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diff --git a/eigen/Eigen/src/QR/CompleteOrthogonalDecomposition.h b/eigen/Eigen/src/QR/CompleteOrthogonalDecomposition.h deleted file mode 100644 index 34c637b..0000000 --- a/eigen/Eigen/src/QR/CompleteOrthogonalDecomposition.h +++ /dev/null @@ -1,562 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2016 Rasmus Munk Larsen <rmlarsen@google.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_COMPLETEORTHOGONALDECOMPOSITION_H -#define EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H - -namespace Eigen { - -namespace internal { -template <typename _MatrixType> -struct traits<CompleteOrthogonalDecomposition<_MatrixType> > - : traits<_MatrixType> { - enum { Flags = 0 }; -}; - -} // end namespace internal - -/** \ingroup QR_Module - * - * \class CompleteOrthogonalDecomposition - * - * \brief Complete orthogonal decomposition (COD) of a matrix. - * - * \param MatrixType the type of the matrix of which we are computing the COD. - * - * This class performs a rank-revealing complete orthogonal decomposition of a - * matrix \b A into matrices \b P, \b Q, \b T, and \b Z such that - * \f[ - * \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, - * \begin{bmatrix} \mathbf{T} & \mathbf{0} \\ - * \mathbf{0} & \mathbf{0} \end{bmatrix} \, \mathbf{Z} - * \f] - * by using Householder transformations. Here, \b P is a permutation matrix, - * \b Q and \b Z are unitary matrices and \b T an upper triangular matrix of - * size rank-by-rank. \b A may be rank deficient. - * - * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. - * - * \sa MatrixBase::completeOrthogonalDecomposition() - */ -template <typename _MatrixType> -class CompleteOrthogonalDecomposition { - public: - typedef _MatrixType MatrixType; - enum { - RowsAtCompileTime = MatrixType::RowsAtCompileTime, - ColsAtCompileTime = MatrixType::ColsAtCompileTime, - MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, - MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime - }; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef typename MatrixType::StorageIndex StorageIndex; - typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType; - typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> - PermutationType; - typedef typename internal::plain_row_type<MatrixType, Index>::type - IntRowVectorType; - typedef typename internal::plain_row_type<MatrixType>::type RowVectorType; - typedef typename internal::plain_row_type<MatrixType, RealScalar>::type - RealRowVectorType; - typedef HouseholderSequence< - MatrixType, typename internal::remove_all< - typename HCoeffsType::ConjugateReturnType>::type> - HouseholderSequenceType; - typedef typename MatrixType::PlainObject PlainObject; - - private: - typedef typename PermutationType::Index PermIndexType; - - public: - /** - * \brief Default Constructor. - * - * The default constructor is useful in cases in which the user intends to - * perform decompositions via - * \c CompleteOrthogonalDecomposition::compute(const* MatrixType&). - */ - CompleteOrthogonalDecomposition() : m_cpqr(), m_zCoeffs(), m_temp() {} - - /** \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 CompleteOrthogonalDecomposition() - */ - CompleteOrthogonalDecomposition(Index rows, Index cols) - : m_cpqr(rows, cols), m_zCoeffs((std::min)(rows, cols)), m_temp(cols) {} - - /** \brief Constructs a complete orthogonal decomposition from a given - * matrix. - * - * This constructor computes the complete orthogonal decomposition of the - * matrix \a matrix by calling the method compute(). The default - * threshold for rank determination will be used. It is a short cut for: - * - * \code - * CompleteOrthogonalDecomposition<MatrixType> cod(matrix.rows(), - * matrix.cols()); - * cod.setThreshold(Default); - * cod.compute(matrix); - * \endcode - * - * \sa compute() - */ - template <typename InputType> - explicit CompleteOrthogonalDecomposition(const EigenBase<InputType>& matrix) - : m_cpqr(matrix.rows(), matrix.cols()), - m_zCoeffs((std::min)(matrix.rows(), matrix.cols())), - m_temp(matrix.cols()) - { - compute(matrix.derived()); - } - - /** \brief Constructs a complete orthogonal decomposition from a given matrix - * - * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref. - * - * \sa CompleteOrthogonalDecomposition(const EigenBase&) - */ - template<typename InputType> - explicit CompleteOrthogonalDecomposition(EigenBase<InputType>& matrix) - : m_cpqr(matrix.derived()), - m_zCoeffs((std::min)(matrix.rows(), matrix.cols())), - m_temp(matrix.cols()) - { - computeInPlace(); - } - - - /** This method computes the minimum-norm solution X to a least squares - * problem \f[\mathrm{minimize} \|A X - B\|, \f] where \b A is the matrix of - * which \c *this is the complete orthogonal decomposition. - * - * \param b the right-hand sides of the problem to solve. - * - * \returns a solution. - * - */ - template <typename Rhs> - inline const Solve<CompleteOrthogonalDecomposition, Rhs> solve( - const MatrixBase<Rhs>& b) const { - eigen_assert(m_cpqr.m_isInitialized && - "CompleteOrthogonalDecomposition is not initialized."); - return Solve<CompleteOrthogonalDecomposition, Rhs>(*this, b.derived()); - } - - HouseholderSequenceType householderQ(void) const; - HouseholderSequenceType matrixQ(void) const { return m_cpqr.householderQ(); } - - /** \returns the matrix \b Z. - */ - MatrixType matrixZ() const { - MatrixType Z = MatrixType::Identity(m_cpqr.cols(), m_cpqr.cols()); - applyZAdjointOnTheLeftInPlace(Z); - return Z.adjoint(); - } - - /** \returns a reference to the matrix where the complete orthogonal - * decomposition is stored - */ - const MatrixType& matrixQTZ() const { return m_cpqr.matrixQR(); } - - /** \returns a reference to the matrix where the complete orthogonal - * decomposition is stored. - * \warning The strict lower part and \code cols() - rank() \endcode right - * columns of this matrix contains internal values. - * Only the upper triangular part should be referenced. To get it, use - * \code matrixT().template triangularView<Upper>() \endcode - * For rank-deficient matrices, use - * \code - * matrixR().topLeftCorner(rank(), rank()).template triangularView<Upper>() - * \endcode - */ - const MatrixType& matrixT() const { return m_cpqr.matrixQR(); } - - template <typename InputType> - CompleteOrthogonalDecomposition& compute(const EigenBase<InputType>& matrix) { - // Compute the column pivoted QR factorization A P = Q R. - m_cpqr.compute(matrix); - computeInPlace(); - return *this; - } - - /** \returns a const reference to the column permutation matrix */ - const PermutationType& colsPermutation() const { - return m_cpqr.colsPermutation(); - } - - /** \returns the absolute value of the determinant of the matrix of which - * *this is the complete orthogonal decomposition. It has only linear - * complexity (that is, O(n) where n is the dimension of the square matrix) - * as the complete orthogonal decomposition has already been computed. - * - * \note This is only for square matrices. - * - * \warning a determinant can be very big or small, so for matrices - * of large enough dimension, there is a risk of overflow/underflow. - * One way to work around that is to use logAbsDeterminant() instead. - * - * \sa logAbsDeterminant(), MatrixBase::determinant() - */ - typename MatrixType::RealScalar absDeterminant() const; - - /** \returns the natural log of the absolute value of the determinant of the - * matrix of which *this is the complete orthogonal decomposition. It has - * only linear complexity (that is, O(n) where n is the dimension of the - * square matrix) as the complete orthogonal decomposition has already been - * computed. - * - * \note This is only for square matrices. - * - * \note This method is useful to work around the risk of overflow/underflow - * that's inherent to determinant computation. - * - * \sa absDeterminant(), MatrixBase::determinant() - */ - typename MatrixType::RealScalar logAbsDeterminant() const; - - /** \returns the rank of the matrix of which *this is the complete orthogonal - * 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 { return m_cpqr.rank(); } - - /** \returns the dimension of the kernel of the matrix of which *this is the - * complete orthogonal 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 { return m_cpqr.dimensionOfKernel(); } - - /** \returns true if the matrix of which *this is the 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 { return m_cpqr.isInjective(); } - - /** \returns true if the matrix of which *this is the 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 { return m_cpqr.isSurjective(); } - - /** \returns true if the matrix of which *this is the complete orthogonal - * 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 { return m_cpqr.isInvertible(); } - - /** \returns the pseudo-inverse of the matrix of which *this is the complete - * orthogonal decomposition. - * \warning: Do not compute \c this->pseudoInverse()*rhs to solve a linear systems. - * It is more efficient and numerically stable to call \c this->solve(rhs). - */ - inline const Inverse<CompleteOrthogonalDecomposition> pseudoInverse() const - { - return Inverse<CompleteOrthogonalDecomposition>(*this); - } - - inline Index rows() const { return m_cpqr.rows(); } - inline Index cols() const { return m_cpqr.cols(); } - - /** \returns a const reference to the vector of Householder coefficients used - * to represent the factor \c Q. - * - * For advanced uses only. - */ - inline const HCoeffsType& hCoeffs() const { return m_cpqr.hCoeffs(); } - - /** \returns a const reference to the vector of Householder coefficients - * used to represent the factor \c Z. - * - * For advanced uses only. - */ - const HCoeffsType& zCoeffs() const { return m_zCoeffs; } - - /** 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. - * Most be called before calling compute(). - * - * 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) - */ - CompleteOrthogonalDecomposition& setThreshold(const RealScalar& threshold) { - m_cpqr.setThreshold(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 qr.setThreshold(Eigen::Default); \endcode - * - * See the documentation of setThreshold(const RealScalar&). - */ - CompleteOrthogonalDecomposition& setThreshold(Default_t) { - m_cpqr.setThreshold(Default); - 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 { return m_cpqr.threshold(); } - - /** \returns the number of nonzero pivots in the complete orthogonal - * 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 { return m_cpqr.nonzeroPivots(); } - - /** \returns the absolute value of the biggest pivot, i.e. the biggest - * diagonal coefficient of R. - */ - inline RealScalar maxPivot() const { return m_cpqr.maxPivot(); } - - /** \brief Reports whether the complete orthogonal decomposition was - * succesful. - * - * \note This function always returns \c Success. It is provided for - * compatibility - * with other factorization routines. - * \returns \c Success - */ - ComputationInfo info() const { - eigen_assert(m_cpqr.m_isInitialized && "Decomposition is not initialized."); - return Success; - } - -#ifndef EIGEN_PARSED_BY_DOXYGEN - template <typename RhsType, typename DstType> - EIGEN_DEVICE_FUNC void _solve_impl(const RhsType& rhs, DstType& dst) const; -#endif - - protected: - static void check_template_parameters() { - EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); - } - - void computeInPlace(); - - /** Overwrites \b rhs with \f$ \mathbf{Z}^* * \mathbf{rhs} \f$. - */ - template <typename Rhs> - void applyZAdjointOnTheLeftInPlace(Rhs& rhs) const; - - ColPivHouseholderQR<MatrixType> m_cpqr; - HCoeffsType m_zCoeffs; - RowVectorType m_temp; -}; - -template <typename MatrixType> -typename MatrixType::RealScalar -CompleteOrthogonalDecomposition<MatrixType>::absDeterminant() const { - return m_cpqr.absDeterminant(); -} - -template <typename MatrixType> -typename MatrixType::RealScalar -CompleteOrthogonalDecomposition<MatrixType>::logAbsDeterminant() const { - return m_cpqr.logAbsDeterminant(); -} - -/** Performs the complete orthogonal decomposition of the given matrix \a - * matrix. The result of the factorization is stored into \c *this, and a - * reference to \c *this is returned. - * - * \sa class CompleteOrthogonalDecomposition, - * CompleteOrthogonalDecomposition(const MatrixType&) - */ -template <typename MatrixType> -void CompleteOrthogonalDecomposition<MatrixType>::computeInPlace() -{ - check_template_parameters(); - - // the column permutation is stored as int indices, so just to be sure: - eigen_assert(m_cpqr.cols() <= NumTraits<int>::highest()); - - const Index rank = m_cpqr.rank(); - const Index cols = m_cpqr.cols(); - const Index rows = m_cpqr.rows(); - m_zCoeffs.resize((std::min)(rows, cols)); - m_temp.resize(cols); - - if (rank < cols) { - // We have reduced the (permuted) matrix to the form - // [R11 R12] - // [ 0 R22] - // where R11 is r-by-r (r = rank) upper triangular, R12 is - // r-by-(n-r), and R22 is empty or the norm of R22 is negligible. - // We now compute the complete orthogonal decomposition by applying - // Householder transformations from the right to the upper trapezoidal - // matrix X = [R11 R12] to zero out R12 and obtain the factorization - // [R11 R12] = [T11 0] * Z, where T11 is r-by-r upper triangular and - // Z = Z(0) * Z(1) ... Z(r-1) is an n-by-n orthogonal matrix. - // We store the data representing Z in R12 and m_zCoeffs. - for (Index k = rank - 1; k >= 0; --k) { - if (k != rank - 1) { - // Given the API for Householder reflectors, it is more convenient if - // we swap the leading parts of columns k and r-1 (zero-based) to form - // the matrix X_k = [X(0:k, k), X(0:k, r:n)] - m_cpqr.m_qr.col(k).head(k + 1).swap( - m_cpqr.m_qr.col(rank - 1).head(k + 1)); - } - // Construct Householder reflector Z(k) to zero out the last row of X_k, - // i.e. choose Z(k) such that - // [X(k, k), X(k, r:n)] * Z(k) = [beta, 0, .., 0]. - RealScalar beta; - m_cpqr.m_qr.row(k) - .tail(cols - rank + 1) - .makeHouseholderInPlace(m_zCoeffs(k), beta); - m_cpqr.m_qr(k, rank - 1) = beta; - if (k > 0) { - // Apply Z(k) to the first k rows of X_k - m_cpqr.m_qr.topRightCorner(k, cols - rank + 1) - .applyHouseholderOnTheRight( - m_cpqr.m_qr.row(k).tail(cols - rank).transpose(), m_zCoeffs(k), - &m_temp(0)); - } - if (k != rank - 1) { - // Swap X(0:k,k) back to its proper location. - m_cpqr.m_qr.col(k).head(k + 1).swap( - m_cpqr.m_qr.col(rank - 1).head(k + 1)); - } - } - } -} - -template <typename MatrixType> -template <typename Rhs> -void CompleteOrthogonalDecomposition<MatrixType>::applyZAdjointOnTheLeftInPlace( - Rhs& rhs) const { - const Index cols = this->cols(); - const Index nrhs = rhs.cols(); - const Index rank = this->rank(); - Matrix<typename MatrixType::Scalar, Dynamic, 1> temp((std::max)(cols, nrhs)); - for (Index k = 0; k < rank; ++k) { - if (k != rank - 1) { - rhs.row(k).swap(rhs.row(rank - 1)); - } - rhs.middleRows(rank - 1, cols - rank + 1) - .applyHouseholderOnTheLeft( - matrixQTZ().row(k).tail(cols - rank).adjoint(), zCoeffs()(k), - &temp(0)); - if (k != rank - 1) { - rhs.row(k).swap(rhs.row(rank - 1)); - } - } -} - -#ifndef EIGEN_PARSED_BY_DOXYGEN -template <typename _MatrixType> -template <typename RhsType, typename DstType> -void CompleteOrthogonalDecomposition<_MatrixType>::_solve_impl( - const RhsType& rhs, DstType& dst) const { - eigen_assert(rhs.rows() == this->rows()); - - const Index rank = this->rank(); - if (rank == 0) { - dst.setZero(); - return; - } - - // Compute c = Q^* * rhs - // Note that the matrix Q = H_0^* H_1^*... so its inverse is - // Q^* = (H_0 H_1 ...)^T - typename RhsType::PlainObject c(rhs); - c.applyOnTheLeft( - householderSequence(matrixQTZ(), hCoeffs()).setLength(rank).transpose()); - - // Solve T z = c(1:rank, :) - dst.topRows(rank) = matrixT() - .topLeftCorner(rank, rank) - .template triangularView<Upper>() - .solve(c.topRows(rank)); - - const Index cols = this->cols(); - if (rank < cols) { - // Compute y = Z^* * [ z ] - // [ 0 ] - dst.bottomRows(cols - rank).setZero(); - applyZAdjointOnTheLeftInPlace(dst); - } - - // Undo permutation to get x = P^{-1} * y. - dst = colsPermutation() * dst; -} -#endif - -namespace internal { - -template<typename DstXprType, typename MatrixType> -struct Assignment<DstXprType, Inverse<CompleteOrthogonalDecomposition<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename CompleteOrthogonalDecomposition<MatrixType>::Scalar>, Dense2Dense> -{ - typedef CompleteOrthogonalDecomposition<MatrixType> CodType; - typedef Inverse<CodType> SrcXprType; - static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename CodType::Scalar> &) - { - dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.rows())); - } -}; - -} // end namespace internal - -/** \returns the matrix Q as a sequence of householder transformations */ -template <typename MatrixType> -typename CompleteOrthogonalDecomposition<MatrixType>::HouseholderSequenceType -CompleteOrthogonalDecomposition<MatrixType>::householderQ() const { - return m_cpqr.householderQ(); -} - -/** \return the complete orthogonal decomposition of \c *this. - * - * \sa class CompleteOrthogonalDecomposition - */ -template <typename Derived> -const CompleteOrthogonalDecomposition<typename MatrixBase<Derived>::PlainObject> -MatrixBase<Derived>::completeOrthogonalDecomposition() const { - return CompleteOrthogonalDecomposition<PlainObject>(eval()); -} - -} // end namespace Eigen - -#endif // EIGEN_COMPLETEORTHOGONALDECOMPOSITION_H |