| // This file is part of Eigen, a lightweight C++ template library | |
| // for linear algebra. | |
| // | |
| // Copyright (C) 2010 Vincent Lejeune | |
| // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr> | |
| // | |
| // This Source Code Form is subject to the terms of the Mozilla | |
| // Public License v. 2.0. If a copy of the MPL was not distributed | |
| // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. | |
| // This file contains some helper function to deal with block householder reflectors | |
| namespace Eigen { | |
| namespace internal { | |
| /** \internal */ | |
| // template<typename TriangularFactorType,typename VectorsType,typename CoeffsType> | |
| // void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs) | |
| // { | |
| // typedef typename VectorsType::Scalar Scalar; | |
| // const Index nbVecs = vectors.cols(); | |
| // eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs); | |
| // | |
| // for(Index i = 0; i < nbVecs; i++) | |
| // { | |
| // Index rs = vectors.rows() - i; | |
| // // Warning, note that hCoeffs may alias with vectors. | |
| // // It is then necessary to copy it before modifying vectors(i,i). | |
| // typename CoeffsType::Scalar h = hCoeffs(i); | |
| // // This hack permits to pass trough nested Block<> and Transpose<> expressions. | |
| // Scalar *Vii_ptr = const_cast<Scalar*>(vectors.data() + vectors.outerStride()*i + vectors.innerStride()*i); | |
| // Scalar Vii = *Vii_ptr; | |
| // *Vii_ptr = Scalar(1); | |
| // triFactor.col(i).head(i).noalias() = -h * vectors.block(i, 0, rs, i).adjoint() | |
| // * vectors.col(i).tail(rs); | |
| // *Vii_ptr = Vii; | |
| // // FIXME add .noalias() once the triangular product can work inplace | |
| // triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView<Upper>() | |
| // * triFactor.col(i).head(i); | |
| // triFactor(i,i) = hCoeffs(i); | |
| // } | |
| // } | |
| /** \internal */ | |
| // This variant avoid modifications in vectors | |
| template<typename TriangularFactorType,typename VectorsType,typename CoeffsType> | |
| void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs) | |
| { | |
| const Index nbVecs = vectors.cols(); | |
| eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs); | |
| for(Index i = nbVecs-1; i >=0 ; --i) | |
| { | |
| Index rs = vectors.rows() - i - 1; | |
| Index rt = nbVecs-i-1; | |
| if(rt>0) | |
| { | |
| triFactor.row(i).tail(rt).noalias() = -hCoeffs(i) * vectors.col(i).tail(rs).adjoint() | |
| * vectors.bottomRightCorner(rs, rt).template triangularView<UnitLower>(); | |
| // FIXME use the following line with .noalias() once the triangular product can work inplace | |
| // triFactor.row(i).tail(rt) = triFactor.row(i).tail(rt) * triFactor.bottomRightCorner(rt,rt).template triangularView<Upper>(); | |
| for(Index j=nbVecs-1; j>i; --j) | |
| { | |
| typename TriangularFactorType::Scalar z = triFactor(i,j); | |
| triFactor(i,j) = z * triFactor(j,j); | |
| if(nbVecs-j-1>0) | |
| triFactor.row(i).tail(nbVecs-j-1) += z * triFactor.row(j).tail(nbVecs-j-1); | |
| } | |
| } | |
| triFactor(i,i) = hCoeffs(i); | |
| } | |
| } | |
| /** \internal | |
| * if forward then perform mat = H0 * H1 * H2 * mat | |
| * otherwise perform mat = H2 * H1 * H0 * mat | |
| */ | |
| template<typename MatrixType,typename VectorsType,typename CoeffsType> | |
| void apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vectors, const CoeffsType& hCoeffs, bool forward) | |
| { | |
| enum { TFactorSize = MatrixType::ColsAtCompileTime }; | |
| Index nbVecs = vectors.cols(); | |
| Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, RowMajor> T(nbVecs,nbVecs); | |
| if(forward) make_block_householder_triangular_factor(T, vectors, hCoeffs); | |
| else make_block_householder_triangular_factor(T, vectors, hCoeffs.conjugate()); | |
| const TriangularView<const VectorsType, UnitLower> V(vectors); | |
| // A -= V T V^* A | |
| Matrix<typename MatrixType::Scalar,VectorsType::ColsAtCompileTime,MatrixType::ColsAtCompileTime, | |
| (VectorsType::MaxColsAtCompileTime==1 && MatrixType::MaxColsAtCompileTime!=1)?RowMajor:ColMajor, | |
| VectorsType::MaxColsAtCompileTime,MatrixType::MaxColsAtCompileTime> tmp = V.adjoint() * mat; | |
| // FIXME add .noalias() once the triangular product can work inplace | |
| if(forward) tmp = T.template triangularView<Upper>() * tmp; | |
| else tmp = T.template triangularView<Upper>().adjoint() * tmp; | |
| mat.noalias() -= V * tmp; | |
| } | |
| } // end namespace internal | |
| } // end namespace Eigen | |