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Diffstat (limited to 'third_party/eigen3/Eigen/src/LU/PartialPivLU.h')
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diff --git a/third_party/eigen3/Eigen/src/LU/PartialPivLU.h b/third_party/eigen3/Eigen/src/LU/PartialPivLU.h deleted file mode 100644 index 1d389ecac7..0000000000 --- a/third_party/eigen3/Eigen/src/LU/PartialPivLU.h +++ /dev/null @@ -1,506 +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 { - -/** \ingroup LU_Module - * - * \class PartialPivLU - * - * \brief LU decomposition of a matrix with partial pivoting, and related features - * - * \param 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(). - * - * \sa MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU - */ -template<typename _MatrixType> class PartialPivLU -{ - public: - - typedef _MatrixType MatrixType; - enum { - RowsAtCompileTime = MatrixType::RowsAtCompileTime, - ColsAtCompileTime = MatrixType::ColsAtCompileTime, - Options = MatrixType::Options, - MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, - MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime - }; - typedef typename MatrixType::Scalar Scalar; - typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; - typedef typename internal::traits<MatrixType>::StorageKind StorageKind; - typedef typename MatrixType::Index Index; - typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationType; - typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> TranspositionType; - - - /** - * \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() - */ - 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. - */ - PartialPivLU(const MatrixType& matrix); - - PartialPivLU& compute(const MatrixType& matrix); - - /** \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; - } - - /** 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 internal::solve_retval<PartialPivLU, Rhs> - solve(const MatrixBase<Rhs>& b) const - { - eigen_assert(m_isInitialized && "PartialPivLU is not initialized."); - return internal::solve_retval<PartialPivLU, Rhs>(*this, b.derived()); - } - - /** \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 internal::solve_retval<PartialPivLU,typename MatrixType::IdentityReturnType> inverse() const - { - eigen_assert(m_isInitialized && "PartialPivLU is not initialized."); - return internal::solve_retval<PartialPivLU,typename MatrixType::IdentityReturnType> - (*this, MatrixType::Identity(m_lu.rows(), m_lu.cols())); - } - - /** \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() - */ - typename internal::traits<MatrixType>::Scalar determinant() const; - - MatrixType reconstructedMatrix() const; - - inline Index rows() const { return m_lu.rows(); } - inline Index cols() const { return m_lu.cols(); } - - protected: - MatrixType m_lu; - PermutationType m_p; - TranspositionType m_rowsTranspositions; - Index m_det_p; - bool m_isInitialized; -}; - -template<typename MatrixType> -PartialPivLU<MatrixType>::PartialPivLU() - : m_lu(), - m_p(), - m_rowsTranspositions(), - 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_det_p(0), - m_isInitialized(false) -{ -} - -template<typename MatrixType> -PartialPivLU<MatrixType>::PartialPivLU(const MatrixType& matrix) - : m_lu(matrix.rows(), matrix.rows()), - m_p(matrix.rows()), - m_rowsTranspositions(matrix.rows()), - m_det_p(0), - m_isInitialized(false) -{ - compute(matrix); -} - -namespace internal { - -/** \internal This is the blocked version of fullpivlu_unblocked() */ -template<typename Scalar, int StorageOrder, typename PivIndex> -struct partial_lu_impl -{ - // FIXME add a stride to Map, so that the following mapping becomes easier, - // another option would be to create an expression being able to automatically - // warp any Map, Matrix, and Block expressions as a unique type, but since that's exactly - // a Map + stride, why not adding a stride to Map, and convenient ctors from a Matrix, - // and Block. - typedef Map<Matrix<Scalar, Dynamic, Dynamic, StorageOrder> > MapLU; - typedef Block<MapLU, Dynamic, Dynamic> MatrixType; - typedef Block<MatrixType,Dynamic,Dynamic> BlockType; - typedef typename MatrixType::RealScalar RealScalar; - typedef typename MatrixType::Index Index; - - /** \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(MatrixType& lu, PivIndex* row_transpositions, PivIndex& nb_transpositions) - { - const Index rows = lu.rows(); - const Index cols = lu.cols(); - const Index size = (std::min)(rows,cols); - nb_transpositions = 0; - Index first_zero_pivot = -1; - for(Index k = 0; k < size; ++k) - { - Index rrows = rows-k-1; - Index rcols = cols-k-1; - - Index row_of_biggest_in_col; - RealScalar biggest_in_corner - = lu.col(k).tail(rows-k).cwiseAbs().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 != RealScalar(0)) - { - if(k != row_of_biggest_in_col) - { - lu.row(k).swap(lu.row(row_of_biggest_in_col)); - ++nb_transpositions; - } - - // FIXME shall we introduce a safe quotient expression in cas 1/lu.coeff(k,k) - // overflow but not the actual quotient? - lu.col(k).tail(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(rrows,rcols).noalias() -= lu.col(k).tail(rrows) * lu.row(k).tail(rcols); - } - 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 instanciations to the strict minimum - * 2 - avoid infinite recursion of the instanciations 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) - { - MapLU lu1(lu_data,StorageOrder==RowMajor?rows:luStride,StorageOrder==RowMajor?luStride:cols); - MatrixType lu(lu1,0,0,rows,cols); - - const Index size = (std::min)(rows,cols); - - // if the matrix is too small, no blocking: - if(size<=16) - { - 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,0,0,rows,k); - BlockType A_2(lu,0,k+bs,rows,tsize); - BlockType A11(lu,k,k,bs,bs); - BlockType A12(lu,k,k+bs,bs,tsize); - BlockType A21(lu,k+bs,k,trows,bs); - BlockType A22(lu,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] += 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::Index& nb_transpositions) -{ - eigen_assert(lu.cols() == row_transpositions.size()); - eigen_assert((&row_transpositions.coeffRef(1)-&row_transpositions.coeffRef(0)) == 1); - - partial_lu_impl - <typename MatrixType::Scalar, MatrixType::Flags&RowMajorBit?RowMajor:ColMajor, typename TranspositionType::Index> - ::blocked_lu(lu.rows(), lu.cols(), &lu.coeffRef(0,0), lu.outerStride(), &row_transpositions.coeffRef(0), nb_transpositions); -} - -} // end namespace internal - -template<typename MatrixType> -PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const MatrixType& matrix) -{ - // the row permutation is stored as int indices, so just to be sure: - eigen_assert(matrix.rows()<NumTraits<int>::highest()); - - m_lu = matrix; - - eigen_assert(matrix.rows() == matrix.cols() && "PartialPivLU is only for square (and moreover invertible) matrices"); - const Index size = matrix.rows(); - - m_rowsTranspositions.resize(size); - - typename TranspositionType::Index 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; - return *this; -} - -template<typename MatrixType> -typename internal::traits<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 of solve() *****************************************************/ - -namespace internal { - -template<typename _MatrixType, typename Rhs> -struct solve_retval<PartialPivLU<_MatrixType>, Rhs> - : solve_retval_base<PartialPivLU<_MatrixType>, Rhs> -{ - EIGEN_MAKE_SOLVE_HELPERS(PartialPivLU<_MatrixType>,Rhs) - - template<typename Dest> void evalTo(Dest& 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. - */ - - eigen_assert(rhs().rows() == dec().matrixLU().rows()); - - // Step 1 - dst = dec().permutationP() * rhs(); - - // Step 2 - dec().matrixLU().template triangularView<UnitLower>().solveInPlace(dst); - - // Step 3 - dec().matrixLU().template triangularView<Upper>().solveInPlace(dst); - } -}; - -} // end namespace internal - -/******** MatrixBase methods *******/ - -/** \lu_module - * - * \return the partial-pivoting LU decomposition of \c *this. - * - * \sa class PartialPivLU - */ -#ifndef __CUDACC__ -template<typename Derived> -inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject> -MatrixBase<Derived>::partialPivLu() const -{ - return PartialPivLU<PlainObject>(eval()); -} -#endif - -#if EIGEN2_SUPPORT_STAGE > STAGE20_RESOLVE_API_CONFLICTS -/** \lu_module - * - * Synonym of partialPivLu(). - * - * \return the partial-pivoting LU decomposition of \c *this. - * - * \sa class PartialPivLU - */ -#ifndef __CUDACC__ -template<typename Derived> -inline const PartialPivLU<typename MatrixBase<Derived>::PlainObject> -MatrixBase<Derived>::lu() const -{ - return PartialPivLU<PlainObject>(eval()); -} -#endif - -#endif - -} // end namespace Eigen - -#endif // EIGEN_PARTIALLU_H |