diff options
Diffstat (limited to 'Eigen/src/SVD/JacobiSVD.h')
| -rw-r--r-- | Eigen/src/SVD/JacobiSVD.h | 80 |
1 files changed, 23 insertions, 57 deletions
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h index 3ab8a4c8a..444187ae7 100644 --- a/Eigen/src/SVD/JacobiSVD.h +++ b/Eigen/src/SVD/JacobiSVD.h @@ -550,7 +550,7 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD * according to the specified problem size. * \sa JacobiSVD() */ - JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0) + explicit JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0) { allocate(rows, cols, computationOptions); } @@ -565,7 +565,7 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not * available with the (non-default) FullPivHouseholderQR preconditioner. */ - JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0) + explicit JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0) { compute(matrix, computationOptions); } @@ -593,27 +593,12 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD return compute(matrix, m_computationOptions); } - /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A. - * - * \param b the right-hand-side of the equation to solve. - * - * \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V. - * - * \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving. - * In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$. - */ - template<typename Rhs> - inline const internal::solve_retval<JacobiSVD, Rhs> - solve(const MatrixBase<Rhs>& b) const - { - eigen_assert(m_isInitialized && "JacobiSVD is not initialized."); - eigen_assert(computeU() && computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice)."); - return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived()); - } - using Base::computeU; using Base::computeV; - + using Base::rows; + using Base::cols; + using Base::rank; + private: void allocate(Index rows, Index cols, unsigned int computationOptions); @@ -643,6 +628,7 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols; internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows; + MatrixType m_scaledMatrix; }; template<typename MatrixType, int QRPreconditioner> @@ -689,8 +675,9 @@ void JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, u : 0); m_workMatrix.resize(m_diagSize, m_diagSize); - if(m_cols>m_rows) m_qr_precond_morecols.allocate(*this); - if(m_rows>m_cols) m_qr_precond_morerows.allocate(*this); + if(m_cols>m_rows) m_qr_precond_morecols.allocate(*this); + if(m_rows>m_cols) m_qr_precond_morerows.allocate(*this); + if(m_cols!=m_cols) m_scaledMatrix.resize(rows,cols); } template<typename MatrixType, int QRPreconditioner> @@ -707,21 +694,26 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig // limit for very small denormal numbers to be considered zero in order to avoid infinite loops (see bug 286) const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min(); + // Scaling factor to reduce over/under-flows + RealScalar scale = matrix.cwiseAbs().maxCoeff(); + if(scale==RealScalar(0)) scale = RealScalar(1); + /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */ - if(!m_qr_precond_morecols.run(*this, matrix) && !m_qr_precond_morerows.run(*this, matrix)) + if(m_rows!=m_cols) + { + m_scaledMatrix = matrix / scale; + m_qr_precond_morecols.run(*this, m_scaledMatrix); + m_qr_precond_morerows.run(*this, m_scaledMatrix); + } + else { - m_workMatrix = matrix.block(0,0,m_diagSize,m_diagSize); + m_workMatrix = matrix.block(0,0,m_diagSize,m_diagSize) / scale; if(m_computeFullU) m_matrixU.setIdentity(m_rows,m_rows); if(m_computeThinU) m_matrixU.setIdentity(m_rows,m_diagSize); if(m_computeFullV) m_matrixV.setIdentity(m_cols,m_cols); if(m_computeThinV) m_matrixV.setIdentity(m_cols, m_diagSize); } - - // Scaling factor to reduce over/under-flows - RealScalar scale = m_workMatrix.cwiseAbs().maxCoeff(); - if(scale==RealScalar(0)) scale = RealScalar(1); - m_workMatrix /= scale; /*** step 2. The main Jacobi SVD iteration. ***/ @@ -739,8 +731,7 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig // if this 2x2 sub-matrix is not diagonal already... // notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't // keep us iterating forever. Similarly, small denormal numbers are considered zero. - EIGEN_USING_STD_MATH(max); - RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)), + RealScalar threshold = numext::maxi(considerAsZero, precision * numext::maxi(abs(m_workMatrix.coeff(p,p)), abs(m_workMatrix.coeff(q,q)))); // We compare both values to threshold instead of calling max to be robust to NaN (See bug 791) if(abs(m_workMatrix.coeff(p,q))>threshold || abs(m_workMatrix.coeff(q,p)) > threshold) @@ -799,31 +790,6 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig return *this; } -namespace internal { -template<typename _MatrixType, int QRPreconditioner, typename Rhs> -struct solve_retval<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs> - : solve_retval_base<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs> -{ - typedef JacobiSVD<_MatrixType, QRPreconditioner> JacobiSVDType; - EIGEN_MAKE_SOLVE_HELPERS(JacobiSVDType,Rhs) - - template<typename Dest> void evalTo(Dest& dst) const - { - eigen_assert(rhs().rows() == dec().rows()); - - // A = U S V^* - // So A^{-1} = V S^{-1} U^* - - Matrix<Scalar, Dynamic, Rhs::ColsAtCompileTime, 0, _MatrixType::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime> tmp; - Index rank = dec().rank(); - - tmp.noalias() = dec().matrixU().leftCols(rank).adjoint() * rhs(); - tmp = dec().singularValues().head(rank).asDiagonal().inverse() * tmp; - dst = dec().matrixV().leftCols(rank) * tmp; - } -}; -} // end namespace internal - #ifndef __CUDACC__ /** \svd_module * |