diff options
Diffstat (limited to 'src/Eigen/src/LU')
| -rw-r--r-- | src/Eigen/src/LU/Determinant.h | 117 | ||||
| -rw-r--r-- | src/Eigen/src/LU/FullPivLU.h | 877 | ||||
| -rw-r--r-- | src/Eigen/src/LU/InverseImpl.h | 432 | ||||
| -rw-r--r-- | src/Eigen/src/LU/PartialPivLU.h | 624 | ||||
| -rw-r--r-- | src/Eigen/src/LU/PartialPivLU_LAPACKE.h | 83 | ||||
| -rw-r--r-- | src/Eigen/src/LU/arch/InverseSize4.h | 351 |
6 files changed, 0 insertions, 2484 deletions
diff --git a/src/Eigen/src/LU/Determinant.h b/src/Eigen/src/LU/Determinant.h deleted file mode 100644 index 3a41e6f..0000000 --- a/src/Eigen/src/LU/Determinant.h +++ /dev/null @@ -1,117 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com> -// -// 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_DETERMINANT_H -#define EIGEN_DETERMINANT_H - -namespace Eigen { - -namespace internal { - -template<typename Derived> -EIGEN_DEVICE_FUNC -inline const typename Derived::Scalar bruteforce_det3_helper -(const MatrixBase<Derived>& matrix, int a, int b, int c) -{ - return matrix.coeff(0,a) - * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b)); -} - -template<typename Derived, - int DeterminantType = Derived::RowsAtCompileTime -> struct determinant_impl -{ - static inline typename traits<Derived>::Scalar run(const Derived& m) - { - if(Derived::ColsAtCompileTime==Dynamic && m.rows()==0) - return typename traits<Derived>::Scalar(1); - return m.partialPivLu().determinant(); - } -}; - -template<typename Derived> struct determinant_impl<Derived, 1> -{ - static inline EIGEN_DEVICE_FUNC - typename traits<Derived>::Scalar run(const Derived& m) - { - return m.coeff(0,0); - } -}; - -template<typename Derived> struct determinant_impl<Derived, 2> -{ - static inline EIGEN_DEVICE_FUNC - typename traits<Derived>::Scalar run(const Derived& m) - { - return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1); - } -}; - -template<typename Derived> struct determinant_impl<Derived, 3> -{ - static inline EIGEN_DEVICE_FUNC - typename traits<Derived>::Scalar run(const Derived& m) - { - return bruteforce_det3_helper(m,0,1,2) - - bruteforce_det3_helper(m,1,0,2) - + bruteforce_det3_helper(m,2,0,1); - } -}; - -template<typename Derived> struct determinant_impl<Derived, 4> -{ - typedef typename traits<Derived>::Scalar Scalar; - static EIGEN_DEVICE_FUNC - Scalar run(const Derived& m) - { - Scalar d2_01 = det2(m, 0, 1); - Scalar d2_02 = det2(m, 0, 2); - Scalar d2_03 = det2(m, 0, 3); - Scalar d2_12 = det2(m, 1, 2); - Scalar d2_13 = det2(m, 1, 3); - Scalar d2_23 = det2(m, 2, 3); - Scalar d3_0 = det3(m, 1,d2_23, 2,d2_13, 3,d2_12); - Scalar d3_1 = det3(m, 0,d2_23, 2,d2_03, 3,d2_02); - Scalar d3_2 = det3(m, 0,d2_13, 1,d2_03, 3,d2_01); - Scalar d3_3 = det3(m, 0,d2_12, 1,d2_02, 2,d2_01); - return internal::pmadd(-m(0,3),d3_0, m(1,3)*d3_1) + - internal::pmadd(-m(2,3),d3_2, m(3,3)*d3_3); - } -protected: - static EIGEN_DEVICE_FUNC - Scalar det2(const Derived& m, Index i0, Index i1) - { - return m(i0,0) * m(i1,1) - m(i1,0) * m(i0,1); - } - - static EIGEN_DEVICE_FUNC - Scalar det3(const Derived& m, Index i0, const Scalar& d0, Index i1, const Scalar& d1, Index i2, const Scalar& d2) - { - return internal::pmadd(m(i0,2), d0, internal::pmadd(-m(i1,2), d1, m(i2,2)*d2)); - } -}; - -} // end namespace internal - -/** \lu_module - * - * \returns the determinant of this matrix - */ -template<typename Derived> -EIGEN_DEVICE_FUNC -inline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const -{ - eigen_assert(rows() == cols()); - typedef typename internal::nested_eval<Derived,Base::RowsAtCompileTime>::type Nested; - return internal::determinant_impl<typename internal::remove_all<Nested>::type>::run(derived()); -} - -} // end namespace Eigen - -#endif // EIGEN_DETERMINANT_H diff --git a/src/Eigen/src/LU/FullPivLU.h b/src/Eigen/src/LU/FullPivLU.h deleted file mode 100644 index ba1749f..0000000 --- a/src/Eigen/src/LU/FullPivLU.h +++ /dev/null @@ -1,877 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com> -// -// 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_LU_H -#define EIGEN_LU_H - -namespace Eigen { - -namespace internal { -template<typename _MatrixType> struct traits<FullPivLU<_MatrixType> > - : traits<_MatrixType> -{ - typedef MatrixXpr XprKind; - typedef SolverStorage StorageKind; - typedef int StorageIndex; - enum { Flags = 0 }; -}; - -} // end namespace internal - -/** \ingroup LU_Module - * - * \class FullPivLU - * - * \brief LU decomposition of a matrix with complete pivoting, and related features - * - * \tparam _MatrixType the type of the matrix of which we are computing the LU decomposition - * - * This class represents a LU decomposition of any matrix, with complete pivoting: the matrix A is - * decomposed as \f$ A = P^{-1} L U Q^{-1} \f$ where L is unit-lower-triangular, U is - * upper-triangular, and P and Q are permutation matrices. This is a rank-revealing LU - * decomposition. The eigenvalues (diagonal coefficients) of U are sorted in such a way that any - * zeros are at the end. - * - * This decomposition provides the generic approach to solving systems of linear equations, computing - * the rank, invertibility, inverse, kernel, and determinant. - * - * This LU decomposition is very stable and well tested with large matrices. However there are use cases where the SVD - * decomposition is inherently more stable and/or flexible. For example, when computing the kernel of a matrix, - * working with the SVD allows to select the smallest singular values of the matrix, something that - * the LU decomposition doesn't see. - * - * The data of the LU decomposition can be directly accessed through the methods matrixLU(), - * permutationP(), permutationQ(). - * - * As an example, here is how the original matrix can be retrieved: - * \include class_FullPivLU.cpp - * Output: \verbinclude class_FullPivLU.out - * - * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. - * - * \sa MatrixBase::fullPivLu(), MatrixBase::determinant(), MatrixBase::inverse() - */ -template<typename _MatrixType> class FullPivLU - : public SolverBase<FullPivLU<_MatrixType> > -{ - public: - typedef _MatrixType MatrixType; - typedef SolverBase<FullPivLU> Base; - friend class SolverBase<FullPivLU>; - - EIGEN_GENERIC_PUBLIC_INTERFACE(FullPivLU) - enum { - MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, - MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime - }; - typedef typename internal::plain_row_type<MatrixType, StorageIndex>::type IntRowVectorType; - typedef typename internal::plain_col_type<MatrixType, StorageIndex>::type IntColVectorType; - typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationQType; - typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationPType; - typedef typename MatrixType::PlainObject PlainObject; - - /** - * \brief Default Constructor. - * - * The default constructor is useful in cases in which the user intends to - * perform decompositions via LU::compute(const MatrixType&). - */ - FullPivLU(); - - /** \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 FullPivLU() - */ - FullPivLU(Index rows, Index cols); - - /** Constructor. - * - * \param matrix the matrix of which to compute the LU decomposition. - * It is required to be nonzero. - */ - template<typename InputType> - explicit FullPivLU(const EigenBase<InputType>& matrix); - - /** \brief Constructs a LU factorization from a given matrix - * - * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref. - * - * \sa FullPivLU(const EigenBase&) - */ - template<typename InputType> - explicit FullPivLU(EigenBase<InputType>& matrix); - - /** Computes the LU decomposition of the given matrix. - * - * \param matrix the matrix of which to compute the LU decomposition. - * It is required to be nonzero. - * - * \returns a reference to *this - */ - template<typename InputType> - FullPivLU& compute(const EigenBase<InputType>& matrix) { - m_lu = matrix.derived(); - computeInPlace(); - return *this; - } - - /** \returns the LU decomposition matrix: the upper-triangular part is U, the - * unit-lower-triangular part is L (at least for square matrices; in the non-square - * case, special care is needed, see the documentation of class FullPivLU). - * - * \sa matrixL(), matrixU() - */ - inline const MatrixType& matrixLU() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return m_lu; - } - - /** \returns the number of nonzero pivots in the LU decomposition. - * Here nonzero is meant in the exact sense, not in a fuzzy sense. - * So that notion isn't really intrinsically interesting, but it is - * still useful when implementing algorithms. - * - * \sa rank() - */ - inline Index nonzeroPivots() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return m_nonzero_pivots; - } - - /** \returns the absolute value of the biggest pivot, i.e. the biggest - * diagonal coefficient of U. - */ - RealScalar maxPivot() const { return m_maxpivot; } - - /** \returns the permutation matrix P - * - * \sa permutationQ() - */ - EIGEN_DEVICE_FUNC inline const PermutationPType& permutationP() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return m_p; - } - - /** \returns the permutation matrix Q - * - * \sa permutationP() - */ - inline const PermutationQType& permutationQ() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return m_q; - } - - /** \returns the kernel of the matrix, also called its null-space. The columns of the returned matrix - * will form a basis of the kernel. - * - * \note If the kernel has dimension zero, then the returned matrix is a column-vector filled with zeros. - * - * \note This method has to determine which pivots should be considered nonzero. - * For that, it uses the threshold value that you can control by calling - * setThreshold(const RealScalar&). - * - * Example: \include FullPivLU_kernel.cpp - * Output: \verbinclude FullPivLU_kernel.out - * - * \sa image() - */ - inline const internal::kernel_retval<FullPivLU> kernel() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return internal::kernel_retval<FullPivLU>(*this); - } - - /** \returns the image of the matrix, also called its column-space. The columns of the returned matrix - * will form a basis of the image (column-space). - * - * \param originalMatrix the original matrix, of which *this is the LU decomposition. - * The reason why it is needed to pass it here, is that this allows - * a large optimization, as otherwise this method would need to reconstruct it - * from the LU decomposition. - * - * \note If the image has dimension zero, then the returned matrix is a column-vector filled with zeros. - * - * \note This method has to determine which pivots should be considered nonzero. - * For that, it uses the threshold value that you can control by calling - * setThreshold(const RealScalar&). - * - * Example: \include FullPivLU_image.cpp - * Output: \verbinclude FullPivLU_image.out - * - * \sa kernel() - */ - inline const internal::image_retval<FullPivLU> - image(const MatrixType& originalMatrix) const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return internal::image_retval<FullPivLU>(*this, originalMatrix); - } - - #ifdef EIGEN_PARSED_BY_DOXYGEN - /** \return a solution x to the equation Ax=b, where A is the matrix of which - * *this is the LU decomposition. - * - * \param b the right-hand-side of the equation to solve. Can be a vector or a matrix, - * the only requirement in order for the equation to make sense is that - * b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition. - * - * \returns a solution. - * - * \note_about_checking_solutions - * - * \note_about_arbitrary_choice_of_solution - * \note_about_using_kernel_to_study_multiple_solutions - * - * Example: \include FullPivLU_solve.cpp - * Output: \verbinclude FullPivLU_solve.out - * - * \sa TriangularView::solve(), kernel(), inverse() - */ - template<typename Rhs> - inline const Solve<FullPivLU, Rhs> - solve(const MatrixBase<Rhs>& b) const; - #endif - - /** \returns an estimate of the reciprocal condition number of the matrix of which \c *this is - the LU decomposition. - */ - inline RealScalar rcond() const - { - eigen_assert(m_isInitialized && "PartialPivLU is not initialized."); - return internal::rcond_estimate_helper(m_l1_norm, *this); - } - - /** \returns the determinant of the matrix of which - * *this is the LU decomposition. It has only linear complexity - * (that is, O(n) where n is the dimension of the square matrix) - * as the LU decomposition has already been computed. - * - * \note This is only for square matrices. - * - * \note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers - * optimized paths. - * - * \warning a determinant can be very big or small, so for matrices - * of large enough dimension, there is a risk of overflow/underflow. - * - * \sa MatrixBase::determinant() - */ - typename internal::traits<MatrixType>::Scalar determinant() const; - - /** Allows to prescribe a threshold to be used by certain methods, such as rank(), - * who need to determine when pivots are to be considered nonzero. This is not used for the - * LU decomposition itself. - * - * When it needs to get the threshold value, Eigen calls threshold(). By default, this - * uses a formula to automatically determine a reasonable threshold. - * Once you have called the present method setThreshold(const RealScalar&), - * your value is used instead. - * - * \param threshold The new value to use as the threshold. - * - * A pivot will be considered nonzero if its absolute value is strictly greater than - * \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$ - * where maxpivot is the biggest pivot. - * - * If you want to come back to the default behavior, call setThreshold(Default_t) - */ - FullPivLU& setThreshold(const RealScalar& threshold) - { - m_usePrescribedThreshold = true; - m_prescribedThreshold = threshold; - return *this; - } - - /** Allows to come back to the default behavior, letting Eigen use its default formula for - * determining the threshold. - * - * You should pass the special object Eigen::Default as parameter here. - * \code lu.setThreshold(Eigen::Default); \endcode - * - * See the documentation of setThreshold(const RealScalar&). - */ - FullPivLU& setThreshold(Default_t) - { - m_usePrescribedThreshold = false; - return *this; - } - - /** Returns the threshold that will be used by certain methods such as rank(). - * - * See the documentation of setThreshold(const RealScalar&). - */ - RealScalar threshold() const - { - eigen_assert(m_isInitialized || m_usePrescribedThreshold); - return m_usePrescribedThreshold ? m_prescribedThreshold - // this formula comes from experimenting (see "LU precision tuning" thread on the list) - // and turns out to be identical to Higham's formula used already in LDLt. - : NumTraits<Scalar>::epsilon() * RealScalar(m_lu.diagonalSize()); - } - - /** \returns the rank of the matrix of which *this is the LU decomposition. - * - * \note This method has to determine which pivots should be considered nonzero. - * For that, it uses the threshold value that you can control by calling - * setThreshold(const RealScalar&). - */ - inline Index rank() const - { - using std::abs; - eigen_assert(m_isInitialized && "LU is not initialized."); - RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold(); - Index result = 0; - for(Index i = 0; i < m_nonzero_pivots; ++i) - result += (abs(m_lu.coeff(i,i)) > premultiplied_threshold); - return result; - } - - /** \returns the dimension of the kernel of the matrix of which *this is the LU decomposition. - * - * \note This method has to determine which pivots should be considered nonzero. - * For that, it uses the threshold value that you can control by calling - * setThreshold(const RealScalar&). - */ - inline Index dimensionOfKernel() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return cols() - rank(); - } - - /** \returns true if the matrix of which *this is the LU decomposition represents an injective - * linear map, i.e. has trivial kernel; false otherwise. - * - * \note This method has to determine which pivots should be considered nonzero. - * For that, it uses the threshold value that you can control by calling - * setThreshold(const RealScalar&). - */ - inline bool isInjective() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return rank() == cols(); - } - - /** \returns true if the matrix of which *this is the LU decomposition represents a surjective - * linear map; false otherwise. - * - * \note This method has to determine which pivots should be considered nonzero. - * For that, it uses the threshold value that you can control by calling - * setThreshold(const RealScalar&). - */ - inline bool isSurjective() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return rank() == rows(); - } - - /** \returns true if the matrix of which *this is the LU decomposition is invertible. - * - * \note This method has to determine which pivots should be considered nonzero. - * For that, it uses the threshold value that you can control by calling - * setThreshold(const RealScalar&). - */ - inline bool isInvertible() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - return isInjective() && (m_lu.rows() == m_lu.cols()); - } - - /** \returns the inverse of the matrix of which *this is the LU decomposition. - * - * \note If this matrix is not invertible, the returned matrix has undefined coefficients. - * Use isInvertible() to first determine whether this matrix is invertible. - * - * \sa MatrixBase::inverse() - */ - inline const Inverse<FullPivLU> inverse() const - { - eigen_assert(m_isInitialized && "LU is not initialized."); - eigen_assert(m_lu.rows() == m_lu.cols() && "You can't take the inverse of a non-square matrix!"); - return Inverse<FullPivLU>(*this); - } - - MatrixType reconstructedMatrix() const; - - EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR - inline Index rows() const EIGEN_NOEXCEPT { return m_lu.rows(); } - EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR - inline Index cols() const EIGEN_NOEXCEPT { return m_lu.cols(); } - - #ifndef EIGEN_PARSED_BY_DOXYGEN - template<typename RhsType, typename DstType> - void _solve_impl(const RhsType &rhs, DstType &dst) const; - - template<bool Conjugate, typename RhsType, typename DstType> - void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const; - #endif - - protected: - - static void check_template_parameters() - { - EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); - } - - void computeInPlace(); - - MatrixType m_lu; - PermutationPType m_p; - PermutationQType m_q; - IntColVectorType m_rowsTranspositions; - IntRowVectorType m_colsTranspositions; - Index m_nonzero_pivots; - RealScalar m_l1_norm; - RealScalar m_maxpivot, m_prescribedThreshold; - signed char m_det_pq; - bool m_isInitialized, m_usePrescribedThreshold; -}; - -template<typename MatrixType> -FullPivLU<MatrixType>::FullPivLU() - : m_isInitialized(false), m_usePrescribedThreshold(false) -{ -} - -template<typename MatrixType> -FullPivLU<MatrixType>::FullPivLU(Index rows, Index cols) - : m_lu(rows, cols), - m_p(rows), - m_q(cols), - m_rowsTranspositions(rows), - m_colsTranspositions(cols), - m_isInitialized(false), - m_usePrescribedThreshold(false) -{ -} - -template<typename MatrixType> -template<typename InputType> -FullPivLU<MatrixType>::FullPivLU(const EigenBase<InputType>& matrix) - : m_lu(matrix.rows(), matrix.cols()), - m_p(matrix.rows()), - m_q(matrix.cols()), - m_rowsTranspositions(matrix.rows()), - m_colsTranspositions(matrix.cols()), - m_isInitialized(false), - m_usePrescribedThreshold(false) -{ - compute(matrix.derived()); -} - -template<typename MatrixType> -template<typename InputType> -FullPivLU<MatrixType>::FullPivLU(EigenBase<InputType>& matrix) - : m_lu(matrix.derived()), - m_p(matrix.rows()), - m_q(matrix.cols()), - m_rowsTranspositions(matrix.rows()), - m_colsTranspositions(matrix.cols()), - m_isInitialized(false), - m_usePrescribedThreshold(false) -{ - computeInPlace(); -} - -template<typename MatrixType> -void FullPivLU<MatrixType>::computeInPlace() -{ - check_template_parameters(); - - // the permutations are stored as int indices, so just to be sure: - eigen_assert(m_lu.rows()<=NumTraits<int>::highest() && m_lu.cols()<=NumTraits<int>::highest()); - - m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff(); - - const Index size = m_lu.diagonalSize(); - const Index rows = m_lu.rows(); - const Index cols = m_lu.cols(); - - // will store the transpositions, before we accumulate them at the end. - // can't accumulate on-the-fly because that will be done in reverse order for the rows. - m_rowsTranspositions.resize(m_lu.rows()); - m_colsTranspositions.resize(m_lu.cols()); - Index number_of_transpositions = 0; // number of NONTRIVIAL transpositions, i.e. m_rowsTranspositions[i]!=i - - m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case) - m_maxpivot = RealScalar(0); - - for(Index k = 0; k < size; ++k) - { - // First, we need to find the pivot. - - // biggest coefficient in the remaining bottom-right corner (starting at row k, col k) - Index row_of_biggest_in_corner, col_of_biggest_in_corner; - typedef internal::scalar_score_coeff_op<Scalar> Scoring; - typedef typename Scoring::result_type Score; - Score biggest_in_corner; - biggest_in_corner = m_lu.bottomRightCorner(rows-k, cols-k) - .unaryExpr(Scoring()) - .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner); - row_of_biggest_in_corner += k; // correct the values! since they were computed in the corner, - col_of_biggest_in_corner += k; // need to add k to them. - - if(biggest_in_corner==Score(0)) - { - // before exiting, make sure to initialize the still uninitialized transpositions - // in a sane state without destroying what we already have. - m_nonzero_pivots = k; - for(Index i = k; i < size; ++i) - { - m_rowsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i); - m_colsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i); - } - break; - } - - RealScalar abs_pivot = internal::abs_knowing_score<Scalar>()(m_lu(row_of_biggest_in_corner, col_of_biggest_in_corner), biggest_in_corner); - if(abs_pivot > m_maxpivot) m_maxpivot = abs_pivot; - - // Now that we've found the pivot, we need to apply the row/col swaps to - // bring it to the location (k,k). - - m_rowsTranspositions.coeffRef(k) = internal::convert_index<StorageIndex>(row_of_biggest_in_corner); - m_colsTranspositions.coeffRef(k) = internal::convert_index<StorageIndex>(col_of_biggest_in_corner); - if(k != row_of_biggest_in_corner) { - m_lu.row(k).swap(m_lu.row(row_of_biggest_in_corner)); - ++number_of_transpositions; - } - if(k != col_of_biggest_in_corner) { - m_lu.col(k).swap(m_lu.col(col_of_biggest_in_corner)); - ++number_of_transpositions; - } - - // Now that the pivot is at the right location, we update the remaining - // bottom-right corner by Gaussian elimination. - - if(k<rows-1) - m_lu.col(k).tail(rows-k-1) /= m_lu.coeff(k,k); - if(k<size-1) - m_lu.block(k+1,k+1,rows-k-1,cols-k-1).noalias() -= m_lu.col(k).tail(rows-k-1) * m_lu.row(k).tail(cols-k-1); - } - - // the main loop is over, we still have to accumulate the transpositions to find the - // permutations P and Q - - m_p.setIdentity(rows); - for(Index k = size-1; k >= 0; --k) - m_p.applyTranspositionOnTheRight(k, m_rowsTranspositions.coeff(k)); - - m_q.setIdentity(cols); - for(Index k = 0; k < size; ++k) - m_q.applyTranspositionOnTheRight(k, m_colsTranspositions.coeff(k)); - - m_det_pq = (number_of_transpositions%2) ? -1 : 1; - - m_isInitialized = true; -} - -template<typename MatrixType> -typename internal::traits<MatrixType>::Scalar FullPivLU<MatrixType>::determinant() const -{ - eigen_assert(m_isInitialized && "LU is not initialized."); - eigen_assert(m_lu.rows() == m_lu.cols() && "You can't take the determinant of a non-square matrix!"); - return Scalar(m_det_pq) * Scalar(m_lu.diagonal().prod()); -} - -/** \returns the matrix represented by the decomposition, - * i.e., it returns the product: \f$ P^{-1} L U Q^{-1} \f$. - * This function is provided for debug purposes. */ -template<typename MatrixType> -MatrixType FullPivLU<MatrixType>::reconstructedMatrix() const -{ - eigen_assert(m_isInitialized && "LU is not initialized."); - const Index smalldim = (std::min)(m_lu.rows(), m_lu.cols()); - // LU - MatrixType res(m_lu.rows(),m_lu.cols()); - // FIXME the .toDenseMatrix() should not be needed... - res = m_lu.leftCols(smalldim) - .template triangularView<UnitLower>().toDenseMatrix() - * m_lu.topRows(smalldim) - .template triangularView<Upper>().toDenseMatrix(); - - // P^{-1}(LU) - res = m_p.inverse() * res; - - // (P^{-1}LU)Q^{-1} - res = res * m_q.inverse(); - - return res; -} - -/********* Implementation of kernel() **************************************************/ - -namespace internal { -template<typename _MatrixType> -struct kernel_retval<FullPivLU<_MatrixType> > - : kernel_retval_base<FullPivLU<_MatrixType> > -{ - EIGEN_MAKE_KERNEL_HELPERS(FullPivLU<_MatrixType>) - - enum { MaxSmallDimAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED( - MatrixType::MaxColsAtCompileTime, - MatrixType::MaxRowsAtCompileTime) - }; - - template<typename Dest> void evalTo(Dest& dst) const - { - using std::abs; - const Index cols = dec().matrixLU().cols(), dimker = cols - rank(); - if(dimker == 0) - { - // The Kernel is just {0}, so it doesn't have a basis properly speaking, but let's - // avoid crashing/asserting as that depends on floating point calculations. Let's - // just return a single column vector filled with zeros. - dst.setZero(); - return; - } - - /* Let us use the following lemma: - * - * Lemma: If the matrix A has the LU decomposition PAQ = LU, - * then Ker A = Q(Ker U). - * - * Proof: trivial: just keep in mind that P, Q, L are invertible. - */ - - /* Thus, all we need to do is to compute Ker U, and then apply Q. - * - * U is upper triangular, with eigenvalues sorted so that any zeros appear at the end. - * Thus, the diagonal of U ends with exactly - * dimKer zero's. Let us use that to construct dimKer linearly - * independent vectors in Ker U. - */ - - Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank()); - RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold(); - Index p = 0; - for(Index i = 0; i < dec().nonzeroPivots(); ++i) - if(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold) - pivots.coeffRef(p++) = i; - eigen_internal_assert(p == rank()); - - // we construct a temporaty trapezoid matrix m, by taking the U matrix and - // permuting the rows and cols to bring the nonnegligible pivots to the top of - // the main diagonal. We need that to be able to apply our triangular solvers. - // FIXME when we get triangularView-for-rectangular-matrices, this can be simplified - Matrix<typename MatrixType::Scalar, Dynamic, Dynamic, MatrixType::Options, - MaxSmallDimAtCompileTime, MatrixType::MaxColsAtCompileTime> - m(dec().matrixLU().block(0, 0, rank(), cols)); - for(Index i = 0; i < rank(); ++i) - { - if(i) m.row(i).head(i).setZero(); - m.row(i).tail(cols-i) = dec().matrixLU().row(pivots.coeff(i)).tail(cols-i); - } - m.block(0, 0, rank(), rank()); - m.block(0, 0, rank(), rank()).template triangularView<StrictlyLower>().setZero(); - for(Index i = 0; i < rank(); ++i) - m.col(i).swap(m.col(pivots.coeff(i))); - - // ok, we have our trapezoid matrix, we can apply the triangular solver. - // notice that the math behind this suggests that we should apply this to the - // negative of the RHS, but for performance we just put the negative sign elsewhere, see below. - m.topLeftCorner(rank(), rank()) - .template triangularView<Upper>().solveInPlace( - m.topRightCorner(rank(), dimker) - ); - - // now we must undo the column permutation that we had applied! - for(Index i = rank()-1; i >= 0; --i) - m.col(i).swap(m.col(pivots.coeff(i))); - - // see the negative sign in the next line, that's what we were talking about above. - for(Index i = 0; i < rank(); ++i) dst.row(dec().permutationQ().indices().coeff(i)) = -m.row(i).tail(dimker); - for(Index i = rank(); i < cols; ++i) dst.row(dec().permutationQ().indices().coeff(i)).setZero(); - for(Index k = 0; k < dimker; ++k) dst.coeffRef(dec().permutationQ().indices().coeff(rank()+k), k) = Scalar(1); - } -}; - -/***** Implementation of image() *****************************************************/ - -template<typename _MatrixType> -struct image_retval<FullPivLU<_MatrixType> > - : image_retval_base<FullPivLU<_MatrixType> > -{ - EIGEN_MAKE_IMAGE_HELPERS(FullPivLU<_MatrixType>) - - enum { MaxSmallDimAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED( - MatrixType::MaxColsAtCompileTime, - MatrixType::MaxRowsAtCompileTime) - }; - - template<typename Dest> void evalTo(Dest& dst) const - { - using std::abs; - if(rank() == 0) - { - // The Image is just {0}, so it doesn't have a basis properly speaking, but let's - // avoid crashing/asserting as that depends on floating point calculations. Let's - // just return a single column vector filled with zeros. - dst.setZero(); - return; - } - - Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank()); - RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold(); - Index p = 0; - for(Index i = 0; i < dec().nonzeroPivots(); ++i) - if(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold) - pivots.coeffRef(p++) = i; - eigen_internal_assert(p == rank()); - - for(Index i = 0; i < rank(); ++i) - dst.col(i) = originalMatrix().col(dec().permutationQ().indices().coeff(pivots.coeff(i))); - } -}; - -/***** Implementation of solve() *****************************************************/ - -} // end namespace internal - -#ifndef EIGEN_PARSED_BY_DOXYGEN -template<typename _MatrixType> -template<typename RhsType, typename DstType> -void FullPivLU<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &dst) const -{ - /* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1}. - * So we proceed as follows: - * Step 1: compute c = P * rhs. - * Step 2: replace c by the solution x to Lx = c. Exists because L is invertible. - * Step 3: replace c by the solution x to Ux = c. May or may not exist. - * Step 4: result = Q * c; - */ - - const Index rows = this->rows(), - cols = this->cols(), - nonzero_pivots = this->rank(); - const Index smalldim = (std::min)(rows, cols); - - if(nonzero_pivots == 0) - { - dst.setZero(); - return; - } - - typename RhsType::PlainObject c(rhs.rows(), rhs.cols()); - - // Step 1 - c = permutationP() * rhs; - - // Step 2 - m_lu.topLeftCorner(smalldim,smalldim) - .template triangularView<UnitLower>() - .solveInPlace(c.topRows(smalldim)); - if(rows>cols) - c.bottomRows(rows-cols) -= m_lu.bottomRows(rows-cols) * c.topRows(cols); - - // Step 3 - m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots) - .template triangularView<Upper>() - .solveInPlace(c.topRows(nonzero_pivots)); - - // Step 4 - for(Index i = 0; i < nonzero_pivots; ++i) - dst.row(permutationQ().indices().coeff(i)) = c.row(i); - for(Index i = nonzero_pivots; i < m_lu.cols(); ++i) - dst.row(permutationQ().indices().coeff(i)).setZero(); -} - -template<typename _MatrixType> -template<bool Conjugate, typename RhsType, typename DstType> -void FullPivLU<_MatrixType>::_solve_impl_transposed(const RhsType &rhs, DstType &dst) const -{ - /* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1}, - * and since permutations are real and unitary, we can write this - * as A^T = Q U^T L^T P, - * So we proceed as follows: - * Step 1: compute c = Q^T rhs. - * Step 2: replace c by the solution x to U^T x = c. May or may not exist. - * Step 3: replace c by the solution x to L^T x = c. - * Step 4: result = P^T c. - * If Conjugate is true, replace "^T" by "^*" above. - */ - - const Index rows = this->rows(), cols = this->cols(), - nonzero_pivots = this->rank(); - const Index smalldim = (std::min)(rows, cols); - - if(nonzero_pivots == 0) - { - dst.setZero(); - return; - } - - typename RhsType::PlainObject c(rhs.rows(), rhs.cols()); - - // Step 1 - c = permutationQ().inverse() * rhs; - - // Step 2 - m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots) - .template triangularView<Upper>() - .transpose() - .template conjugateIf<Conjugate>() - .solveInPlace(c.topRows(nonzero_pivots)); - - // Step 3 - m_lu.topLeftCorner(smalldim, smalldim) - .template triangularView<UnitLower>() - .transpose() - .template conjugateIf<Conjugate>() - .solveInPlace(c.topRows(smalldim)); - - // Step 4 - PermutationPType invp = permutationP().inverse().eval(); - for(Index i = 0; i < smalldim; ++i) - dst.row(invp.indices().coeff(i)) = c.row(i); - for(Index i = smalldim; i < rows; ++i) - dst.row(invp.indices().coeff(i)).setZero(); -} - -#endif - -namespace internal { - - -/***** Implementation of inverse() *****************************************************/ -template<typename DstXprType, typename MatrixType> -struct Assignment<DstXprType, Inverse<FullPivLU<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename FullPivLU<MatrixType>::Scalar>, Dense2Dense> -{ - typedef FullPivLU<MatrixType> LuType; - typedef Inverse<LuType> SrcXprType; - static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename MatrixType::Scalar> &) - { - dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols())); - } -}; -} // end namespace internal - -/******* MatrixBase methods *****************************************************************/ - -/** \lu_module - * - * \return the full-pivoting LU decomposition of \c *this. - * - * \sa class FullPivLU - */ -template<typename Derived> -inline const FullPivLU<typename MatrixBase<Derived>::PlainObject> -MatrixBase<Derived>::fullPivLu() const -{ - return FullPivLU<PlainObject>(eval()); -} - -} // end namespace Eigen - -#endif // EIGEN_LU_H diff --git a/src/Eigen/src/LU/InverseImpl.h b/src/Eigen/src/LU/InverseImpl.h deleted file mode 100644 index a40cefa..0000000 --- a/src/Eigen/src/LU/InverseImpl.h +++ /dev/null @@ -1,432 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008-2010 Benoit Jacob <jacob.benoit.1@gmail.com> -// Copyright (C) 2014 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_INVERSE_IMPL_H -#define EIGEN_INVERSE_IMPL_H - -namespace Eigen { - -namespace internal { - -/********************************** -*** General case implementation *** -**********************************/ - -template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime> -struct compute_inverse -{ - EIGEN_DEVICE_FUNC - static inline void run(const MatrixType& matrix, ResultType& result) - { - result = matrix.partialPivLu().inverse(); - } -}; - -template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime> -struct compute_inverse_and_det_with_check { /* nothing! general case not supported. */ }; - -/**************************** -*** Size 1 implementation *** -****************************/ - -template<typename MatrixType, typename ResultType> -struct compute_inverse<MatrixType, ResultType, 1> -{ - EIGEN_DEVICE_FUNC - static inline void run(const MatrixType& matrix, ResultType& result) - { - typedef typename MatrixType::Scalar Scalar; - internal::evaluator<MatrixType> matrixEval(matrix); - result.coeffRef(0,0) = Scalar(1) / matrixEval.coeff(0,0); - } -}; - -template<typename MatrixType, typename ResultType> -struct compute_inverse_and_det_with_check<MatrixType, ResultType, 1> -{ - EIGEN_DEVICE_FUNC - static inline void run( - const MatrixType& matrix, - const typename MatrixType::RealScalar& absDeterminantThreshold, - ResultType& result, - typename ResultType::Scalar& determinant, - bool& invertible - ) - { - using std::abs; - determinant = matrix.coeff(0,0); - invertible = abs(determinant) > absDeterminantThreshold; - if(invertible) result.coeffRef(0,0) = typename ResultType::Scalar(1) / determinant; - } -}; - -/**************************** -*** Size 2 implementation *** -****************************/ - -template<typename MatrixType, typename ResultType> -EIGEN_DEVICE_FUNC -inline void compute_inverse_size2_helper( - const MatrixType& matrix, const typename ResultType::Scalar& invdet, - ResultType& result) -{ - typename ResultType::Scalar temp = matrix.coeff(0,0); - result.coeffRef(0,0) = matrix.coeff(1,1) * invdet; - result.coeffRef(1,0) = -matrix.coeff(1,0) * invdet; - result.coeffRef(0,1) = -matrix.coeff(0,1) * invdet; - result.coeffRef(1,1) = temp * invdet; -} - -template<typename MatrixType, typename ResultType> -struct compute_inverse<MatrixType, ResultType, 2> -{ - EIGEN_DEVICE_FUNC - static inline void run(const MatrixType& matrix, ResultType& result) - { - typedef typename ResultType::Scalar Scalar; - const Scalar invdet = typename MatrixType::Scalar(1) / matrix.determinant(); - compute_inverse_size2_helper(matrix, invdet, result); - } -}; - -template<typename MatrixType, typename ResultType> -struct compute_inverse_and_det_with_check<MatrixType, ResultType, 2> -{ - EIGEN_DEVICE_FUNC - static inline void run( - const MatrixType& matrix, - const typename MatrixType::RealScalar& absDeterminantThreshold, - ResultType& inverse, - typename ResultType::Scalar& determinant, - bool& invertible - ) - { - using std::abs; - typedef typename ResultType::Scalar Scalar; - determinant = matrix.determinant(); - invertible = abs(determinant) > absDeterminantThreshold; - if(!invertible) return; - const Scalar invdet = Scalar(1) / determinant; - compute_inverse_size2_helper(matrix, invdet, inverse); - } -}; - -/**************************** -*** Size 3 implementation *** -****************************/ - -template<typename MatrixType, int i, int j> -EIGEN_DEVICE_FUNC -inline typename MatrixType::Scalar cofactor_3x3(const MatrixType& m) -{ - enum { - i1 = (i+1) % 3, - i2 = (i+2) % 3, - j1 = (j+1) % 3, - j2 = (j+2) % 3 - }; - return m.coeff(i1, j1) * m.coeff(i2, j2) - - m.coeff(i1, j2) * m.coeff(i2, j1); -} - -template<typename MatrixType, typename ResultType> -EIGEN_DEVICE_FUNC -inline void compute_inverse_size3_helper( - const MatrixType& matrix, - const typename ResultType::Scalar& invdet, - const Matrix<typename ResultType::Scalar,3,1>& cofactors_col0, - ResultType& result) -{ - // Compute cofactors in a way that avoids aliasing issues. - typedef typename ResultType::Scalar Scalar; - const Scalar c01 = cofactor_3x3<MatrixType,0,1>(matrix) * invdet; - const Scalar c11 = cofactor_3x3<MatrixType,1,1>(matrix) * invdet; - const Scalar c02 = cofactor_3x3<MatrixType,0,2>(matrix) * invdet; - result.coeffRef(1,2) = cofactor_3x3<MatrixType,2,1>(matrix) * invdet; - result.coeffRef(2,1) = cofactor_3x3<MatrixType,1,2>(matrix) * invdet; - result.coeffRef(2,2) = cofactor_3x3<MatrixType,2,2>(matrix) * invdet; - result.coeffRef(1,0) = c01; - result.coeffRef(1,1) = c11; - result.coeffRef(2,0) = c02; - result.row(0) = cofactors_col0 * invdet; -} - -template<typename MatrixType, typename ResultType> -struct compute_inverse<MatrixType, ResultType, 3> -{ - EIGEN_DEVICE_FUNC - static inline void run(const MatrixType& matrix, ResultType& result) - { - typedef typename ResultType::Scalar Scalar; - Matrix<typename MatrixType::Scalar,3,1> cofactors_col0; - cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix); - cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix); - cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix); - const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum(); - const Scalar invdet = Scalar(1) / det; - compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result); - } -}; - -template<typename MatrixType, typename ResultType> -struct compute_inverse_and_det_with_check<MatrixType, ResultType, 3> -{ - EIGEN_DEVICE_FUNC - static inline void run( - const MatrixType& matrix, - const typename MatrixType::RealScalar& absDeterminantThreshold, - ResultType& inverse, - typename ResultType::Scalar& determinant, - bool& invertible - ) - { - typedef typename ResultType::Scalar Scalar; - Matrix<Scalar,3,1> cofactors_col0; - cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix); - cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix); - cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix); - determinant = (cofactors_col0.cwiseProduct(matrix.col(0))).sum(); - invertible = Eigen::numext::abs(determinant) > absDeterminantThreshold; - if(!invertible) return; - const Scalar invdet = Scalar(1) / determinant; - compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse); - } -}; - -/**************************** -*** Size 4 implementation *** -****************************/ - -template<typename Derived> -EIGEN_DEVICE_FUNC -inline const typename Derived::Scalar general_det3_helper -(const MatrixBase<Derived>& matrix, int i1, int i2, int i3, int j1, int j2, int j3) -{ - return matrix.coeff(i1,j1) - * (matrix.coeff(i2,j2) * matrix.coeff(i3,j3) - matrix.coeff(i2,j3) * matrix.coeff(i3,j2)); -} - -template<typename MatrixType, int i, int j> -EIGEN_DEVICE_FUNC -inline typename MatrixType::Scalar cofactor_4x4(const MatrixType& matrix) -{ - enum { - i1 = (i+1) % 4, - i2 = (i+2) % 4, - i3 = (i+3) % 4, - j1 = (j+1) % 4, - j2 = (j+2) % 4, - j3 = (j+3) % 4 - }; - return general_det3_helper(matrix, i1, i2, i3, j1, j2, j3) - + general_det3_helper(matrix, i2, i3, i1, j1, j2, j3) - + general_det3_helper(matrix, i3, i1, i2, j1, j2, j3); -} - -template<int Arch, typename Scalar, typename MatrixType, typename ResultType> -struct compute_inverse_size4 -{ - EIGEN_DEVICE_FUNC - static void run(const MatrixType& matrix, ResultType& result) - { - result.coeffRef(0,0) = cofactor_4x4<MatrixType,0,0>(matrix); - result.coeffRef(1,0) = -cofactor_4x4<MatrixType,0,1>(matrix); - result.coeffRef(2,0) = cofactor_4x4<MatrixType,0,2>(matrix); - result.coeffRef(3,0) = -cofactor_4x4<MatrixType,0,3>(matrix); - result.coeffRef(0,2) = cofactor_4x4<MatrixType,2,0>(matrix); - result.coeffRef(1,2) = -cofactor_4x4<MatrixType,2,1>(matrix); - result.coeffRef(2,2) = cofactor_4x4<MatrixType,2,2>(matrix); - result.coeffRef(3,2) = -cofactor_4x4<MatrixType,2,3>(matrix); - result.coeffRef(0,1) = -cofactor_4x4<MatrixType,1,0>(matrix); - result.coeffRef(1,1) = cofactor_4x4<MatrixType,1,1>(matrix); - result.coeffRef(2,1) = -cofactor_4x4<MatrixType,1,2>(matrix); - result.coeffRef(3,1) = cofactor_4x4<MatrixType,1,3>(matrix); - result.coeffRef(0,3) = -cofactor_4x4<MatrixType,3,0>(matrix); - result.coeffRef(1,3) = cofactor_4x4<MatrixType,3,1>(matrix); - result.coeffRef(2,3) = -cofactor_4x4<MatrixType,3,2>(matrix); - result.coeffRef(3,3) = cofactor_4x4<MatrixType,3,3>(matrix); - result /= (matrix.col(0).cwiseProduct(result.row(0).transpose())).sum(); - } -}; - -template<typename MatrixType, typename ResultType> -struct compute_inverse<MatrixType, ResultType, 4> - : compute_inverse_size4<Architecture::Target, typename MatrixType::Scalar, - MatrixType, ResultType> -{ -}; - -template<typename MatrixType, typename ResultType> -struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4> -{ - EIGEN_DEVICE_FUNC - static inline void run( - const MatrixType& matrix, - const typename MatrixType::RealScalar& absDeterminantThreshold, - ResultType& inverse, - typename ResultType::Scalar& determinant, - bool& invertible - ) - { - using std::abs; - determinant = matrix.determinant(); - invertible = abs(determinant) > absDeterminantThreshold; - if(invertible && extract_data(matrix) != extract_data(inverse)) { - compute_inverse<MatrixType, ResultType>::run(matrix, inverse); - } - else if(invertible) { - MatrixType matrix_t = matrix; - compute_inverse<MatrixType, ResultType>::run(matrix_t, inverse); - } - } -}; - -/************************* -*** MatrixBase methods *** -*************************/ - -} // end namespace internal - -namespace internal { - -// Specialization for "dense = dense_xpr.inverse()" -template<typename DstXprType, typename XprType> -struct Assignment<DstXprType, Inverse<XprType>, internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar>, Dense2Dense> -{ - typedef Inverse<XprType> SrcXprType; - EIGEN_DEVICE_FUNC - static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar> &) - { - Index dstRows = src.rows(); - Index dstCols = src.cols(); - if((dst.rows()!=dstRows) || (dst.cols()!=dstCols)) - dst.resize(dstRows, dstCols); - - const int Size = EIGEN_PLAIN_ENUM_MIN(XprType::ColsAtCompileTime,DstXprType::ColsAtCompileTime); - EIGEN_ONLY_USED_FOR_DEBUG(Size); - eigen_assert(( (Size<=1) || (Size>4) || (extract_data(src.nestedExpression())!=extract_data(dst))) - && "Aliasing problem detected in inverse(), you need to do inverse().eval() here."); - - typedef typename internal::nested_eval<XprType,XprType::ColsAtCompileTime>::type ActualXprType; - typedef typename internal::remove_all<ActualXprType>::type ActualXprTypeCleanded; - - ActualXprType actual_xpr(src.nestedExpression()); - - compute_inverse<ActualXprTypeCleanded, DstXprType>::run(actual_xpr, dst); - } -}; - - -} // end namespace internal - -/** \lu_module - * - * \returns the matrix inverse of this matrix. - * - * For small fixed sizes up to 4x4, this method uses cofactors. - * In the general case, this method uses class PartialPivLU. - * - * \note This matrix must be invertible, otherwise the result is undefined. If you need an - * invertibility check, do the following: - * \li for fixed sizes up to 4x4, use computeInverseAndDetWithCheck(). - * \li for the general case, use class FullPivLU. - * - * Example: \include MatrixBase_inverse.cpp - * Output: \verbinclude MatrixBase_inverse.out - * - * \sa computeInverseAndDetWithCheck() - */ -template<typename Derived> -EIGEN_DEVICE_FUNC -inline const Inverse<Derived> MatrixBase<Derived>::inverse() const -{ - EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsInteger,THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES) - eigen_assert(rows() == cols()); - return Inverse<Derived>(derived()); -} - -/** \lu_module - * - * Computation of matrix inverse and determinant, with invertibility check. - * - * This is only for fixed-size square matrices of size up to 4x4. - * - * Notice that it will trigger a copy of input matrix when trying to do the inverse in place. - * - * \param inverse Reference to the matrix in which to store the inverse. - * \param determinant Reference to the variable in which to store the determinant. - * \param invertible Reference to the bool variable in which to store whether the matrix is invertible. - * \param absDeterminantThreshold Optional parameter controlling the invertibility check. - * The matrix will be declared invertible if the absolute value of its - * determinant is greater than this threshold. - * - * Example: \include MatrixBase_computeInverseAndDetWithCheck.cpp - * Output: \verbinclude MatrixBase_computeInverseAndDetWithCheck.out - * - * \sa inverse(), computeInverseWithCheck() - */ -template<typename Derived> -template<typename ResultType> -inline void MatrixBase<Derived>::computeInverseAndDetWithCheck( - ResultType& inverse, - typename ResultType::Scalar& determinant, - bool& invertible, - const RealScalar& absDeterminantThreshold - ) const -{ - // i'd love to put some static assertions there, but SFINAE means that they have no effect... - eigen_assert(rows() == cols()); - // for 2x2, it's worth giving a chance to avoid evaluating. - // for larger sizes, evaluating has negligible cost and limits code size. - typedef typename internal::conditional< - RowsAtCompileTime == 2, - typename internal::remove_all<typename internal::nested_eval<Derived, 2>::type>::type, - PlainObject - >::type MatrixType; - internal::compute_inverse_and_det_with_check<MatrixType, ResultType>::run - (derived(), absDeterminantThreshold, inverse, determinant, invertible); -} - -/** \lu_module - * - * Computation of matrix inverse, with invertibility check. - * - * This is only for fixed-size square matrices of size up to 4x4. - * - * Notice that it will trigger a copy of input matrix when trying to do the inverse in place. - * - * \param inverse Reference to the matrix in which to store the inverse. - * \param invertible Reference to the bool variable in which to store whether the matrix is invertible. - * \param absDeterminantThreshold Optional parameter controlling the invertibility check. - * The matrix will be declared invertible if the absolute value of its - * determinant is greater than this threshold. - * - * Example: \include MatrixBase_computeInverseWithCheck.cpp - * Output: \verbinclude MatrixBase_computeInverseWithCheck.out - * - * \sa inverse(), computeInverseAndDetWithCheck() - */ -template<typename Derived> -template<typename ResultType> -inline void MatrixBase<Derived>::computeInverseWithCheck( - ResultType& inverse, - bool& invertible, - const RealScalar& absDeterminantThreshold - ) const -{ - Scalar determinant; - // i'd love to put some static assertions there, but SFINAE means that they have no effect... - eigen_assert(rows() == cols()); - computeInverseAndDetWithCheck(inverse,determinant,invertible,absDeterminantThreshold); -} - -} // end namespace Eigen - -#endif // EIGEN_INVERSE_IMPL_H diff --git a/src/Eigen/src/LU/PartialPivLU.h b/src/Eigen/src/LU/PartialPivLU.h deleted file mode 100644 index 34aed72..0000000 --- a/src/Eigen/src/LU/PartialPivLU.h +++ /dev/null @@ -1,624 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com> -// Copyright (C) 2009 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_PARTIALLU_H -#define EIGEN_PARTIALLU_H - -namespace Eigen { - -namespace internal { -template<typename _MatrixType> struct traits<PartialPivLU<_MatrixType> > - : traits<_MatrixType> -{ - typedef MatrixXpr XprKind; - typedef SolverStorage StorageKind; - typedef int StorageIndex; - typedef traits<_MatrixType> BaseTraits; - enum { - Flags = BaseTraits::Flags & RowMajorBit, - CoeffReadCost = Dynamic - }; -}; - -template<typename T,typename Derived> -struct enable_if_ref; -// { -// typedef Derived type; -// }; - -template<typename T,typename Derived> -struct enable_if_ref<Ref<T>,Derived> { - typedef Derived type; -}; - -} // end namespace internal - -/** \ingroup LU_Module - * - * \class PartialPivLU - * - * \brief LU decomposition of a matrix with partial pivoting, and related features - * - * \tparam _MatrixType the type of the matrix of which we are computing the LU decomposition - * - * This class represents a LU decomposition of a \b square \b invertible matrix, with partial pivoting: the matrix A - * is decomposed as A = PLU where L is unit-lower-triangular, U is upper-triangular, and P - * is a permutation matrix. - * - * Typically, partial pivoting LU decomposition is only considered numerically stable for square invertible - * matrices. Thus LAPACK's dgesv and dgesvx require the matrix to be square and invertible. The present class - * does the same. It will assert that the matrix is square, but it won't (actually it can't) check that the - * matrix is invertible: it is your task to check that you only use this decomposition on invertible matrices. - * - * The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided - * by class FullPivLU. - * - * This is \b not a rank-revealing LU decomposition. Many features are intentionally absent from this class, - * such as rank computation. If you need these features, use class FullPivLU. - * - * This LU decomposition is suitable to invert invertible matrices. It is what MatrixBase::inverse() uses - * in the general case. - * On the other hand, it is \b not suitable to determine whether a given matrix is invertible. - * - * The data of the LU decomposition can be directly accessed through the methods matrixLU(), permutationP(). - * - * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. - * - * \sa MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU - */ -template<typename _MatrixType> class PartialPivLU - : public SolverBase<PartialPivLU<_MatrixType> > -{ - public: - - typedef _MatrixType MatrixType; - typedef SolverBase<PartialPivLU> Base; - friend class SolverBase<PartialPivLU>; - - EIGEN_GENERIC_PUBLIC_INTERFACE(PartialPivLU) - enum { - MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, - MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime - }; - typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType; - typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType; - typedef typename MatrixType::PlainObject PlainObject; - - /** - * \brief Default Constructor. - * - * The default constructor is useful in cases in which the user intends to - * perform decompositions via PartialPivLU::compute(const MatrixType&). - */ - PartialPivLU(); - - /** \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 PartialPivLU() - */ - explicit PartialPivLU(Index size); - - /** Constructor. - * - * \param matrix the matrix of which to compute the LU decomposition. - * - * \warning The matrix should have full rank (e.g. if it's square, it should be invertible). - * If you need to deal with non-full rank, use class FullPivLU instead. - */ - template<typename InputType> - explicit PartialPivLU(const EigenBase<InputType>& matrix); - - /** Constructor for \link InplaceDecomposition inplace decomposition \endlink - * - * \param matrix the matrix of which to compute the LU decomposition. - * - * \warning The matrix should have full rank (e.g. if it's square, it should be invertible). - * If you need to deal with non-full rank, use class FullPivLU instead. - */ - template<typename InputType> - explicit PartialPivLU(EigenBase<InputType>& matrix); - - template<typename InputType> - PartialPivLU& compute(const EigenBase<InputType>& matrix) { - m_lu = matrix.derived(); - compute(); - return *this; - } - - /** \returns the LU decomposition matrix: the upper-triangular part is U, the - * unit-lower-triangular part is L (at least for square matrices; in the non-square - * case, special care is needed, see the documentation of class FullPivLU). - * - * \sa matrixL(), matrixU() - */ - inline const MatrixType& matrixLU() const - { - eigen_assert(m_isInitialized && "PartialPivLU is not initialized."); - return m_lu; - } - - /** \returns the permutation matrix P. - */ - inline const PermutationType& permutationP() const - { - eigen_assert(m_isInitialized && "PartialPivLU is not initialized."); - return m_p; - } - - #ifdef EIGEN_PARSED_BY_DOXYGEN - /** This method returns the solution x to the equation Ax=b, where A is the matrix of which - * *this is the LU decomposition. - * - * \param b the right-hand-side of the equation to solve. Can be a vector or a matrix, - * the only requirement in order for the equation to make sense is that - * b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition. - * - * \returns the solution. - * - * Example: \include PartialPivLU_solve.cpp - * Output: \verbinclude PartialPivLU_solve.out - * - * Since this PartialPivLU class assumes anyway that the matrix A is invertible, the solution - * theoretically exists and is unique regardless of b. - * - * \sa TriangularView::solve(), inverse(), computeInverse() - */ - template<typename Rhs> - inline const Solve<PartialPivLU, Rhs> - solve(const MatrixBase<Rhs>& b) const; - #endif - - /** \returns an estimate of the reciprocal condition number of the matrix of which \c *this is - the LU decomposition. - */ - inline RealScalar rcond() const - { - eigen_assert(m_isInitialized && "PartialPivLU is not initialized."); - return internal::rcond_estimate_helper(m_l1_norm, *this); - } - - /** \returns the inverse of the matrix of which *this is the LU decomposition. - * - * \warning The matrix being decomposed here is assumed to be invertible. If you need to check for - * invertibility, use class FullPivLU instead. - * - * \sa MatrixBase::inverse(), LU::inverse() - */ - inline const Inverse<PartialPivLU> inverse() const - { - eigen_assert(m_isInitialized && "PartialPivLU is not initialized."); - return Inverse<PartialPivLU>(*this); - } - - /** \returns the determinant of the matrix of which - * *this is the LU decomposition. It has only linear complexity - * (that is, O(n) where n is the dimension of the square matrix) - * as the LU decomposition has already been computed. - * - * \note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers - * optimized paths. - * - * \warning a determinant can be very big or small, so for matrices - * of large enough dimension, there is a risk of overflow/underflow. - * - * \sa MatrixBase::determinant() - */ - Scalar determinant() const; - - MatrixType reconstructedMatrix() const; - - EIGEN_CONSTEXPR inline Index rows() const EIGEN_NOEXCEPT { return m_lu.rows(); } - EIGEN_CONSTEXPR inline Index cols() const EIGEN_NOEXCEPT { return m_lu.cols(); } - - #ifndef EIGEN_PARSED_BY_DOXYGEN - template<typename RhsType, typename DstType> - EIGEN_DEVICE_FUNC - void _solve_impl(const RhsType &rhs, DstType &dst) const { - /* The decomposition PA = LU can be rewritten as A = P^{-1} L U. - * So we proceed as follows: - * Step 1: compute c = Pb. - * Step 2: replace c by the solution x to Lx = c. - * Step 3: replace c by the solution x to Ux = c. - */ - - // Step 1 - dst = permutationP() * rhs; - - // Step 2 - m_lu.template triangularView<UnitLower>().solveInPlace(dst); - - // Step 3 - m_lu.template triangularView<Upper>().solveInPlace(dst); - } - - template<bool Conjugate, typename RhsType, typename DstType> - EIGEN_DEVICE_FUNC - void _solve_impl_transposed(const RhsType &rhs, DstType &dst) const { - /* The decomposition PA = LU can be rewritten as A^T = U^T L^T P. - * So we proceed as follows: - * Step 1: compute c as the solution to L^T c = b - * Step 2: replace c by the solution x to U^T x = c. - * Step 3: update c = P^-1 c. - */ - - eigen_assert(rhs.rows() == m_lu.cols()); - - // Step 1 - dst = m_lu.template triangularView<Upper>().transpose() - .template conjugateIf<Conjugate>().solve(rhs); - // Step 2 - m_lu.template triangularView<UnitLower>().transpose() - .template conjugateIf<Conjugate>().solveInPlace(dst); - // Step 3 - dst = permutationP().transpose() * dst; - } - #endif - - protected: - - static void check_template_parameters() - { - EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); - } - - void compute(); - - MatrixType m_lu; - PermutationType m_p; - TranspositionType m_rowsTranspositions; - RealScalar m_l1_norm; - signed char m_det_p; - bool m_isInitialized; -}; - -template<typename MatrixType> -PartialPivLU<MatrixType>::PartialPivLU() - : m_lu(), - m_p(), - m_rowsTranspositions(), - m_l1_norm(0), - m_det_p(0), - m_isInitialized(false) -{ -} - -template<typename MatrixType> -PartialPivLU<MatrixType>::PartialPivLU(Index size) - : m_lu(size, size), - m_p(size), - m_rowsTranspositions(size), - m_l1_norm(0), - m_det_p(0), - m_isInitialized(false) -{ -} - -template<typename MatrixType> -template<typename InputType> -PartialPivLU<MatrixType>::PartialPivLU(const EigenBase<InputType>& matrix) - : m_lu(matrix.rows(),matrix.cols()), - m_p(matrix.rows()), - m_rowsTranspositions(matrix.rows()), - m_l1_norm(0), - m_det_p(0), - m_isInitialized(false) -{ - compute(matrix.derived()); -} - -template<typename MatrixType> -template<typename InputType> -PartialPivLU<MatrixType>::PartialPivLU(EigenBase<InputType>& matrix) - : m_lu(matrix.derived()), - m_p(matrix.rows()), - m_rowsTranspositions(matrix.rows()), - m_l1_norm(0), - m_det_p(0), - m_isInitialized(false) -{ - compute(); -} - -namespace internal { - -/** \internal This is the blocked version of fullpivlu_unblocked() */ -template<typename Scalar, int StorageOrder, typename PivIndex, int SizeAtCompileTime=Dynamic> -struct partial_lu_impl -{ - static const int UnBlockedBound = 16; - static const bool UnBlockedAtCompileTime = SizeAtCompileTime!=Dynamic && SizeAtCompileTime<=UnBlockedBound; - static const int ActualSizeAtCompileTime = UnBlockedAtCompileTime ? SizeAtCompileTime : Dynamic; - // Remaining rows and columns at compile-time: - static const int RRows = SizeAtCompileTime==2 ? 1 : Dynamic; - static const int RCols = SizeAtCompileTime==2 ? 1 : Dynamic; - typedef Matrix<Scalar, ActualSizeAtCompileTime, ActualSizeAtCompileTime, StorageOrder> MatrixType; - typedef Ref<MatrixType> MatrixTypeRef; - typedef Ref<Matrix<Scalar, Dynamic, Dynamic, StorageOrder> > BlockType; - typedef typename MatrixType::RealScalar RealScalar; - - /** \internal performs the LU decomposition in-place of the matrix \a lu - * using an unblocked algorithm. - * - * In addition, this function returns the row transpositions in the - * vector \a row_transpositions which must have a size equal to the number - * of columns of the matrix \a lu, and an integer \a nb_transpositions - * which returns the actual number of transpositions. - * - * \returns The index of the first pivot which is exactly zero if any, or a negative number otherwise. - */ - static Index unblocked_lu(MatrixTypeRef& lu, PivIndex* row_transpositions, PivIndex& nb_transpositions) - { - typedef scalar_score_coeff_op<Scalar> Scoring; - typedef typename Scoring::result_type Score; - const Index rows = lu.rows(); - const Index cols = lu.cols(); - const Index size = (std::min)(rows,cols); - // For small compile-time matrices it is worth processing the last row separately: - // speedup: +100% for 2x2, +10% for others. - const Index endk = UnBlockedAtCompileTime ? size-1 : size; - nb_transpositions = 0; - Index first_zero_pivot = -1; - for(Index k = 0; k < endk; ++k) - { - int rrows = internal::convert_index<int>(rows-k-1); - int rcols = internal::convert_index<int>(cols-k-1); - - Index row_of_biggest_in_col; - Score biggest_in_corner - = lu.col(k).tail(rows-k).unaryExpr(Scoring()).maxCoeff(&row_of_biggest_in_col); - row_of_biggest_in_col += k; - - row_transpositions[k] = PivIndex(row_of_biggest_in_col); - - if(biggest_in_corner != Score(0)) - { - if(k != row_of_biggest_in_col) - { - lu.row(k).swap(lu.row(row_of_biggest_in_col)); - ++nb_transpositions; - } - - lu.col(k).tail(fix<RRows>(rrows)) /= lu.coeff(k,k); - } - else if(first_zero_pivot==-1) - { - // the pivot is exactly zero, we record the index of the first pivot which is exactly 0, - // and continue the factorization such we still have A = PLU - first_zero_pivot = k; - } - - if(k<rows-1) - lu.bottomRightCorner(fix<RRows>(rrows),fix<RCols>(rcols)).noalias() -= lu.col(k).tail(fix<RRows>(rrows)) * lu.row(k).tail(fix<RCols>(rcols)); - } - - // special handling of the last entry - if(UnBlockedAtCompileTime) - { - Index k = endk; - row_transpositions[k] = PivIndex(k); - if (Scoring()(lu(k, k)) == Score(0) && first_zero_pivot == -1) - first_zero_pivot = k; - } - - return first_zero_pivot; - } - - /** \internal performs the LU decomposition in-place of the matrix represented - * by the variables \a rows, \a cols, \a lu_data, and \a lu_stride using a - * recursive, blocked algorithm. - * - * In addition, this function returns the row transpositions in the - * vector \a row_transpositions which must have a size equal to the number - * of columns of the matrix \a lu, and an integer \a nb_transpositions - * which returns the actual number of transpositions. - * - * \returns The index of the first pivot which is exactly zero if any, or a negative number otherwise. - * - * \note This very low level interface using pointers, etc. is to: - * 1 - reduce the number of instantiations to the strict minimum - * 2 - avoid infinite recursion of the instantiations with Block<Block<Block<...> > > - */ - static Index blocked_lu(Index rows, Index cols, Scalar* lu_data, Index luStride, PivIndex* row_transpositions, PivIndex& nb_transpositions, Index maxBlockSize=256) - { - MatrixTypeRef lu = MatrixType::Map(lu_data,rows, cols, OuterStride<>(luStride)); - - const Index size = (std::min)(rows,cols); - - // if the matrix is too small, no blocking: - if(UnBlockedAtCompileTime || size<=UnBlockedBound) - { - return unblocked_lu(lu, row_transpositions, nb_transpositions); - } - - // automatically adjust the number of subdivisions to the size - // of the matrix so that there is enough sub blocks: - Index blockSize; - { - blockSize = size/8; - blockSize = (blockSize/16)*16; - blockSize = (std::min)((std::max)(blockSize,Index(8)), maxBlockSize); - } - - nb_transpositions = 0; - Index first_zero_pivot = -1; - for(Index k = 0; k < size; k+=blockSize) - { - Index bs = (std::min)(size-k,blockSize); // actual size of the block - Index trows = rows - k - bs; // trailing rows - Index tsize = size - k - bs; // trailing size - - // partition the matrix: - // A00 | A01 | A02 - // lu = A_0 | A_1 | A_2 = A10 | A11 | A12 - // A20 | A21 | A22 - BlockType A_0 = lu.block(0,0,rows,k); - BlockType A_2 = lu.block(0,k+bs,rows,tsize); - BlockType A11 = lu.block(k,k,bs,bs); - BlockType A12 = lu.block(k,k+bs,bs,tsize); - BlockType A21 = lu.block(k+bs,k,trows,bs); - BlockType A22 = lu.block(k+bs,k+bs,trows,tsize); - - PivIndex nb_transpositions_in_panel; - // recursively call the blocked LU algorithm on [A11^T A21^T]^T - // with a very small blocking size: - Index ret = blocked_lu(trows+bs, bs, &lu.coeffRef(k,k), luStride, - row_transpositions+k, nb_transpositions_in_panel, 16); - if(ret>=0 && first_zero_pivot==-1) - first_zero_pivot = k+ret; - - nb_transpositions += nb_transpositions_in_panel; - // update permutations and apply them to A_0 - for(Index i=k; i<k+bs; ++i) - { - Index piv = (row_transpositions[i] += internal::convert_index<PivIndex>(k)); - A_0.row(i).swap(A_0.row(piv)); - } - - if(trows) - { - // apply permutations to A_2 - for(Index i=k;i<k+bs; ++i) - A_2.row(i).swap(A_2.row(row_transpositions[i])); - - // A12 = A11^-1 A12 - A11.template triangularView<UnitLower>().solveInPlace(A12); - - A22.noalias() -= A21 * A12; - } - } - return first_zero_pivot; - } -}; - -/** \internal performs the LU decomposition with partial pivoting in-place. - */ -template<typename MatrixType, typename TranspositionType> -void partial_lu_inplace(MatrixType& lu, TranspositionType& row_transpositions, typename TranspositionType::StorageIndex& nb_transpositions) -{ - // Special-case of zero matrix. - if (lu.rows() == 0 || lu.cols() == 0) { - nb_transpositions = 0; - return; - } - eigen_assert(lu.cols() == row_transpositions.size()); - eigen_assert(row_transpositions.size() < 2 || (&row_transpositions.coeffRef(1)-&row_transpositions.coeffRef(0)) == 1); - - partial_lu_impl - < typename MatrixType::Scalar, MatrixType::Flags&RowMajorBit?RowMajor:ColMajor, - typename TranspositionType::StorageIndex, - EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::RowsAtCompileTime,MatrixType::ColsAtCompileTime)> - ::blocked_lu(lu.rows(), lu.cols(), &lu.coeffRef(0,0), lu.outerStride(), &row_transpositions.coeffRef(0), nb_transpositions); -} - -} // end namespace internal - -template<typename MatrixType> -void PartialPivLU<MatrixType>::compute() -{ - check_template_parameters(); - - // the row permutation is stored as int indices, so just to be sure: - eigen_assert(m_lu.rows()<NumTraits<int>::highest()); - - if(m_lu.cols()>0) - m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff(); - else - m_l1_norm = RealScalar(0); - - eigen_assert(m_lu.rows() == m_lu.cols() && "PartialPivLU is only for square (and moreover invertible) matrices"); - const Index size = m_lu.rows(); - - m_rowsTranspositions.resize(size); - - typename TranspositionType::StorageIndex nb_transpositions; - internal::partial_lu_inplace(m_lu, m_rowsTranspositions, nb_transpositions); - m_det_p = (nb_transpositions%2) ? -1 : 1; - - m_p = m_rowsTranspositions; - - m_isInitialized = true; -} - -template<typename MatrixType> -typename PartialPivLU<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() const -{ - eigen_assert(m_isInitialized && "PartialPivLU is not initialized."); - return Scalar(m_det_p) * m_lu.diagonal().prod(); -} - -/** \returns the matrix represented by the decomposition, - * i.e., it returns the product: P^{-1} L U. - * This function is provided for debug purpose. */ -template<typename MatrixType> -MatrixType PartialPivLU<MatrixType>::reconstructedMatrix() const -{ - eigen_assert(m_isInitialized && "LU is not initialized."); - // LU - MatrixType res = m_lu.template triangularView<UnitLower>().toDenseMatrix() - * m_lu.template triangularView<Upper>(); - - // P^{-1}(LU) - res = m_p.inverse() * res; - - return res; -} - -/***** Implementation details *****************************************************/ - -namespace internal { - -/***** Implementation of inverse() *****************************************************/ -template<typename DstXprType, typename MatrixType> -struct Assignment<DstXprType, Inverse<PartialPivLU<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename PartialPivLU<MatrixType>::Scalar>, Dense2Dense> -{ - typedef PartialPivLU<MatrixType> LuType; - typedef Inverse<LuType> SrcXprType; - static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename LuType::Scalar> &) - { - dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols())); - } -}; -} // end namespace internal - -/******** MatrixBase methods *******/ - -/** \lu_module - * - * \return the partial-pivoting LU decomposition of \c *this. - * - * \sa class PartialPivLU - */ -template<typename Derived> -inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject> -MatrixBase<Derived>::partialPivLu() const -{ - return PartialPivLU<PlainObject>(eval()); -} - -/** \lu_module - * - * Synonym of partialPivLu(). - * - * \return the partial-pivoting LU decomposition of \c *this. - * - * \sa class PartialPivLU - */ -template<typename Derived> -inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject> -MatrixBase<Derived>::lu() const -{ - return PartialPivLU<PlainObject>(eval()); -} - -} // end namespace Eigen - -#endif // EIGEN_PARTIALLU_H diff --git a/src/Eigen/src/LU/PartialPivLU_LAPACKE.h b/src/Eigen/src/LU/PartialPivLU_LAPACKE.h deleted file mode 100644 index 755168a..0000000 --- a/src/Eigen/src/LU/PartialPivLU_LAPACKE.h +++ /dev/null @@ -1,83 +0,0 @@ -/* - Copyright (c) 2011, Intel Corporation. All rights reserved. - - Redistribution and use in source and binary forms, with or without modification, - are permitted provided that the following conditions are met: - - * Redistributions of source code must retain the above copyright notice, this - list of conditions and the following disclaimer. - * Redistributions in binary form must reproduce the above copyright notice, - this list of conditions and the following disclaimer in the documentation - and/or other materials provided with the distribution. - * Neither the name of Intel Corporation nor the names of its contributors may - be used to endorse or promote products derived from this software without - specific prior written permission. - - THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND - ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED - WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE - DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR - ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES - (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; - LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON - ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT - (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS - SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. - - ******************************************************************************** - * Content : Eigen bindings to LAPACKe - * LU decomposition with partial pivoting based on LAPACKE_?getrf function. - ******************************************************************************** -*/ - -#ifndef EIGEN_PARTIALLU_LAPACK_H -#define EIGEN_PARTIALLU_LAPACK_H - -namespace Eigen { - -namespace internal { - -/** \internal Specialization for the data types supported by LAPACKe */ - -#define EIGEN_LAPACKE_LU_PARTPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX) \ -template<int StorageOrder> \ -struct partial_lu_impl<EIGTYPE, StorageOrder, lapack_int> \ -{ \ - /* \internal performs the LU decomposition in-place of the matrix represented */ \ - static lapack_int blocked_lu(Index rows, Index cols, EIGTYPE* lu_data, Index luStride, lapack_int* row_transpositions, lapack_int& nb_transpositions, lapack_int maxBlockSize=256) \ - { \ - EIGEN_UNUSED_VARIABLE(maxBlockSize);\ - lapack_int matrix_order, first_zero_pivot; \ - lapack_int m, n, lda, *ipiv, info; \ - EIGTYPE* a; \ -/* Set up parameters for ?getrf */ \ - matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \ - lda = convert_index<lapack_int>(luStride); \ - a = lu_data; \ - ipiv = row_transpositions; \ - m = convert_index<lapack_int>(rows); \ - n = convert_index<lapack_int>(cols); \ - nb_transpositions = 0; \ -\ - info = LAPACKE_##LAPACKE_PREFIX##getrf( matrix_order, m, n, (LAPACKE_TYPE*)a, lda, ipiv ); \ -\ - for(int i=0;i<m;i++) { ipiv[i]--; if (ipiv[i]!=i) nb_transpositions++; } \ -\ - eigen_assert(info >= 0); \ -/* something should be done with nb_transpositions */ \ -\ - first_zero_pivot = info; \ - return first_zero_pivot; \ - } \ -}; - -EIGEN_LAPACKE_LU_PARTPIV(double, double, d) -EIGEN_LAPACKE_LU_PARTPIV(float, float, s) -EIGEN_LAPACKE_LU_PARTPIV(dcomplex, lapack_complex_double, z) -EIGEN_LAPACKE_LU_PARTPIV(scomplex, lapack_complex_float, c) - -} // end namespace internal - -} // end namespace Eigen - -#endif // EIGEN_PARTIALLU_LAPACK_H diff --git a/src/Eigen/src/LU/arch/InverseSize4.h b/src/Eigen/src/LU/arch/InverseSize4.h deleted file mode 100644 index a232ffc..0000000 --- a/src/Eigen/src/LU/arch/InverseSize4.h +++ /dev/null @@ -1,351 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2001 Intel Corporation -// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr> -// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> -// -// 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/. -// -// The algorithm below is a reimplementation of former \src\LU\Inverse_SSE.h using PacketMath. -// inv(M) = M#/|M|, where inv(M), M# and |M| denote the inverse of M, -// adjugate of M and determinant of M respectively. M# is computed block-wise -// using specific formulae. For proof, see: -// https://lxjk.github.io/2017/09/03/Fast-4x4-Matrix-Inverse-with-SSE-SIMD-Explained.html -// Variable names are adopted from \src\LU\Inverse_SSE.h. -// -// The SSE code for the 4x4 float and double matrix inverse in former (deprecated) \src\LU\Inverse_SSE.h -// comes from the following Intel's library: -// http://software.intel.com/en-us/articles/optimized-matrix-library-for-use-with-the-intel-pentiumr-4-processors-sse2-instructions/ -// -// Here is the respective copyright and license statement: -// -// Copyright (c) 2001 Intel Corporation. -// -// Permition is granted to use, copy, distribute and prepare derivative works -// of this library for any purpose and without fee, provided, that the above -// copyright notice and this statement appear in all copies. -// Intel makes no representations about the suitability of this software for -// any purpose, and specifically disclaims all warranties. -// See LEGAL.TXT for all the legal information. -// -// TODO: Unify implementations of different data types (i.e. float and double). -#ifndef EIGEN_INVERSE_SIZE_4_H -#define EIGEN_INVERSE_SIZE_4_H - -namespace Eigen -{ -namespace internal -{ -template <typename MatrixType, typename ResultType> -struct compute_inverse_size4<Architecture::Target, float, MatrixType, ResultType> -{ - enum - { - MatrixAlignment = traits<MatrixType>::Alignment, - ResultAlignment = traits<ResultType>::Alignment, - StorageOrdersMatch = (MatrixType::Flags & RowMajorBit) == (ResultType::Flags & RowMajorBit) - }; - typedef typename conditional<(MatrixType::Flags & LinearAccessBit), MatrixType const &, typename MatrixType::PlainObject>::type ActualMatrixType; - - static void run(const MatrixType &mat, ResultType &result) - { - ActualMatrixType matrix(mat); - - const float* data = matrix.data(); - const Index stride = matrix.innerStride(); - Packet4f _L1 = ploadt<Packet4f,MatrixAlignment>(data); - Packet4f _L2 = ploadt<Packet4f,MatrixAlignment>(data + stride*4); - Packet4f _L3 = ploadt<Packet4f,MatrixAlignment>(data + stride*8); - Packet4f _L4 = ploadt<Packet4f,MatrixAlignment>(data + stride*12); - - // Four 2x2 sub-matrices of the input matrix - // input = [[A, B], - // [C, D]] - Packet4f A, B, C, D; - - if (!StorageOrdersMatch) - { - A = vec4f_unpacklo(_L1, _L2); - B = vec4f_unpacklo(_L3, _L4); - C = vec4f_unpackhi(_L1, _L2); - D = vec4f_unpackhi(_L3, _L4); - } - else - { - A = vec4f_movelh(_L1, _L2); - B = vec4f_movehl(_L2, _L1); - C = vec4f_movelh(_L3, _L4); - D = vec4f_movehl(_L4, _L3); - } - - Packet4f AB, DC; - - // AB = A# * B, where A# denotes the adjugate of A, and * denotes matrix product. - AB = pmul(vec4f_swizzle2(A, A, 3, 3, 0, 0), B); - AB = psub(AB, pmul(vec4f_swizzle2(A, A, 1, 1, 2, 2), vec4f_swizzle2(B, B, 2, 3, 0, 1))); - - // DC = D#*C - DC = pmul(vec4f_swizzle2(D, D, 3, 3, 0, 0), C); - DC = psub(DC, pmul(vec4f_swizzle2(D, D, 1, 1, 2, 2), vec4f_swizzle2(C, C, 2, 3, 0, 1))); - - // determinants of the sub-matrices - Packet4f dA, dB, dC, dD; - - dA = pmul(vec4f_swizzle2(A, A, 3, 3, 1, 1), A); - dA = psub(dA, vec4f_movehl(dA, dA)); - - dB = pmul(vec4f_swizzle2(B, B, 3, 3, 1, 1), B); - dB = psub(dB, vec4f_movehl(dB, dB)); - - dC = pmul(vec4f_swizzle2(C, C, 3, 3, 1, 1), C); - dC = psub(dC, vec4f_movehl(dC, dC)); - - dD = pmul(vec4f_swizzle2(D, D, 3, 3, 1, 1), D); - dD = psub(dD, vec4f_movehl(dD, dD)); - - Packet4f d, d1, d2; - - d = pmul(vec4f_swizzle2(DC, DC, 0, 2, 1, 3), AB); - d = padd(d, vec4f_movehl(d, d)); - d = padd(d, vec4f_swizzle2(d, d, 1, 0, 0, 0)); - d1 = pmul(dA, dD); - d2 = pmul(dB, dC); - - // determinant of the input matrix, det = |A||D| + |B||C| - trace(A#*B*D#*C) - Packet4f det = vec4f_duplane(psub(padd(d1, d2), d), 0); - - // reciprocal of the determinant of the input matrix, rd = 1/det - Packet4f rd = pdiv(pset1<Packet4f>(1.0f), det); - - // Four sub-matrices of the inverse - Packet4f iA, iB, iC, iD; - - // iD = D*|A| - C*A#*B - iD = pmul(vec4f_swizzle2(C, C, 0, 0, 2, 2), vec4f_movelh(AB, AB)); - iD = padd(iD, pmul(vec4f_swizzle2(C, C, 1, 1, 3, 3), vec4f_movehl(AB, AB))); - iD = psub(pmul(D, vec4f_duplane(dA, 0)), iD); - - // iA = A*|D| - B*D#*C - iA = pmul(vec4f_swizzle2(B, B, 0, 0, 2, 2), vec4f_movelh(DC, DC)); - iA = padd(iA, pmul(vec4f_swizzle2(B, B, 1, 1, 3, 3), vec4f_movehl(DC, DC))); - iA = psub(pmul(A, vec4f_duplane(dD, 0)), iA); - - // iB = C*|B| - D * (A#B)# = C*|B| - D*B#*A - iB = pmul(D, vec4f_swizzle2(AB, AB, 3, 0, 3, 0)); - iB = psub(iB, pmul(vec4f_swizzle2(D, D, 1, 0, 3, 2), vec4f_swizzle2(AB, AB, 2, 1, 2, 1))); - iB = psub(pmul(C, vec4f_duplane(dB, 0)), iB); - - // iC = B*|C| - A * (D#C)# = B*|C| - A*C#*D - iC = pmul(A, vec4f_swizzle2(DC, DC, 3, 0, 3, 0)); - iC = psub(iC, pmul(vec4f_swizzle2(A, A, 1, 0, 3, 2), vec4f_swizzle2(DC, DC, 2, 1, 2, 1))); - iC = psub(pmul(B, vec4f_duplane(dC, 0)), iC); - - const float sign_mask[4] = {0.0f, numext::bit_cast<float>(0x80000000u), numext::bit_cast<float>(0x80000000u), 0.0f}; - const Packet4f p4f_sign_PNNP = ploadu<Packet4f>(sign_mask); - rd = pxor(rd, p4f_sign_PNNP); - iA = pmul(iA, rd); - iB = pmul(iB, rd); - iC = pmul(iC, rd); - iD = pmul(iD, rd); - - Index res_stride = result.outerStride(); - float *res = result.data(); - - pstoret<float, Packet4f, ResultAlignment>(res + 0, vec4f_swizzle2(iA, iB, 3, 1, 3, 1)); - pstoret<float, Packet4f, ResultAlignment>(res + res_stride, vec4f_swizzle2(iA, iB, 2, 0, 2, 0)); - pstoret<float, Packet4f, ResultAlignment>(res + 2 * res_stride, vec4f_swizzle2(iC, iD, 3, 1, 3, 1)); - pstoret<float, Packet4f, ResultAlignment>(res + 3 * res_stride, vec4f_swizzle2(iC, iD, 2, 0, 2, 0)); - } -}; - -#if !(defined EIGEN_VECTORIZE_NEON && !(EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG)) -// same algorithm as above, except that each operand is split into -// halves for two registers to hold. -template <typename MatrixType, typename ResultType> -struct compute_inverse_size4<Architecture::Target, double, MatrixType, ResultType> -{ - enum - { - MatrixAlignment = traits<MatrixType>::Alignment, - ResultAlignment = traits<ResultType>::Alignment, - StorageOrdersMatch = (MatrixType::Flags & RowMajorBit) == (ResultType::Flags & RowMajorBit) - }; - typedef typename conditional<(MatrixType::Flags & LinearAccessBit), - MatrixType const &, - typename MatrixType::PlainObject>::type - ActualMatrixType; - - static void run(const MatrixType &mat, ResultType &result) - { - ActualMatrixType matrix(mat); - - // Four 2x2 sub-matrices of the input matrix, each is further divided into upper and lower - // row e.g. A1, upper row of A, A2, lower row of A - // input = [[A, B], = [[[A1, [B1, - // [C, D]] A2], B2]], - // [[C1, [D1, - // C2], D2]]] - - Packet2d A1, A2, B1, B2, C1, C2, D1, D2; - - const double* data = matrix.data(); - const Index stride = matrix.innerStride(); - if (StorageOrdersMatch) - { - A1 = ploadt<Packet2d,MatrixAlignment>(data + stride*0); - B1 = ploadt<Packet2d,MatrixAlignment>(data + stride*2); - A2 = ploadt<Packet2d,MatrixAlignment>(data + stride*4); - B2 = ploadt<Packet2d,MatrixAlignment>(data + stride*6); - C1 = ploadt<Packet2d,MatrixAlignment>(data + stride*8); - D1 = ploadt<Packet2d,MatrixAlignment>(data + stride*10); - C2 = ploadt<Packet2d,MatrixAlignment>(data + stride*12); - D2 = ploadt<Packet2d,MatrixAlignment>(data + stride*14); - } - else - { - Packet2d temp; - A1 = ploadt<Packet2d,MatrixAlignment>(data + stride*0); - C1 = ploadt<Packet2d,MatrixAlignment>(data + stride*2); - A2 = ploadt<Packet2d,MatrixAlignment>(data + stride*4); - C2 = ploadt<Packet2d,MatrixAlignment>(data + stride*6); - temp = A1; - A1 = vec2d_unpacklo(A1, A2); - A2 = vec2d_unpackhi(temp, A2); - - temp = C1; - C1 = vec2d_unpacklo(C1, C2); - C2 = vec2d_unpackhi(temp, C2); - - B1 = ploadt<Packet2d,MatrixAlignment>(data + stride*8); - D1 = ploadt<Packet2d,MatrixAlignment>(data + stride*10); - B2 = ploadt<Packet2d,MatrixAlignment>(data + stride*12); - D2 = ploadt<Packet2d,MatrixAlignment>(data + stride*14); - - temp = B1; - B1 = vec2d_unpacklo(B1, B2); - B2 = vec2d_unpackhi(temp, B2); - - temp = D1; - D1 = vec2d_unpacklo(D1, D2); - D2 = vec2d_unpackhi(temp, D2); - } - - // determinants of the sub-matrices - Packet2d dA, dB, dC, dD; - - dA = vec2d_swizzle2(A2, A2, 1); - dA = pmul(A1, dA); - dA = psub(dA, vec2d_duplane(dA, 1)); - - dB = vec2d_swizzle2(B2, B2, 1); - dB = pmul(B1, dB); - dB = psub(dB, vec2d_duplane(dB, 1)); - - dC = vec2d_swizzle2(C2, C2, 1); - dC = pmul(C1, dC); - dC = psub(dC, vec2d_duplane(dC, 1)); - - dD = vec2d_swizzle2(D2, D2, 1); - dD = pmul(D1, dD); - dD = psub(dD, vec2d_duplane(dD, 1)); - - Packet2d DC1, DC2, AB1, AB2; - - // AB = A# * B, where A# denotes the adjugate of A, and * denotes matrix product. - AB1 = pmul(B1, vec2d_duplane(A2, 1)); - AB2 = pmul(B2, vec2d_duplane(A1, 0)); - AB1 = psub(AB1, pmul(B2, vec2d_duplane(A1, 1))); - AB2 = psub(AB2, pmul(B1, vec2d_duplane(A2, 0))); - - // DC = D#*C - DC1 = pmul(C1, vec2d_duplane(D2, 1)); - DC2 = pmul(C2, vec2d_duplane(D1, 0)); - DC1 = psub(DC1, pmul(C2, vec2d_duplane(D1, 1))); - DC2 = psub(DC2, pmul(C1, vec2d_duplane(D2, 0))); - - Packet2d d1, d2; - - // determinant of the input matrix, det = |A||D| + |B||C| - trace(A#*B*D#*C) - Packet2d det; - - // reciprocal of the determinant of the input matrix, rd = 1/det - Packet2d rd; - - d1 = pmul(AB1, vec2d_swizzle2(DC1, DC2, 0)); - d2 = pmul(AB2, vec2d_swizzle2(DC1, DC2, 3)); - rd = padd(d1, d2); - rd = padd(rd, vec2d_duplane(rd, 1)); - - d1 = pmul(dA, dD); - d2 = pmul(dB, dC); - - det = padd(d1, d2); - det = psub(det, rd); - det = vec2d_duplane(det, 0); - rd = pdiv(pset1<Packet2d>(1.0), det); - - // rows of four sub-matrices of the inverse - Packet2d iA1, iA2, iB1, iB2, iC1, iC2, iD1, iD2; - - // iD = D*|A| - C*A#*B - iD1 = pmul(AB1, vec2d_duplane(C1, 0)); - iD2 = pmul(AB1, vec2d_duplane(C2, 0)); - iD1 = padd(iD1, pmul(AB2, vec2d_duplane(C1, 1))); - iD2 = padd(iD2, pmul(AB2, vec2d_duplane(C2, 1))); - dA = vec2d_duplane(dA, 0); - iD1 = psub(pmul(D1, dA), iD1); - iD2 = psub(pmul(D2, dA), iD2); - - // iA = A*|D| - B*D#*C - iA1 = pmul(DC1, vec2d_duplane(B1, 0)); - iA2 = pmul(DC1, vec2d_duplane(B2, 0)); - iA1 = padd(iA1, pmul(DC2, vec2d_duplane(B1, 1))); - iA2 = padd(iA2, pmul(DC2, vec2d_duplane(B2, 1))); - dD = vec2d_duplane(dD, 0); - iA1 = psub(pmul(A1, dD), iA1); - iA2 = psub(pmul(A2, dD), iA2); - - // iB = C*|B| - D * (A#B)# = C*|B| - D*B#*A - iB1 = pmul(D1, vec2d_swizzle2(AB2, AB1, 1)); - iB2 = pmul(D2, vec2d_swizzle2(AB2, AB1, 1)); - iB1 = psub(iB1, pmul(vec2d_swizzle2(D1, D1, 1), vec2d_swizzle2(AB2, AB1, 2))); - iB2 = psub(iB2, pmul(vec2d_swizzle2(D2, D2, 1), vec2d_swizzle2(AB2, AB1, 2))); - dB = vec2d_duplane(dB, 0); - iB1 = psub(pmul(C1, dB), iB1); - iB2 = psub(pmul(C2, dB), iB2); - - // iC = B*|C| - A * (D#C)# = B*|C| - A*C#*D - iC1 = pmul(A1, vec2d_swizzle2(DC2, DC1, 1)); - iC2 = pmul(A2, vec2d_swizzle2(DC2, DC1, 1)); - iC1 = psub(iC1, pmul(vec2d_swizzle2(A1, A1, 1), vec2d_swizzle2(DC2, DC1, 2))); - iC2 = psub(iC2, pmul(vec2d_swizzle2(A2, A2, 1), vec2d_swizzle2(DC2, DC1, 2))); - dC = vec2d_duplane(dC, 0); - iC1 = psub(pmul(B1, dC), iC1); - iC2 = psub(pmul(B2, dC), iC2); - - const double sign_mask1[2] = {0.0, numext::bit_cast<double>(0x8000000000000000ull)}; - const double sign_mask2[2] = {numext::bit_cast<double>(0x8000000000000000ull), 0.0}; - const Packet2d sign_PN = ploadu<Packet2d>(sign_mask1); - const Packet2d sign_NP = ploadu<Packet2d>(sign_mask2); - d1 = pxor(rd, sign_PN); - d2 = pxor(rd, sign_NP); - - Index res_stride = result.outerStride(); - double *res = result.data(); - pstoret<double, Packet2d, ResultAlignment>(res + 0, pmul(vec2d_swizzle2(iA2, iA1, 3), d1)); - pstoret<double, Packet2d, ResultAlignment>(res + res_stride, pmul(vec2d_swizzle2(iA2, iA1, 0), d2)); - pstoret<double, Packet2d, ResultAlignment>(res + 2, pmul(vec2d_swizzle2(iB2, iB1, 3), d1)); - pstoret<double, Packet2d, ResultAlignment>(res + res_stride + 2, pmul(vec2d_swizzle2(iB2, iB1, 0), d2)); - pstoret<double, Packet2d, ResultAlignment>(res + 2 * res_stride, pmul(vec2d_swizzle2(iC2, iC1, 3), d1)); - pstoret<double, Packet2d, ResultAlignment>(res + 3 * res_stride, pmul(vec2d_swizzle2(iC2, iC1, 0), d2)); - pstoret<double, Packet2d, ResultAlignment>(res + 2 * res_stride + 2, pmul(vec2d_swizzle2(iD2, iD1, 3), d1)); - pstoret<double, Packet2d, ResultAlignment>(res + 3 * res_stride + 2, pmul(vec2d_swizzle2(iD2, iD1, 0), d2)); - } -}; -#endif -} // namespace internal -} // namespace Eigen -#endif |