| User | Revision | Line number | New contents of line |
|---|
| 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 |