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diff --git a/eigen/Eigen/src/QR/FullPivHouseholderQR.h b/eigen/Eigen/src/QR/FullPivHouseholderQR.h deleted file mode 100644 index e489bdd..0000000 --- a/eigen/Eigen/src/QR/FullPivHouseholderQR.h +++ /dev/null @@ -1,676 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008-2009 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/. - -#ifndef EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H -#define EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H - -namespace Eigen { - -namespace internal { - -template<typename _MatrixType> struct traits<FullPivHouseholderQR<_MatrixType> > - : traits<_MatrixType> -{ - enum { Flags = 0 }; -}; - -template<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType; - -template<typename MatrixType> -struct traits<FullPivHouseholderQRMatrixQReturnType<MatrixType> > -{ - typedef typename MatrixType::PlainObject ReturnType; -}; - -} // end namespace internal - -/** \ingroup QR_Module - * - * \class FullPivHouseholderQR - * - * \brief Householder rank-revealing QR decomposition of a matrix with full pivoting - * - * \tparam _MatrixType the type of the matrix of which we are computing the QR decomposition - * - * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b P', \b Q and \b R - * such that - * \f[ - * \mathbf{P} \, \mathbf{A} \, \mathbf{P}' = \mathbf{Q} \, \mathbf{R} - * \f] - * by using Householder transformations. Here, \b P and \b P' are permutation matrices, \b Q a unitary matrix - * and \b R an upper triangular matrix. - * - * This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal - * numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR. - * - * This class supports the \link InplaceDecomposition inplace decomposition \endlink mechanism. - * - * \sa MatrixBase::fullPivHouseholderQr() - */ -template<typename _MatrixType> class FullPivHouseholderQR -{ - 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; - // FIXME should be int - typedef typename MatrixType::StorageIndex StorageIndex; - typedef internal::FullPivHouseholderQRMatrixQReturnType<MatrixType> MatrixQReturnType; - typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType; - typedef Matrix<StorageIndex, 1, - EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime,RowsAtCompileTime), RowMajor, 1, - EIGEN_SIZE_MIN_PREFER_FIXED(MaxColsAtCompileTime,MaxRowsAtCompileTime)> IntDiagSizeVectorType; - typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType; - typedef typename internal::plain_row_type<MatrixType>::type RowVectorType; - typedef typename internal::plain_col_type<MatrixType>::type ColVectorType; - typedef typename MatrixType::PlainObject PlainObject; - - /** \brief Default Constructor. - * - * The default constructor is useful in cases in which the user intends to - * perform decompositions via FullPivHouseholderQR::compute(const MatrixType&). - */ - FullPivHouseholderQR() - : m_qr(), - m_hCoeffs(), - m_rows_transpositions(), - m_cols_transpositions(), - m_cols_permutation(), - m_temp(), - m_isInitialized(false), - m_usePrescribedThreshold(false) {} - - /** \brief Default Constructor with memory preallocation - * - * Like the default constructor but with preallocation of the internal data - * according to the specified problem \a size. - * \sa FullPivHouseholderQR() - */ - FullPivHouseholderQR(Index rows, Index cols) - : m_qr(rows, cols), - m_hCoeffs((std::min)(rows,cols)), - m_rows_transpositions((std::min)(rows,cols)), - m_cols_transpositions((std::min)(rows,cols)), - m_cols_permutation(cols), - m_temp(cols), - m_isInitialized(false), - m_usePrescribedThreshold(false) {} - - /** \brief Constructs a QR factorization from a given matrix - * - * This constructor computes the QR factorization of the matrix \a matrix by calling - * the method compute(). It is a short cut for: - * - * \code - * FullPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols()); - * qr.compute(matrix); - * \endcode - * - * \sa compute() - */ - template<typename InputType> - explicit FullPivHouseholderQR(const EigenBase<InputType>& matrix) - : m_qr(matrix.rows(), matrix.cols()), - m_hCoeffs((std::min)(matrix.rows(), matrix.cols())), - m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())), - m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())), - m_cols_permutation(matrix.cols()), - m_temp(matrix.cols()), - m_isInitialized(false), - m_usePrescribedThreshold(false) - { - compute(matrix.derived()); - } - - /** \brief Constructs a QR factorization from a given matrix - * - * This overloaded constructor is provided for \link InplaceDecomposition inplace decomposition \endlink when \c MatrixType is a Eigen::Ref. - * - * \sa FullPivHouseholderQR(const EigenBase&) - */ - template<typename InputType> - explicit FullPivHouseholderQR(EigenBase<InputType>& matrix) - : m_qr(matrix.derived()), - m_hCoeffs((std::min)(matrix.rows(), matrix.cols())), - m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())), - m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())), - m_cols_permutation(matrix.cols()), - m_temp(matrix.cols()), - m_isInitialized(false), - m_usePrescribedThreshold(false) - { - computeInPlace(); - } - - /** This method finds a solution x to the equation Ax=b, where A is the matrix of which - * \c *this is the QR decomposition. - * - * \param b the right-hand-side of the equation to solve. - * - * \returns the exact or least-square solution if the rank is greater or equal to the number of columns of A, - * and an arbitrary solution otherwise. - * - * \note_about_checking_solutions - * - * \note_about_arbitrary_choice_of_solution - * - * Example: \include FullPivHouseholderQR_solve.cpp - * Output: \verbinclude FullPivHouseholderQR_solve.out - */ - template<typename Rhs> - inline const Solve<FullPivHouseholderQR, Rhs> - solve(const MatrixBase<Rhs>& b) const - { - eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized."); - return Solve<FullPivHouseholderQR, Rhs>(*this, b.derived()); - } - - /** \returns Expression object representing the matrix Q - */ - MatrixQReturnType matrixQ(void) const; - - /** \returns a reference to the matrix where the Householder QR decomposition is stored - */ - const MatrixType& matrixQR() const - { - eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized."); - return m_qr; - } - - template<typename InputType> - FullPivHouseholderQR& compute(const EigenBase<InputType>& matrix); - - /** \returns a const reference to the column permutation matrix */ - const PermutationType& colsPermutation() const - { - eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized."); - return m_cols_permutation; - } - - /** \returns a const reference to the vector of indices representing the rows transpositions */ - const IntDiagSizeVectorType& rowsTranspositions() const - { - eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized."); - return m_rows_transpositions; - } - - /** \returns the absolute value of the determinant of the matrix of which - * *this is the QR decomposition. It has only linear complexity - * (that is, O(n) where n is the dimension of the square matrix) - * as the QR 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 QR decomposition. It has only linear complexity - * (that is, O(n) where n is the dimension of the square matrix) - * as the QR 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 QR 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 && "FullPivHouseholderQR 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_qr.coeff(i,i)) > premultiplied_threshold); - return result; - } - - /** \returns the dimension of the kernel of the matrix of which *this is the QR 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 && "FullPivHouseholderQR is not initialized."); - return cols() - rank(); - } - - /** \returns true if the matrix of which *this is the QR 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 && "FullPivHouseholderQR is not initialized."); - return rank() == cols(); - } - - /** \returns true if the matrix of which *this is the QR 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 && "FullPivHouseholderQR is not initialized."); - return rank() == rows(); - } - - /** \returns true if the matrix of which *this is the QR 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 && "FullPivHouseholderQR is not initialized."); - return isInjective() && isSurjective(); - } - - /** \returns the inverse of the matrix of which *this is the QR decomposition. - * - * \note If this matrix is not invertible, the returned matrix has undefined coefficients. - * Use isInvertible() to first determine whether this matrix is invertible. - */ - inline const Inverse<FullPivHouseholderQR> inverse() const - { - eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized."); - return Inverse<FullPivHouseholderQR>(*this); - } - - inline Index rows() const { return m_qr.rows(); } - inline Index cols() const { return m_qr.cols(); } - - /** \returns a const reference to the vector of Householder coefficients used to represent the factor \c Q. - * - * For advanced uses only. - */ - const HCoeffsType& hCoeffs() const { return m_hCoeffs; } - - /** 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 - * QR 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) - */ - FullPivHouseholderQR& 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 qr.setThreshold(Eigen::Default); \endcode - * - * See the documentation of setThreshold(const RealScalar&). - */ - FullPivHouseholderQR& 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_qr.diagonalSize()); - } - - /** \returns the number of nonzero pivots in the QR 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; } - - #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(); - - MatrixType m_qr; - HCoeffsType m_hCoeffs; - IntDiagSizeVectorType m_rows_transpositions; - IntDiagSizeVectorType m_cols_transpositions; - PermutationType m_cols_permutation; - RowVectorType m_temp; - bool m_isInitialized, m_usePrescribedThreshold; - RealScalar m_prescribedThreshold, m_maxpivot; - Index m_nonzero_pivots; - RealScalar m_precision; - Index m_det_pq; -}; - -template<typename MatrixType> -typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::absDeterminant() const -{ - using std::abs; - eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized."); - eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!"); - return abs(m_qr.diagonal().prod()); -} - -template<typename MatrixType> -typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::logAbsDeterminant() const -{ - eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized."); - eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!"); - return m_qr.diagonal().cwiseAbs().array().log().sum(); -} - -/** Performs the QR factorization 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 FullPivHouseholderQR, FullPivHouseholderQR(const MatrixType&) - */ -template<typename MatrixType> -template<typename InputType> -FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const EigenBase<InputType>& matrix) -{ - m_qr = matrix.derived(); - computeInPlace(); - return *this; -} - -template<typename MatrixType> -void FullPivHouseholderQR<MatrixType>::computeInPlace() -{ - check_template_parameters(); - - using std::abs; - Index rows = m_qr.rows(); - Index cols = m_qr.cols(); - Index size = (std::min)(rows,cols); - - - m_hCoeffs.resize(size); - - m_temp.resize(cols); - - m_precision = NumTraits<Scalar>::epsilon() * RealScalar(size); - - m_rows_transpositions.resize(size); - m_cols_transpositions.resize(size); - Index number_of_transpositions = 0; - - RealScalar biggest(0); - - 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) - { - 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 score = m_qr.bottomRightCorner(rows-k, cols-k) - .unaryExpr(Scoring()) - .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner); - row_of_biggest_in_corner += k; - col_of_biggest_in_corner += k; - RealScalar biggest_in_corner = internal::abs_knowing_score<Scalar>()(m_qr(row_of_biggest_in_corner, col_of_biggest_in_corner), score); - if(k==0) biggest = biggest_in_corner; - - // if the corner is negligible, then we have less than full rank, and we can finish early - if(internal::isMuchSmallerThan(biggest_in_corner, biggest, m_precision)) - { - m_nonzero_pivots = k; - for(Index i = k; i < size; i++) - { - m_rows_transpositions.coeffRef(i) = i; - m_cols_transpositions.coeffRef(i) = i; - m_hCoeffs.coeffRef(i) = Scalar(0); - } - break; - } - - m_rows_transpositions.coeffRef(k) = row_of_biggest_in_corner; - m_cols_transpositions.coeffRef(k) = col_of_biggest_in_corner; - if(k != row_of_biggest_in_corner) { - m_qr.row(k).tail(cols-k).swap(m_qr.row(row_of_biggest_in_corner).tail(cols-k)); - ++number_of_transpositions; - } - if(k != col_of_biggest_in_corner) { - m_qr.col(k).swap(m_qr.col(col_of_biggest_in_corner)); - ++number_of_transpositions; - } - - RealScalar beta; - m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta); - m_qr.coeffRef(k,k) = beta; - - // remember the maximum absolute value of diagonal coefficients - if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta); - - m_qr.bottomRightCorner(rows-k, cols-k-1) - .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1)); - } - - m_cols_permutation.setIdentity(cols); - for(Index k = 0; k < size; ++k) - m_cols_permutation.applyTranspositionOnTheRight(k, m_cols_transpositions.coeff(k)); - - m_det_pq = (number_of_transpositions%2) ? -1 : 1; - m_isInitialized = true; -} - -#ifndef EIGEN_PARSED_BY_DOXYGEN -template<typename _MatrixType> -template<typename RhsType, typename DstType> -void FullPivHouseholderQR<_MatrixType>::_solve_impl(const RhsType &rhs, DstType &dst) const -{ - eigen_assert(rhs.rows() == rows()); - const Index l_rank = rank(); - - // FIXME introduce nonzeroPivots() and use it here. and more generally, - // make the same improvements in this dec as in FullPivLU. - if(l_rank==0) - { - dst.setZero(); - return; - } - - typename RhsType::PlainObject c(rhs); - - Matrix<Scalar,1,RhsType::ColsAtCompileTime> temp(rhs.cols()); - for (Index k = 0; k < l_rank; ++k) - { - Index remainingSize = rows()-k; - c.row(k).swap(c.row(m_rows_transpositions.coeff(k))); - c.bottomRightCorner(remainingSize, rhs.cols()) - .applyHouseholderOnTheLeft(m_qr.col(k).tail(remainingSize-1), - m_hCoeffs.coeff(k), &temp.coeffRef(0)); - } - - m_qr.topLeftCorner(l_rank, l_rank) - .template triangularView<Upper>() - .solveInPlace(c.topRows(l_rank)); - - for(Index i = 0; i < l_rank; ++i) dst.row(m_cols_permutation.indices().coeff(i)) = c.row(i); - for(Index i = l_rank; i < cols(); ++i) dst.row(m_cols_permutation.indices().coeff(i)).setZero(); -} -#endif - -namespace internal { - -template<typename DstXprType, typename MatrixType> -struct Assignment<DstXprType, Inverse<FullPivHouseholderQR<MatrixType> >, internal::assign_op<typename DstXprType::Scalar,typename FullPivHouseholderQR<MatrixType>::Scalar>, Dense2Dense> -{ - typedef FullPivHouseholderQR<MatrixType> QrType; - typedef Inverse<QrType> SrcXprType; - static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename QrType::Scalar> &) - { - dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols())); - } -}; - -/** \ingroup QR_Module - * - * \brief Expression type for return value of FullPivHouseholderQR::matrixQ() - * - * \tparam MatrixType type of underlying dense matrix - */ -template<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType - : public ReturnByValue<FullPivHouseholderQRMatrixQReturnType<MatrixType> > -{ -public: - typedef typename FullPivHouseholderQR<MatrixType>::IntDiagSizeVectorType IntDiagSizeVectorType; - typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType; - typedef Matrix<typename MatrixType::Scalar, 1, MatrixType::RowsAtCompileTime, RowMajor, 1, - MatrixType::MaxRowsAtCompileTime> WorkVectorType; - - FullPivHouseholderQRMatrixQReturnType(const MatrixType& qr, - const HCoeffsType& hCoeffs, - const IntDiagSizeVectorType& rowsTranspositions) - : m_qr(qr), - m_hCoeffs(hCoeffs), - m_rowsTranspositions(rowsTranspositions) - {} - - template <typename ResultType> - void evalTo(ResultType& result) const - { - const Index rows = m_qr.rows(); - WorkVectorType workspace(rows); - evalTo(result, workspace); - } - - template <typename ResultType> - void evalTo(ResultType& result, WorkVectorType& workspace) const - { - using numext::conj; - // compute the product H'_0 H'_1 ... H'_n-1, - // where H_k is the k-th Householder transformation I - h_k v_k v_k' - // and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...] - const Index rows = m_qr.rows(); - const Index cols = m_qr.cols(); - const Index size = (std::min)(rows, cols); - workspace.resize(rows); - result.setIdentity(rows, rows); - for (Index k = size-1; k >= 0; k--) - { - result.block(k, k, rows-k, rows-k) - .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), conj(m_hCoeffs.coeff(k)), &workspace.coeffRef(k)); - result.row(k).swap(result.row(m_rowsTranspositions.coeff(k))); - } - } - - Index rows() const { return m_qr.rows(); } - Index cols() const { return m_qr.rows(); } - -protected: - typename MatrixType::Nested m_qr; - typename HCoeffsType::Nested m_hCoeffs; - typename IntDiagSizeVectorType::Nested m_rowsTranspositions; -}; - -// template<typename MatrixType> -// struct evaluator<FullPivHouseholderQRMatrixQReturnType<MatrixType> > -// : public evaluator<ReturnByValue<FullPivHouseholderQRMatrixQReturnType<MatrixType> > > -// {}; - -} // end namespace internal - -template<typename MatrixType> -inline typename FullPivHouseholderQR<MatrixType>::MatrixQReturnType FullPivHouseholderQR<MatrixType>::matrixQ() const -{ - eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized."); - return MatrixQReturnType(m_qr, m_hCoeffs, m_rows_transpositions); -} - -/** \return the full-pivoting Householder QR decomposition of \c *this. - * - * \sa class FullPivHouseholderQR - */ -template<typename Derived> -const FullPivHouseholderQR<typename MatrixBase<Derived>::PlainObject> -MatrixBase<Derived>::fullPivHouseholderQr() const -{ - return FullPivHouseholderQR<PlainObject>(eval()); -} - -} // end namespace Eigen - -#endif // EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H |