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Diffstat (limited to 'Eigen/src/QR/ColPivotingHouseholderQR.h')
| -rw-r--r-- | Eigen/src/QR/ColPivotingHouseholderQR.h | 266 |
1 files changed, 266 insertions, 0 deletions
diff --git a/Eigen/src/QR/ColPivotingHouseholderQR.h b/Eigen/src/QR/ColPivotingHouseholderQR.h new file mode 100644 index 000000000..ed4b84f63 --- /dev/null +++ b/Eigen/src/QR/ColPivotingHouseholderQR.h @@ -0,0 +1,266 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008-2009 Gael Guennebaud <g.gael@free.fr> +// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> +// +// 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 <http://www.gnu.org/licenses/>. + +#ifndef EIGEN_COLPIVOTINGHOUSEHOLDERQR_H +#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_H + +/** \ingroup QR_Module + * \nonstableyet + * + * \class ColPivotingHouseholderQR + * + * \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::colPivotingHouseholderQr() + */ +template<typename MatrixType> class ColPivotingHouseholderQR +{ + 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<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixQType; + typedef Matrix<Scalar, DiagSizeAtCompileTime, 1> HCoeffsType; + typedef Matrix<int, 1, ColsAtCompileTime> IntRowVectorType; + typedef Matrix<int, RowsAtCompileTime, 1> IntColVectorType; + typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType; + typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType; + typedef Matrix<RealScalar, 1, ColsAtCompileTime> RealRowVectorType; + + /** + * \brief Default Constructor. + * + * The default constructor is useful in cases in which the user intends to + * perform decompositions via ColPivotingHouseholderQR::compute(const MatrixType&). + */ + ColPivotingHouseholderQR() : m_qr(), m_hCoeffs(), m_isInitialized(false) {} + + ColPivotingHouseholderQR(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 ColPivotingHouseholderQR_solve.cpp + * Output: \verbinclude ColPivotingHouseholderQR_solve.out + */ + template<typename OtherDerived, typename ResultType> + void solve(const MatrixBase<OtherDerived>& 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; } + + ColPivotingHouseholderQR& compute(const MatrixType& matrix); + + const IntRowVectorType& colsPermutation() const + { + ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized."); + return m_cols_permutation; + } + + inline int rank() const + { + ei_assert(m_isInitialized && "ColPivotingHouseholderQR is not initialized."); + return m_rank; + } + + protected: + MatrixType m_qr; + HCoeffsType m_hCoeffs; + IntRowVectorType m_cols_permutation; + bool m_isInitialized; + RealScalar m_precision; + int m_rank; + int m_det_pq; +}; + +#ifndef EIGEN_HIDE_HEAVY_CODE + +template<typename MatrixType> +ColPivotingHouseholderQR<MatrixType>& ColPivotingHouseholderQR<MatrixType>::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); + + m_precision = epsilon<Scalar>() * size; + + IntRowVectorType cols_transpositions(matrix.cols()); + m_cols_permutation.resize(matrix.cols()); + int number_of_transpositions = 0; + + RealRowVectorType colSqNorms(cols); + for(int k = 0; k < cols; ++k) + colSqNorms.coeffRef(k) = m_qr.col(k).squaredNorm(); + RealScalar biggestColSqNorm = colSqNorms.maxCoeff(); + + for (int k = 0; k < size; ++k) + { + int biggest_col_in_corner; + RealScalar biggestColSqNormInCorner = colSqNorms.end(cols-k).maxCoeff(&biggest_col_in_corner); + biggest_col_in_corner += k; + + // if the corner is negligible, then we have less than full rank, and we can finish early + if(ei_isMuchSmallerThan(biggestColSqNormInCorner, biggestColSqNorm, m_precision)) + { + m_rank = k; + for(int i = k; i < size; i++) + { + cols_transpositions.coeffRef(i) = i; + m_hCoeffs.coeffRef(i) = Scalar(0); + } + break; + } + + cols_transpositions.coeffRef(k) = biggest_col_in_corner; + if(k != biggest_col_in_corner) { + m_qr.col(k).swap(m_qr.col(biggest_col_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; + + 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)); + + colSqNorms.end(cols-k-1) -= m_qr.row(k).end(cols-k-1).cwise().abs2(); + } + + 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<typename MatrixType> +template<typename OtherDerived, typename ResultType> +void ColPivotingHouseholderQR<MatrixType>::solve( + const MatrixBase<OtherDerived>& b, + ResultType *result +) const +{ + ei_assert(m_isInitialized && "ColPivotingHouseholderQR 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<Scalar,1,MatrixType::ColsAtCompileTime> temp(cols); + for (int k = 0; k < m_rank; ++k) + { + int remainingSize = rows-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<UpperTriangular>() + .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<typename MatrixType> +MatrixType ColPivotingHouseholderQR<MatrixType>::matrixQ() const +{ + ei_assert(m_isInitialized && "ColPivotingHouseholderQR 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<Scalar,1,MatrixType::RowsAtCompileTime> 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)); + } + return res; +} + +#endif // EIGEN_HIDE_HEAVY_CODE + +/** \return the column-pivoting Householder QR decomposition of \c *this. + * + * \sa class ColPivotingHouseholderQR + */ +template<typename Derived> +const ColPivotingHouseholderQR<typename MatrixBase<Derived>::PlainMatrixType> +MatrixBase<Derived>::colPivotingHouseholderQr() const +{ + return ColPivotingHouseholderQR<PlainMatrixType>(eval()); +} + + +#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H |