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src/QR/FullPivHouseholderQR.h@1:3b8049da21b8, 2019-09-24 (annotated)

Committer:
jsoh91
Date:
Tue Sep 24 00:18:23 2019 +0000
Revision:
1:3b8049da21b8
Parent:
0:13a5d365ba16 
ignore and revise some of error parts

Who changed what in which revision?

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ykuroda 0:13a5d365ba16 1 // This file is part of Eigen, a lightweight C++ template library
ykuroda 0:13a5d365ba16 2 // for linear algebra.
ykuroda 0:13a5d365ba16 3 //
ykuroda 0:13a5d365ba16 4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
ykuroda 0:13a5d365ba16 5 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
ykuroda 0:13a5d365ba16 6 //
ykuroda 0:13a5d365ba16 7 // This Source Code Form is subject to the terms of the Mozilla
ykuroda 0:13a5d365ba16 8 // Public License v. 2.0. If a copy of the MPL was not distributed
ykuroda 0:13a5d365ba16 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
ykuroda 0:13a5d365ba16 10
ykuroda 0:13a5d365ba16 11 #ifndef EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
ykuroda 0:13a5d365ba16 12 #define EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
ykuroda 0:13a5d365ba16 13
ykuroda 0:13a5d365ba16 14 namespace Eigen {
ykuroda 0:13a5d365ba16 15
ykuroda 0:13a5d365ba16 16 namespace internal {
ykuroda 0:13a5d365ba16 17
ykuroda 0:13a5d365ba16 18 template<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType;
ykuroda 0:13a5d365ba16 19
ykuroda 0:13a5d365ba16 20 template<typename MatrixType>
ykuroda 0:13a5d365ba16 21 struct traits<FullPivHouseholderQRMatrixQReturnType<MatrixType> >
ykuroda 0:13a5d365ba16 22 {
ykuroda 0:13a5d365ba16 23 typedef typename MatrixType::PlainObject ReturnType;
ykuroda 0:13a5d365ba16 24 };
ykuroda 0:13a5d365ba16 25
ykuroda 0:13a5d365ba16 26 }
ykuroda 0:13a5d365ba16 27
ykuroda 0:13a5d365ba16 28 /** \ingroup QR_Module
ykuroda 0:13a5d365ba16 29 *
ykuroda 0:13a5d365ba16 30 * \class FullPivHouseholderQR
ykuroda 0:13a5d365ba16 31 *
ykuroda 0:13a5d365ba16 32 * \brief Householder rank-revealing QR decomposition of a matrix with full pivoting
ykuroda 0:13a5d365ba16 33 *
ykuroda 0:13a5d365ba16 34 * \param MatrixType the type of the matrix of which we are computing the QR decomposition
ykuroda 0:13a5d365ba16 35 *
ykuroda 0:13a5d365ba16 36 * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
ykuroda 0:13a5d365ba16 37 * such that
ykuroda 0:13a5d365ba16 38 * \f[
ykuroda 0:13a5d365ba16 39 * \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \mathbf{R}
ykuroda 0:13a5d365ba16 40 * \f]
ykuroda 0:13a5d365ba16 41 * by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an
ykuroda 0:13a5d365ba16 42 * upper triangular matrix.
ykuroda 0:13a5d365ba16 43 *
ykuroda 0:13a5d365ba16 44 * This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal
ykuroda 0:13a5d365ba16 45 * numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR.
ykuroda 0:13a5d365ba16 46 *
ykuroda 0:13a5d365ba16 47 * \sa MatrixBase::fullPivHouseholderQr()
ykuroda 0:13a5d365ba16 48 */
ykuroda 0:13a5d365ba16 49 template<typename _MatrixType> class FullPivHouseholderQR
ykuroda 0:13a5d365ba16 50 {
ykuroda 0:13a5d365ba16 51 public:
ykuroda 0:13a5d365ba16 52
ykuroda 0:13a5d365ba16 53 typedef _MatrixType MatrixType;
ykuroda 0:13a5d365ba16 54 enum {
ykuroda 0:13a5d365ba16 55 RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ykuroda 0:13a5d365ba16 56 ColsAtCompileTime = MatrixType::ColsAtCompileTime,
ykuroda 0:13a5d365ba16 57 Options = MatrixType::Options,
ykuroda 0:13a5d365ba16 58 MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
ykuroda 0:13a5d365ba16 59 MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
ykuroda 0:13a5d365ba16 60 };
ykuroda 0:13a5d365ba16 61 typedef typename MatrixType::Scalar Scalar;
ykuroda 0:13a5d365ba16 62 typedef typename MatrixType::RealScalar RealScalar;
ykuroda 0:13a5d365ba16 63 typedef typename MatrixType::Index Index;
ykuroda 0:13a5d365ba16 64 typedef internal::FullPivHouseholderQRMatrixQReturnType<MatrixType> MatrixQReturnType;
ykuroda 0:13a5d365ba16 65 typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
ykuroda 0:13a5d365ba16 66 typedef Matrix<Index, 1,
ykuroda 0:13a5d365ba16 67 EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime,RowsAtCompileTime), RowMajor, 1,
ykuroda 0:13a5d365ba16 68 EIGEN_SIZE_MIN_PREFER_FIXED(MaxColsAtCompileTime,MaxRowsAtCompileTime)> IntDiagSizeVectorType;
ykuroda 0:13a5d365ba16 69 typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;
ykuroda 0:13a5d365ba16 70 typedef typename internal::plain_row_type<MatrixType>::type RowVectorType;
ykuroda 0:13a5d365ba16 71 typedef typename internal::plain_col_type<MatrixType>::type ColVectorType;
ykuroda 0:13a5d365ba16 72
ykuroda 0:13a5d365ba16 73 /** \brief Default Constructor.
ykuroda 0:13a5d365ba16 74 *
ykuroda 0:13a5d365ba16 75 * The default constructor is useful in cases in which the user intends to
ykuroda 0:13a5d365ba16 76 * perform decompositions via FullPivHouseholderQR::compute(const MatrixType&).
ykuroda 0:13a5d365ba16 77 */
ykuroda 0:13a5d365ba16 78 FullPivHouseholderQR()
ykuroda 0:13a5d365ba16 79 : m_qr(),
ykuroda 0:13a5d365ba16 80 m_hCoeffs(),
ykuroda 0:13a5d365ba16 81 m_rows_transpositions(),
ykuroda 0:13a5d365ba16 82 m_cols_transpositions(),
ykuroda 0:13a5d365ba16 83 m_cols_permutation(),
ykuroda 0:13a5d365ba16 84 m_temp(),
ykuroda 0:13a5d365ba16 85 m_isInitialized(false),
ykuroda 0:13a5d365ba16 86 m_usePrescribedThreshold(false) {}
ykuroda 0:13a5d365ba16 87
ykuroda 0:13a5d365ba16 88 /** \brief Default Constructor with memory preallocation
ykuroda 0:13a5d365ba16 89 *
ykuroda 0:13a5d365ba16 90 * Like the default constructor but with preallocation of the internal data
ykuroda 0:13a5d365ba16 91 * according to the specified problem \a size.
ykuroda 0:13a5d365ba16 92 * \sa FullPivHouseholderQR()
ykuroda 0:13a5d365ba16 93 */
ykuroda 0:13a5d365ba16 94 FullPivHouseholderQR(Index rows, Index cols)
ykuroda 0:13a5d365ba16 95 : m_qr(rows, cols),
ykuroda 0:13a5d365ba16 96 m_hCoeffs((std::min)(rows,cols)),
ykuroda 0:13a5d365ba16 97 m_rows_transpositions((std::min)(rows,cols)),
ykuroda 0:13a5d365ba16 98 m_cols_transpositions((std::min)(rows,cols)),
ykuroda 0:13a5d365ba16 99 m_cols_permutation(cols),
ykuroda 0:13a5d365ba16 100 m_temp(cols),
ykuroda 0:13a5d365ba16 101 m_isInitialized(false),
ykuroda 0:13a5d365ba16 102 m_usePrescribedThreshold(false) {}
ykuroda 0:13a5d365ba16 103
ykuroda 0:13a5d365ba16 104 /** \brief Constructs a QR factorization from a given matrix
ykuroda 0:13a5d365ba16 105 *
ykuroda 0:13a5d365ba16 106 * This constructor computes the QR factorization of the matrix \a matrix by calling
ykuroda 0:13a5d365ba16 107 * the method compute(). It is a short cut for:
ykuroda 0:13a5d365ba16 108 *
ykuroda 0:13a5d365ba16 109 * \code
ykuroda 0:13a5d365ba16 110 * FullPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());
ykuroda 0:13a5d365ba16 111 * qr.compute(matrix);
ykuroda 0:13a5d365ba16 112 * \endcode
ykuroda 0:13a5d365ba16 113 *
ykuroda 0:13a5d365ba16 114 * \sa compute()
ykuroda 0:13a5d365ba16 115 */
ykuroda 0:13a5d365ba16 116 FullPivHouseholderQR(const MatrixType& matrix)
ykuroda 0:13a5d365ba16 117 : m_qr(matrix.rows(), matrix.cols()),
ykuroda 0:13a5d365ba16 118 m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),
ykuroda 0:13a5d365ba16 119 m_rows_transpositions((std::min)(matrix.rows(), matrix.cols())),
ykuroda 0:13a5d365ba16 120 m_cols_transpositions((std::min)(matrix.rows(), matrix.cols())),
ykuroda 0:13a5d365ba16 121 m_cols_permutation(matrix.cols()),
ykuroda 0:13a5d365ba16 122 m_temp(matrix.cols()),
ykuroda 0:13a5d365ba16 123 m_isInitialized(false),
ykuroda 0:13a5d365ba16 124 m_usePrescribedThreshold(false)
ykuroda 0:13a5d365ba16 125 {
ykuroda 0:13a5d365ba16 126 compute(matrix);
ykuroda 0:13a5d365ba16 127 }
ykuroda 0:13a5d365ba16 128
ykuroda 0:13a5d365ba16 129 /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
ykuroda 0:13a5d365ba16 130 * \c *this is the QR decomposition.
ykuroda 0:13a5d365ba16 131 *
ykuroda 0:13a5d365ba16 132 * \param b the right-hand-side of the equation to solve.
ykuroda 0:13a5d365ba16 133 *
ykuroda 0:13a5d365ba16 134 * \returns the exact or least-square solution if the rank is greater or equal to the number of columns of A,
ykuroda 0:13a5d365ba16 135 * and an arbitrary solution otherwise.
ykuroda 0:13a5d365ba16 136 *
ykuroda 0:13a5d365ba16 137 * \note The case where b is a matrix is not yet implemented. Also, this
ykuroda 0:13a5d365ba16 138 * code is space inefficient.
ykuroda 0:13a5d365ba16 139 *
ykuroda 0:13a5d365ba16 140 * \note_about_checking_solutions
ykuroda 0:13a5d365ba16 141 *
ykuroda 0:13a5d365ba16 142 * \note_about_arbitrary_choice_of_solution
ykuroda 0:13a5d365ba16 143 *
ykuroda 0:13a5d365ba16 144 * Example: \include FullPivHouseholderQR_solve.cpp
ykuroda 0:13a5d365ba16 145 * Output: \verbinclude FullPivHouseholderQR_solve.out
ykuroda 0:13a5d365ba16 146 */
ykuroda 0:13a5d365ba16 147 template<typename Rhs>
ykuroda 0:13a5d365ba16 148 inline const internal::solve_retval<FullPivHouseholderQR, Rhs>
ykuroda 0:13a5d365ba16 149 solve(const MatrixBase<Rhs>& b) const
ykuroda 0:13a5d365ba16 150 {
ykuroda 0:13a5d365ba16 151 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 152 return internal::solve_retval<FullPivHouseholderQR, Rhs>(*this, b.derived());
ykuroda 0:13a5d365ba16 153 }
ykuroda 0:13a5d365ba16 154
ykuroda 0:13a5d365ba16 155 /** \returns Expression object representing the matrix Q
ykuroda 0:13a5d365ba16 156 */
ykuroda 0:13a5d365ba16 157 MatrixQReturnType matrixQ(void) const;
ykuroda 0:13a5d365ba16 158
ykuroda 0:13a5d365ba16 159 /** \returns a reference to the matrix where the Householder QR decomposition is stored
ykuroda 0:13a5d365ba16 160 */
ykuroda 0:13a5d365ba16 161 const MatrixType& matrixQR() const
ykuroda 0:13a5d365ba16 162 {
ykuroda 0:13a5d365ba16 163 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 164 return m_qr;
ykuroda 0:13a5d365ba16 165 }
ykuroda 0:13a5d365ba16 166
ykuroda 0:13a5d365ba16 167 FullPivHouseholderQR& compute(const MatrixType& matrix);
ykuroda 0:13a5d365ba16 168
ykuroda 0:13a5d365ba16 169 /** \returns a const reference to the column permutation matrix */
ykuroda 0:13a5d365ba16 170 const PermutationType& colsPermutation() const
ykuroda 0:13a5d365ba16 171 {
ykuroda 0:13a5d365ba16 172 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 173 return m_cols_permutation;
ykuroda 0:13a5d365ba16 174 }
ykuroda 0:13a5d365ba16 175
ykuroda 0:13a5d365ba16 176 /** \returns a const reference to the vector of indices representing the rows transpositions */
ykuroda 0:13a5d365ba16 177 const IntDiagSizeVectorType& rowsTranspositions() const
ykuroda 0:13a5d365ba16 178 {
ykuroda 0:13a5d365ba16 179 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 180 return m_rows_transpositions;
ykuroda 0:13a5d365ba16 181 }
ykuroda 0:13a5d365ba16 182
ykuroda 0:13a5d365ba16 183 /** \returns the absolute value of the determinant of the matrix of which
ykuroda 0:13a5d365ba16 184 * *this is the QR decomposition. It has only linear complexity
ykuroda 0:13a5d365ba16 185 * (that is, O(n) where n is the dimension of the square matrix)
ykuroda 0:13a5d365ba16 186 * as the QR decomposition has already been computed.
ykuroda 0:13a5d365ba16 187 *
ykuroda 0:13a5d365ba16 188 * \note This is only for square matrices.
ykuroda 0:13a5d365ba16 189 *
ykuroda 0:13a5d365ba16 190 * \warning a determinant can be very big or small, so for matrices
ykuroda 0:13a5d365ba16 191 * of large enough dimension, there is a risk of overflow/underflow.
ykuroda 0:13a5d365ba16 192 * One way to work around that is to use logAbsDeterminant() instead.
ykuroda 0:13a5d365ba16 193 *
ykuroda 0:13a5d365ba16 194 * \sa logAbsDeterminant(), MatrixBase::determinant()
ykuroda 0:13a5d365ba16 195 */
ykuroda 0:13a5d365ba16 196 typename MatrixType::RealScalar absDeterminant() const;
ykuroda 0:13a5d365ba16 197
ykuroda 0:13a5d365ba16 198 /** \returns the natural log of the absolute value of the determinant of the matrix of which
ykuroda 0:13a5d365ba16 199 * *this is the QR decomposition. It has only linear complexity
ykuroda 0:13a5d365ba16 200 * (that is, O(n) where n is the dimension of the square matrix)
ykuroda 0:13a5d365ba16 201 * as the QR decomposition has already been computed.
ykuroda 0:13a5d365ba16 202 *
ykuroda 0:13a5d365ba16 203 * \note This is only for square matrices.
ykuroda 0:13a5d365ba16 204 *
ykuroda 0:13a5d365ba16 205 * \note This method is useful to work around the risk of overflow/underflow that's inherent
ykuroda 0:13a5d365ba16 206 * to determinant computation.
ykuroda 0:13a5d365ba16 207 *
ykuroda 0:13a5d365ba16 208 * \sa absDeterminant(), MatrixBase::determinant()
ykuroda 0:13a5d365ba16 209 */
ykuroda 0:13a5d365ba16 210 typename MatrixType::RealScalar logAbsDeterminant() const;
ykuroda 0:13a5d365ba16 211
ykuroda 0:13a5d365ba16 212 /** \returns the rank of the matrix of which *this is the QR decomposition.
ykuroda 0:13a5d365ba16 213 *
ykuroda 0:13a5d365ba16 214 * \note This method has to determine which pivots should be considered nonzero.
ykuroda 0:13a5d365ba16 215 * For that, it uses the threshold value that you can control by calling
ykuroda 0:13a5d365ba16 216 * setThreshold(const RealScalar&).
ykuroda 0:13a5d365ba16 217 */
ykuroda 0:13a5d365ba16 218 inline Index rank() const
ykuroda 0:13a5d365ba16 219 {
ykuroda 0:13a5d365ba16 220 using std::abs;
ykuroda 0:13a5d365ba16 221 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 222 RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
ykuroda 0:13a5d365ba16 223 Index result = 0;
ykuroda 0:13a5d365ba16 224 for(Index i = 0; i < m_nonzero_pivots; ++i)
ykuroda 0:13a5d365ba16 225 result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);
ykuroda 0:13a5d365ba16 226 return result;
ykuroda 0:13a5d365ba16 227 }
ykuroda 0:13a5d365ba16 228
ykuroda 0:13a5d365ba16 229 /** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
ykuroda 0:13a5d365ba16 230 *
ykuroda 0:13a5d365ba16 231 * \note This method has to determine which pivots should be considered nonzero.
ykuroda 0:13a5d365ba16 232 * For that, it uses the threshold value that you can control by calling
ykuroda 0:13a5d365ba16 233 * setThreshold(const RealScalar&).
ykuroda 0:13a5d365ba16 234 */
ykuroda 0:13a5d365ba16 235 inline Index dimensionOfKernel() const
ykuroda 0:13a5d365ba16 236 {
ykuroda 0:13a5d365ba16 237 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 238 return cols() - rank();
ykuroda 0:13a5d365ba16 239 }
ykuroda 0:13a5d365ba16 240
ykuroda 0:13a5d365ba16 241 /** \returns true if the matrix of which *this is the QR decomposition represents an injective
ykuroda 0:13a5d365ba16 242 * linear map, i.e. has trivial kernel; false otherwise.
ykuroda 0:13a5d365ba16 243 *
ykuroda 0:13a5d365ba16 244 * \note This method has to determine which pivots should be considered nonzero.
ykuroda 0:13a5d365ba16 245 * For that, it uses the threshold value that you can control by calling
ykuroda 0:13a5d365ba16 246 * setThreshold(const RealScalar&).
ykuroda 0:13a5d365ba16 247 */
ykuroda 0:13a5d365ba16 248 inline bool isInjective() const
ykuroda 0:13a5d365ba16 249 {
ykuroda 0:13a5d365ba16 250 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 251 return rank() == cols();
ykuroda 0:13a5d365ba16 252 }
ykuroda 0:13a5d365ba16 253
ykuroda 0:13a5d365ba16 254 /** \returns true if the matrix of which *this is the QR decomposition represents a surjective
ykuroda 0:13a5d365ba16 255 * linear map; false otherwise.
ykuroda 0:13a5d365ba16 256 *
ykuroda 0:13a5d365ba16 257 * \note This method has to determine which pivots should be considered nonzero.
ykuroda 0:13a5d365ba16 258 * For that, it uses the threshold value that you can control by calling
ykuroda 0:13a5d365ba16 259 * setThreshold(const RealScalar&).
ykuroda 0:13a5d365ba16 260 */
ykuroda 0:13a5d365ba16 261 inline bool isSurjective() const
ykuroda 0:13a5d365ba16 262 {
ykuroda 0:13a5d365ba16 263 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 264 return rank() == rows();
ykuroda 0:13a5d365ba16 265 }
ykuroda 0:13a5d365ba16 266
ykuroda 0:13a5d365ba16 267 /** \returns true if the matrix of which *this is the QR decomposition is invertible.
ykuroda 0:13a5d365ba16 268 *
ykuroda 0:13a5d365ba16 269 * \note This method has to determine which pivots should be considered nonzero.
ykuroda 0:13a5d365ba16 270 * For that, it uses the threshold value that you can control by calling
ykuroda 0:13a5d365ba16 271 * setThreshold(const RealScalar&).
ykuroda 0:13a5d365ba16 272 */
ykuroda 0:13a5d365ba16 273 inline bool isInvertible() const
ykuroda 0:13a5d365ba16 274 {
ykuroda 0:13a5d365ba16 275 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 276 return isInjective() && isSurjective();
ykuroda 0:13a5d365ba16 277 }
ykuroda 0:13a5d365ba16 278
ykuroda 0:13a5d365ba16 279 /** \returns the inverse of the matrix of which *this is the QR decomposition.
ykuroda 0:13a5d365ba16 280 *
ykuroda 0:13a5d365ba16 281 * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
ykuroda 0:13a5d365ba16 282 * Use isInvertible() to first determine whether this matrix is invertible.
ykuroda 0:13a5d365ba16 283 */ inline const
ykuroda 0:13a5d365ba16 284 internal::solve_retval<FullPivHouseholderQR, typename MatrixType::IdentityReturnType>
ykuroda 0:13a5d365ba16 285 inverse() const
ykuroda 0:13a5d365ba16 286 {
ykuroda 0:13a5d365ba16 287 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 288 return internal::solve_retval<FullPivHouseholderQR,typename MatrixType::IdentityReturnType>
ykuroda 0:13a5d365ba16 289 (*this, MatrixType::Identity(m_qr.rows(), m_qr.cols()));
ykuroda 0:13a5d365ba16 290 }
ykuroda 0:13a5d365ba16 291
ykuroda 0:13a5d365ba16 292 inline Index rows() const { return m_qr.rows(); }
ykuroda 0:13a5d365ba16 293 inline Index cols() const { return m_qr.cols(); }
ykuroda 0:13a5d365ba16 294
ykuroda 0:13a5d365ba16 295 /** \returns a const reference to the vector of Householder coefficients used to represent the factor \c Q.
ykuroda 0:13a5d365ba16 296 *
ykuroda 0:13a5d365ba16 297 * For advanced uses only.
ykuroda 0:13a5d365ba16 298 */
ykuroda 0:13a5d365ba16 299 const HCoeffsType& hCoeffs() const { return m_hCoeffs; }
ykuroda 0:13a5d365ba16 300
ykuroda 0:13a5d365ba16 301 /** Allows to prescribe a threshold to be used by certain methods, such as rank(),
ykuroda 0:13a5d365ba16 302 * who need to determine when pivots are to be considered nonzero. This is not used for the
ykuroda 0:13a5d365ba16 303 * QR decomposition itself.
ykuroda 0:13a5d365ba16 304 *
ykuroda 0:13a5d365ba16 305 * When it needs to get the threshold value, Eigen calls threshold(). By default, this
ykuroda 0:13a5d365ba16 306 * uses a formula to automatically determine a reasonable threshold.
ykuroda 0:13a5d365ba16 307 * Once you have called the present method setThreshold(const RealScalar&),
ykuroda 0:13a5d365ba16 308 * your value is used instead.
ykuroda 0:13a5d365ba16 309 *
ykuroda 0:13a5d365ba16 310 * \param threshold The new value to use as the threshold.
ykuroda 0:13a5d365ba16 311 *
ykuroda 0:13a5d365ba16 312 * A pivot will be considered nonzero if its absolute value is strictly greater than
ykuroda 0:13a5d365ba16 313 * \f$ \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \f$
ykuroda 0:13a5d365ba16 314 * where maxpivot is the biggest pivot.
ykuroda 0:13a5d365ba16 315 *
ykuroda 0:13a5d365ba16 316 * If you want to come back to the default behavior, call setThreshold(Default_t)
ykuroda 0:13a5d365ba16 317 */
ykuroda 0:13a5d365ba16 318 FullPivHouseholderQR& setThreshold(const RealScalar& threshold)
ykuroda 0:13a5d365ba16 319 {
ykuroda 0:13a5d365ba16 320 m_usePrescribedThreshold = true;
ykuroda 0:13a5d365ba16 321 m_prescribedThreshold = threshold;
ykuroda 0:13a5d365ba16 322 return *this;
ykuroda 0:13a5d365ba16 323 }
ykuroda 0:13a5d365ba16 324
ykuroda 0:13a5d365ba16 325 /** Allows to come back to the default behavior, letting Eigen use its default formula for
ykuroda 0:13a5d365ba16 326 * determining the threshold.
ykuroda 0:13a5d365ba16 327 *
ykuroda 0:13a5d365ba16 328 * You should pass the special object Eigen::Default as parameter here.
ykuroda 0:13a5d365ba16 329 * \code qr.setThreshold(Eigen::Default); \endcode
ykuroda 0:13a5d365ba16 330 *
ykuroda 0:13a5d365ba16 331 * See the documentation of setThreshold(const RealScalar&).
ykuroda 0:13a5d365ba16 332 */
ykuroda 0:13a5d365ba16 333 FullPivHouseholderQR& setThreshold(Default_t)
ykuroda 0:13a5d365ba16 334 {
ykuroda 0:13a5d365ba16 335 m_usePrescribedThreshold = false;
ykuroda 0:13a5d365ba16 336 return *this;
ykuroda 0:13a5d365ba16 337 }
ykuroda 0:13a5d365ba16 338
ykuroda 0:13a5d365ba16 339 /** Returns the threshold that will be used by certain methods such as rank().
ykuroda 0:13a5d365ba16 340 *
ykuroda 0:13a5d365ba16 341 * See the documentation of setThreshold(const RealScalar&).
ykuroda 0:13a5d365ba16 342 */
ykuroda 0:13a5d365ba16 343 RealScalar threshold() const
ykuroda 0:13a5d365ba16 344 {
ykuroda 0:13a5d365ba16 345 eigen_assert(m_isInitialized || m_usePrescribedThreshold);
ykuroda 0:13a5d365ba16 346 return m_usePrescribedThreshold ? m_prescribedThreshold
ykuroda 0:13a5d365ba16 347 // this formula comes from experimenting (see "LU precision tuning" thread on the list)
ykuroda 0:13a5d365ba16 348 // and turns out to be identical to Higham's formula used already in LDLt.
ykuroda 0:13a5d365ba16 349 : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());
ykuroda 0:13a5d365ba16 350 }
ykuroda 0:13a5d365ba16 351
ykuroda 0:13a5d365ba16 352 /** \returns the number of nonzero pivots in the QR decomposition.
ykuroda 0:13a5d365ba16 353 * Here nonzero is meant in the exact sense, not in a fuzzy sense.
ykuroda 0:13a5d365ba16 354 * So that notion isn't really intrinsically interesting, but it is
ykuroda 0:13a5d365ba16 355 * still useful when implementing algorithms.
ykuroda 0:13a5d365ba16 356 *
ykuroda 0:13a5d365ba16 357 * \sa rank()
ykuroda 0:13a5d365ba16 358 */
ykuroda 0:13a5d365ba16 359 inline Index nonzeroPivots() const
ykuroda 0:13a5d365ba16 360 {
ykuroda 0:13a5d365ba16 361 eigen_assert(m_isInitialized && "LU is not initialized.");
ykuroda 0:13a5d365ba16 362 return m_nonzero_pivots;
ykuroda 0:13a5d365ba16 363 }
ykuroda 0:13a5d365ba16 364
ykuroda 0:13a5d365ba16 365 /** \returns the absolute value of the biggest pivot, i.e. the biggest
ykuroda 0:13a5d365ba16 366 * diagonal coefficient of U.
ykuroda 0:13a5d365ba16 367 */
ykuroda 0:13a5d365ba16 368 RealScalar maxPivot() const { return m_maxpivot; }
ykuroda 0:13a5d365ba16 369
ykuroda 0:13a5d365ba16 370 protected:
ykuroda 0:13a5d365ba16 371
ykuroda 0:13a5d365ba16 372 static void check_template_parameters()
ykuroda 0:13a5d365ba16 373 {
ykuroda 0:13a5d365ba16 374 EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
ykuroda 0:13a5d365ba16 375 }
ykuroda 0:13a5d365ba16 376
ykuroda 0:13a5d365ba16 377 MatrixType m_qr;
ykuroda 0:13a5d365ba16 378 HCoeffsType m_hCoeffs;
ykuroda 0:13a5d365ba16 379 IntDiagSizeVectorType m_rows_transpositions;
ykuroda 0:13a5d365ba16 380 IntDiagSizeVectorType m_cols_transpositions;
ykuroda 0:13a5d365ba16 381 PermutationType m_cols_permutation;
ykuroda 0:13a5d365ba16 382 RowVectorType m_temp;
ykuroda 0:13a5d365ba16 383 bool m_isInitialized, m_usePrescribedThreshold;
ykuroda 0:13a5d365ba16 384 RealScalar m_prescribedThreshold, m_maxpivot;
ykuroda 0:13a5d365ba16 385 Index m_nonzero_pivots;
ykuroda 0:13a5d365ba16 386 RealScalar m_precision;
ykuroda 0:13a5d365ba16 387 Index m_det_pq;
ykuroda 0:13a5d365ba16 388 };
ykuroda 0:13a5d365ba16 389
ykuroda 0:13a5d365ba16 390 template<typename MatrixType>
ykuroda 0:13a5d365ba16 391 typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::absDeterminant() const
ykuroda 0:13a5d365ba16 392 {
ykuroda 0:13a5d365ba16 393 using std::abs;
ykuroda 0:13a5d365ba16 394 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 395 eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
ykuroda 0:13a5d365ba16 396 return abs(m_qr.diagonal().prod());
ykuroda 0:13a5d365ba16 397 }
ykuroda 0:13a5d365ba16 398
ykuroda 0:13a5d365ba16 399 template<typename MatrixType>
ykuroda 0:13a5d365ba16 400 typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::logAbsDeterminant() const
ykuroda 0:13a5d365ba16 401 {
ykuroda 0:13a5d365ba16 402 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 403 eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
ykuroda 0:13a5d365ba16 404 return m_qr.diagonal().cwiseAbs().array().log().sum();
ykuroda 0:13a5d365ba16 405 }
ykuroda 0:13a5d365ba16 406
ykuroda 0:13a5d365ba16 407 /** Performs the QR factorization of the given matrix \a matrix. The result of
ykuroda 0:13a5d365ba16 408 * the factorization is stored into \c *this, and a reference to \c *this
ykuroda 0:13a5d365ba16 409 * is returned.
ykuroda 0:13a5d365ba16 410 *
ykuroda 0:13a5d365ba16 411 * \sa class FullPivHouseholderQR, FullPivHouseholderQR(const MatrixType&)
ykuroda 0:13a5d365ba16 412 */
ykuroda 0:13a5d365ba16 413 template<typename MatrixType>
ykuroda 0:13a5d365ba16 414 FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
ykuroda 0:13a5d365ba16 415 {
ykuroda 0:13a5d365ba16 416 check_template_parameters();
ykuroda 0:13a5d365ba16 417
ykuroda 0:13a5d365ba16 418 using std::abs;
ykuroda 0:13a5d365ba16 419 Index rows = matrix.rows();
ykuroda 0:13a5d365ba16 420 Index cols = matrix.cols();
ykuroda 0:13a5d365ba16 421 Index size = (std::min)(rows,cols);
ykuroda 0:13a5d365ba16 422
ykuroda 0:13a5d365ba16 423 m_qr = matrix;
ykuroda 0:13a5d365ba16 424 m_hCoeffs.resize(size);
ykuroda 0:13a5d365ba16 425
ykuroda 0:13a5d365ba16 426 m_temp.resize(cols);
ykuroda 0:13a5d365ba16 427
ykuroda 0:13a5d365ba16 428 m_precision = NumTraits<Scalar>::epsilon() * RealScalar(size);
ykuroda 0:13a5d365ba16 429
ykuroda 0:13a5d365ba16 430 m_rows_transpositions.resize(size);
ykuroda 0:13a5d365ba16 431 m_cols_transpositions.resize(size);
ykuroda 0:13a5d365ba16 432 Index number_of_transpositions = 0;
ykuroda 0:13a5d365ba16 433
ykuroda 0:13a5d365ba16 434 RealScalar biggest(0);
ykuroda 0:13a5d365ba16 435
ykuroda 0:13a5d365ba16 436 m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case)
ykuroda 0:13a5d365ba16 437 m_maxpivot = RealScalar(0);
ykuroda 0:13a5d365ba16 438
ykuroda 0:13a5d365ba16 439 for (Index k = 0; k < size; ++k)
ykuroda 0:13a5d365ba16 440 {
ykuroda 0:13a5d365ba16 441 Index row_of_biggest_in_corner, col_of_biggest_in_corner;
ykuroda 0:13a5d365ba16 442 RealScalar biggest_in_corner;
ykuroda 0:13a5d365ba16 443
ykuroda 0:13a5d365ba16 444 biggest_in_corner = m_qr.bottomRightCorner(rows-k, cols-k)
ykuroda 0:13a5d365ba16 445 .cwiseAbs()
ykuroda 0:13a5d365ba16 446 .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
ykuroda 0:13a5d365ba16 447 row_of_biggest_in_corner += k;
ykuroda 0:13a5d365ba16 448 col_of_biggest_in_corner += k;
ykuroda 0:13a5d365ba16 449 if(k==0) biggest = biggest_in_corner;
ykuroda 0:13a5d365ba16 450
ykuroda 0:13a5d365ba16 451 // if the corner is negligible, then we have less than full rank, and we can finish early
ykuroda 0:13a5d365ba16 452 if(internal::isMuchSmallerThan(biggest_in_corner, biggest, m_precision))
ykuroda 0:13a5d365ba16 453 {
ykuroda 0:13a5d365ba16 454 m_nonzero_pivots = k;
ykuroda 0:13a5d365ba16 455 for(Index i = k; i < size; i++)
ykuroda 0:13a5d365ba16 456 {
ykuroda 0:13a5d365ba16 457 m_rows_transpositions.coeffRef(i) = i;
ykuroda 0:13a5d365ba16 458 m_cols_transpositions.coeffRef(i) = i;
ykuroda 0:13a5d365ba16 459 m_hCoeffs.coeffRef(i) = Scalar(0);
ykuroda 0:13a5d365ba16 460 }
ykuroda 0:13a5d365ba16 461 break;
ykuroda 0:13a5d365ba16 462 }
ykuroda 0:13a5d365ba16 463
ykuroda 0:13a5d365ba16 464 m_rows_transpositions.coeffRef(k) = row_of_biggest_in_corner;
ykuroda 0:13a5d365ba16 465 m_cols_transpositions.coeffRef(k) = col_of_biggest_in_corner;
ykuroda 0:13a5d365ba16 466 if(k != row_of_biggest_in_corner) {
ykuroda 0:13a5d365ba16 467 m_qr.row(k).tail(cols-k).swap(m_qr.row(row_of_biggest_in_corner).tail(cols-k));
ykuroda 0:13a5d365ba16 468 ++number_of_transpositions;
ykuroda 0:13a5d365ba16 469 }
ykuroda 0:13a5d365ba16 470 if(k != col_of_biggest_in_corner) {
ykuroda 0:13a5d365ba16 471 m_qr.col(k).swap(m_qr.col(col_of_biggest_in_corner));
ykuroda 0:13a5d365ba16 472 ++number_of_transpositions;
ykuroda 0:13a5d365ba16 473 }
ykuroda 0:13a5d365ba16 474
ykuroda 0:13a5d365ba16 475 RealScalar beta;
ykuroda 0:13a5d365ba16 476 m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
ykuroda 0:13a5d365ba16 477 m_qr.coeffRef(k,k) = beta;
ykuroda 0:13a5d365ba16 478
ykuroda 0:13a5d365ba16 479 // remember the maximum absolute value of diagonal coefficients
ykuroda 0:13a5d365ba16 480 if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
ykuroda 0:13a5d365ba16 481
ykuroda 0:13a5d365ba16 482 m_qr.bottomRightCorner(rows-k, cols-k-1)
ykuroda 0:13a5d365ba16 483 .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
ykuroda 0:13a5d365ba16 484 }
ykuroda 0:13a5d365ba16 485
ykuroda 0:13a5d365ba16 486 m_cols_permutation.setIdentity(cols);
ykuroda 0:13a5d365ba16 487 for(Index k = 0; k < size; ++k)
ykuroda 0:13a5d365ba16 488 m_cols_permutation.applyTranspositionOnTheRight(k, m_cols_transpositions.coeff(k));
ykuroda 0:13a5d365ba16 489
ykuroda 0:13a5d365ba16 490 m_det_pq = (number_of_transpositions%2) ? -1 : 1;
ykuroda 0:13a5d365ba16 491 m_isInitialized = true;
ykuroda 0:13a5d365ba16 492
ykuroda 0:13a5d365ba16 493 return *this;
ykuroda 0:13a5d365ba16 494 }
ykuroda 0:13a5d365ba16 495
ykuroda 0:13a5d365ba16 496 namespace internal {
ykuroda 0:13a5d365ba16 497
ykuroda 0:13a5d365ba16 498 template<typename _MatrixType, typename Rhs>
ykuroda 0:13a5d365ba16 499 struct solve_retval<FullPivHouseholderQR<_MatrixType>, Rhs>
ykuroda 0:13a5d365ba16 500 : solve_retval_base<FullPivHouseholderQR<_MatrixType>, Rhs>
ykuroda 0:13a5d365ba16 501 {
ykuroda 0:13a5d365ba16 502 EIGEN_MAKE_SOLVE_HELPERS(FullPivHouseholderQR<_MatrixType>,Rhs)
ykuroda 0:13a5d365ba16 503
ykuroda 0:13a5d365ba16 504 template<typename Dest> void evalTo(Dest& dst) const
ykuroda 0:13a5d365ba16 505 {
ykuroda 0:13a5d365ba16 506 const Index rows = dec().rows(), cols = dec().cols();
ykuroda 0:13a5d365ba16 507 eigen_assert(rhs().rows() == rows);
ykuroda 0:13a5d365ba16 508
ykuroda 0:13a5d365ba16 509 // FIXME introduce nonzeroPivots() and use it here. and more generally,
ykuroda 0:13a5d365ba16 510 // make the same improvements in this dec as in FullPivLU.
ykuroda 0:13a5d365ba16 511 if(dec().rank()==0)
ykuroda 0:13a5d365ba16 512 {
ykuroda 0:13a5d365ba16 513 dst.setZero();
ykuroda 0:13a5d365ba16 514 return;
ykuroda 0:13a5d365ba16 515 }
ykuroda 0:13a5d365ba16 516
ykuroda 0:13a5d365ba16 517 typename Rhs::PlainObject c(rhs());
ykuroda 0:13a5d365ba16 518
ykuroda 0:13a5d365ba16 519 Matrix<Scalar,1,Rhs::ColsAtCompileTime> temp(rhs().cols());
ykuroda 0:13a5d365ba16 520 for (Index k = 0; k < dec().rank(); ++k)
ykuroda 0:13a5d365ba16 521 {
ykuroda 0:13a5d365ba16 522 Index remainingSize = rows-k;
ykuroda 0:13a5d365ba16 523 c.row(k).swap(c.row(dec().rowsTranspositions().coeff(k)));
ykuroda 0:13a5d365ba16 524 c.bottomRightCorner(remainingSize, rhs().cols())
ykuroda 0:13a5d365ba16 525 .applyHouseholderOnTheLeft(dec().matrixQR().col(k).tail(remainingSize-1),
ykuroda 0:13a5d365ba16 526 dec().hCoeffs().coeff(k), &temp.coeffRef(0));
ykuroda 0:13a5d365ba16 527 }
ykuroda 0:13a5d365ba16 528
ykuroda 0:13a5d365ba16 529 dec().matrixQR()
ykuroda 0:13a5d365ba16 530 .topLeftCorner(dec().rank(), dec().rank())
ykuroda 0:13a5d365ba16 531 .template triangularView<Upper>()
ykuroda 0:13a5d365ba16 532 .solveInPlace(c.topRows(dec().rank()));
ykuroda 0:13a5d365ba16 533
ykuroda 0:13a5d365ba16 534 for(Index i = 0; i < dec().rank(); ++i) dst.row(dec().colsPermutation().indices().coeff(i)) = c.row(i);
ykuroda 0:13a5d365ba16 535 for(Index i = dec().rank(); i < cols; ++i) dst.row(dec().colsPermutation().indices().coeff(i)).setZero();
ykuroda 0:13a5d365ba16 536 }
ykuroda 0:13a5d365ba16 537 };
ykuroda 0:13a5d365ba16 538
ykuroda 0:13a5d365ba16 539 /** \ingroup QR_Module
ykuroda 0:13a5d365ba16 540 *
ykuroda 0:13a5d365ba16 541 * \brief Expression type for return value of FullPivHouseholderQR::matrixQ()
ykuroda 0:13a5d365ba16 542 *
ykuroda 0:13a5d365ba16 543 * \tparam MatrixType type of underlying dense matrix
ykuroda 0:13a5d365ba16 544 */
ykuroda 0:13a5d365ba16 545 template<typename MatrixType> struct FullPivHouseholderQRMatrixQReturnType
ykuroda 0:13a5d365ba16 546 : public ReturnByValue<FullPivHouseholderQRMatrixQReturnType<MatrixType> >
ykuroda 0:13a5d365ba16 547 {
ykuroda 0:13a5d365ba16 548 public:
ykuroda 0:13a5d365ba16 549 typedef typename MatrixType::Index Index;
ykuroda 0:13a5d365ba16 550 typedef typename FullPivHouseholderQR<MatrixType>::IntDiagSizeVectorType IntDiagSizeVectorType;
ykuroda 0:13a5d365ba16 551 typedef typename internal::plain_diag_type<MatrixType>::type HCoeffsType;
ykuroda 0:13a5d365ba16 552 typedef Matrix<typename MatrixType::Scalar, 1, MatrixType::RowsAtCompileTime, RowMajor, 1,
ykuroda 0:13a5d365ba16 553 MatrixType::MaxRowsAtCompileTime> WorkVectorType;
ykuroda 0:13a5d365ba16 554
ykuroda 0:13a5d365ba16 555 FullPivHouseholderQRMatrixQReturnType(const MatrixType& qr,
ykuroda 0:13a5d365ba16 556 const HCoeffsType& hCoeffs,
ykuroda 0:13a5d365ba16 557 const IntDiagSizeVectorType& rowsTranspositions)
ykuroda 0:13a5d365ba16 558 : m_qr(qr),
ykuroda 0:13a5d365ba16 559 m_hCoeffs(hCoeffs),
ykuroda 0:13a5d365ba16 560 m_rowsTranspositions(rowsTranspositions)
ykuroda 0:13a5d365ba16 561 {}
ykuroda 0:13a5d365ba16 562
ykuroda 0:13a5d365ba16 563 template <typename ResultType>
ykuroda 0:13a5d365ba16 564 void evalTo(ResultType& result) const
ykuroda 0:13a5d365ba16 565 {
ykuroda 0:13a5d365ba16 566 const Index rows = m_qr.rows();
ykuroda 0:13a5d365ba16 567 WorkVectorType workspace(rows);
ykuroda 0:13a5d365ba16 568 evalTo(result, workspace);
ykuroda 0:13a5d365ba16 569 }
ykuroda 0:13a5d365ba16 570
ykuroda 0:13a5d365ba16 571 template <typename ResultType>
ykuroda 0:13a5d365ba16 572 void evalTo(ResultType& result, WorkVectorType& workspace) const
ykuroda 0:13a5d365ba16 573 {
ykuroda 0:13a5d365ba16 574 using numext::conj;
ykuroda 0:13a5d365ba16 575 // compute the product H'_0 H'_1 ... H'_n-1,
ykuroda 0:13a5d365ba16 576 // where H_k is the k-th Householder transformation I - h_k v_k v_k'
ykuroda 0:13a5d365ba16 577 // and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
ykuroda 0:13a5d365ba16 578 const Index rows = m_qr.rows();
ykuroda 0:13a5d365ba16 579 const Index cols = m_qr.cols();
ykuroda 0:13a5d365ba16 580 const Index size = (std::min)(rows, cols);
ykuroda 0:13a5d365ba16 581 workspace.resize(rows);
ykuroda 0:13a5d365ba16 582 result.setIdentity(rows, rows);
ykuroda 0:13a5d365ba16 583 for (Index k = size-1; k >= 0; k--)
ykuroda 0:13a5d365ba16 584 {
ykuroda 0:13a5d365ba16 585 result.block(k, k, rows-k, rows-k)
ykuroda 0:13a5d365ba16 586 .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), conj(m_hCoeffs.coeff(k)), &workspace.coeffRef(k));
ykuroda 0:13a5d365ba16 587 result.row(k).swap(result.row(m_rowsTranspositions.coeff(k)));
ykuroda 0:13a5d365ba16 588 }
ykuroda 0:13a5d365ba16 589 }
ykuroda 0:13a5d365ba16 590
ykuroda 0:13a5d365ba16 591 Index rows() const { return m_qr.rows(); }
ykuroda 0:13a5d365ba16 592 Index cols() const { return m_qr.rows(); }
ykuroda 0:13a5d365ba16 593
ykuroda 0:13a5d365ba16 594 protected:
ykuroda 0:13a5d365ba16 595 typename MatrixType::Nested m_qr;
ykuroda 0:13a5d365ba16 596 typename HCoeffsType::Nested m_hCoeffs;
ykuroda 0:13a5d365ba16 597 typename IntDiagSizeVectorType::Nested m_rowsTranspositions;
ykuroda 0:13a5d365ba16 598 };
ykuroda 0:13a5d365ba16 599
ykuroda 0:13a5d365ba16 600 } // end namespace internal
ykuroda 0:13a5d365ba16 601
ykuroda 0:13a5d365ba16 602 template<typename MatrixType>
ykuroda 0:13a5d365ba16 603 inline typename FullPivHouseholderQR<MatrixType>::MatrixQReturnType FullPivHouseholderQR<MatrixType>::matrixQ() const
ykuroda 0:13a5d365ba16 604 {
ykuroda 0:13a5d365ba16 605 eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
ykuroda 0:13a5d365ba16 606 return MatrixQReturnType(m_qr, m_hCoeffs, m_rows_transpositions);
ykuroda 0:13a5d365ba16 607 }
ykuroda 0:13a5d365ba16 608
ykuroda 0:13a5d365ba16 609 /** \return the full-pivoting Householder QR decomposition of \c *this.
ykuroda 0:13a5d365ba16 610 *
ykuroda 0:13a5d365ba16 611 * \sa class FullPivHouseholderQR
ykuroda 0:13a5d365ba16 612 */
ykuroda 0:13a5d365ba16 613 template<typename Derived>
ykuroda 0:13a5d365ba16 614 const FullPivHouseholderQR<typename MatrixBase<Derived>::PlainObject>
ykuroda 0:13a5d365ba16 615 MatrixBase<Derived>::fullPivHouseholderQr() const
ykuroda 0:13a5d365ba16 616 {
ykuroda 0:13a5d365ba16 617 return FullPivHouseholderQR<PlainObject>(eval());
ykuroda 0:13a5d365ba16 618 }
ykuroda 0:13a5d365ba16 619
ykuroda 0:13a5d365ba16 620 } // end namespace Eigen
ykuroda 0:13a5d365ba16 621
ykuroda 0:13a5d365ba16 622 #endif // EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H