BlockHouseholder.h
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2010 Vincent Lejeune
5 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10 
11 #ifndef EIGEN_BLOCK_HOUSEHOLDER_H
12 #define EIGEN_BLOCK_HOUSEHOLDER_H
13 
14 // This file contains some helper function to deal with block householder reflectors
15 
16 namespace Eigen {
17 
18 namespace internal {
19 
21 // template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
22 // void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
23 // {
24 // typedef typename VectorsType::Scalar Scalar;
25 // const Index nbVecs = vectors.cols();
26 // eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);
27 //
28 // for(Index i = 0; i < nbVecs; i++)
29 // {
30 // Index rs = vectors.rows() - i;
31 // // Warning, note that hCoeffs may alias with vectors.
32 // // It is then necessary to copy it before modifying vectors(i,i).
33 // typename CoeffsType::Scalar h = hCoeffs(i);
34 // // This hack permits to pass trough nested Block<> and Transpose<> expressions.
35 // Scalar *Vii_ptr = const_cast<Scalar*>(vectors.data() + vectors.outerStride()*i + vectors.innerStride()*i);
36 // Scalar Vii = *Vii_ptr;
37 // *Vii_ptr = Scalar(1);
38 // triFactor.col(i).head(i).noalias() = -h * vectors.block(i, 0, rs, i).adjoint()
39 // * vectors.col(i).tail(rs);
40 // *Vii_ptr = Vii;
41 // // FIXME add .noalias() once the triangular product can work inplace
42 // triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView<Upper>()
43 // * triFactor.col(i).head(i);
44 // triFactor(i,i) = hCoeffs(i);
45 // }
46 // }
47 
49 // This variant avoid modifications in vectors
50 template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
51 void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
52 {
53  const Index nbVecs = vectors.cols();
54  eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);
55 
56  for(Index i = nbVecs-1; i >=0 ; --i)
57  {
58  Index rs = vectors.rows() - i - 1;
59  Index rt = nbVecs-i-1;
60 
61  if(rt>0)
62  {
63  triFactor.row(i).tail(rt).noalias() = -hCoeffs(i) * vectors.col(i).tail(rs).adjoint()
64  * vectors.bottomRightCorner(rs, rt).template triangularView<UnitLower>();
65 
66  // FIXME use the following line with .noalias() once the triangular product can work inplace
67  // triFactor.row(i).tail(rt) = triFactor.row(i).tail(rt) * triFactor.bottomRightCorner(rt,rt).template triangularView<Upper>();
68  for(Index j=nbVecs-1; j>i; --j)
69  {
70  typename TriangularFactorType::Scalar z = triFactor(i,j);
71  triFactor(i,j) = z * triFactor(j,j);
72  if(nbVecs-j-1>0)
73  triFactor.row(i).tail(nbVecs-j-1) += z * triFactor.row(j).tail(nbVecs-j-1);
74  }
75 
76  }
77  triFactor(i,i) = hCoeffs(i);
78  }
79 }
80 
85 template<typename MatrixType,typename VectorsType,typename CoeffsType>
86 void apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vectors, const CoeffsType& hCoeffs, bool forward)
87 {
88  enum { TFactorSize = MatrixType::ColsAtCompileTime };
89  Index nbVecs = vectors.cols();
91 
92  if(forward) make_block_householder_triangular_factor(T, vectors, hCoeffs);
93  else make_block_householder_triangular_factor(T, vectors, hCoeffs.conjugate());
95 
96  // A -= V T V^* A
97  Matrix<typename MatrixType::Scalar,VectorsType::ColsAtCompileTime,MatrixType::ColsAtCompileTime,
98  (VectorsType::MaxColsAtCompileTime==1 && MatrixType::MaxColsAtCompileTime!=1)?RowMajor:ColMajor,
99  VectorsType::MaxColsAtCompileTime,MatrixType::MaxColsAtCompileTime> tmp = V.adjoint() * mat;
100  // FIXME add .noalias() once the triangular product can work inplace
101  if(forward) tmp = T.template triangularView<Upper>() * tmp;
102  else tmp = T.template triangularView<Upper>().adjoint() * tmp;
103  mat.noalias() -= V * tmp;
104 }
105 
106 } // end namespace internal
107 
108 } // end namespace Eigen
109 
110 #endif // EIGEN_BLOCK_HOUSEHOLDER_H
SCALAR Scalar
Definition: bench_gemm.cpp:46
void adjoint(const MatrixType &m)
Definition: adjoint.cpp:67
void apply_block_householder_on_the_left(MatrixType &mat, const VectorsType &vectors, const CoeffsType &hCoeffs, bool forward)
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
MatrixXf MatrixType
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
#define eigen_assert(x)
Definition: Macros.h:1037
Eigen::Triplet< double > T
Expression of a triangular part in a matrix.
The matrix class, also used for vectors and row-vectors.
void make_block_householder_triangular_factor(TriangularFactorType &triFactor, const VectorsType &vectors, const CoeffsType &hCoeffs)
std::ptrdiff_t j


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autogenerated on Tue Jul 4 2023 02:33:59