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// |
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// Copyright (c) 2024 INRIA |
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// |
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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< |
| 378 |
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TridiagonalSymmetricMatrixApplyOnTheLeftReturnType<LhsMatrixType, TridiagonalSymmetricMatrix>> |
| 379 |
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{ |
| 380 |
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typedef TridiagonalSymmetricMatrixApplyOnTheLeftReturnType Self; |
| 381 |
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typedef typename traits<Self>::PlainMatrixType PlainMatrixType; |
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| 383 |
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TridiagonalSymmetricMatrixApplyOnTheLeftReturnType( |
| 384 |
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const LhsMatrixType & lhs, const TridiagonalSymmetricMatrix & rhs) |
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: m_lhs(lhs) |
| 386 |
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, m_rhs(rhs) |
| 387 |
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{ |
| 388 |
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} |
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| 390 |
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template<typename ResultType> |
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inline void evalTo(ResultType & result) const |
| 392 |
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{ |
| 393 |
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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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| 396 |
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assert(cols() >= 1); |
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assert(rows() >= 1); |
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| 399 |
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const Eigen::DenseIndex reduced_size = cols() - 1; |
| 400 |
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// Main diagonal |
| 401 |
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result.noalias() = m_lhs * m_rhs.diagonal().asDiagonal(); |
| 402 |
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// Upper diagonal |
| 403 |
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result.rightCols(reduced_size).noalias() += |
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m_lhs.leftCols(reduced_size) * m_rhs.subDiagonal().conjugate().asDiagonal(); |
| 405 |
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// Sub diagonal |
| 406 |
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result.leftCols(reduced_size).noalias() += |
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m_lhs.rightCols(reduced_size) * m_rhs.subDiagonal().asDiagonal(); |
| 408 |
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} |
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| 410 |
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EIGEN_CONSTEXPR Eigen::Index rows() const EIGEN_NOEXCEPT |
| 411 |
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{ |
| 412 |
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return m_lhs.rows(); |
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} |
| 414 |
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EIGEN_CONSTEXPR Eigen::Index cols() const EIGEN_NOEXCEPT |
| 415 |
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{ |
| 416 |
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return m_rhs.cols(); |
| 417 |
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} |
| 418 |
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| 419 |
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protected: |
| 420 |
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const LhsMatrixType & m_lhs; |
| 421 |
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const TridiagonalSymmetricMatrix & m_rhs; |
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}; |
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| 424 |
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template<typename _TridiagonalSymmetricMatrix> |
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struct TridiagonalSymmetricMatrixInverse |
| 426 |
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: public Eigen::ReturnByValue<TridiagonalSymmetricMatrixInverse<_TridiagonalSymmetricMatrix>> |
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{ |
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typedef _TridiagonalSymmetricMatrix TridiagonalSymmetricMatrix; |
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typedef TridiagonalSymmetricMatrixInverse Self; |
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typedef typename TridiagonalSymmetricMatrix::Scalar Scalar; |
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enum |
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{ |
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Options = TridiagonalSymmetricMatrix::Options |
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}; |
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| 436 |
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typedef typename TridiagonalSymmetricMatrix::CoeffVectorType CoeffVectorType; |
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typedef typename traits<Self>::PlainMatrixType PlainMatrixType; |
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| 439 |
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explicit TridiagonalSymmetricMatrixInverse( |
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const TridiagonalSymmetricMatrix & tridiagonal_matrix) |
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: tridiagonal_matrix(tridiagonal_matrix) |
| 442 |
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, m_size(tridiagonal_matrix.rows()) |
| 443 |
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, m_diagonal(m_size) |
| 444 |
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, m_sub_diagonal(m_size - 1) |
| 445 |
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{ |
| 446 |
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eval(); |
| 447 |
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} |
| 448 |
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| 449 |
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const TridiagonalSymmetricMatrix & inverse() const |
| 450 |
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{ |
| 451 |
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return tridiagonal_matrix; |
| 452 |
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} |
| 453 |
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| 454 |
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template<typename MatrixDerived> |
| 455 |
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TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType<Self, MatrixDerived> |
| 456 |
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applyOnTheRight(const Eigen::MatrixBase<MatrixDerived> & mat) const |
| 457 |
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{ |
| 458 |
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typedef TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType<Self, MatrixDerived> |
| 459 |
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ReturnType; |
| 460 |
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return ReturnType(*this, mat.derived()); |
| 461 |
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} |
| 462 |
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| 463 |
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template<typename MatrixDerived> |
| 464 |
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inline TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType<Self, MatrixDerived> |
| 465 |
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operator*(const Eigen::MatrixBase<MatrixDerived> & mat) const |
| 466 |
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{ |
| 467 |
|
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return this->applyOnTheRight(mat.derived()); |
| 468 |
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} |
| 469 |
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| 470 |
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template<typename ResultType> |
| 471 |
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inline void evalTo(ResultType & result) const |
| 472 |
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{ |
| 473 |
|
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PINOCCHIO_CHECK_ARGUMENT_SIZE(result.rows(), rows()); |
| 474 |
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PINOCCHIO_CHECK_ARGUMENT_SIZE(result.cols(), cols()); |
| 475 |
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|
| 476 |
|
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assert(cols() >= 1); |
| 477 |
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✗ |
assert(rows() >= 1); |
| 478 |
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|
| 479 |
|
✗ |
const auto & b = m_diagonal; |
| 480 |
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const auto & c = tridiagonal_matrix.subDiagonal(); |
| 481 |
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const auto & w = m_sub_diagonal; |
| 482 |
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|
| 483 |
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// Forward sweep |
| 484 |
|
✗ |
result.setIdentity(); |
| 485 |
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✗ |
for (Eigen::DenseIndex i = 1; i < m_size; ++i) |
| 486 |
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{ |
| 487 |
|
✗ |
result.row(i).head(i) -= w[i - 1] * result.row(i - 1).head(i); |
| 488 |
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} |
| 489 |
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|
| 490 |
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// Backward sweep |
| 491 |
|
✗ |
result.row(m_size - 1) /= b[m_size - 1]; |
| 492 |
|
✗ |
for (Eigen::DenseIndex i = m_size - 2; i >= 0; --i) |
| 493 |
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{ |
| 494 |
|
✗ |
result.row(i) -= c[i] * result.row(i + 1); |
| 495 |
|
✗ |
result.row(i) /= b[i]; |
| 496 |
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} |
| 497 |
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} |
| 498 |
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|
| 499 |
|
✗ |
EIGEN_CONSTEXPR Eigen::Index rows() const EIGEN_NOEXCEPT |
| 500 |
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{ |
| 501 |
|
✗ |
return m_size; |
| 502 |
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} |
| 503 |
|
✗ |
EIGEN_CONSTEXPR Eigen::Index cols() const EIGEN_NOEXCEPT |
| 504 |
|
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{ |
| 505 |
|
✗ |
return m_size; |
| 506 |
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} |
| 507 |
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|
| 508 |
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protected: |
| 509 |
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template<typename T, typename MatrixDerived> |
| 510 |
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friend struct TridiagonalSymmetricMatrixInverseApplyOnTheRightReturnType; |
| 511 |
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|
| 512 |
|
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/// \brief Forward sweep of https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm |
| 513 |
|
✗ |
void eval() |
| 514 |
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|
{ |
| 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 |
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|
} |
| 526 |
|
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|
| 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 |
|
|
|