diff options
| -rw-r--r-- | Eigen/LU | 1 | ||||
| -rw-r--r-- | Eigen/src/Core/MatrixBase.h | 1 | ||||
| -rw-r--r-- | Eigen/src/Core/util/ForwardDeclarations.h | 1 | ||||
| -rw-r--r-- | Eigen/src/LU/Determinant.h | 2 | ||||
| -rw-r--r-- | Eigen/src/LU/Inverse.h | 3 | ||||
| -rw-r--r-- | Eigen/src/LU/PartialLU.h | 262 |
6 files changed, 267 insertions, 3 deletions
@@ -19,6 +19,7 @@ namespace Eigen { */ #include "src/LU/LU.h" +#include "src/LU/PartialLU.h" #include "src/LU/Determinant.h" #include "src/LU/Inverse.h" diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h index 13b66af73..7df9f307b 100644 --- a/Eigen/src/Core/MatrixBase.h +++ b/Eigen/src/Core/MatrixBase.h @@ -623,6 +623,7 @@ template<typename Derived> class MatrixBase /////////// LU module /////////// const LU<PlainMatrixType> lu() const; + const PartialLU<PlainMatrixType> partialLu() const; const PlainMatrixType inverse() const; void computeInverse(PlainMatrixType *result) const; Scalar determinant() const; diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h index 11fed05ec..9ef708194 100644 --- a/Eigen/src/Core/util/ForwardDeclarations.h +++ b/Eigen/src/Core/util/ForwardDeclarations.h @@ -109,6 +109,7 @@ template<typename MatrixType,int RowFactor,int ColFactor> class Replicate; template<typename MatrixType, int Direction = BothDirections> class Reverse; template<typename MatrixType> class LU; +template<typename MatrixType> class PartialLU; template<typename MatrixType> class QR; template<typename MatrixType> class SVD; template<typename MatrixType> class LLT; diff --git a/Eigen/src/LU/Determinant.h b/Eigen/src/LU/Determinant.h index 4f435054a..fc3454435 100644 --- a/Eigen/src/LU/Determinant.h +++ b/Eigen/src/LU/Determinant.h @@ -51,7 +51,7 @@ template<typename Derived, { static inline typename ei_traits<Derived>::Scalar run(const Derived& m) { - return m.lu().determinant(); + return m.partialLu().determinant(); } }; diff --git a/Eigen/src/LU/Inverse.h b/Eigen/src/LU/Inverse.h index 3d4d63489..722de82a3 100644 --- a/Eigen/src/LU/Inverse.h +++ b/Eigen/src/LU/Inverse.h @@ -170,8 +170,7 @@ struct ei_compute_inverse { static inline void run(const MatrixType& matrix, MatrixType* result) { - LU<MatrixType> lu(matrix); - lu.computeInverse(result); + matrix.partialLu().computeInverse(result); } }; diff --git a/Eigen/src/LU/PartialLU.h b/Eigen/src/LU/PartialLU.h new file mode 100644 index 000000000..7fdbeac38 --- /dev/null +++ b/Eigen/src/LU/PartialLU.h @@ -0,0 +1,262 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. Eigen itself is part of the KDE project. +// +// Copyright (C) 2006-2009 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_PARTIALLU_H +#define EIGEN_PARTIALLU_H + +/** \ingroup LU_Module + * + * \class PartialLU + * + * \brief LU decomposition of a matrix with partial pivoting, and related features + * + * \param MatrixType the type of the matrix of which we are computing the LU decomposition + * + * This class represents a LU decomposition of a \b square \b invertible matrix, with partial pivoting: the matrix A + * is decomposed as A = PLU where L is unit-lower-triangular, U is upper-triangular, and P + * is a permutation matrix. + * + * Typically, partial pivoting LU decomposition is only considered numerically stable for square invertible matrices. + * So in this class, we plainly require that and take advantage of that to do some simplifications and optimizations. + * This class will assert that the matrix is square, but it won't (actually it can't) check that the matrix is invertible: + * it is your task to check that you only use this decomposition on invertible matrices. + * + * The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided by class LU. + * + * This is \b not a rank-revealing LU decomposition. Many features are intentionally absent from this class, + * such as rank computation. If you need these features, use class LU. + * + * This LU decomposition is suitable to invert invertible matrices. It is what MatrixBase::inverse() uses. On the other hand, + * it is \b not suitable to determine whether a given matrix is invertible. + * + * The data of the LU decomposition can be directly accessed through the methods matrixLU(), permutationP(). + * + * \sa MatrixBase::partialLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class LU + */ +template<typename MatrixType> class PartialLU +{ + public: + + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; + typedef Matrix<int, 1, MatrixType::ColsAtCompileTime> IntRowVectorType; + typedef Matrix<int, MatrixType::RowsAtCompileTime, 1> IntColVectorType; + typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType; + typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType; + + enum { MaxSmallDimAtCompileTime = EIGEN_ENUM_MIN( + MatrixType::MaxColsAtCompileTime, + MatrixType::MaxRowsAtCompileTime) + }; + + /** Constructor. + * + * \param matrix the matrix of which to compute the LU decomposition. + * + * \warning The matrix should have full rank (e.g. if it's square, it should be invertible). + * If you need to deal with non-full rank, use class LU instead. + */ + PartialLU(const MatrixType& matrix); + + /** \returns the LU decomposition matrix: the upper-triangular part is U, the + * unit-lower-triangular part is L (at least for square matrices; in the non-square + * case, special care is needed, see the documentation of class LU). + * + * \sa matrixL(), matrixU() + */ + inline const MatrixType& matrixLU() const + { + return m_lu; + } + + /** \returns a vector of integers, whose size is the number of rows of the matrix being decomposed, + * representing the P permutation i.e. the permutation of the rows. For its precise meaning, + * see the examples given in the documentation of class LU. + */ + inline const IntColVectorType& permutationP() const + { + return m_p; + } + + /** This method finds the solution x to the equation Ax=b, where A is the matrix of which + * *this is the LU decomposition. Since if this partial pivoting decomposition the matrix is assumed + * to have full rank, such a solution is assumed to exist and to be unique. + * + * \warning Again, if your matrix may not have full rank, use class LU instead. See LU::solve(). + * + * \param b the right-hand-side of the equation to solve. Can be a vector or a matrix, + * the only requirement in order for the equation to make sense is that + * b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition. + * \param result a pointer to the vector or 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. + * + * Example: \include PartialLU_solve.cpp + * Output: \verbinclude PartialLU_solve.out + * + * \sa MatrixBase::solveTriangular(), inverse(), computeInverse() + */ + template<typename OtherDerived, typename ResultType> + void solve(const MatrixBase<OtherDerived>& b, ResultType *result) const; + + /** \returns the determinant of the matrix of which + * *this is the LU decomposition. It has only linear complexity + * (that is, O(n) where n is the dimension of the square matrix) + * as the LU decomposition has already been computed. + * + * \note For fixed-size matrices of size up to 4, MatrixBase::determinant() offers + * optimized paths. + * + * \warning a determinant can be very big or small, so for matrices + * of large enough dimension, there is a risk of overflow/underflow. + * + * \sa MatrixBase::determinant() + */ + typename ei_traits<MatrixType>::Scalar determinant() const; + + /** Computes the inverse of the matrix of which *this is the LU decomposition. + * + * \param result a pointer to the matrix into which to store the inverse. Resized if needed. + * + * \warning The matrix being decomposed here is assumed to be invertible. If you need to check for + * invertibility, use class LU instead. + * + * \sa MatrixBase::computeInverse(), inverse() + */ + inline void computeInverse(MatrixType *result) const + { + solve(MatrixType::Identity(m_lu.rows(), m_lu.cols()), result); + } + + /** \returns the inverse of the matrix of which *this is the LU decomposition. + * + * \warning The matrix being decomposed here is assumed to be invertible. If you need to check for + * invertibility, use class LU instead. + * + * \sa computeInverse(), MatrixBase::inverse() + */ + inline MatrixType inverse() const + { + MatrixType result; + computeInverse(&result); + return result; + } + + protected: + const MatrixType& m_originalMatrix; + MatrixType m_lu; + IntColVectorType m_p; + int m_det_p; +}; + +template<typename MatrixType> +PartialLU<MatrixType>::PartialLU(const MatrixType& matrix) + : m_originalMatrix(matrix), + m_lu(matrix), + m_p(matrix.rows()) +{ + ei_assert(matrix.rows() == matrix.cols() && "PartialLU is only for square (and moreover invertible) matrices"); + const int size = matrix.rows(); + + IntColVectorType rows_transpositions(size); + int number_of_transpositions = 0; + + for(int k = 0; k < size; ++k) + { + int row_of_biggest_in_col; + m_lu.block(k,k,size-k,1).cwise().abs().maxCoeff(&row_of_biggest_in_col); + row_of_biggest_in_col += k; + + rows_transpositions.coeffRef(k) = row_of_biggest_in_col; + + if(k != row_of_biggest_in_col) { + m_lu.row(k).swap(m_lu.row(row_of_biggest_in_col)); + ++number_of_transpositions; + } + + if(k<size-1) { + m_lu.col(k).end(size-k-1) /= m_lu.coeff(k,k); + for(int col = k + 1; col < size; ++col) + m_lu.col(col).end(size-k-1) -= m_lu.col(k).end(size-k-1) * m_lu.coeff(k,col); + } + } + + for(int k = 0; k < size; ++k) m_p.coeffRef(k) = k; + for(int k = size-1; k >= 0; --k) + std::swap(m_p.coeffRef(k), m_p.coeffRef(rows_transpositions.coeff(k))); + + m_det_p = (number_of_transpositions%2) ? -1 : 1; +} + +template<typename MatrixType> +typename ei_traits<MatrixType>::Scalar PartialLU<MatrixType>::determinant() const +{ + return Scalar(m_det_p) * m_lu.diagonal().prod(); +} + +template<typename MatrixType> +template<typename OtherDerived, typename ResultType> +void PartialLU<MatrixType>::solve( + const MatrixBase<OtherDerived>& b, + ResultType *result +) const +{ + /* The decomposition PA = LU can be rewritten as A = P^{-1} L U. + * So we proceed as follows: + * Step 1: compute c = Pb. + * Step 2: replace c by the solution x to Lx = c. Exists because L is invertible. + * Step 3: replace c by the solution x to Ux = c. Check if a solution really exists. + */ + + const int size = m_lu.rows(); + ei_assert(b.rows() == size); + + result->resize(size, b.cols()); + + // Step 1 + for(int i = 0; i < size; ++i) result->row(m_p.coeff(i)) = b.row(i); + + // Step 2 + m_lu.template marked<UnitLowerTriangular>() + .solveTriangularInPlace(*result); + + // Step 3 + m_lu.template marked<UpperTriangular>() + .solveTriangularInPlace(*result); +} + +/** \lu_module + * + * \return the LU decomposition of \c *this. + * + * \sa class LU + */ +template<typename Derived> +inline const PartialLU<typename MatrixBase<Derived>::PlainMatrixType> +MatrixBase<Derived>::partialLu() const +{ + return PartialLU<PlainMatrixType>(eval()); +} + +#endif // EIGEN_PARTIALLU_H |