diff options
Diffstat (limited to 'Eigen/src/Cholesky')
| -rw-r--r-- | Eigen/src/Cholesky/LDLT.h | 66 | ||||
| -rw-r--r-- | Eigen/src/Cholesky/LLT.h | 53 |
2 files changed, 90 insertions, 29 deletions
diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h index c3cc3746c..538aff956 100644 --- a/Eigen/src/Cholesky/LDLT.h +++ b/Eigen/src/Cholesky/LDLT.h @@ -13,7 +13,7 @@ #ifndef EIGEN_LDLT_H #define EIGEN_LDLT_H -namespace Eigen { +namespace Eigen { namespace internal { template<typename MatrixType, int UpLo> struct LDLT_Traits; @@ -73,11 +73,11 @@ template<typename _MatrixType, int _UpLo> class LDLT * The default constructor is useful in cases in which the user intends to * perform decompositions via LDLT::compute(const MatrixType&). */ - LDLT() - : m_matrix(), - m_transpositions(), + LDLT() + : m_matrix(), + m_transpositions(), m_sign(internal::ZeroSign), - m_isInitialized(false) + m_isInitialized(false) {} /** \brief Default Constructor with memory preallocation @@ -168,7 +168,7 @@ template<typename _MatrixType, int _UpLo> class LDLT * \note_about_checking_solutions * * More precisely, this method solves \f$ A x = b \f$ using the decomposition \f$ A = P^T L D L^* P \f$ - * by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$, + * by solving the systems \f$ P^T y_1 = b \f$, \f$ L y_2 = y_1 \f$, \f$ D y_3 = y_2 \f$, * \f$ L^* y_4 = y_3 \f$ and \f$ P x = y_4 \f$ in succession. If the matrix \f$ A \f$ is singular, then * \f$ D \f$ will also be singular (all the other matrices are invertible). In that case, the * least-square solution of \f$ D y_3 = y_2 \f$ is computed. This does not mean that this function @@ -192,6 +192,15 @@ template<typename _MatrixType, int _UpLo> class LDLT template<typename InputType> LDLT& compute(const EigenBase<InputType>& matrix); + /** \returns an estimate of the reciprocal condition number of the matrix of + * which \c *this is the LDLT decomposition. + */ + RealScalar rcond() const + { + eigen_assert(m_isInitialized && "LDLT is not initialized."); + return internal::rcond_estimate_helper(m_l1_norm, *this); + } + template <typename Derived> LDLT& rankUpdate(const MatrixBase<Derived>& w, const RealScalar& alpha=1); @@ -207,6 +216,13 @@ template<typename _MatrixType, int _UpLo> class LDLT MatrixType reconstructedMatrix() const; + /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint. + * + * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as: + * \code x = decomposition.adjoint().solve(b) \endcode + */ + const LDLT& adjoint() const { return *this; }; + inline Index rows() const { return m_matrix.rows(); } inline Index cols() const { return m_matrix.cols(); } @@ -220,7 +236,7 @@ template<typename _MatrixType, int _UpLo> class LDLT eigen_assert(m_isInitialized && "LDLT is not initialized."); return Success; } - + #ifndef EIGEN_PARSED_BY_DOXYGEN template<typename RhsType, typename DstType> EIGEN_DEVICE_FUNC @@ -228,7 +244,7 @@ template<typename _MatrixType, int _UpLo> class LDLT #endif protected: - + static void check_template_parameters() { EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); @@ -241,6 +257,7 @@ template<typename _MatrixType, int _UpLo> class LDLT * is not stored), and the diagonal entries correspond to D. */ MatrixType m_matrix; + RealScalar m_l1_norm; TranspositionType m_transpositions; TmpMatrixType m_temporary; internal::SignMatrix m_sign; @@ -266,8 +283,8 @@ template<> struct ldlt_inplace<Lower> if (size <= 1) { transpositions.setIdentity(); - if (numext::real(mat.coeff(0,0)) > 0) sign = PositiveSemiDef; - else if (numext::real(mat.coeff(0,0)) < 0) sign = NegativeSemiDef; + if (numext::real(mat.coeff(0,0)) > static_cast<RealScalar>(0) ) sign = PositiveSemiDef; + else if (numext::real(mat.coeff(0,0)) < static_cast<RealScalar>(0)) sign = NegativeSemiDef; else sign = ZeroSign; return true; } @@ -314,7 +331,7 @@ template<> struct ldlt_inplace<Lower> if(rs>0) A21.noalias() -= A20 * temp.head(k); } - + // In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot // was smaller than the cutoff value. However, since LDLT is not rank-revealing // we should only make sure that we do not introduce INF or NaN values. @@ -324,12 +341,12 @@ template<> struct ldlt_inplace<Lower> A21 /= realAkk; if (sign == PositiveSemiDef) { - if (realAkk < 0) sign = Indefinite; + if (realAkk < static_cast<RealScalar>(0)) sign = Indefinite; } else if (sign == NegativeSemiDef) { - if (realAkk > 0) sign = Indefinite; + if (realAkk > static_cast<RealScalar>(0)) sign = Indefinite; } else if (sign == ZeroSign) { - if (realAkk > 0) sign = PositiveSemiDef; - else if (realAkk < 0) sign = NegativeSemiDef; + if (realAkk > static_cast<RealScalar>(0)) sign = PositiveSemiDef; + else if (realAkk < static_cast<RealScalar>(0)) sign = NegativeSemiDef; } } @@ -433,12 +450,25 @@ template<typename InputType> LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a) { check_template_parameters(); - + eigen_assert(a.rows()==a.cols()); const Index size = a.rows(); m_matrix = a.derived(); + // Compute matrix L1 norm = max abs column sum. + m_l1_norm = RealScalar(0); + // TODO move this code to SelfAdjointView + for (Index col = 0; col < size; ++col) { + RealScalar abs_col_sum; + if (_UpLo == Lower) + abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>(); + else + abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>(); + if (abs_col_sum > m_l1_norm) + m_l1_norm = abs_col_sum; + } + m_transpositions.resize(size); m_isInitialized = false; m_temporary.resize(size); @@ -466,7 +496,7 @@ LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Deri eigen_assert(m_matrix.rows()==size); } else - { + { m_matrix.resize(size,size); m_matrix.setZero(); m_transpositions.resize(size); @@ -505,7 +535,7 @@ void LDLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) cons // diagonal element is not well justified and leads to numerical issues in some cases. // Moreover, Lapack's xSYTRS routines use 0 for the tolerance. RealScalar tolerance = RealScalar(1) / NumTraits<RealScalar>::highest(); - + for (Index i = 0; i < vecD.size(); ++i) { if(abs(vecD(i)) > tolerance) diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h index 74cf5bfe1..19578b216 100644 --- a/Eigen/src/Cholesky/LLT.h +++ b/Eigen/src/Cholesky/LLT.h @@ -10,7 +10,7 @@ #ifndef EIGEN_LLT_H #define EIGEN_LLT_H -namespace Eigen { +namespace Eigen { namespace internal{ template<typename MatrixType, int UpLo> struct LLT_Traits; @@ -40,7 +40,7 @@ template<typename MatrixType, int UpLo> struct LLT_Traits; * * Example: \include LLT_example.cpp * Output: \verbinclude LLT_example.out - * + * * \sa MatrixBase::llt(), SelfAdjointView::llt(), class LDLT */ /* HEY THIS DOX IS DISABLED BECAUSE THERE's A BUG EITHER HERE OR IN LDLT ABOUT THAT (OR BOTH) @@ -135,6 +135,16 @@ template<typename _MatrixType, int _UpLo> class LLT template<typename InputType> LLT& compute(const EigenBase<InputType>& matrix); + /** \returns an estimate of the reciprocal condition number of the matrix of + * which \c *this is the Cholesky decomposition. + */ + RealScalar rcond() const + { + eigen_assert(m_isInitialized && "LLT is not initialized."); + eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative"); + return internal::rcond_estimate_helper(m_l1_norm, *this); + } + /** \returns the LLT decomposition matrix * * TODO: document the storage layout @@ -159,12 +169,19 @@ template<typename _MatrixType, int _UpLo> class LLT return m_info; } + /** \returns the adjoint of \c *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint. + * + * This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as: + * \code x = decomposition.adjoint().solve(b) \endcode + */ + const LLT& adjoint() const { return *this; }; + inline Index rows() const { return m_matrix.rows(); } inline Index cols() const { return m_matrix.cols(); } template<typename VectorType> LLT rankUpdate(const VectorType& vec, const RealScalar& sigma = 1); - + #ifndef EIGEN_PARSED_BY_DOXYGEN template<typename RhsType, typename DstType> EIGEN_DEVICE_FUNC @@ -172,17 +189,18 @@ template<typename _MatrixType, int _UpLo> class LLT #endif protected: - + static void check_template_parameters() { EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); } - + /** \internal * Used to compute and store L * The strict upper part is not used and even not initialized. */ MatrixType m_matrix; + RealScalar m_l1_norm; bool m_isInitialized; ComputationInfo m_info; }; @@ -268,7 +286,7 @@ template<typename Scalar> struct llt_inplace<Scalar, Lower> static Index unblocked(MatrixType& mat) { using std::sqrt; - + eigen_assert(mat.rows()==mat.cols()); const Index size = mat.rows(); for(Index k = 0; k < size; ++k) @@ -328,7 +346,7 @@ template<typename Scalar> struct llt_inplace<Scalar, Lower> return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); } }; - + template<typename Scalar> struct llt_inplace<Scalar, Upper> { typedef typename NumTraits<Scalar>::Real RealScalar; @@ -387,12 +405,25 @@ template<typename InputType> LLT<MatrixType,_UpLo>& LLT<MatrixType,_UpLo>::compute(const EigenBase<InputType>& a) { check_template_parameters(); - + eigen_assert(a.rows()==a.cols()); const Index size = a.rows(); m_matrix.resize(size, size); m_matrix = a.derived(); + // Compute matrix L1 norm = max abs column sum. + m_l1_norm = RealScalar(0); + // TODO move this code to SelfAdjointView + for (Index col = 0; col < size; ++col) { + RealScalar abs_col_sum; + if (_UpLo == Lower) + abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>(); + else + abs_col_sum = m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>(); + if (abs_col_sum > m_l1_norm) + m_l1_norm = abs_col_sum; + } + m_isInitialized = true; bool ok = Traits::inplace_decomposition(m_matrix); m_info = ok ? Success : NumericalIssue; @@ -419,7 +450,7 @@ LLT<_MatrixType,_UpLo> LLT<_MatrixType,_UpLo>::rankUpdate(const VectorType& v, c return *this; } - + #ifndef EIGEN_PARSED_BY_DOXYGEN template<typename _MatrixType,int _UpLo> template<typename RhsType, typename DstType> @@ -431,7 +462,7 @@ void LLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const #endif /** \internal use x = llt_object.solve(x); - * + * * This is the \em in-place version of solve(). * * \param bAndX represents both the right-hand side matrix b and result x. @@ -483,7 +514,7 @@ SelfAdjointView<MatrixType, UpLo>::llt() const return LLT<PlainObject,UpLo>(m_matrix); } #endif // __CUDACC__ - + } // end namespace Eigen #endif // EIGEN_LLT_H |