Options>> |
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{ |
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typedef _Scalar Scalar; |
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enum |
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{ |
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Options = _Options |
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}; |
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typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Options> PlainMatrixType; |
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}; |
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template<typename TridiagonalSymmetricMatrix, typename MatrixDerived> |
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struct TridiagonalSymmetricMatrixApplyOnTheRightReturnType; |
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template<typename TridiagonalSymmetricMatrix, typename MatrixDerived> |
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struct traits< |
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TridiagonalSymmetricMatrixApplyOnTheRightReturnType<TridiagonalSymmetricMatrix, MatrixDerived>> |
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: public traits<TridiagonalSymmetricMatrix> |
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{ |
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}; |
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template<typename MatrixDerived, typename TridiagonalSymmetricMatrix> |
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struct TridiagonalSymmetricMatrixApplyOnTheLeftReturnType; |
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template<typename MatrixDerived, typename TridiagonalSymmetricMatrix> |
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struct traits< |
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TridiagonalSymmetricMatrixApplyOnTheLeftReturnType<MatrixDerived, TridiagonalSymmetricMatrix>> |
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: public traits<TridiagonalSymmetricMatrix> |
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{ |
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}; |
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template<typename TridiagonalSymmetricMatrix> |
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struct TridiagonalSymmetricMatrixInverse; |
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template<typename TridiagonalSymmetricMatrix> |
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struct traits<TridiagonalSymmetricMatrixInverse<TridiagonalSymmetricMatrix>> |
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: public traits<TridiagonalSymmetricMatrix> |
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{ |
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}; |
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template<typename TridiagonalSymmetricMatrixInverse, typename MatrixDerived> |
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struct TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType; |
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template<typename TridiagonalSymmetricMatrixInverse, typename MatrixDerived> |
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struct traits<TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType< |
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TridiagonalSymmetricMatrixInverse, |
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MatrixDerived>> : public traits<TridiagonalSymmetricMatrixInverse> |
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{ |
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}; |
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} // namespace pinocchio |
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namespace Eigen |
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{ |
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namespace internal |
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{ |
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template<typename Scalar, int Options> |
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struct traits<pinocchio::TridiagonalSymmetricMatrixTpl<Scalar, Options>> |
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: public traits<typename pinocchio::traits< |
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pinocchio::TridiagonalSymmetricMatrixTpl<Scalar, Options>>::PlainMatrixType> |
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{ |
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typedef pinocchio::traits<pinocchio::TridiagonalSymmetricMatrixTpl<Scalar, Options>> Base; |
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typedef typename Base::PlainMatrixType ReturnType; |
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enum |
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{ |
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Flags = 0 |
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}; |
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}; |
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template<typename TridiagonalSymmetricMatrix, typename MatrixDerived> |
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struct traits<pinocchio::TridiagonalSymmetricMatrixApplyOnTheRightReturnType< |
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TridiagonalSymmetricMatrix, |
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MatrixDerived>> |
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: public traits< |
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typename pinocchio::traits<pinocchio::TridiagonalSymmetricMatrixApplyOnTheRightReturnType< |
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TridiagonalSymmetricMatrix, |
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MatrixDerived>>::PlainMatrixType> |
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{ |
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typedef pinocchio::traits<pinocchio::TridiagonalSymmetricMatrixApplyOnTheRightReturnType< |
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TridiagonalSymmetricMatrix, |
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MatrixDerived>> |
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Base; |
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typedef typename Base::PlainMatrixType ReturnType; |
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enum |
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{ |
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Flags = 0 |
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}; |
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}; |
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template<typename MatrixDerived, typename TridiagonalSymmetricMatrix> |
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struct traits<pinocchio::TridiagonalSymmetricMatrixApplyOnTheLeftReturnType< |
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MatrixDerived, |
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TridiagonalSymmetricMatrix>> |
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: public traits< |
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typename pinocchio::traits<pinocchio::TridiagonalSymmetricMatrixApplyOnTheLeftReturnType< |
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MatrixDerived, |
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TridiagonalSymmetricMatrix>>::PlainMatrixType> |
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{ |
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typedef pinocchio::traits<pinocchio::TridiagonalSymmetricMatrixApplyOnTheLeftReturnType< |
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MatrixDerived, |
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TridiagonalSymmetricMatrix>> |
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Base; |
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typedef typename Base::PlainMatrixType ReturnType; |
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enum |
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{ |
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Flags = 0 |
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}; |
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}; |
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template<typename TridiagonalSymmetricMatrix> |
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struct traits<pinocchio::TridiagonalSymmetricMatrixInverse<TridiagonalSymmetricMatrix>> |
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: public traits<TridiagonalSymmetricMatrix> |
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{ |
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}; |
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template<typename TridiagonalSymmetricMatrixInverse, typename MatrixDerived> |
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struct traits<pinocchio::TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType< |
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TridiagonalSymmetricMatrixInverse, |
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MatrixDerived>> |
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: public traits<typename pinocchio::traits< |
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pinocchio::TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType< |
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TridiagonalSymmetricMatrixInverse, |
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MatrixDerived>>::PlainMatrixType> |
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{ |
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typedef pinocchio::traits< |
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pinocchio::TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType< |
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TridiagonalSymmetricMatrixInverse, |
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MatrixDerived>> |
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Base; |
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typedef typename Base::PlainMatrixType ReturnType; |
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enum |
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{ |
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Flags = 0 |
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}; |
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}; |
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} // namespace internal |
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} // namespace Eigen |
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namespace pinocchio |
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{ |
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/// \brief Dynamic size Tridiagonal symmetric matrix type |
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/// This class is in practice used in Lanczos decomposition |
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template<typename _Scalar, int _Options> |
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struct TridiagonalSymmetricMatrixTpl |
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: public Eigen::ReturnByValue<TridiagonalSymmetricMatrixTpl<_Scalar, _Options>> |
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{ |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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typedef TridiagonalSymmetricMatrixTpl Self; |
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typedef _Scalar Scalar; |
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enum |
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{ |
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Options = _Options |
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}; |
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typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1, Options> CoeffVectorType; |
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typedef typename traits<Self>::PlainMatrixType PlainMatrixType; |
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/// \brief Default constructor from a given size |
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explicit TridiagonalSymmetricMatrixTpl(const Eigen::DenseIndex size) |
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: m_size(size) |
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, m_diagonal(size) |
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, m_sub_diagonal(size - 1) |
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{ |
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assert(size > 0 && "size should be greater than 0."); |
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} |
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bool operator==(const TridiagonalSymmetricMatrixTpl & other) const |
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{ |
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if (this == &other) |
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return true; |
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return diagonal() == other.diagonal() && subDiagonal() == other.subDiagonal(); |
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} |
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bool operator!=(const TridiagonalSymmetricMatrixTpl & other) const |
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{ |
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return !(*this == other); |
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} |
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TridiagonalSymmetricMatrixInverse<Self> inverse() const |
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{ |
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return TridiagonalSymmetricMatrixInverse<Self>(*this); |
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} |
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CoeffVectorType & diagonal() |
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{ |
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return m_diagonal; |
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} |
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const CoeffVectorType & diagonal() const |
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{ |
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return m_diagonal; |
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} |
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CoeffVectorType & subDiagonal() |
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{ |
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return m_sub_diagonal; |
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} |
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const CoeffVectorType & subDiagonal() const |
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{ |
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return m_sub_diagonal; |
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} |
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void setIdentity() |
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{ |
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diagonal().setOnes(); |
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subDiagonal().setZero(); |
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} |
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bool isIdentity(const Scalar prec = Eigen::NumTraits<Scalar>::dummy_precision()) const |
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{ |
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return subDiagonal().isZero(prec) && diagonal().isOnes(prec); |
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} |
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void setZero() |
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{ |
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diagonal().setZero(); |
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subDiagonal().setZero(); |
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} |
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bool isZero(const Scalar prec = Eigen::NumTraits<Scalar>::dummy_precision()) const |
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{ |
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return subDiagonal().isZero(prec) && diagonal().isZero(prec); |
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} |
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void setRandom() |
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{ |
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diagonal().setRandom(); |
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subDiagonal().setRandom(); |
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} |
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bool isDiagonal(const Scalar prec = Eigen::NumTraits<Scalar>::dummy_precision()) const |
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{ |
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return subDiagonal().isZero(prec); |
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} |
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template<typename VectorCoeffType> |
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void setDiagonal(const Eigen::MatrixBase<VectorCoeffType> & diagonal_coefficients) |
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{ |
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PINOCCHIO_CHECK_ARGUMENT_SIZE(diagonal_coefficients.size(), cols()); |
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static_assert( |
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VectorCoeffType::IsVectorAtCompileTime, |
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"VectorCoeffType should be a vector type at compile time"); |
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diagonal() = diagonal_coefficients; |
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subDiagonal().setZero(); |
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} |
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EIGEN_CONSTEXPR Eigen::Index rows() const EIGEN_NOEXCEPT |
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{ |
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return m_size; |
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} |
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EIGEN_CONSTEXPR Eigen::Index cols() const EIGEN_NOEXCEPT |
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{ |
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return m_size; |
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} |
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PlainMatrixType matrix() const |
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{ |
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return PlainMatrixType(*this); |
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} |
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template<typename ResultType> |
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inline void evalTo(ResultType & result) const |
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{ |
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result.setZero(); |
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result.template diagonal<1>() = subDiagonal().conjugate(); |
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result.diagonal() = diagonal(); |
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result.template diagonal<-1>() = subDiagonal(); |
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} |
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template<typename MatrixDerived> |
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TridiagonalSymmetricMatrixApplyOnTheRightReturnType<Self, MatrixDerived> |
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applyOnTheRight(const Eigen::MatrixBase<MatrixDerived> & mat) const |
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{ |
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typedef TridiagonalSymmetricMatrixApplyOnTheRightReturnType<Self, MatrixDerived> ReturnType; |
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return ReturnType(*this, mat.derived()); |
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} |
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template<typename MatrixDerived> |
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TridiagonalSymmetricMatrixApplyOnTheLeftReturnType<MatrixDerived, Self> |
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applyOnTheLeft(const Eigen::MatrixBase<MatrixDerived> & mat) const |
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{ |
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typedef TridiagonalSymmetricMatrixApplyOnTheLeftReturnType<MatrixDerived, Self> ReturnType; |
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return ReturnType(mat.derived(), *this); |
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} |
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template<typename MatrixDerived> |
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inline TridiagonalSymmetricMatrixApplyOnTheRightReturnType<Self, MatrixDerived> |
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operator*(const Eigen::MatrixBase<MatrixDerived> & mat) const |
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{ |
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return this->applyOnTheRight(mat.derived()); |
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} |
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protected: |
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Eigen::DenseIndex m_size; |
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CoeffVectorType m_diagonal; |
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CoeffVectorType m_sub_diagonal; |
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}; |
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template<typename LhsMatrixType, typename S, int O> |
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TridiagonalSymmetricMatrixApplyOnTheLeftReturnType< |
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LhsMatrixType, |
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TridiagonalSymmetricMatrixTpl<S, O>> |
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operator*( |
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const Eigen::MatrixBase<LhsMatrixType> & lhs, const TridiagonalSymmetricMatrixTpl<S, O> & rhs) |
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{ |
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return rhs.applyOnTheLeft(lhs); |
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} |
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template<typename TridiagonalSymmetricMatrix, typename RhsMatrixType> |
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struct TridiagonalSymmetricMatrixApplyOnTheRightReturnType |
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: public Eigen::ReturnByValue<TridiagonalSymmetricMatrixApplyOnTheRightReturnType< |
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TridiagonalSymmetricMatrix, |
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RhsMatrixType>> |
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{ |
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typedef TridiagonalSymmetricMatrixApplyOnTheRightReturnType Self; |
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typedef typename traits<Self>::PlainMatrixType PlainMatrixType; |
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TridiagonalSymmetricMatrixApplyOnTheRightReturnType( |
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const TridiagonalSymmetricMatrix & lhs, const RhsMatrixType & rhs) |
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: m_lhs(lhs) |
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, m_rhs(rhs) |
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{ |
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} |
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template<typename ResultType> |
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inline void evalTo(ResultType & result) const |
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{ |
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PINOCCHIO_CHECK_ARGUMENT_SIZE(result.rows(), rows()); |
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PINOCCHIO_CHECK_ARGUMENT_SIZE(result.cols(), cols()); |
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assert(cols() >= 1); |
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assert(rows() >= 1); |
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const Eigen::DenseIndex reduced_size = cols() - 1; |
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// Main diagonal |
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result.noalias() = m_lhs.diagonal().asDiagonal() * m_rhs; |
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// Upper diagonal |
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result.topRows(reduced_size).noalias() += |
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m_lhs.subDiagonal().conjugate().asDiagonal() * m_rhs.bottomRows(reduced_size); |
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// Sub diagonal |
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result.bottomRows(reduced_size).noalias() += |
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m_lhs.subDiagonal().asDiagonal() * m_rhs.topRows(reduced_size); |
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} |
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EIGEN_CONSTEXPR Eigen::Index rows() const EIGEN_NOEXCEPT |
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{ |
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return m_lhs.rows(); |
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} |
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EIGEN_CONSTEXPR Eigen::Index cols() const EIGEN_NOEXCEPT |
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{ |
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return m_rhs.cols(); |
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} |
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protected: |
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const TridiagonalSymmetricMatrix & m_lhs; |
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const RhsMatrixType & m_rhs; |
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}; |
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template<typename LhsMatrixType, typename TridiagonalSymmetricMatrix> |
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struct TridiagonalSymmetricMatrixApplyOnTheLeftReturnType |
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: public Eigen::ReturnByValue< |
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TridiagonalSymmetricMatrixApplyOnTheLeftReturnType<LhsMatrixType, TridiagonalSymmetricMatrix>> |
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{ |
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typedef TridiagonalSymmetricMatrixApplyOnTheLeftReturnType Self; |
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typedef typename traits<Self>::PlainMatrixType PlainMatrixType; |
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TridiagonalSymmetricMatrixApplyOnTheLeftReturnType( |
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const LhsMatrixType & lhs, const TridiagonalSymmetricMatrix & rhs) |
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: m_lhs(lhs) |
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, m_rhs(rhs) |
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{ |
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} |
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template<typename ResultType> |
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inline void evalTo(ResultType & result) const |
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{ |
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PINOCCHIO_CHECK_ARGUMENT_SIZE(result.rows(), rows()); |
394 |
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✗ |
PINOCCHIO_CHECK_ARGUMENT_SIZE(result.cols(), cols()); |
395 |
|
|
|
396 |
|
✗ |
assert(cols() >= 1); |
397 |
|
✗ |
assert(rows() >= 1); |
398 |
|
|
|
399 |
|
✗ |
const Eigen::DenseIndex reduced_size = cols() - 1; |
400 |
|
|
// Main diagonal |
401 |
|
✗ |
result.noalias() = m_lhs * m_rhs.diagonal().asDiagonal(); |
402 |
|
|
// Upper diagonal |
403 |
|
✗ |
result.rightCols(reduced_size).noalias() += |
404 |
|
✗ |
m_lhs.leftCols(reduced_size) * m_rhs.subDiagonal().conjugate().asDiagonal(); |
405 |
|
|
// Sub diagonal |
406 |
|
✗ |
result.leftCols(reduced_size).noalias() += |
407 |
|
✗ |
m_lhs.rightCols(reduced_size) * m_rhs.subDiagonal().asDiagonal(); |
408 |
|
|
} |
409 |
|
|
|
410 |
|
✗ |
EIGEN_CONSTEXPR Eigen::Index rows() const EIGEN_NOEXCEPT |
411 |
|
|
{ |
412 |
|
✗ |
return m_lhs.rows(); |
413 |
|
|
} |
414 |
|
✗ |
EIGEN_CONSTEXPR Eigen::Index cols() const EIGEN_NOEXCEPT |
415 |
|
|
{ |
416 |
|
✗ |
return m_rhs.cols(); |
417 |
|
|
} |
418 |
|
|
|
419 |
|
|
protected: |
420 |
|
|
const LhsMatrixType & m_lhs; |
421 |
|
|
const TridiagonalSymmetricMatrix & m_rhs; |
422 |
|
|
}; |
423 |
|
|
|
424 |
|
|
template<typename _TridiagonalSymmetricMatrix> |
425 |
|
|
struct TridiagonalSymmetricMatrixInverse |
426 |
|
|
: public Eigen::ReturnByValue<TridiagonalSymmetricMatrixInverse<_TridiagonalSymmetricMatrix>> |
427 |
|
|
{ |
428 |
|
|
typedef _TridiagonalSymmetricMatrix TridiagonalSymmetricMatrix; |
429 |
|
|
typedef TridiagonalSymmetricMatrixInverse Self; |
430 |
|
|
typedef typename TridiagonalSymmetricMatrix::Scalar Scalar; |
431 |
|
|
enum |
432 |
|
|
{ |
433 |
|
|
Options = TridiagonalSymmetricMatrix::Options |
434 |
|
|
}; |
435 |
|
|
|
436 |
|
|
typedef typename TridiagonalSymmetricMatrix::CoeffVectorType CoeffVectorType; |
437 |
|
|
typedef typename traits<Self>::PlainMatrixType PlainMatrixType; |
438 |
|
|
|
439 |
|
✗ |
explicit TridiagonalSymmetricMatrixInverse( |
440 |
|
|
const TridiagonalSymmetricMatrix & tridiagonal_matrix) |
441 |
|
✗ |
: tridiagonal_matrix(tridiagonal_matrix) |
442 |
|
✗ |
, m_size(tridiagonal_matrix.rows()) |
443 |
|
✗ |
, m_diagonal(m_size) |
444 |
|
✗ |
, m_sub_diagonal(m_size - 1) |
445 |
|
|
{ |
446 |
|
✗ |
eval(); |
447 |
|
|
} |
448 |
|
|
|
449 |
|
✗ |
const TridiagonalSymmetricMatrix & inverse() const |
450 |
|
|
{ |
451 |
|
✗ |
return tridiagonal_matrix; |
452 |
|
|
} |
453 |
|
|
|
454 |
|
|
template<typename MatrixDerived> |
455 |
|
|
TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType<Self, MatrixDerived> |
456 |
|
✗ |
applyOnTheRight(const Eigen::MatrixBase<MatrixDerived> & mat) const |
457 |
|
|
{ |
458 |
|
|
typedef TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType<Self, MatrixDerived> |
459 |
|
|
ReturnType; |
460 |
|
✗ |
return ReturnType(*this, mat.derived()); |
461 |
|
|
} |
462 |
|
|
|
463 |
|
|
template<typename MatrixDerived> |
464 |
|
|
inline TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType<Self, MatrixDerived> |
465 |
|
✗ |
operator*(const Eigen::MatrixBase<MatrixDerived> & mat) const |
466 |
|
|
{ |
467 |
|
✗ |
return this->applyOnTheRight(mat.derived()); |
468 |
|
|
} |
469 |
|
|
|
470 |
|
|
template<typename ResultType> |
471 |
|
✗ |
inline void evalTo(ResultType & result) const |
472 |
|
|
{ |
473 |
|
✗ |
PINOCCHIO_CHECK_ARGUMENT_SIZE(result.rows(), rows()); |
474 |
|
✗ |
PINOCCHIO_CHECK_ARGUMENT_SIZE(result.cols(), cols()); |
475 |
|
|
|
476 |
|
✗ |
assert(cols() >= 1); |
477 |
|
✗ |
assert(rows() >= 1); |
478 |
|
|
|
479 |
|
✗ |
const auto & b = m_diagonal; |
480 |
|
✗ |
const auto & c = tridiagonal_matrix.subDiagonal(); |
481 |
|
✗ |
const auto & w = m_sub_diagonal; |
482 |
|
|
|
483 |
|
|
// Forward sweep |
484 |
|
✗ |
result.setIdentity(); |
485 |
|
✗ |
for (Eigen::DenseIndex i = 1; i < m_size; ++i) |
486 |
|
|
{ |
487 |
|
✗ |
result.row(i).head(i) -= w[i - 1] * result.row(i - 1).head(i); |
488 |
|
|
} |
489 |
|
|
|
490 |
|
|
// Backward sweep |
491 |
|
✗ |
result.row(m_size - 1) /= b[m_size - 1]; |
492 |
|
✗ |
for (Eigen::DenseIndex i = m_size - 2; i >= 0; --i) |
493 |
|
|
{ |
494 |
|
✗ |
result.row(i) -= c[i] * result.row(i + 1); |
495 |
|
✗ |
result.row(i) /= b[i]; |
496 |
|
|
} |
497 |
|
|
} |
498 |
|
|
|
499 |
|
✗ |
EIGEN_CONSTEXPR Eigen::Index rows() const EIGEN_NOEXCEPT |
500 |
|
|
{ |
501 |
|
✗ |
return m_size; |
502 |
|
|
} |
503 |
|
✗ |
EIGEN_CONSTEXPR Eigen::Index cols() const EIGEN_NOEXCEPT |
504 |
|
|
{ |
505 |
|
✗ |
return m_size; |
506 |
|
|
} |
507 |
|
|
|
508 |
|
|
protected: |
509 |
|
|
template<typename T, typename MatrixDerived> |
510 |
|
|
friend struct TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType; |
511 |
|
|
|
512 |
|
|
/// \brief Forward sweep of https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm |
513 |
|
✗ |
void eval() |
514 |
|
|
{ |
515 |
|
✗ |
m_diagonal = tridiagonal_matrix.diagonal(); |
516 |
|
✗ |
m_sub_diagonal = tridiagonal_matrix.subDiagonal(); |
517 |
|
✗ |
auto & w = m_sub_diagonal; |
518 |
|
✗ |
auto & b = m_diagonal; |
519 |
|
✗ |
const auto & c = tridiagonal_matrix.subDiagonal(); |
520 |
|
✗ |
for (Eigen::DenseIndex i = 1; i < m_size; ++i) |
521 |
|
|
{ |
522 |
|
✗ |
w.coeffRef(i - 1) /= b[i - 1]; |
523 |
|
✗ |
m_diagonal.coeffRef(i) -= w[i - 1] * c[i - 1]; |
524 |
|
|
} |
525 |
|
|
} |
526 |
|
|
|
527 |
|
|
const TridiagonalSymmetricMatrix & tridiagonal_matrix; |
528 |
|
|
Eigen::DenseIndex m_size; |
529 |
|
|
CoeffVectorType m_diagonal; |
530 |
|
|
CoeffVectorType m_sub_diagonal; |
531 |
|
|
}; |
532 |
|
|
|
533 |
|
|
template<typename TridiagonalSymmetricMatrixInverse, typename RhsMatrixType> |
534 |
|
|
struct TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType |
535 |
|
|
: public Eigen::ReturnByValue<TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType< |
536 |
|
|
TridiagonalSymmetricMatrixInverse, |
537 |
|
|
RhsMatrixType>> |
538 |
|
|
{ |
539 |
|
|
typedef TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType Self; |
540 |
|
|
typedef typename traits<Self>::PlainMatrixType PlainMatrixType; |
541 |
|
|
|
542 |
|
✗ |
TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType( |
543 |
|
|
const TridiagonalSymmetricMatrixInverse & lhs, const RhsMatrixType & rhs) |
544 |
|
✗ |
: m_lhs(lhs) |
545 |
|
✗ |
, m_rhs(rhs) |
546 |
|
|
{ |
547 |
|
|
} |
548 |
|
|
|
549 |
|
|
template<typename ResultType> |
550 |
|
✗ |
inline void evalTo(ResultType & result) const |
551 |
|
|
{ |
552 |
|
✗ |
PINOCCHIO_CHECK_ARGUMENT_SIZE(result.rows(), rows()); |
553 |
|
✗ |
PINOCCHIO_CHECK_ARGUMENT_SIZE(result.cols(), cols()); |
554 |
|
|
|
555 |
|
✗ |
assert(cols() >= 1); |
556 |
|
✗ |
assert(rows() >= 1); |
557 |
|
|
|
558 |
|
✗ |
const Eigen::DenseIndex size = m_lhs.rows(); |
559 |
|
✗ |
const auto & b = m_lhs.m_diagonal; |
560 |
|
✗ |
const auto & c = m_lhs.tridiagonal_matrix.subDiagonal(); |
561 |
|
✗ |
const auto & w = m_lhs.m_sub_diagonal; |
562 |
|
|
|
563 |
|
|
// Forward sweep |
564 |
|
✗ |
result = m_rhs; |
565 |
|
✗ |
for (Eigen::DenseIndex i = 1; i < size; ++i) |
566 |
|
|
{ |
567 |
|
✗ |
result.row(i) -= w[i - 1] * result.row(i - 1); |
568 |
|
|
} |
569 |
|
|
|
570 |
|
|
// Backward sweep |
571 |
|
✗ |
result.row(size - 1) /= b[size - 1]; |
572 |
|
✗ |
for (Eigen::DenseIndex i = size - 2; i >= 0; --i) |
573 |
|
|
{ |
574 |
|
✗ |
result.row(i) -= c[i] * result.row(i + 1); |
575 |
|
✗ |
result.row(i) /= b[i]; |
576 |
|
|
} |
577 |
|
|
} |
578 |
|
|
|
579 |
|
✗ |
EIGEN_CONSTEXPR Eigen::Index rows() const EIGEN_NOEXCEPT |
580 |
|
|
{ |
581 |
|
✗ |
return m_lhs.rows(); |
582 |
|
|
} |
583 |
|
✗ |
EIGEN_CONSTEXPR Eigen::Index cols() const EIGEN_NOEXCEPT |
584 |
|
|
{ |
585 |
|
✗ |
return m_rhs.cols(); |
586 |
|
|
} |
587 |
|
|
|
588 |
|
|
protected: |
589 |
|
|
const TridiagonalSymmetricMatrixInverse & m_lhs; |
590 |
|
|
const RhsMatrixType & m_rhs; |
591 |
|
|
}; |
592 |
|
|
} // namespace pinocchio |
593 |
|
|
|
594 |
|
|
#endif // #ifndef __pinocchio_math_tridiagonal_matrix_hpp__ |
595 |
|
|
|