From 22d07ec2e3324d09c7dff36c9642f0ed74f3e994 Mon Sep 17 00:00:00 2001 From: Gael Guennebaud Date: Thu, 17 Jun 2010 18:30:47 +0200 Subject: Add blocking inside HouseholderQR based on code from Vincent Lejeune. This is all internal stuff for now. --- Eigen/src/Householder/BlockHouseholder.h | 76 ++++++++++++++++++++++++++++++++ Eigen/src/QR/HouseholderQR.h | 58 +++++++++++++++++++++++- 2 files changed, 132 insertions(+), 2 deletions(-) create mode 100644 Eigen/src/Householder/BlockHouseholder.h (limited to 'Eigen/src') diff --git a/Eigen/src/Householder/BlockHouseholder.h b/Eigen/src/Householder/BlockHouseholder.h new file mode 100644 index 000000000..c17ca10e0 --- /dev/null +++ b/Eigen/src/Householder/BlockHouseholder.h @@ -0,0 +1,76 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2010 Vincent Lejeune +// Copyright (C) 2010 Gael Guennebaud +// +// Eigen is free software; you can redistribute it and/or +// modify it under the terms of the GNU Lesser General Public +// License as published by the Free Software Foundation; either +// version 3 of the License, or (at your option) any later version. +// +// Alternatively, you can redistribute it and/or +// modify it under the terms of the GNU General Public License as +// published by the Free Software Foundation; either version 2 of +// the License, or (at your option) any later version. +// +// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY +// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the +// GNU General Public License for more details. +// +// You should have received a copy of the GNU Lesser General Public +// License and a copy of the GNU General Public License along with +// Eigen. If not, see . + +#ifndef EIGEN_BLOCK_HOUSEHOLDER_H +#define EIGEN_BLOCK_HOUSEHOLDER_H + +// This file contains some helper function to deal with block householder reflectors + +/** \internal */ +template +void ei_make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs) +{ + typedef typename TriangularFactorType::Index Index; + typedef typename VectorsType::Scalar Scalar; + const Index nbVecs = vectors.cols(); + ei_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs); + + for(Index i = 0; i < nbVecs; i++) + { + Index rs = vectors.rows() - i; + Scalar Vii = vectors(i,i); + vectors.const_cast_derived().coeffRef(i,i) = Scalar(1); + triFactor.col(i).head(i).noalias() = vectors.block(i, 0, rs, i).adjoint() + * vectors.col(i).tail(rs); + triFactor.col(i).head(i) *= -hCoeffs(i); + vectors.const_cast_derived().coeffRef(i, i) = Vii; + // FIXME add .noalias() once the triangular product can work inplace + triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView() + * triFactor.col(i).head(i); + triFactor(i,i) = hCoeffs(i); + } +} + +/** \internal */ +template +void ei_apply_block_householder_on_the_left(MatrixType& mat, const VectorsType& vectors, const CoeffsType& hCoeffs) +{ + typedef typename MatrixType::Index Index; + enum { TFactorSize = MatrixType::ColsAtCompileTime }; + Index nbVecs = vectors.cols(); + Matrix T(nbVecs,nbVecs); + ei_make_block_householder_triangular_factor(T, vectors, hCoeffs); + + const TriangularView& V(vectors); + + // A -= V T V^* A + Matrix tmp = V.adjoint() * mat; + // FIXME add .noalias() once the triangular product can work inplace + tmp = T.template triangularView().adjoint() * tmp; + mat.noalias() -= V * tmp; +} + + +#endif // EIGEN_BLOCK_HOUSEHOLDER_H diff --git a/Eigen/src/QR/HouseholderQR.h b/Eigen/src/QR/HouseholderQR.h index c977c2e33..29044e905 100644 --- a/Eigen/src/QR/HouseholderQR.h +++ b/Eigen/src/QR/HouseholderQR.h @@ -1,8 +1,9 @@ // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // -// Copyright (C) 2008-2009 Gael Guennebaud +// Copyright (C) 2008-2010 Gael Guennebaud // Copyright (C) 2009 Benoit Jacob +// Copyright (C) 2010 Vincent Lejeune // // Eigen is free software; you can redistribute it and/or // modify it under the terms of the GNU Lesser General Public @@ -229,6 +230,59 @@ void ei_householder_qr_inplace_unblocked(MatrixQR& mat, HCoeffs& hCoeffs, typena } } +/** \internal */ +template +void ei_householder_qr_inplace_blocked(MatrixQR& mat, HCoeffs& hCoeffs, + typename MatrixQR::Index maxBlockSize=32, + typename MatrixQR::Scalar* tempData = 0) +{ + typedef typename MatrixQR::Index Index; + typedef typename MatrixQR::Scalar Scalar; + typedef typename MatrixQR::RealScalar RealScalar; + typedef Block BlockType; + + Index rows = mat.rows(); + Index cols = mat.cols(); + Index size = std::min(rows, cols); + + typedef Matrix TempType; + TempType tempVector; + if(tempData==0) + { + tempVector.resize(cols); + tempData = tempVector.data(); + } + + Index blockSize = std::min(maxBlockSize,size); + + int k = 0; + for (k = 0; k < size; k += blockSize) + { + Index bs = std::min(size-k,blockSize); // actual size of the block + Index tcols = cols - k - bs; // trailing columns + Index brows = rows-k; // rows of the block + + // partition the matrix: + // A00 | A01 | A02 + // mat = A10 | A11 | A12 + // A20 | A21 | A22 + // and performs the qr dec of [A11^T A12^T]^T + // and update [A21^T A22^T]^T using level 3 operations. + // Finally, the algorithm continue on A22 + + BlockType A11_21 = mat.block(k,k,brows,bs); + Block hCoeffsSegment = hCoeffs.segment(k,bs); + + ei_householder_qr_inplace_unblocked(A11_21, hCoeffsSegment, tempData); + + if(tcols) + { + BlockType A21_22 = mat.block(k,k+bs,brows,tcols); + ei_apply_block_householder_on_the_left(A21_22,A11_21,hCoeffsSegment.adjoint()); + } + } +} + template HouseholderQR& HouseholderQR::compute(const MatrixType& matrix) { @@ -241,7 +295,7 @@ HouseholderQR& HouseholderQR::compute(const MatrixType& m_temp.resize(cols); - ei_householder_qr_inplace_unblocked(m_qr, m_hCoeffs, m_temp.data()); + ei_householder_qr_inplace_blocked(m_qr, m_hCoeffs, 48, m_temp.data()); m_isInitialized = true; return *this; -- cgit v1.2.3