BlockHouseholder.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2010 Vincent Lejeune
00005 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
00006 //
00007 // This Source Code Form is subject to the terms of the Mozilla
00008 // Public License v. 2.0. If a copy of the MPL was not distributed
00009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00010 
00011 #ifndef EIGEN_BLOCK_HOUSEHOLDER_H
00012 #define EIGEN_BLOCK_HOUSEHOLDER_H
00013 
00014 // This file contains some helper function to deal with block householder reflectors
00015 
00016 namespace Eigen { 
00017 
00018 namespace internal {
00019 
00020 /** \internal */
00021 template<typename TriangularFactorType,typename VectorsType,typename CoeffsType>
00022 void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)
00023 {
00024   typedef typename TriangularFactorType::Index Index;
00025   typedef typename VectorsType::Scalar Scalar;
00026   const Index nbVecs = vectors.cols();
00027   eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);
00028 
00029   for(Index i = 0; i < nbVecs; i++)
00030   {
00031     Index rs = vectors.rows() - i;
00032     Scalar Vii = vectors(i,i);
00033     vectors.const_cast_derived().coeffRef(i,i) = Scalar(1);
00034     triFactor.col(i).head(i).noalias() = -hCoeffs(i) * vectors.block(i, 0, rs, i).adjoint()
00035                                        * vectors.col(i).tail(rs);
00036     vectors.const_cast_derived().coeffRef(i, i) = Vii;
00037     // FIXME add .noalias() once the triangular product can work inplace
00038     triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView<Upper>()
00039                              * triFactor.col(i).head(i);
00040     triFactor(i,i) = hCoeffs(i);
00041   }
00042 }
00043 
00044 /** \internal */
00045 template<typename MatrixType,typename VectorsType,typename CoeffsType>
00046 void apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vectors, const CoeffsType& hCoeffs)
00047 {
00048   typedef typename MatrixType::Index Index;
00049   enum { TFactorSize = MatrixType::ColsAtCompileTime };
00050   Index nbVecs = vectors.cols();
00051   Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, ColMajor> T(nbVecs,nbVecs);
00052   make_block_householder_triangular_factor(T, vectors, hCoeffs);
00053 
00054   const TriangularView<const VectorsType, UnitLower>& V(vectors);
00055 
00056   // A -= V T V^* A
00057   Matrix<typename MatrixType::Scalar,VectorsType::ColsAtCompileTime,MatrixType::ColsAtCompileTime,0,
00058          VectorsType::MaxColsAtCompileTime,MatrixType::MaxColsAtCompileTime> tmp = V.adjoint() * mat;
00059   // FIXME add .noalias() once the triangular product can work inplace
00060   tmp = T.template triangularView<Upper>().adjoint() * tmp;
00061   mat.noalias() -= V * tmp;
00062 }
00063 
00064 } // end namespace internal
00065 
00066 } // end namespace Eigen
00067 
00068 #endif // EIGEN_BLOCK_HOUSEHOLDER_H