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Diffstat (limited to 'extern/Eigen2/Eigen/src/QR/QR.h')
| -rw-r--r-- | extern/Eigen2/Eigen/src/QR/QR.h | 334 |
1 files changed, 0 insertions, 334 deletions
diff --git a/extern/Eigen2/Eigen/src/QR/QR.h b/extern/Eigen2/Eigen/src/QR/QR.h deleted file mode 100644 index 90751dd428d..00000000000 --- a/extern/Eigen2/Eigen/src/QR/QR.h +++ /dev/null @@ -1,334 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> -// -// 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_QR_H -#define EIGEN_QR_H - -/** \ingroup QR_Module - * \nonstableyet - * - * \class QR - * - * \brief QR decomposition of a matrix - * - * \param MatrixType the type of the matrix of which we are computing the QR decomposition - * - * This class performs a QR decomposition using Householder transformations. The result is - * stored in a compact way compatible with LAPACK. - * - * \sa MatrixBase::qr() - */ -template<typename MatrixType> class QR -{ - public: - - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::RealScalar RealScalar; - typedef Block<MatrixType, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixRBlockType; - typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixTypeR; - typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; - - /** - * \brief Default Constructor. - * - * The default constructor is useful in cases in which the user intends to - * perform decompositions via QR::compute(const MatrixType&). - */ - QR() : m_qr(), m_hCoeffs(), m_isInitialized(false) {} - - QR(const MatrixType& matrix) - : m_qr(matrix.rows(), matrix.cols()), - m_hCoeffs(matrix.cols()), - m_isInitialized(false) - { - compute(matrix); - } - - /** \deprecated use isInjective() - * \returns whether or not the matrix is of full rank - * - * \note Since the rank is computed only once, i.e. the first time it is needed, this - * method almost does not perform any further computation. - */ - EIGEN_DEPRECATED bool isFullRank() const - { - ei_assert(m_isInitialized && "QR is not initialized."); - return rank() == m_qr.cols(); - } - - /** \returns the rank of the matrix of which *this is the QR decomposition. - * - * \note Since the rank is computed only once, i.e. the first time it is needed, this - * method almost does not perform any further computation. - */ - int rank() const; - - /** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition. - * - * \note Since the rank is computed only once, i.e. the first time it is needed, this - * method almost does not perform any further computation. - */ - inline int dimensionOfKernel() const - { - ei_assert(m_isInitialized && "QR is not initialized."); - return m_qr.cols() - rank(); - } - - /** \returns true if the matrix of which *this is the QR decomposition represents an injective - * linear map, i.e. has trivial kernel; false otherwise. - * - * \note Since the rank is computed only once, i.e. the first time it is needed, this - * method almost does not perform any further computation. - */ - inline bool isInjective() const - { - ei_assert(m_isInitialized && "QR is not initialized."); - return rank() == m_qr.cols(); - } - - /** \returns true if the matrix of which *this is the QR decomposition represents a surjective - * linear map; false otherwise. - * - * \note Since the rank is computed only once, i.e. the first time it is needed, this - * method almost does not perform any further computation. - */ - inline bool isSurjective() const - { - ei_assert(m_isInitialized && "QR is not initialized."); - return rank() == m_qr.rows(); - } - - /** \returns true if the matrix of which *this is the QR decomposition is invertible. - * - * \note Since the rank is computed only once, i.e. the first time it is needed, this - * method almost does not perform any further computation. - */ - inline bool isInvertible() const - { - ei_assert(m_isInitialized && "QR is not initialized."); - return isInjective() && isSurjective(); - } - - /** \returns a read-only expression of the matrix R of the actual the QR decomposition */ - const Part<NestByValue<MatrixRBlockType>, UpperTriangular> - matrixR(void) const - { - ei_assert(m_isInitialized && "QR is not initialized."); - int cols = m_qr.cols(); - return MatrixRBlockType(m_qr, 0, 0, cols, cols).nestByValue().template part<UpperTriangular>(); - } - - /** 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. - * - * \returns true if any solution exists, false if no solution exists. - * - * \note If there exist more than one solution, this method will arbitrarily choose one. - * If you need a complete analysis of the space of solutions, take the one solution obtained - * by this method and add to it elements of the kernel, as determined by kernel(). - * - * \note The case where b is a matrix is not yet implemented. Also, this - * code is space inefficient. - * - * Example: \include QR_solve.cpp - * Output: \verbinclude QR_solve.out - * - * \sa MatrixBase::solveTriangular(), kernel(), computeKernel(), inverse(), computeInverse() - */ - template<typename OtherDerived, typename ResultType> - bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const; - - MatrixType matrixQ(void) const; - - void compute(const MatrixType& matrix); - - protected: - MatrixType m_qr; - VectorType m_hCoeffs; - mutable int m_rank; - mutable bool m_rankIsUptodate; - bool m_isInitialized; -}; - -/** \returns the rank of the matrix of which *this is the QR decomposition. */ -template<typename MatrixType> -int QR<MatrixType>::rank() const -{ - ei_assert(m_isInitialized && "QR is not initialized."); - if (!m_rankIsUptodate) - { - RealScalar maxCoeff = m_qr.diagonal().cwise().abs().maxCoeff(); - int n = m_qr.cols(); - m_rank = 0; - while(m_rank<n && !ei_isMuchSmallerThan(m_qr.diagonal().coeff(m_rank), maxCoeff)) - ++m_rank; - m_rankIsUptodate = true; - } - return m_rank; -} - -#ifndef EIGEN_HIDE_HEAVY_CODE - -template<typename MatrixType> -void QR<MatrixType>::compute(const MatrixType& matrix) -{ - m_rankIsUptodate = false; - m_qr = matrix; - m_hCoeffs.resize(matrix.cols()); - - int rows = matrix.rows(); - int cols = matrix.cols(); - RealScalar eps2 = precision<RealScalar>()*precision<RealScalar>(); - - for (int k = 0; k < cols; ++k) - { - int remainingSize = rows-k; - - RealScalar beta; - Scalar v0 = m_qr.col(k).coeff(k); - - if (remainingSize==1) - { - if (NumTraits<Scalar>::IsComplex) - { - // Householder transformation on the remaining single scalar - beta = ei_abs(v0); - if (ei_real(v0)>0) - beta = -beta; - m_qr.coeffRef(k,k) = beta; - m_hCoeffs.coeffRef(k) = (beta - v0) / beta; - } - else - { - m_hCoeffs.coeffRef(k) = 0; - } - } - else if ((beta=m_qr.col(k).end(remainingSize-1).squaredNorm())>eps2) - // FIXME what about ei_imag(v0) ?? - { - // form k-th Householder vector - beta = ei_sqrt(ei_abs2(v0)+beta); - if (ei_real(v0)>=0.) - beta = -beta; - m_qr.col(k).end(remainingSize-1) /= v0-beta; - m_qr.coeffRef(k,k) = beta; - Scalar h = m_hCoeffs.coeffRef(k) = (beta - v0) / beta; - - // apply the Householder transformation (I - h v v') to remaining columns, i.e., - // R <- (I - h v v') * R where v = [1,m_qr(k+1,k), m_qr(k+2,k), ...] - int remainingCols = cols - k -1; - if (remainingCols>0) - { - m_qr.coeffRef(k,k) = Scalar(1); - m_qr.corner(BottomRight, remainingSize, remainingCols) -= ei_conj(h) * m_qr.col(k).end(remainingSize) - * (m_qr.col(k).end(remainingSize).adjoint() * m_qr.corner(BottomRight, remainingSize, remainingCols)); - m_qr.coeffRef(k,k) = beta; - } - } - else - { - m_hCoeffs.coeffRef(k) = 0; - } - } - m_isInitialized = true; -} - -template<typename MatrixType> -template<typename OtherDerived, typename ResultType> -bool QR<MatrixType>::solve( - const MatrixBase<OtherDerived>& b, - ResultType *result -) const -{ - ei_assert(m_isInitialized && "QR is not initialized."); - const int rows = m_qr.rows(); - ei_assert(b.rows() == rows); - result->resize(rows, b.cols()); - - // TODO(keir): There is almost certainly a faster way to multiply by - // Q^T without explicitly forming matrixQ(). Investigate. - *result = matrixQ().transpose()*b; - - if(!isSurjective()) - { - // is result is in the image of R ? - RealScalar biggest_in_res = result->corner(TopLeft, m_rank, result->cols()).cwise().abs().maxCoeff(); - for(int col = 0; col < result->cols(); ++col) - for(int row = m_rank; row < result->rows(); ++row) - if(!ei_isMuchSmallerThan(result->coeff(row,col), biggest_in_res)) - return false; - } - m_qr.corner(TopLeft, m_rank, m_rank) - .template marked<UpperTriangular>() - .solveTriangularInPlace(result->corner(TopLeft, m_rank, result->cols())); - - return true; -} - -/** \returns the matrix Q */ -template<typename MatrixType> -MatrixType QR<MatrixType>::matrixQ() const -{ - ei_assert(m_isInitialized && "QR is not initialized."); - // compute the product Q_0 Q_1 ... Q_n-1, - // where Q_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(); - MatrixType res = MatrixType::Identity(rows, cols); - for (int k = cols-1; k >= 0; k--) - { - // to make easier the computation of the transformation, let's temporarily - // overwrite m_qr(k,k) such that the end of m_qr.col(k) is exactly our Householder vector. - Scalar beta = m_qr.coeff(k,k); - m_qr.const_cast_derived().coeffRef(k,k) = 1; - int endLength = rows-k; - res.corner(BottomRight,endLength, cols-k) -= ((m_hCoeffs.coeff(k) * m_qr.col(k).end(endLength)) - * (m_qr.col(k).end(endLength).adjoint() * res.corner(BottomRight,endLength, cols-k)).lazy()).lazy(); - m_qr.const_cast_derived().coeffRef(k,k) = beta; - } - return res; -} - -#endif // EIGEN_HIDE_HEAVY_CODE - -/** \return the QR decomposition of \c *this. - * - * \sa class QR - */ -template<typename Derived> -const QR<typename MatrixBase<Derived>::PlainMatrixType> -MatrixBase<Derived>::qr() const -{ - return QR<PlainMatrixType>(eval()); -} - - -#endif // EIGEN_QR_H |