diff options
Diffstat (limited to 'unsupported/Eigen/src/IterativeSolvers/DGMRES.h')
| -rw-r--r-- | unsupported/Eigen/src/IterativeSolvers/DGMRES.h | 122 |
1 files changed, 60 insertions, 62 deletions
diff --git a/unsupported/Eigen/src/IterativeSolvers/DGMRES.h b/unsupported/Eigen/src/IterativeSolvers/DGMRES.h index bae04fc30..5ae011b75 100644 --- a/unsupported/Eigen/src/IterativeSolvers/DGMRES.h +++ b/unsupported/Eigen/src/IterativeSolvers/DGMRES.h @@ -10,7 +10,7 @@ #ifndef EIGEN_DGMRES_H #define EIGEN_DGMRES_H -#include <Eigen/Eigenvalues> +#include "../../../../Eigen/Eigenvalues" namespace Eigen { @@ -39,7 +39,6 @@ template <typename VectorType, typename IndexType> void sortWithPermutation (VectorType& vec, IndexType& perm, typename IndexType::Scalar& ncut) { eigen_assert(vec.size() == perm.size()); - typedef typename IndexType::Scalar Index; bool flag; for (Index k = 0; k < ncut; k++) { @@ -58,7 +57,7 @@ void sortWithPermutation (VectorType& vec, IndexType& perm, typename IndexType:: } /** - * \ingroup IterativeLInearSolvers_Module + * \ingroup IterativeLinearSolvers_Module * \brief A Restarted GMRES with deflation. * This class implements a modification of the GMRES solver for * sparse linear systems. The basis is built with modified @@ -89,7 +88,7 @@ void sortWithPermutation (VectorType& vec, IndexType& perm, typename IndexType:: * [1] D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid * Algebraic Solvers for Linear Systems Arising from Compressible * Flows, Computers and Fluids, In Press, - * http://dx.doi.org/10.1016/j.compfluid.2012.03.023 + * https://doi.org/10.1016/j.compfluid.2012.03.023 * [2] K. Burrage and J. Erhel, On the performance of various * adaptive preconditioned GMRES strategies, 5(1998), 101-121. * [3] J. Erhel, K. Burrage and B. Pohl, Restarted GMRES @@ -110,9 +109,9 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> > using Base::m_tolerance; public: using Base::_solve_impl; + using Base::_solve_with_guess_impl; typedef _MatrixType MatrixType; typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::Index Index; typedef typename MatrixType::StorageIndex StorageIndex; typedef typename MatrixType::RealScalar RealScalar; typedef _Preconditioner Preconditioner; @@ -143,44 +142,30 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> > /** \internal */ template<typename Rhs,typename Dest> - void _solve_with_guess_impl(const Rhs& b, Dest& x) const - { - bool failed = false; - for(int j=0; j<b.cols(); ++j) - { - m_iterations = Base::maxIterations(); - m_error = Base::m_tolerance; - - typename Dest::ColXpr xj(x,j); - dgmres(matrix(), b.col(j), xj, Base::m_preconditioner); - } - m_info = failed ? NumericalIssue - : m_error <= Base::m_tolerance ? Success - : NoConvergence; - m_isInitialized = true; - } - - /** \internal */ - template<typename Rhs,typename Dest> - void _solve_impl(const Rhs& b, MatrixBase<Dest>& x) const + void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const { - x = b; - _solve_with_guess_impl(b,x.derived()); + EIGEN_STATIC_ASSERT(Rhs::ColsAtCompileTime==1 || Dest::ColsAtCompileTime==1, YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX); + + m_iterations = Base::maxIterations(); + m_error = Base::m_tolerance; + + dgmres(matrix(), b, x, Base::m_preconditioner); } + /** * Get the restart value */ - int restart() { return m_restart; } + Index restart() { return m_restart; } /** * Set the restart value (default is 30) */ - void set_restart(const int restart) { m_restart=restart; } + void set_restart(const Index restart) { m_restart=restart; } /** * Set the number of eigenvalues to deflate at each restart */ - void setEigenv(const int neig) + void setEigenv(const Index neig) { m_neig = neig; if (neig+1 > m_maxNeig) m_maxNeig = neig+1; // To allow for complex conjugates @@ -189,12 +174,12 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> > /** * Get the size of the deflation subspace size */ - int deflSize() {return m_r; } + Index deflSize() {return m_r; } /** * Set the maximum size of the deflation subspace */ - void setMaxEigenv(const int maxNeig) { m_maxNeig = maxNeig; } + void setMaxEigenv(const Index maxNeig) { m_maxNeig = maxNeig; } protected: // DGMRES algorithm @@ -202,27 +187,27 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> > void dgmres(const MatrixType& mat,const Rhs& rhs, Dest& x, const Preconditioner& precond) const; // Perform one cycle of GMRES template<typename Dest> - int dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, int& nbIts) const; + Index dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, Index& nbIts) const; // Compute data to use for deflation - int dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const; + Index dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const; // Apply deflation to a vector template<typename RhsType, typename DestType> - int dgmresApplyDeflation(const RhsType& In, DestType& Out) const; + Index dgmresApplyDeflation(const RhsType& In, DestType& Out) const; ComplexVector schurValues(const ComplexSchur<DenseMatrix>& schurofH) const; ComplexVector schurValues(const RealSchur<DenseMatrix>& schurofH) const; // Init data for deflation void dgmresInitDeflation(Index& rows) const; mutable DenseMatrix m_V; // Krylov basis vectors mutable DenseMatrix m_H; // Hessenberg matrix - mutable DenseMatrix m_Hes; // Initial hessenberg matrix wihout Givens rotations applied + mutable DenseMatrix m_Hes; // Initial hessenberg matrix without Givens rotations applied mutable Index m_restart; // Maximum size of the Krylov subspace mutable DenseMatrix m_U; // Vectors that form the basis of the invariant subspace mutable DenseMatrix m_MU; // matrix operator applied to m_U (for next cycles) mutable DenseMatrix m_T; /* T=U^T*M^{-1}*A*U */ mutable PartialPivLU<DenseMatrix> m_luT; // LU factorization of m_T mutable StorageIndex m_neig; //Number of eigenvalues to extract at each restart - mutable int m_r; // Current number of deflated eigenvalues, size of m_U - mutable int m_maxNeig; // Maximum number of eigenvalues to deflate + mutable Index m_r; // Current number of deflated eigenvalues, size of m_U + mutable Index m_maxNeig; // Maximum number of eigenvalues to deflate mutable RealScalar m_lambdaN; //Modulus of the largest eigenvalue of A mutable bool m_isDeflAllocated; mutable bool m_isDeflInitialized; @@ -243,18 +228,30 @@ template<typename Rhs, typename Dest> void DGMRES<_MatrixType, _Preconditioner>::dgmres(const MatrixType& mat,const Rhs& rhs, Dest& x, const Preconditioner& precond) const { + const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)(); + + RealScalar normRhs = rhs.norm(); + if(normRhs <= considerAsZero) + { + x.setZero(); + m_error = 0; + return; + } + //Initialization - int n = mat.rows(); + m_isDeflInitialized = false; + Index n = mat.rows(); DenseVector r0(n); - int nbIts = 0; + Index nbIts = 0; m_H.resize(m_restart+1, m_restart); m_Hes.resize(m_restart, m_restart); m_V.resize(n,m_restart+1); - //Initial residual vector and intial norm - x = precond.solve(x); + //Initial residual vector and initial norm + if(x.squaredNorm()==0) + x = precond.solve(rhs); r0 = rhs - mat * x; RealScalar beta = r0.norm(); - RealScalar normRhs = rhs.norm(); + m_error = beta/normRhs; if(m_error < m_tolerance) m_info = Success; @@ -267,8 +264,10 @@ void DGMRES<_MatrixType, _Preconditioner>::dgmres(const MatrixType& mat,const Rh dgmresCycle(mat, precond, x, r0, beta, normRhs, nbIts); // Compute the new residual vector for the restart - if (nbIts < m_iterations && m_info == NoConvergence) - r0 = rhs - mat * x; + if (nbIts < m_iterations && m_info == NoConvergence) { + r0 = rhs - mat * x; + beta = r0.norm(); + } } } @@ -284,7 +283,7 @@ void DGMRES<_MatrixType, _Preconditioner>::dgmres(const MatrixType& mat,const Rh */ template< typename _MatrixType, typename _Preconditioner> template<typename Dest> -int DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, int& nbIts) const +Index DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, Index& nbIts) const { //Initialization DenseVector g(m_restart+1); // Right hand side of the least square problem @@ -293,8 +292,8 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, con m_V.col(0) = r0/beta; m_info = NoConvergence; std::vector<JacobiRotation<Scalar> >gr(m_restart); // Givens rotations - int it = 0; // Number of inner iterations - int n = mat.rows(); + Index it = 0; // Number of inner iterations + Index n = mat.rows(); DenseVector tv1(n), tv2(n); //Temporary vectors while (m_info == NoConvergence && it < m_restart && nbIts < m_iterations) { @@ -312,7 +311,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, con // Orthogonalize it with the previous basis in the basis using modified Gram-Schmidt Scalar coef; - for (int i = 0; i <= it; ++i) + for (Index i = 0; i <= it; ++i) { coef = tv1.dot(m_V.col(i)); tv1 = tv1 - coef * m_V.col(i); @@ -328,7 +327,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, con // FIXME Check for happy breakdown // Update Hessenberg matrix with Givens rotations - for (int i = 1; i <= it; ++i) + for (Index i = 1; i <= it; ++i) { m_H.col(it).applyOnTheLeft(i-1,i,gr[i-1].adjoint()); } @@ -394,7 +393,6 @@ inline typename DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_Matr template< typename _MatrixType, typename _Preconditioner> inline typename DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_MatrixType, _Preconditioner>::schurValues(const RealSchur<DenseMatrix>& schurofH) const { - typedef typename MatrixType::Index Index; const DenseMatrix& T = schurofH.matrixT(); Index it = T.rows(); ComplexVector eig(it); @@ -418,7 +416,7 @@ inline typename DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_Matr } template< typename _MatrixType, typename _Preconditioner> -int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const +Index DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const { // First, find the Schur form of the Hessenberg matrix H typename internal::conditional<NumTraits<Scalar>::IsComplex, ComplexSchur<DenseMatrix>, RealSchur<DenseMatrix> >::type schurofH; @@ -433,8 +431,8 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri // Reorder the absolute values of Schur values DenseRealVector modulEig(it); - for (int j=0; j<it; ++j) modulEig(j) = std::abs(eig(j)); - perm.setLinSpaced(it,0,it-1); + for (Index j=0; j<it; ++j) modulEig(j) = std::abs(eig(j)); + perm.setLinSpaced(it,0,internal::convert_index<StorageIndex>(it-1)); internal::sortWithPermutation(modulEig, perm, neig); if (!m_lambdaN) @@ -442,7 +440,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri m_lambdaN = (std::max)(modulEig.maxCoeff(), m_lambdaN); } //Count the real number of extracted eigenvalues (with complex conjugates) - int nbrEig = 0; + Index nbrEig = 0; while (nbrEig < neig) { if(eig(perm(it-nbrEig-1)).imag() == RealScalar(0)) nbrEig++; @@ -451,7 +449,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri // Extract the Schur vectors corresponding to the smallest Ritz values DenseMatrix Sr(it, nbrEig); Sr.setZero(); - for (int j = 0; j < nbrEig; j++) + for (Index j = 0; j < nbrEig; j++) { Sr.col(j) = schurofH.matrixU().col(perm(it-j-1)); } @@ -462,8 +460,8 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri if (m_r) { // Orthogonalize X against m_U using modified Gram-Schmidt - for (int j = 0; j < nbrEig; j++) - for (int k =0; k < m_r; k++) + for (Index j = 0; j < nbrEig; j++) + for (Index k =0; k < m_r; k++) X.col(j) = X.col(j) - (m_U.col(k).dot(X.col(j)))*m_U.col(k); } @@ -473,7 +471,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri dgmresInitDeflation(m); DenseMatrix MX(m, nbrEig); DenseVector tv1(m); - for (int j = 0; j < nbrEig; j++) + for (Index j = 0; j < nbrEig; j++) { tv1 = mat * X.col(j); MX.col(j) = precond.solve(tv1); @@ -488,8 +486,8 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri } // Save X into m_U and m_MX in m_MU - for (int j = 0; j < nbrEig; j++) m_U.col(m_r+j) = X.col(j); - for (int j = 0; j < nbrEig; j++) m_MU.col(m_r+j) = MX.col(j); + for (Index j = 0; j < nbrEig; j++) m_U.col(m_r+j) = X.col(j); + for (Index j = 0; j < nbrEig; j++) m_MU.col(m_r+j) = MX.col(j); // Increase the size of the invariant subspace m_r += nbrEig; @@ -502,7 +500,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri } template<typename _MatrixType, typename _Preconditioner> template<typename RhsType, typename DestType> -int DGMRES<_MatrixType, _Preconditioner>::dgmresApplyDeflation(const RhsType &x, DestType &y) const +Index DGMRES<_MatrixType, _Preconditioner>::dgmresApplyDeflation(const RhsType &x, DestType &y) const { DenseVector x1 = m_U.leftCols(m_r).transpose() * x; y = x + m_U.leftCols(m_r) * ( m_lambdaN * m_luT.solve(x1) - x1); |