cart-elc

Source code for CART-ELC
git clone git://git.laack.co/cart-elc.git
Log | Files | Refs | README | LICENSE

BlockHouseholder.h (4784B)

      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   
     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>
     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>
     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