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 <[email protected]>
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
20 /** \internal */
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
48 /** \internal */
49 // This variant avoid modifications in vectors
50 template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
make_block_householder_triangular_factor(TriangularFactorType & triFactor,const VectorsType & vectors,const CoeffsType & hCoeffs)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
81 /** \internal
82 * if forward then perform mat = H0 * H1 * H2 * mat
83 * otherwise perform mat = H2 * H1 * H0 * mat
84 */
85 template<typename MatrixType,typename VectorsType,typename CoeffsType>
apply_block_householder_on_the_left(MatrixType & mat,const VectorsType & vectors,const CoeffsType & hCoeffs,bool forward)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();
90 Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, RowMajor> T(nbVecs,nbVecs);
91
92 if(forward) make_block_householder_triangular_factor(T, vectors, hCoeffs);
93 else make_block_householder_triangular_factor(T, vectors, hCoeffs.conjugate());
94 const TriangularView<const VectorsType, UnitLower> V(vectors);
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
111