diff options
Diffstat (limited to 'Eigen/src/QR/ColPivHouseholderQR.h')
| -rw-r--r-- | Eigen/src/QR/ColPivHouseholderQR.h | 131 |
1 files changed, 78 insertions, 53 deletions
diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h index 172e4a89f..7c559f952 100644 --- a/Eigen/src/QR/ColPivHouseholderQR.h +++ b/Eigen/src/QR/ColPivHouseholderQR.h @@ -11,7 +11,7 @@ #ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H #define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H -namespace Eigen { +namespace Eigen { namespace internal { template<typename _MatrixType> struct traits<ColPivHouseholderQR<_MatrixType> > @@ -28,14 +28,14 @@ template<typename _MatrixType> struct traits<ColPivHouseholderQR<_MatrixType> > * * \brief Householder rank-revealing QR decomposition of a matrix with column-pivoting * - * \param MatrixType the type of the matrix of which we are computing the QR decomposition + * \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 Q and \b R - * such that + * such that * \f[ * \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R} * \f] - * by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an + * by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an * upper triangular matrix. * * This decomposition performs column pivoting in order to be rank-revealing and improve @@ -67,11 +67,11 @@ template<typename _MatrixType> class ColPivHouseholderQR 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::StorageIndex PermIndexType; - + public: /** @@ -86,7 +86,8 @@ template<typename _MatrixType> class ColPivHouseholderQR m_colsPermutation(), m_colsTranspositions(), m_temp(), - m_colSqNorms(), + m_colNormsUpdated(), + m_colNormsDirect(), m_isInitialized(false), m_usePrescribedThreshold(false) {} @@ -102,7 +103,8 @@ template<typename _MatrixType> class ColPivHouseholderQR m_colsPermutation(PermIndexType(cols)), m_colsTranspositions(cols), m_temp(cols), - m_colSqNorms(cols), + m_colNormsUpdated(cols), + m_colNormsDirect(cols), m_isInitialized(false), m_usePrescribedThreshold(false) {} @@ -110,12 +112,12 @@ template<typename _MatrixType> class ColPivHouseholderQR * * This constructor computes the QR factorization of the matrix \a matrix by calling * the method compute(). It is a short cut for: - * + * * \code * ColPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols()); * qr.compute(matrix); * \endcode - * + * * \sa compute() */ template<typename InputType> @@ -125,7 +127,8 @@ template<typename _MatrixType> class ColPivHouseholderQR m_colsPermutation(PermIndexType(matrix.cols())), m_colsTranspositions(matrix.cols()), m_temp(matrix.cols()), - m_colSqNorms(matrix.cols()), + m_colNormsUpdated(matrix.cols()), + m_colNormsDirect(matrix.cols()), m_isInitialized(false), m_usePrescribedThreshold(false) { @@ -160,7 +163,7 @@ template<typename _MatrixType> class ColPivHouseholderQR HouseholderSequenceType householderQ() const; HouseholderSequenceType matrixQ() const { - return householderQ(); + return householderQ(); } /** \returns a reference to the matrix where the Householder QR decomposition is stored @@ -170,14 +173,14 @@ template<typename _MatrixType> class ColPivHouseholderQR eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized."); return m_qr; } - - /** \returns a reference to the matrix where the result Householder QR is stored - * \warning The strict lower part of this matrix contains internal values. + + /** \returns a reference to the matrix where the result Householder QR is stored + * \warning The strict lower part of this matrix contains internal values. * Only the upper triangular part should be referenced. To get it, use * \code matrixR().template triangularView<Upper>() \endcode - * For rank-deficient matrices, use - * \code - * matrixR().topLeftCorner(rank(), rank()).template triangularView<Upper>() + * For rank-deficient matrices, use + * \code + * matrixR().topLeftCorner(rank(), rank()).template triangularView<Upper>() * \endcode */ const MatrixType& matrixR() const @@ -185,7 +188,7 @@ template<typename _MatrixType> class ColPivHouseholderQR eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized."); return m_qr; } - + template<typename InputType> ColPivHouseholderQR& compute(const EigenBase<InputType>& matrix); @@ -305,9 +308,9 @@ template<typename _MatrixType> class ColPivHouseholderQR 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; } @@ -380,19 +383,19 @@ template<typename _MatrixType> class ColPivHouseholderQR * diagonal coefficient of R. */ RealScalar maxPivot() const { return m_maxpivot; } - + /** \brief Reports whether the QR factorization was succesful. * - * \note This function always returns \c Success. It is provided for compatibility + * \note This function always returns \c Success. It is provided for compatibility * with other factorization routines. - * \returns \c Success + * \returns \c Success */ ComputationInfo info() const { eigen_assert(m_isInitialized && "Decomposition is not initialized."); return Success; } - + #ifndef EIGEN_PARSED_BY_DOXYGEN template<typename RhsType, typename DstType> EIGEN_DEVICE_FUNC @@ -400,20 +403,23 @@ template<typename _MatrixType> class ColPivHouseholderQR #endif protected: - + + friend class CompleteOrthogonalDecomposition<MatrixType>; + static void check_template_parameters() { EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); } - + void computeInPlace(); - + MatrixType m_qr; HCoeffsType m_hCoeffs; PermutationType m_colsPermutation; IntRowVectorType m_colsTranspositions; RowVectorType m_temp; - RealRowVectorType m_colSqNorms; + RealRowVectorType m_colNormsUpdated; + RealRowVectorType m_colNormsDirect; bool m_isInitialized, m_usePrescribedThreshold; RealScalar m_prescribedThreshold, m_maxpivot; Index m_nonzero_pivots; @@ -448,14 +454,14 @@ template<typename InputType> ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const EigenBase<InputType>& matrix) { check_template_parameters(); - + // the column permutation is stored as int indices, so just to be sure: eigen_assert(matrix.cols()<=NumTraits<int>::highest()); m_qr = matrix; - + computeInPlace(); - + return *this; } @@ -463,10 +469,11 @@ template<typename MatrixType> void ColPivHouseholderQR<MatrixType>::computeInPlace() { using std::abs; + Index rows = m_qr.rows(); Index cols = m_qr.cols(); Index size = m_qr.diagonalSize(); - + m_hCoeffs.resize(size); m_temp.resize(cols); @@ -474,31 +481,28 @@ void ColPivHouseholderQR<MatrixType>::computeInPlace() m_colsTranspositions.resize(m_qr.cols()); Index number_of_transpositions = 0; - m_colSqNorms.resize(cols); - for(Index k = 0; k < cols; ++k) - m_colSqNorms.coeffRef(k) = m_qr.col(k).squaredNorm(); + m_colNormsUpdated.resize(cols); + m_colNormsDirect.resize(cols); + for (Index k = 0; k < cols; ++k) { + // colNormsDirect(k) caches the most recent directly computed norm of + // column k. + m_colNormsDirect.coeffRef(k) = m_qr.col(k).norm(); + m_colNormsUpdated.coeffRef(k) = m_colNormsDirect.coeffRef(k); + } - RealScalar threshold_helper = m_colSqNorms.maxCoeff() * numext::abs2(NumTraits<Scalar>::epsilon()) / RealScalar(rows); + RealScalar threshold_helper = numext::abs2(m_colNormsUpdated.maxCoeff() * NumTraits<Scalar>::epsilon()) / RealScalar(rows); + RealScalar norm_downdate_threshold = numext::sqrt(NumTraits<Scalar>::epsilon()); 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 look up in our table m_colSqNorms which column has the biggest squared norm + // first, we look up in our table m_colNormsUpdated which column has the biggest norm Index biggest_col_index; - RealScalar biggest_col_sq_norm = m_colSqNorms.tail(cols-k).maxCoeff(&biggest_col_index); + RealScalar biggest_col_sq_norm = numext::abs2(m_colNormsUpdated.tail(cols-k).maxCoeff(&biggest_col_index)); biggest_col_index += k; - // since our table m_colSqNorms accumulates imprecision at every step, we must now recompute - // the actual squared norm of the selected column. - // Note that not doing so does result in solve() sometimes returning inf/nan values - // when running the unit test with 1000 repetitions. - biggest_col_sq_norm = m_qr.col(biggest_col_index).tail(rows-k).squaredNorm(); - - // we store that back into our table: it can't hurt to correct our table. - m_colSqNorms.coeffRef(biggest_col_index) = biggest_col_sq_norm; - // Track the number of meaningful pivots but do not stop the decomposition to make // sure that the initial matrix is properly reproduced. See bug 941. if(m_nonzero_pivots==size && biggest_col_sq_norm < threshold_helper * RealScalar(rows-k)) @@ -508,7 +512,8 @@ void ColPivHouseholderQR<MatrixType>::computeInPlace() m_colsTranspositions.coeffRef(k) = biggest_col_index; if(k != biggest_col_index) { m_qr.col(k).swap(m_qr.col(biggest_col_index)); - std::swap(m_colSqNorms.coeffRef(k), m_colSqNorms.coeffRef(biggest_col_index)); + std::swap(m_colNormsUpdated.coeffRef(k), m_colNormsUpdated.coeffRef(biggest_col_index)); + std::swap(m_colNormsDirect.coeffRef(k), m_colNormsDirect.coeffRef(biggest_col_index)); ++number_of_transpositions; } @@ -526,8 +531,28 @@ void ColPivHouseholderQR<MatrixType>::computeInPlace() 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)); - // update our table of squared norms of the columns - m_colSqNorms.tail(cols-k-1) -= m_qr.row(k).tail(cols-k-1).cwiseAbs2(); + // update our table of norms of the columns + for (Index j = k + 1; j < cols; ++j) { + // The following implements the stable norm downgrade step discussed in + // http://www.netlib.org/lapack/lawnspdf/lawn176.pdf + // and used in LAPACK routines xGEQPF and xGEQP3. + // See lines 278-297 in http://www.netlib.org/lapack/explore-html/dc/df4/sgeqpf_8f_source.html + if (m_colNormsUpdated.coeffRef(j) != 0) { + RealScalar temp = abs(m_qr.coeffRef(k, j)) / m_colNormsUpdated.coeffRef(j); + temp = (RealScalar(1) + temp) * (RealScalar(1) - temp); + temp = temp < 0 ? 0 : temp; + RealScalar temp2 = temp * numext::abs2(m_colNormsUpdated.coeffRef(j) / + m_colNormsDirect.coeffRef(j)); + if (temp2 <= norm_downdate_threshold) { + // The updated norm has become too inaccurate so re-compute the column + // norm directly. + m_colNormsDirect.coeffRef(j) = m_qr.col(j).tail(rows - k - 1).norm(); + m_colNormsUpdated.coeffRef(j) = m_colNormsDirect.coeffRef(j); + } else { + m_colNormsUpdated.coeffRef(j) *= numext::sqrt(temp); + } + } + } } m_colsPermutation.setIdentity(PermIndexType(cols)); @@ -578,7 +603,7 @@ struct Assignment<DstXprType, Inverse<ColPivHouseholderQR<MatrixType> >, interna typedef ColPivHouseholderQR<MatrixType> QrType; typedef Inverse<QrType> SrcXprType; static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar> &) - { + { dst = src.nestedExpression().solve(MatrixType::Identity(src.rows(), src.cols())); } }; |