diff options
Diffstat (limited to 'Eigen/src/SVD/SVDBase.h')
| -rw-r--r-- | Eigen/src/SVD/SVDBase.h | 41 |
1 files changed, 41 insertions, 0 deletions
diff --git a/Eigen/src/SVD/SVDBase.h b/Eigen/src/SVD/SVDBase.h index 61b01fb8a..27b732b80 100644 --- a/Eigen/src/SVD/SVDBase.h +++ b/Eigen/src/SVD/SVDBase.h @@ -190,6 +190,30 @@ public: inline Index rows() const { return m_rows; } inline Index cols() const { return m_cols; } + + /** \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 Solve<Derived, Rhs> + solve(const MatrixBase<Rhs>& b) const + { + eigen_assert(m_isInitialized && "SVD is not initialized."); + eigen_assert(computeU() && computeV() && "SVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice)."); + return Solve<Derived, Rhs>(derived(), b.derived()); + } + + #ifndef EIGEN_PARSED_BY_DOXYGEN + template<typename RhsType, typename DstType> + EIGEN_DEVICE_FUNC + void _solve_impl(const RhsType &rhs, DstType &dst) const; + #endif protected: // return true if already allocated @@ -220,6 +244,23 @@ protected: }; +#ifndef EIGEN_PARSED_BY_DOXYGEN +template<typename Derived> +template<typename RhsType, typename DstType> +void SVDBase<Derived>::_solve_impl(const RhsType &rhs, DstType &dst) const +{ + eigen_assert(rhs.rows() == rows()); + + // A = U S V^* + // So A^{-1} = V S^{-1} U^* + + Matrix<Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp; + Index l_rank = rank(); + tmp.noalias() = m_matrixU.leftCols(l_rank).adjoint() * rhs; + tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp; + dst = m_matrixV.leftCols(l_rank) * tmp; +} +#endif template<typename MatrixType> bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions) |