diff options
Diffstat (limited to 'extern/Eigen3/Eigen/src/Cholesky/LDLT.h')
| -rw-r--r-- | extern/Eigen3/Eigen/src/Cholesky/LDLT.h | 61 |
1 files changed, 31 insertions, 30 deletions
diff --git a/extern/Eigen3/Eigen/src/Cholesky/LDLT.h b/extern/Eigen3/Eigen/src/Cholesky/LDLT.h index d026418f8a9..abd30bd916d 100644 --- a/extern/Eigen3/Eigen/src/Cholesky/LDLT.h +++ b/extern/Eigen3/Eigen/src/Cholesky/LDLT.h @@ -235,6 +235,11 @@ template<typename _MatrixType, int _UpLo> class LDLT } protected: + + static void check_template_parameters() + { + EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar); + } /** \internal * Used to compute and store the Cholesky decomposition A = L D L^* = U^* D U. @@ -274,30 +279,13 @@ template<> struct ldlt_inplace<Lower> return true; } - RealScalar cutoff(0), biggest_in_corner; - for (Index k = 0; k < size; ++k) { // Find largest diagonal element Index index_of_biggest_in_corner; - biggest_in_corner = mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner); + mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner); index_of_biggest_in_corner += k; - if(k == 0) - { - // The biggest overall is the point of reference to which further diagonals - // are compared; if any diagonal is negligible compared - // to the largest overall, the algorithm bails. - cutoff = abs(NumTraits<Scalar>::epsilon() * biggest_in_corner); - } - - // Finish early if the matrix is not full rank. - if(biggest_in_corner < cutoff) - { - for(Index i = k; i < size; i++) transpositions.coeffRef(i) = i; - break; - } - transpositions.coeffRef(k) = index_of_biggest_in_corner; if(k != index_of_biggest_in_corner) { @@ -328,15 +316,20 @@ template<> struct ldlt_inplace<Lower> if(k>0) { - temp.head(k) = mat.diagonal().head(k).asDiagonal() * A10.adjoint(); + temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint(); mat.coeffRef(k,k) -= (A10 * temp.head(k)).value(); if(rs>0) A21.noalias() -= A20 * temp.head(k); } - if((rs>0) && (abs(mat.coeffRef(k,k)) > cutoff)) - A21 /= mat.coeffRef(k,k); - + + // In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot + // was smaller than the cutoff value. However, soince LDLT is not rank-revealing + // we should only make sure we do not introduce INF or NaN values. + // LAPACK also uses 0 as the cutoff value. RealScalar realAkk = numext::real(mat.coeffRef(k,k)); + if((rs>0) && (abs(realAkk) > RealScalar(0))) + A21 /= realAkk; + if (sign == PositiveSemiDef) { if (realAkk < 0) sign = Indefinite; } else if (sign == NegativeSemiDef) { @@ -446,6 +439,8 @@ template<typename MatrixType> struct LDLT_Traits<MatrixType,Upper> template<typename MatrixType, int _UpLo> LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a) { + check_template_parameters(); + eigen_assert(a.rows()==a.cols()); const Index size = a.rows(); @@ -454,6 +449,7 @@ LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a) m_transpositions.resize(size); m_isInitialized = false; m_temporary.resize(size); + m_sign = internal::ZeroSign; internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, m_sign); @@ -468,7 +464,7 @@ LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::compute(const MatrixType& a) */ template<typename MatrixType, int _UpLo> template<typename Derived> -LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename NumTraits<typename MatrixType::Scalar>::Real& sigma) +LDLT<MatrixType,_UpLo>& LDLT<MatrixType,_UpLo>::rankUpdate(const MatrixBase<Derived>& w, const typename LDLT<MatrixType,_UpLo>::RealScalar& sigma) { const Index size = w.rows(); if (m_isInitialized) @@ -514,16 +510,21 @@ struct solve_retval<LDLT<_MatrixType,_UpLo>, Rhs> using std::abs; using std::max; typedef typename LDLTType::MatrixType MatrixType; - typedef typename LDLTType::Scalar Scalar; typedef typename LDLTType::RealScalar RealScalar; - const Diagonal<const MatrixType> vectorD = dec().vectorD(); - RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() * NumTraits<Scalar>::epsilon(), - RealScalar(1) / NumTraits<RealScalar>::highest()); // motivated by LAPACK's xGELSS + const typename Diagonal<const MatrixType>::RealReturnType vectorD(dec().vectorD()); + // In some previous versions, tolerance was set to the max of 1/highest and the maximal diagonal entry * epsilon + // as motivated by LAPACK's xGELSS: + // RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() *NumTraits<RealScalar>::epsilon(),RealScalar(1) / NumTraits<RealScalar>::highest()); + // However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest + // diagonal element is not well justified and to numerical issues in some cases. + // Moreover, Lapack's xSYTRS routines use 0 for the tolerance. + RealScalar tolerance = RealScalar(1) / NumTraits<RealScalar>::highest(); + for (Index i = 0; i < vectorD.size(); ++i) { if(abs(vectorD(i)) > tolerance) - dst.row(i) /= vectorD(i); + dst.row(i) /= vectorD(i); else - dst.row(i).setZero(); + dst.row(i).setZero(); } // dst = L^-T (D^-1 L^-1 P b) @@ -576,7 +577,7 @@ MatrixType LDLT<MatrixType,_UpLo>::reconstructedMatrix() const // L^* P res = matrixU() * res; // D(L^*P) - res = vectorD().asDiagonal() * res; + res = vectorD().real().asDiagonal() * res; // L(DL^*P) res = matrixL() * res; // P^T (LDL^*P) |