diff options
Diffstat (limited to 'runtimes/nn/depend/external/eigen/Eigen/src/Cholesky/LLT.h')
| -rw-r--r-- | runtimes/nn/depend/external/eigen/Eigen/src/Cholesky/LLT.h | 534 |
1 files changed, 0 insertions, 534 deletions
diff --git a/runtimes/nn/depend/external/eigen/Eigen/src/Cholesky/LLT.h b/runtimes/nn/depend/external/eigen/Eigen/src/Cholesky/LLT.h deleted file mode 100644 index 87ca8d423..000000000 --- a/runtimes/nn/depend/external/eigen/Eigen/src/Cholesky/LLT.h +++ /dev/null @@ -1,534 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -#ifndef EIGEN_LLT_H -#define EIGEN_LLT_H - -namespace Eigen { - -namespace internal{ -template<typename MatrixType, int UpLo> struct LLT_Traits; -} - -/** \ingroup Cholesky_Module - * - * \class LLT - * - * \brief Standard Cholesky decomposition (LL^T) of a matrix and associated features - * - * \tparam _MatrixType the type of the matrix of which we are computing the LL^T Cholesky decomposition - * \tparam _UpLo the triangular part that will be used for the decompositon: Lower (default) or Upper. - * The other triangular part won't be read. - * - * This class performs a LL^T Cholesky decomposition of a symmetric, positive definite - * matrix A such that A = LL^* = U^*U, where L is lower triangular. - * - * While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b, - * for that purpose, we recommend the Cholesky decomposition without square root which is more stable - * and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other - * situations like generalised eigen problems with hermitian matrices. - * - * Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices, - * use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations - * has a solution. - * - * Example: \include LLT_example.cpp - * Output: \verbinclude LLT_example.out - * - * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. - * - * \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) - * Note that during the decomposition, only the upper triangular part of A is considered. Therefore, - * the strict lower part does not have to store correct values. - */ -template<typename _MatrixType, int _UpLo> class LLT -{ - public: - typedef _MatrixType MatrixType; - enum { - RowsAtCompileTime = MatrixType::RowsAtCompileTime, - ColsAtCompileTime = MatrixType::ColsAtCompileTime, - MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime - }; - typedef typename MatrixType::Scalar Scalar; - typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; - typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3 - typedef typename MatrixType::StorageIndex StorageIndex; - - enum { - PacketSize = internal::packet_traits<Scalar>::size, - AlignmentMask = int(PacketSize)-1, - UpLo = _UpLo - }; - - typedef internal::LLT_Traits<MatrixType,UpLo> Traits; - - /** - * \brief Default Constructor. - * - * The default constructor is useful in cases in which the user intends to - * perform decompositions via LLT::compute(const MatrixType&). - */ - LLT() : m_matrix(), m_isInitialized(false) {} - - /** \brief Default Constructor with memory preallocation - * - * Like the default constructor but with preallocation of the internal data - * according to the specified problem \a size. - * \sa LLT() - */ - explicit LLT(Index size) : m_matrix(size, size), - m_isInitialized(false) {} - - template<typename InputType> - explicit LLT(const EigenBase<InputType>& matrix) - : m_matrix(matrix.rows(), matrix.cols()), - m_isInitialized(false) - { - compute(matrix.derived()); - } - - /** \brief Constructs a LDLT factorization from a given matrix - * - * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when - * \c MatrixType is a Eigen::Ref. - * - * \sa LLT(const EigenBase&) - */ - template<typename InputType> - explicit LLT(EigenBase<InputType>& matrix) - : m_matrix(matrix.derived()), - m_isInitialized(false) - { - compute(matrix.derived()); - } - - /** \returns a view of the upper triangular matrix U */ - inline typename Traits::MatrixU matrixU() const - { - eigen_assert(m_isInitialized && "LLT is not initialized."); - return Traits::getU(m_matrix); - } - - /** \returns a view of the lower triangular matrix L */ - inline typename Traits::MatrixL matrixL() const - { - eigen_assert(m_isInitialized && "LLT is not initialized."); - return Traits::getL(m_matrix); - } - - /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A. - * - * Since this LLT class assumes anyway that the matrix A is invertible, the solution - * theoretically exists and is unique regardless of b. - * - * Example: \include LLT_solve.cpp - * Output: \verbinclude LLT_solve.out - * - * \sa solveInPlace(), MatrixBase::llt(), SelfAdjointView::llt() - */ - template<typename Rhs> - inline const Solve<LLT, Rhs> - solve(const MatrixBase<Rhs>& b) const - { - eigen_assert(m_isInitialized && "LLT is not initialized."); - eigen_assert(m_matrix.rows()==b.rows() - && "LLT::solve(): invalid number of rows of the right hand side matrix b"); - return Solve<LLT, Rhs>(*this, b.derived()); - } - - template<typename Derived> - void solveInPlace(MatrixBase<Derived> &bAndX) const; - - 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 - */ - inline const MatrixType& matrixLLT() const - { - eigen_assert(m_isInitialized && "LLT is not initialized."); - return m_matrix; - } - - MatrixType reconstructedMatrix() const; - - - /** \brief Reports whether previous computation was successful. - * - * \returns \c Success if computation was succesful, - * \c NumericalIssue if the matrix.appears to be negative. - */ - ComputationInfo info() const - { - eigen_assert(m_isInitialized && "LLT is not initialized."); - 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 - void _solve_impl(const RhsType &rhs, DstType &dst) const; - #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; -}; - -namespace internal { - -template<typename Scalar, int UpLo> struct llt_inplace; - -template<typename MatrixType, typename VectorType> -static Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma) -{ - using std::sqrt; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef typename MatrixType::ColXpr ColXpr; - typedef typename internal::remove_all<ColXpr>::type ColXprCleaned; - typedef typename ColXprCleaned::SegmentReturnType ColXprSegment; - typedef Matrix<Scalar,Dynamic,1> TempVectorType; - typedef typename TempVectorType::SegmentReturnType TempVecSegment; - - Index n = mat.cols(); - eigen_assert(mat.rows()==n && vec.size()==n); - - TempVectorType temp; - - if(sigma>0) - { - // This version is based on Givens rotations. - // It is faster than the other one below, but only works for updates, - // i.e., for sigma > 0 - temp = sqrt(sigma) * vec; - - for(Index i=0; i<n; ++i) - { - JacobiRotation<Scalar> g; - g.makeGivens(mat(i,i), -temp(i), &mat(i,i)); - - Index rs = n-i-1; - if(rs>0) - { - ColXprSegment x(mat.col(i).tail(rs)); - TempVecSegment y(temp.tail(rs)); - apply_rotation_in_the_plane(x, y, g); - } - } - } - else - { - temp = vec; - RealScalar beta = 1; - for(Index j=0; j<n; ++j) - { - RealScalar Ljj = numext::real(mat.coeff(j,j)); - RealScalar dj = numext::abs2(Ljj); - Scalar wj = temp.coeff(j); - RealScalar swj2 = sigma*numext::abs2(wj); - RealScalar gamma = dj*beta + swj2; - - RealScalar x = dj + swj2/beta; - if (x<=RealScalar(0)) - return j; - RealScalar nLjj = sqrt(x); - mat.coeffRef(j,j) = nLjj; - beta += swj2/dj; - - // Update the terms of L - Index rs = n-j-1; - if(rs) - { - temp.tail(rs) -= (wj/Ljj) * mat.col(j).tail(rs); - if(gamma != 0) - mat.col(j).tail(rs) = (nLjj/Ljj) * mat.col(j).tail(rs) + (nLjj * sigma*numext::conj(wj)/gamma)*temp.tail(rs); - } - } - } - return -1; -} - -template<typename Scalar> struct llt_inplace<Scalar, Lower> -{ - typedef typename NumTraits<Scalar>::Real RealScalar; - template<typename MatrixType> - 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) - { - Index rs = size-k-1; // remaining size - - Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1); - Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k); - Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k); - - RealScalar x = numext::real(mat.coeff(k,k)); - if (k>0) x -= A10.squaredNorm(); - if (x<=RealScalar(0)) - return k; - mat.coeffRef(k,k) = x = sqrt(x); - if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint(); - if (rs>0) A21 /= x; - } - return -1; - } - - template<typename MatrixType> - static Index blocked(MatrixType& m) - { - eigen_assert(m.rows()==m.cols()); - Index size = m.rows(); - if(size<32) - return unblocked(m); - - Index blockSize = size/8; - blockSize = (blockSize/16)*16; - blockSize = (std::min)((std::max)(blockSize,Index(8)), Index(128)); - - for (Index k=0; k<size; k+=blockSize) - { - // partition the matrix: - // A00 | - | - - // lu = A10 | A11 | - - // A20 | A21 | A22 - Index bs = (std::min)(blockSize, size-k); - Index rs = size - k - bs; - Block<MatrixType,Dynamic,Dynamic> A11(m,k, k, bs,bs); - Block<MatrixType,Dynamic,Dynamic> A21(m,k+bs,k, rs,bs); - Block<MatrixType,Dynamic,Dynamic> A22(m,k+bs,k+bs,rs,rs); - - Index ret; - if((ret=unblocked(A11))>=0) return k+ret; - if(rs>0) A11.adjoint().template triangularView<Upper>().template solveInPlace<OnTheRight>(A21); - if(rs>0) A22.template selfadjointView<Lower>().rankUpdate(A21,typename NumTraits<RealScalar>::Literal(-1)); // bottleneck - } - return -1; - } - - template<typename MatrixType, typename VectorType> - static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) - { - return Eigen::internal::llt_rank_update_lower(mat, vec, sigma); - } -}; - -template<typename Scalar> struct llt_inplace<Scalar, Upper> -{ - typedef typename NumTraits<Scalar>::Real RealScalar; - - template<typename MatrixType> - static EIGEN_STRONG_INLINE Index unblocked(MatrixType& mat) - { - Transpose<MatrixType> matt(mat); - return llt_inplace<Scalar, Lower>::unblocked(matt); - } - template<typename MatrixType> - static EIGEN_STRONG_INLINE Index blocked(MatrixType& mat) - { - Transpose<MatrixType> matt(mat); - return llt_inplace<Scalar, Lower>::blocked(matt); - } - template<typename MatrixType, typename VectorType> - static Index rankUpdate(MatrixType& mat, const VectorType& vec, const RealScalar& sigma) - { - Transpose<MatrixType> matt(mat); - return llt_inplace<Scalar, Lower>::rankUpdate(matt, vec.conjugate(), sigma); - } -}; - -template<typename MatrixType> struct LLT_Traits<MatrixType,Lower> -{ - typedef const TriangularView<const MatrixType, Lower> MatrixL; - typedef const TriangularView<const typename MatrixType::AdjointReturnType, Upper> MatrixU; - static inline MatrixL getL(const MatrixType& m) { return MatrixL(m); } - static inline MatrixU getU(const MatrixType& m) { return MatrixU(m.adjoint()); } - static bool inplace_decomposition(MatrixType& m) - { return llt_inplace<typename MatrixType::Scalar, Lower>::blocked(m)==-1; } -}; - -template<typename MatrixType> struct LLT_Traits<MatrixType,Upper> -{ - typedef const TriangularView<const typename MatrixType::AdjointReturnType, Lower> MatrixL; - typedef const TriangularView<const MatrixType, Upper> MatrixU; - static inline MatrixL getL(const MatrixType& m) { return MatrixL(m.adjoint()); } - static inline MatrixU getU(const MatrixType& m) { return MatrixU(m); } - static bool inplace_decomposition(MatrixType& m) - { return llt_inplace<typename MatrixType::Scalar, Upper>::blocked(m)==-1; } -}; - -} // end namespace internal - -/** Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of \a matrix - * - * \returns a reference to *this - * - * Example: \include TutorialLinAlgComputeTwice.cpp - * Output: \verbinclude TutorialLinAlgComputeTwice.out - */ -template<typename MatrixType, int _UpLo> -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; - - return *this; -} - -/** Performs a rank one update (or dowdate) of the current decomposition. - * If A = LL^* before the rank one update, - * then after it we have LL^* = A + sigma * v v^* where \a v must be a vector - * of same dimension. - */ -template<typename _MatrixType, int _UpLo> -template<typename VectorType> -LLT<_MatrixType,_UpLo> LLT<_MatrixType,_UpLo>::rankUpdate(const VectorType& v, const RealScalar& sigma) -{ - EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType); - eigen_assert(v.size()==m_matrix.cols()); - eigen_assert(m_isInitialized); - if(internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix,v,sigma)>=0) - m_info = NumericalIssue; - else - m_info = Success; - - return *this; -} - -#ifndef EIGEN_PARSED_BY_DOXYGEN -template<typename _MatrixType,int _UpLo> -template<typename RhsType, typename DstType> -void LLT<_MatrixType,_UpLo>::_solve_impl(const RhsType &rhs, DstType &dst) const -{ - dst = rhs; - solveInPlace(dst); -} -#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. - * - * This version avoids a copy when the right hand side matrix b is not needed anymore. - * - * \sa LLT::solve(), MatrixBase::llt() - */ -template<typename MatrixType, int _UpLo> -template<typename Derived> -void LLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX) const -{ - eigen_assert(m_isInitialized && "LLT is not initialized."); - eigen_assert(m_matrix.rows()==bAndX.rows()); - matrixL().solveInPlace(bAndX); - matrixU().solveInPlace(bAndX); -} - -/** \returns the matrix represented by the decomposition, - * i.e., it returns the product: L L^*. - * This function is provided for debug purpose. */ -template<typename MatrixType, int _UpLo> -MatrixType LLT<MatrixType,_UpLo>::reconstructedMatrix() const -{ - eigen_assert(m_isInitialized && "LLT is not initialized."); - return matrixL() * matrixL().adjoint().toDenseMatrix(); -} - -/** \cholesky_module - * \returns the LLT decomposition of \c *this - * \sa SelfAdjointView::llt() - */ -template<typename Derived> -inline const LLT<typename MatrixBase<Derived>::PlainObject> -MatrixBase<Derived>::llt() const -{ - return LLT<PlainObject>(derived()); -} - -/** \cholesky_module - * \returns the LLT decomposition of \c *this - * \sa SelfAdjointView::llt() - */ -template<typename MatrixType, unsigned int UpLo> -inline const LLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject, UpLo> -SelfAdjointView<MatrixType, UpLo>::llt() const -{ - return LLT<PlainObject,UpLo>(m_matrix); -} - -} // end namespace Eigen - -#endif // EIGEN_LLT_H |