From 064f3eff959f92190b057ae989137713afb34820 Mon Sep 17 00:00:00 2001 From: giacomo po Date: Thu, 30 Aug 2012 10:01:34 +0200 Subject: [PATCH] first working version. Still no preconditioning --- Eigen/src/IterativeLinearSolvers/MINRES.h | 273 ++++++++++++++++++++++ 1 file changed, 273 insertions(+) create mode 100644 Eigen/src/IterativeLinearSolvers/MINRES.h diff --git a/Eigen/src/IterativeLinearSolvers/MINRES.h b/Eigen/src/IterativeLinearSolvers/MINRES.h new file mode 100644 index 000000000..ca93ebc32 --- /dev/null +++ b/Eigen/src/IterativeLinearSolvers/MINRES.h @@ -0,0 +1,273 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Giacomo Po +// Copyright (C) 2011 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +#ifndef EIGEN_MINRES_H_ +#define EIGEN_MINRES_H_ + + +namespace Eigen { + + namespace internal { + + /** \internal Low-level MINRES algorithm + * \param mat The matrix A + * \param rhs The right hand side vector b + * \param x On input and initial solution, on output the computed solution. + * \param precond A preconditioner being able to efficiently solve for an + * approximation of Ax=b (regardless of b) + * \param iters On input the max number of iteration, on output the number of performed iterations. + * \param tol_error On input the tolerance error, on output an estimation of the relative error. + */ + template + EIGEN_DONT_INLINE + void minres(const MatrixType& mat, const Rhs& rhs, Dest& x, + const Preconditioner& precond, int& iters, + typename Dest::RealScalar& tol_error) + { + typedef typename Dest::RealScalar RealScalar; + typedef typename Dest::Scalar Scalar; + typedef Matrix VectorType; + // initialize + const int maxIters(iters); // initialize maxIters to iters + const int N(mat.cols()); // the size of the matrix + const RealScalar threshold(tol_error); // convergence threshold + VectorType v(VectorType::Zero(N)); + VectorType v_hat(rhs-mat*x); + RealScalar beta(v_hat.norm()); + RealScalar c(1.0); // the cosine of the Givens rotation + RealScalar c_old(1.0); + RealScalar s(0.0); // the sine of the Givens rotation + RealScalar s_old(0.0); // the sine of the Givens rotation + VectorType w(VectorType::Zero(N)); + VectorType w_old(w); + RealScalar eta(beta); + RealScalar norm_rMR=beta; + const RealScalar norm_r0(beta); + + int n = 0; + while ( n < maxIters ){ + + + // Lanczos + VectorType v_old(v); + v=v_hat/beta; + VectorType Av(mat*v); + RealScalar alpha(v.transpose()*Av); + v_hat=Av-alpha*v-beta*v_old; + RealScalar beta_old(beta); + beta=v_hat.norm(); + + // QR + RealScalar c_oold(c_old); + c_old=c; + RealScalar s_oold(s_old); + s_old=s; + RealScalar r1_hat=c_old *alpha-c_oold*s_old *beta_old; + RealScalar r1 =std::pow(std::pow(r1_hat,2)+std::pow(beta,2),0.5); + RealScalar r2 =s_old *alpha+c_oold*c_old*beta_old; + RealScalar r3 =s_oold*beta_old; + + // Givens rotation + c=r1_hat/r1; + s=beta/r1; + + // update + VectorType w_oold(w_old); + w_old=w; + w=(v-r3*w_oold-r2*w_old) /r1; + x += c*eta*w; + norm_rMR *= std::fabs(s); + eta=-s*eta; + //if(norm_rMR/norm_r0 < threshold){ + if ( (mat*x-rhs).norm()/rhs.norm() < threshold){ + break; + } + n++; + } + tol_error = (mat*x-rhs).norm()/rhs.norm(); // return error DOES mat*x NEED TO BE RECOMPUTED??? + iters = n; // return number of iterations + } + + } + + template< typename _MatrixType, int _UpLo=Lower, + typename _Preconditioner = DiagonalPreconditioner > + class MINRES; + + namespace internal { + + template< typename _MatrixType, int _UpLo, typename _Preconditioner> + struct traits > + { + typedef _MatrixType MatrixType; + typedef _Preconditioner Preconditioner; + }; + + } + + /** \ingroup IterativeLinearSolvers_Module + * \brief A minimal residual solver for sparse symmetric problems + * + * This class allows to solve for A.x = b sparse linear problems using the MINRES algorithm + * of Paige and Saunders (1975). The sparse matrix A must be symmetric (possibly indefinite). + * The vectors x and b can be either dense or sparse. + * + * \tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix. + * \tparam _UpLo the triangular part that will be used for the computations. It can be Lower + * or Upper. Default is Lower. + * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner + * + * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() + * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations + * and NumTraits::epsilon() for the tolerance. + * + * This class can be used as the direct solver classes. Here is a typical usage example: + * \code + * int n = 10000; + * VectorXd x(n), b(n); + * SparseMatrix A(n,n); + * // fill A and b + * MINRES > mr; + * mr.compute(A); + * x = mr.solve(b); + * std::cout << "#iterations: " << mr.iterations() << std::endl; + * std::cout << "estimated error: " << mr.error() << std::endl; + * // update b, and solve again + * x = mr.solve(b); + * \endcode + * + * By default the iterations start with x=0 as an initial guess of the solution. + * One can control the start using the solveWithGuess() method. Here is a step by + * step execution example starting with a random guess and printing the evolution + * of the estimated error: + * * \code + * x = VectorXd::Random(n); + * mr.setMaxIterations(1); + * int i = 0; + * do { + * x = mr.solveWithGuess(b,x); + * std::cout << i << " : " << mr.error() << std::endl; + * ++i; + * } while (mr.info()!=Success && i<100); + * \endcode + * Note that such a step by step excution is slightly slower. + * + * \sa class ConjugateGradient, BiCGSTAB, SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner + */ + template< typename _MatrixType, int _UpLo, typename _Preconditioner> + class MINRES : public IterativeSolverBase > + { + + typedef IterativeSolverBase Base; + using Base::mp_matrix; + using Base::m_error; + using Base::m_iterations; + using Base::m_info; + using Base::m_isInitialized; + public: + typedef _MatrixType MatrixType; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::Index Index; + typedef typename MatrixType::RealScalar RealScalar; + typedef _Preconditioner Preconditioner; + + enum {UpLo = _UpLo}; + + public: + + /** Default constructor. */ + MINRES() : Base() {} + + /** Initialize the solver with matrix \a A for further \c Ax=b solving. + * + * This constructor is a shortcut for the default constructor followed + * by a call to compute(). + * + * \warning this class stores a reference to the matrix A as well as some + * precomputed values that depend on it. Therefore, if \a A is changed + * this class becomes invalid. Call compute() to update it with the new + * matrix A, or modify a copy of A. + */ + MINRES(const MatrixType& A) : Base(A) {} + + /** Destructor. */ + ~MINRES(){} + + /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A + * \a x0 as an initial solution. + * + * \sa compute() + */ + template + inline const internal::solve_retval_with_guess + solveWithGuess(const MatrixBase& b, const Guess& x0) const + { + eigen_assert(m_isInitialized && "MINRES is not initialized."); + eigen_assert(Base::rows()==b.rows() + && "MINRES::solve(): invalid number of rows of the right hand side matrix b"); + return internal::solve_retval_with_guess + (*this, b.derived(), x0); + } + + /** \internal */ + template + void _solveWithGuess(const Rhs& b, Dest& x) const + { + m_iterations = Base::maxIterations(); + m_error = Base::m_tolerance; + + for(int j=0; jtemplate selfadjointView(), b.col(j), xj, + Base::m_preconditioner, m_iterations, m_error); + } + + m_isInitialized = true; + m_info = m_error <= Base::m_tolerance ? Success : NoConvergence; + } + + /** \internal */ + template + void _solve(const Rhs& b, Dest& x) const + { + x.setOnes(); + _solveWithGuess(b,x); + } + + protected: + + }; + + namespace internal { + + template + struct solve_retval, Rhs> + : solve_retval_base, Rhs> + { + typedef MINRES<_MatrixType,_UpLo,_Preconditioner> Dec; + EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) + + template void evalTo(Dest& dst) const + { + dec()._solve(rhs(),dst); + } + }; + + } // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_MINRES_H +