1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_HOUSEHOLDER_SEQUENCE_H
#define EIGEN_HOUSEHOLDER_SEQUENCE_H
/** \ingroup Householder_Module
* \householder_module
* \class HouseholderSequence
* \brief Represents a sequence of householder reflections with decreasing size
*
* This class represents a product sequence of householder reflections \f$ H = \Pi_0^{n-1} H_i \f$
* where \f$ H_i \f$ is the i-th householder transformation \f$ I - h_i v_i v_i^* \f$,
* \f$ v_i \f$ is the i-th householder vector \f$ [ 1, m_vectors(i+1,i), m_vectors(i+2,i), ...] \f$
* and \f$ h_i \f$ is the i-th householder coefficient \c m_coeffs[i].
*
* Typical usages are listed below, where H is a HouseholderSequence:
* \code
* A.applyOnTheRight(H); // A = A * H
* A.applyOnTheLeft(H); // A = H * A
* A.applyOnTheRight(H.adjoint()); // A = A * H^*
* A.applyOnTheLeft(H.adjoint()); // A = H^* * A
* MatrixXd Q = H; // conversion to a dense matrix
* \endcode
* In addition to the adjoint, you can also apply the inverse (=adjoint), the transpose, and the conjugate.
*
* \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
*/
namespace internal {
template<typename VectorsType, typename CoeffsType, int Side>
struct traits<HouseholderSequence<VectorsType,CoeffsType,Side> >
{
typedef typename VectorsType::Scalar Scalar;
typedef typename VectorsType::Index Index;
typedef typename VectorsType::StorageKind StorageKind;
enum {
RowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::RowsAtCompileTime
: traits<VectorsType>::ColsAtCompileTime,
ColsAtCompileTime = RowsAtCompileTime,
MaxRowsAtCompileTime = Side==OnTheLeft ? traits<VectorsType>::MaxRowsAtCompileTime
: traits<VectorsType>::MaxColsAtCompileTime,
MaxColsAtCompileTime = MaxRowsAtCompileTime,
Flags = 0
};
};
template<typename VectorsType, typename CoeffsType, int Side>
struct hseq_side_dependent_impl
{
typedef Block<VectorsType, Dynamic, 1> EssentialVectorType;
typedef HouseholderSequence<VectorsType, CoeffsType, OnTheLeft> HouseholderSequenceType;
typedef typename VectorsType::Index Index;
static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)
{
Index start = k+1+h.m_shift;
return Block<VectorsType,Dynamic,1>(h.m_vectors, start, k, h.rows()-start, 1);
}
};
template<typename VectorsType, typename CoeffsType>
struct hseq_side_dependent_impl<VectorsType, CoeffsType, OnTheRight>
{
typedef Transpose<Block<VectorsType, 1, Dynamic> > EssentialVectorType;
typedef HouseholderSequence<VectorsType, CoeffsType, OnTheRight> HouseholderSequenceType;
typedef typename VectorsType::Index Index;
static inline const EssentialVectorType essentialVector(const HouseholderSequenceType& h, Index k)
{
Index start = k+1+h.m_shift;
return Block<VectorsType,1,Dynamic>(h.m_vectors, k, start, 1, h.rows()-start).transpose();
}
};
template<typename OtherScalarType, typename MatrixType> struct matrix_type_times_scalar_type
{
typedef typename scalar_product_traits<OtherScalarType, typename MatrixType::Scalar>::ReturnType
ResultScalar;
typedef Matrix<ResultScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
0, MatrixType::MaxRowsAtCompileTime, MatrixType::MaxColsAtCompileTime> Type;
};
} // end namespace internal
template<typename VectorsType, typename CoeffsType, int Side> class HouseholderSequence
: public EigenBase<HouseholderSequence<VectorsType,CoeffsType,Side> >
{
enum {
RowsAtCompileTime = internal::traits<HouseholderSequence>::RowsAtCompileTime,
ColsAtCompileTime = internal::traits<HouseholderSequence>::ColsAtCompileTime,
MaxRowsAtCompileTime = internal::traits<HouseholderSequence>::MaxRowsAtCompileTime,
MaxColsAtCompileTime = internal::traits<HouseholderSequence>::MaxColsAtCompileTime
};
typedef typename internal::traits<HouseholderSequence>::Scalar Scalar;
typedef typename VectorsType::Index Index;
typedef typename internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::EssentialVectorType
EssentialVectorType;
public:
typedef HouseholderSequence<
VectorsType,
typename internal::meta_if<NumTraits<Scalar>::IsComplex,
typename internal::cleantype<typename CoeffsType::ConjugateReturnType>::type,
CoeffsType>::ret,
Side
> ConjugateReturnType;
HouseholderSequence(const VectorsType& v, const CoeffsType& h, bool trans = false)
: m_vectors(v), m_coeffs(h), m_trans(trans), m_actualVectors(v.diagonalSize()),
m_shift(0)
{
}
HouseholderSequence(const VectorsType& v, const CoeffsType& h, bool trans, Index actualVectors, Index shift)
: m_vectors(v), m_coeffs(h), m_trans(trans), m_actualVectors(actualVectors), m_shift(shift)
{
}
Index rows() const { return Side==OnTheLeft ? m_vectors.rows() : m_vectors.cols(); }
Index cols() const { return rows(); }
const EssentialVectorType essentialVector(Index k) const
{
eigen_assert(k >= 0 && k < m_actualVectors);
return internal::hseq_side_dependent_impl<VectorsType,CoeffsType,Side>::essentialVector(*this, k);
}
HouseholderSequence transpose() const
{ return HouseholderSequence(m_vectors, m_coeffs, !m_trans, m_actualVectors, m_shift); }
ConjugateReturnType conjugate() const
{ return ConjugateReturnType(m_vectors, m_coeffs.conjugate(), m_trans, m_actualVectors, m_shift); }
ConjugateReturnType adjoint() const
{ return ConjugateReturnType(m_vectors, m_coeffs.conjugate(), !m_trans, m_actualVectors, m_shift); }
ConjugateReturnType inverse() const { return adjoint(); }
/** \internal */
template<typename DestType> void evalTo(DestType& dst) const
{
Index vecs = m_actualVectors;
// FIXME find a way to pass this temporary if the user want to
Matrix<Scalar, DestType::RowsAtCompileTime, 1,
AutoAlign|ColMajor, DestType::MaxRowsAtCompileTime, 1> temp(rows());
if( internal::is_same_type<typename internal::cleantype<VectorsType>::type,DestType>::ret
&& internal::extract_data(dst) == internal::extract_data(m_vectors))
{
// in-place
dst.diagonal().setOnes();
dst.template triangularView<StrictlyUpper>().setZero();
for(Index k = vecs-1; k >= 0; --k)
{
Index cornerSize = rows() - k - m_shift;
if(m_trans)
dst.bottomRightCorner(cornerSize, cornerSize)
.applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
else
dst.bottomRightCorner(cornerSize, cornerSize)
.applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
// clear the off diagonal vector
dst.col(k).tail(rows()-k-1).setZero();
}
// clear the remaining columns if needed
for(Index k = 0; k<cols()-vecs ; ++k)
dst.col(k).tail(rows()-k-1).setZero();
}
else
{
dst.setIdentity(rows(), rows());
for(Index k = vecs-1; k >= 0; --k)
{
Index cornerSize = rows() - k - m_shift;
if(m_trans)
dst.bottomRightCorner(cornerSize, cornerSize)
.applyHouseholderOnTheRight(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
else
dst.bottomRightCorner(cornerSize, cornerSize)
.applyHouseholderOnTheLeft(essentialVector(k), m_coeffs.coeff(k), &temp.coeffRef(0));
}
}
}
/** \internal */
template<typename Dest> inline void applyThisOnTheRight(Dest& dst) const
{
Matrix<Scalar,1,Dest::RowsAtCompileTime> temp(dst.rows());
for(Index k = 0; k < m_actualVectors; ++k)
{
Index actual_k = m_trans ? m_actualVectors-k-1 : k;
dst.rightCols(rows()-m_shift-actual_k)
.applyHouseholderOnTheRight(essentialVector(actual_k), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
}
}
/** \internal */
template<typename Dest> inline void applyThisOnTheLeft(Dest& dst) const
{
Matrix<Scalar,1,Dest::ColsAtCompileTime> temp(dst.cols());
for(Index k = 0; k < m_actualVectors; ++k)
{
Index actual_k = m_trans ? k : m_actualVectors-k-1;
dst.bottomRows(rows()-m_shift-actual_k)
.applyHouseholderOnTheLeft(essentialVector(actual_k), m_coeffs.coeff(actual_k), &temp.coeffRef(0));
}
}
template<typename OtherDerived>
typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other) const
{
typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type
res(other.template cast<typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::ResultScalar>());
applyThisOnTheLeft(res);
return res;
}
template<typename OtherDerived> friend
typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type operator*(const MatrixBase<OtherDerived>& other, const HouseholderSequence& h)
{
typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::Type
res(other.template cast<typename internal::matrix_type_times_scalar_type<Scalar, OtherDerived>::ResultScalar>());
h.applyThisOnTheRight(res);
return res;
}
template<typename _VectorsType, typename _CoeffsType, int _Side> friend struct internal::hseq_side_dependent_impl;
protected:
typename VectorsType::Nested m_vectors;
typename CoeffsType::Nested m_coeffs;
bool m_trans;
Index m_actualVectors;
Index m_shift;
};
template<typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType,CoeffsType> householderSequence(const VectorsType& v, const CoeffsType& h, bool trans=false)
{
return HouseholderSequence<VectorsType,CoeffsType,OnTheLeft>(v, h, trans);
}
template<typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType,CoeffsType> householderSequence
(const VectorsType& v, const CoeffsType& h,
bool trans, typename VectorsType::Index actualVectors, typename VectorsType::Index shift)
{
return HouseholderSequence<VectorsType,CoeffsType,OnTheLeft>(v, h, trans, actualVectors, shift);
}
template<typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType,CoeffsType> rightHouseholderSequence(const VectorsType& v, const CoeffsType& h, bool trans=false)
{
return HouseholderSequence<VectorsType,CoeffsType,OnTheRight>(v, h, trans);
}
template<typename VectorsType, typename CoeffsType>
HouseholderSequence<VectorsType,CoeffsType> rightHouseholderSequence
(const VectorsType& v, const CoeffsType& h, bool trans,
typename VectorsType::Index actualVectors, typename VectorsType::Index shift)
{
return HouseholderSequence<VectorsType,CoeffsType,OnTheRight>(v, h, trans, actualVectors, shift);
}
#endif // EIGEN_HOUSEHOLDER_SEQUENCE_H
|
