From 7bedf5e9cb61a10e2be18a3f18ee63d68dbb4acd Mon Sep 17 00:00:00 2001 From: Benoit Jacob Date: Sat, 22 Aug 2009 01:13:21 -0400 Subject: [PATCH] add initial, rough, full-pivoting RRQR decomposition lots of room for improvement! and add Gael a (c) line in Householder.h --- Eigen/QR | 1 + Eigen/src/Householder/Householder.h | 1 + Eigen/src/QR/QR.h | 9 +- Eigen/src/QR/RRQR.h | 286 ++++++++++++++++++++++++++++ test/CMakeLists.txt | 1 + test/rrqr.cpp | 116 +++++++++++ 6 files changed, 410 insertions(+), 4 deletions(-) create mode 100644 Eigen/src/QR/RRQR.h create mode 100644 test/rrqr.cpp diff --git a/Eigen/QR b/Eigen/QR index 151c0b31b..c95f7522a 100644 --- a/Eigen/QR +++ b/Eigen/QR @@ -36,6 +36,7 @@ namespace Eigen { */ #include "src/QR/QR.h" +#include "src/QR/RRQR.h" #include "src/QR/Tridiagonalization.h" #include "src/QR/EigenSolver.h" #include "src/QR/SelfAdjointEigenSolver.h" diff --git a/Eigen/src/Householder/Householder.h b/Eigen/src/Householder/Householder.h index 769ba3d43..8a274d240 100644 --- a/Eigen/src/Householder/Householder.h +++ b/Eigen/src/Householder/Householder.h @@ -2,6 +2,7 @@ // for linear algebra. // // Copyright (C) 2009 Benoit Jacob +// Copyright (C) 2009 Gael Guennebaud // // Eigen is free software; you can redistribute it and/or // modify it under the terms of the GNU Lesser General Public diff --git a/Eigen/src/QR/QR.h b/Eigen/src/QR/QR.h index 90e6f8132..e5da6d691 100644 --- a/Eigen/src/QR/QR.h +++ b/Eigen/src/QR/QR.h @@ -1,7 +1,7 @@ // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // -// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2008-2009 Gael Guennebaud // // Eigen is free software; you can redistribute it and/or // modify it under the terms of the GNU Lesser General Public @@ -39,7 +39,7 @@ * * Note that no pivoting is performed. This is \b not a rank-revealing decomposition. * - * \sa MatrixBase::qr() + * \sa MatrixBase::householderQr() */ template class HouseholderQR { @@ -54,6 +54,7 @@ template class HouseholderQR typedef Block MatrixRBlockType; typedef Matrix MatrixTypeR; typedef Matrix HCoeffsType; + typedef Matrix RowVectorType; /** * \brief Default Constructor. @@ -125,12 +126,12 @@ HouseholderQR& HouseholderQR::compute(const MatrixType& m_qr = matrix; m_hCoeffs.resize(size); - Matrix temp(cols); + RowVectorType temp(cols); for (int k = 0; k < size; ++k) { int remainingRows = rows - k; - int remainingCols = cols - k -1; + int remainingCols = cols - k - 1; RealScalar beta; m_qr.col(k).end(remainingRows).makeHouseholderInPlace(&m_hCoeffs.coeffRef(k), &beta); diff --git a/Eigen/src/QR/RRQR.h b/Eigen/src/QR/RRQR.h new file mode 100644 index 000000000..5e4f009dd --- /dev/null +++ b/Eigen/src/QR/RRQR.h @@ -0,0 +1,286 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud +// Copyright (C) 2009 Benoit Jacob +// +// 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_RRQR_H +#define EIGEN_RRQR_H + +/** \ingroup QR_Module + * \nonstableyet + * + * \class HouseholderRRQR + * + * \brief Householder rank-revealing QR decomposition of a matrix + * + * \param MatrixType the type of the matrix of which we are computing the QR decomposition + * + * This class performs a rank-revealing QR decomposition using Householder transformations. + * + * This decomposition performs full-pivoting in order to be rank-revealing and achieve optimal + * numerical stability. + * + * \sa MatrixBase::householderRrqr() + */ +template class HouseholderRRQR +{ + public: + + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + Options = MatrixType::Options, + DiagSizeAtCompileTime = EIGEN_ENUM_MIN(ColsAtCompileTime,RowsAtCompileTime) + }; + + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + typedef Matrix MatrixQType; + typedef Matrix HCoeffsType; + typedef Matrix IntRowVectorType; + typedef Matrix IntColVectorType; + typedef Matrix RowVectorType; + typedef Matrix ColVectorType; + + /** + * \brief Default Constructor. + * + * The default constructor is useful in cases in which the user intends to + * perform decompositions via HouseholderRRQR::compute(const MatrixType&). + */ + HouseholderRRQR() : m_qr(), m_hCoeffs(), m_isInitialized(false) {} + + HouseholderRRQR(const MatrixType& matrix) + : m_qr(matrix.rows(), matrix.cols()), + m_hCoeffs(std::min(matrix.rows(),matrix.cols())), + m_isInitialized(false) + { + compute(matrix); + } + + /** This method finds a solution x to the equation Ax=b, where A is the matrix of which + * *this is the QR decomposition, if any exists. + * + * \param b the right-hand-side of the equation to solve. + * + * \param result a pointer to the vector/matrix in which to store the solution, if any exists. + * Resized if necessary, so that result->rows()==A.cols() and result->cols()==b.cols(). + * If no solution exists, *result is left with undefined coefficients. + * + * \note The case where b is a matrix is not yet implemented. Also, this + * code is space inefficient. + * + * Example: \include HouseholderRRQR_solve.cpp + * Output: \verbinclude HouseholderRRQR_solve.out + */ + template + void solve(const MatrixBase& b, ResultType *result) const; + + MatrixType matrixQ(void) const; + + /** \returns a reference to the matrix where the Householder QR decomposition is stored + */ + const MatrixType& matrixQR() const { return m_qr; } + + HouseholderRRQR& compute(const MatrixType& matrix); + + const IntRowVectorType& colsPermutation() const + { + ei_assert(m_isInitialized && "RRQR is not initialized."); + return m_cols_permutation; + } + + const IntColVectorType& rowsTranspositions() const + { + ei_assert(m_isInitialized && "RRQR is not initialized."); + return m_rows_transpositions; + } + + inline int rank() const + { + ei_assert(m_isInitialized && "RRQR is not initialized."); + return m_rank; + } + + protected: + MatrixType m_qr; + HCoeffsType m_hCoeffs; + IntColVectorType m_rows_transpositions; + IntRowVectorType m_cols_permutation; + bool m_isInitialized; + RealScalar m_precision; + int m_rank; + int m_det_pq; +}; + +#ifndef EIGEN_HIDE_HEAVY_CODE + +template +HouseholderRRQR& HouseholderRRQR::compute(const MatrixType& matrix) +{ + int rows = matrix.rows(); + int cols = matrix.cols(); + int size = std::min(rows,cols); + m_rank = size; + + m_qr = matrix; + m_hCoeffs.resize(size); + + RowVectorType temp(cols); + + // TODO: experiment to see the best formula + m_precision = epsilon() * size; + + m_rows_transpositions.resize(matrix.rows()); + IntRowVectorType cols_transpositions(matrix.cols()); + m_cols_permutation.resize(matrix.cols()); + int number_of_transpositions = 0; + + RealScalar biggest; + + for (int k = 0; k < size; ++k) + { + int row_of_biggest_in_corner, col_of_biggest_in_corner; + RealScalar biggest_in_corner; + + biggest_in_corner = m_qr.corner(Eigen::BottomRight, rows-k, cols-k) + .cwise().abs() + .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner); + row_of_biggest_in_corner += k; + col_of_biggest_in_corner += k; + if(k==0) biggest = biggest_in_corner; + + // if the corner is negligible, then we have less than full rank, and we can finish early + if(ei_isMuchSmallerThan(biggest_in_corner, biggest, m_precision)) + { + m_rank = k; + for(int i = k; i < size; i++) + { + m_rows_transpositions.coeffRef(i) = i; + cols_transpositions.coeffRef(i) = i; + m_hCoeffs.coeffRef(i) = Scalar(0); + } + break; + } + + m_rows_transpositions.coeffRef(k) = row_of_biggest_in_corner; + cols_transpositions.coeffRef(k) = col_of_biggest_in_corner; + if(k != row_of_biggest_in_corner) { + m_qr.row(k).end(cols-k).swap(m_qr.row(row_of_biggest_in_corner).end(cols-k)); + ++number_of_transpositions; + } + if(k != col_of_biggest_in_corner) { + m_qr.col(k).swap(m_qr.col(col_of_biggest_in_corner)); + ++number_of_transpositions; + } + + RealScalar beta; + m_qr.col(k).end(rows-k).makeHouseholderInPlace(&m_hCoeffs.coeffRef(k), &beta); + m_qr.coeffRef(k,k) = beta; + + // apply H to remaining part of m_qr from the left + m_qr.corner(BottomRight, rows-k, cols-k-1) + .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1)); + } + + for(int k = 0; k < matrix.cols(); ++k) m_cols_permutation.coeffRef(k) = k; + for(int k = 0; k < size; ++k) + std::swap(m_cols_permutation.coeffRef(k), m_cols_permutation.coeffRef(cols_transpositions.coeff(k))); + + m_det_pq = (number_of_transpositions%2) ? -1 : 1; + m_isInitialized = true; + + return *this; +} + +template +template +void HouseholderRRQR::solve( + const MatrixBase& b, + ResultType *result +) const +{ + ei_assert(m_isInitialized && "HouseholderRRQR is not initialized."); + const int rows = m_qr.rows(); + const int cols = b.cols(); + ei_assert(b.rows() == rows); + + typename OtherDerived::PlainMatrixType c(b); + + Matrix temp(cols); + for (int k = 0; k < m_rank; ++k) + { + int remainingSize = rows-k; + c.row(k).swap(c.row(m_rows_transpositions.coeff(k))); + c.corner(BottomRight, remainingSize, cols) + .applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), m_hCoeffs.coeff(k), &temp.coeffRef(0)); + } + + m_qr.corner(TopLeft, m_rank, m_rank) + .template triangularView() + .solveInPlace(c.corner(TopLeft, m_rank, c.cols())); + + result->resize(m_qr.cols(), b.cols()); + for(int i = 0; i < m_rank; ++i) result->row(m_cols_permutation.coeff(i)) = c.row(i); + for(int i = m_rank; i < m_qr.cols(); ++i) result->row(m_cols_permutation.coeff(i)).setZero(); +} + +/** \returns the matrix Q */ +template +MatrixType HouseholderRRQR::matrixQ() const +{ + ei_assert(m_isInitialized && "HouseholderRRQR is not initialized."); + // compute the product H'_0 H'_1 ... H'_n-1, + // where H_k is the k-th Householder transformation I - h_k v_k v_k' + // and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...] + int rows = m_qr.rows(); + int cols = m_qr.cols(); + int size = std::min(rows,cols); + MatrixType res = MatrixType::Identity(rows, rows); + Matrix temp(rows); + for (int k = size-1; k >= 0; k--) + { + res.block(k, k, rows-k, rows-k) + .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k)); + res.row(k).swap(res.row(m_rows_transpositions.coeff(k))); + } + return res; +} + +#endif // EIGEN_HIDE_HEAVY_CODE + +#if 0 +/** \return the Householder QR decomposition of \c *this. + * + * \sa class HouseholderRRQR + */ +template +const HouseholderRRQR::PlainMatrixType> +MatrixBase::householderQr() const +{ + return HouseholderRRQR(eval()); +} +#endif + + +#endif // EIGEN_QR_H diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt index dd8f07386..b79e069b7 100644 --- a/test/CMakeLists.txt +++ b/test/CMakeLists.txt @@ -121,6 +121,7 @@ ei_add_test(lu ${EI_OFLAG}) ei_add_test(determinant) ei_add_test(inverse ${EI_OFLAG}) ei_add_test(qr) +ei_add_test(rrqr) ei_add_test(eigensolver_selfadjoint " " "${GSL_LIBRARIES}") ei_add_test(eigensolver_generic " " "${GSL_LIBRARIES}") ei_add_test(svd) diff --git a/test/rrqr.cpp b/test/rrqr.cpp new file mode 100644 index 000000000..b6cc75d17 --- /dev/null +++ b/test/rrqr.cpp @@ -0,0 +1,116 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud +// Copyright (C) 2009 Benoit Jacob +// +// 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 . + +#include "main.h" +#include + +template void qr() +{ + /* this test covers the following files: QR.h */ + int rows = ei_random(20,200), cols = ei_random(20,200), cols2 = ei_random(20,200); + int rank = ei_random(1, std::min(rows, cols)-1); + + typedef typename MatrixType::Scalar Scalar; + typedef Matrix SquareMatrixType; + typedef Matrix VectorType; + MatrixType m1; + createRandomMatrixOfRank(rank,rows,cols,m1); + HouseholderRRQR qr(m1); + VERIFY_IS_APPROX(rank, qr.rank()); + + MatrixType r = qr.matrixQR(); + // FIXME need better way to construct trapezoid + for(int i = 0; i < rows; i++) for(int j = 0; j < cols; j++) if(i>j) r(i,j) = Scalar(0); + + MatrixType b = qr.matrixQ() * r; + + MatrixType c = MatrixType::Zero(rows,cols); + + for(int i = 0; i < cols; ++i) c.col(qr.colsPermutation().coeff(i)) = b.col(i); + VERIFY_IS_APPROX(m1, c); + + MatrixType m2 = MatrixType::Random(cols,cols2); + MatrixType m3 = m1*m2; + m2 = MatrixType::Random(cols,cols2); + qr.solve(m3, &m2); + VERIFY_IS_APPROX(m3, m1*m2); +} + +template void qr_invertible() +{ + /* this test covers the following files: RRQR.h */ + typedef typename NumTraits::Real RealScalar; + int size = ei_random(10,50); + + MatrixType m1(size, size), m2(size, size), m3(size, size); + m1 = MatrixType::Random(size,size); + + if (ei_is_same_type::ret) + { + // let's build a matrix more stable to inverse + MatrixType a = MatrixType::Random(size,size*2); + m1 += a * a.adjoint(); + } + + HouseholderRRQR qr(m1); + m3 = MatrixType::Random(size,size); + qr.solve(m3, &m2); + VERIFY_IS_APPROX(m3, m1*m2); +} + +template void qr_verify_assert() +{ + MatrixType tmp; + + HouseholderRRQR qr; + VERIFY_RAISES_ASSERT(qr.matrixR()) + VERIFY_RAISES_ASSERT(qr.solve(tmp,&tmp)) + VERIFY_RAISES_ASSERT(qr.matrixQ()) +} + +void test_rrqr() +{ + for(int i = 0; i < 1; i++) { + // FIXME : very weird bug here +// CALL_SUBTEST( qr(Matrix2f()) ); + CALL_SUBTEST( qr() ); + CALL_SUBTEST( qr() ); + CALL_SUBTEST( qr() ); + } + + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST( qr_invertible() ); + CALL_SUBTEST( qr_invertible() ); + CALL_SUBTEST( qr_invertible() ); + CALL_SUBTEST( qr_invertible() ); + } + + CALL_SUBTEST(qr_verify_assert()); + CALL_SUBTEST(qr_verify_assert()); + CALL_SUBTEST(qr_verify_assert()); + CALL_SUBTEST(qr_verify_assert()); + CALL_SUBTEST(qr_verify_assert()); + CALL_SUBTEST(qr_verify_assert()); +}