diff options
author | giacomo po <gpo@ucla.edu> | 2012-09-24 07:47:38 -0700 |
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committer | giacomo po <gpo@ucla.edu> | 2012-09-24 07:47:38 -0700 |
commit | dd7ff3f4934b173fe337916fc9225facbaf955c3 (patch) | |
tree | 89fabcffe80f7be1fa4cec1ef71c06f5988f499a /unsupported | |
parent | 8c5e4fae6186004b8121276f30dd75a8b217eec9 (diff) |
moved MINRES to unsupported. Made unit test.
Diffstat (limited to 'unsupported')
-rw-r--r-- | unsupported/Eigen/IterativeSolvers | 1 | ||||
-rw-r--r-- | unsupported/Eigen/src/IterativeSolvers/MINRES.h | 302 | ||||
-rw-r--r-- | unsupported/test/CMakeLists.txt | 2 | ||||
-rw-r--r-- | unsupported/test/minres.cpp | 33 |
4 files changed, 337 insertions, 1 deletions
diff --git a/unsupported/Eigen/IterativeSolvers b/unsupported/Eigen/IterativeSolvers index 6c6946d91..7a5776d9c 100644 --- a/unsupported/Eigen/IterativeSolvers +++ b/unsupported/Eigen/IterativeSolvers @@ -34,6 +34,7 @@ #include "../../Eigen/Householder" #include "src/IterativeSolvers/GMRES.h" //#include "src/IterativeSolvers/SSORPreconditioner.h" +#include "src/IterativeSolvers/MINRES.h" //@} diff --git a/unsupported/Eigen/src/IterativeSolvers/MINRES.h b/unsupported/Eigen/src/IterativeSolvers/MINRES.h new file mode 100644 index 000000000..d5527a163 --- /dev/null +++ b/unsupported/Eigen/src/IterativeSolvers/MINRES.h @@ -0,0 +1,302 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Giacomo Po <gpo@ucla.edu> +// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr> +// +// 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 right 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<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner> + 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<Scalar,Dynamic,1> VectorType; + + // initialize + const int maxIters(iters); // initialize maxIters to iters + const int N(mat.cols()); // the size of the matrix + const RealScalar rhsNorm2(rhs.squaredNorm()); + const RealScalar threshold2(tol_error*tol_error*rhsNorm2); // convergence threshold + + // Compute initial residual + const VectorType residual(rhs-mat*x); + RealScalar residualNorm2(residual.squaredNorm()); // not needed for original convergnce criterion + + // Initialize preconditioned Lanczos + VectorType v_old(N); // will be initialized inside loop + VectorType v = VectorType::Zero(N); //initialize v + VectorType v_new = residual; //initialize v_new + VectorType w(N); // will be initialized inside loop + VectorType w_new = precond.solve(v_new); // initialize w_new + RealScalar beta; // will be initialized inside loop + RealScalar beta_new2 = v_new.dot(w_new); + assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE"); + RealScalar beta_new = sqrt(beta_new2); + RealScalar beta_one = beta_new; + v_new /= beta_new; + w_new /= beta_new; + // Initialize other variables + 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 p_oold(N); // will be initialized in loop + VectorType p_old(VectorType::Zero(N)); // initialize p_old=0 + VectorType p(p_old); // initialize p=0 + RealScalar eta(1.0); + + int n = 0; + while ( n < maxIters ){ + + // Preconditioned Lanczos + /* Note that there are 4 variants on the Lanczos algorithm. These are + * described in Paige, C. C. (1972). Computational variants of + * the Lanczos method for the eigenproblem. IMA Journal of Applied + * Mathematics, 10(3), 373–381. The current implementation corresonds + * to the case A(2,7) in the paper. It also corresponds to + * algorithm 6.14 in Y. Saad, Iterative Methods for Sparse Linear + * Systems, 2003 p.173. For the preconditioned version see + * A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM (1987). + */ + beta = beta_new; + v_old = v; // update: at first time step, this makes v_old = 0 so value of beta doesn't matter + v = v_new; // update + w = w_new; // update + v_new.noalias() = mat*w - beta*v_old; // compute v_new + const RealScalar alpha = v_new.dot(w); + v_new -= alpha*v; // overwrite v_new + w_new = precond.solve(v_new); // overwrite w_new + beta_new2 = v_new.dot(w_new); // compute beta_new + assert(beta_new2 >= 0 && "PRECONDITIONER IS NOT POSITIVE DEFINITE"); + beta_new = sqrt(beta_new2); // compute beta_new + v_new /= beta_new; // overwrite v_new for next iteration + w_new /= beta_new; // overwrite w_new for next iteration + + // Givens rotation + const RealScalar r2 =s*alpha+c*c_old*beta; // s, s_old, c and c_old are still from previous iteration + const RealScalar r3 =s_old*beta; // s, s_old, c and c_old are still from previous iteration + const RealScalar r1_hat=c*alpha-c_old*s*beta; + const RealScalar r1 =sqrt( std::pow(r1_hat,2) + std::pow(beta_new,2) ); + c_old = c; // store for next iteration + s_old = s; // store for next iteration + c=r1_hat/r1; // new cosine + s=beta_new/r1; // new sine + + // Update solution + p_oold = p_old; + p_old = p; + p=(w-r2*p_old-r3*p_oold) /r1; + x += beta_one*c*eta*p; + residualNorm2 *= s*s; + + if ( residualNorm2 < threshold2){ + break; + } + + eta=-s*eta; // update eta + n++; // increment iteration + } + tol_error = std::sqrt(residualNorm2 / rhsNorm2); // return error + iters = n; // return number of iterations + } + + } + + template< typename _MatrixType, int _UpLo=Lower, + typename _Preconditioner = IdentityPreconditioner> +// typename _Preconditioner = IdentityPreconditioner<typename _MatrixType::Scalar> > // preconditioner must be positive definite + class MINRES; + + namespace internal { + + template< typename _MatrixType, int _UpLo, typename _Preconditioner> + struct traits<MINRES<_MatrixType,_UpLo,_Preconditioner> > + { + 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<Scalar>::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<double> A(n,n); + * // fill A and b + * MINRES<SparseMatrix<double> > 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<MINRES<_MatrixType,_UpLo,_Preconditioner> > + { + + typedef IterativeSolverBase<MINRES> 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<typename Rhs,typename Guess> + inline const internal::solve_retval_with_guess<MINRES, Rhs, Guess> + solveWithGuess(const MatrixBase<Rhs>& 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 + <MINRES, Rhs, Guess>(*this, b.derived(), x0); + } + + /** \internal */ + template<typename Rhs,typename Dest> + void _solveWithGuess(const Rhs& b, Dest& x) const + { + m_iterations = Base::maxIterations(); + m_error = Base::m_tolerance; + + for(int j=0; j<b.cols(); ++j) + { + m_iterations = Base::maxIterations(); + m_error = Base::m_tolerance; + + typename Dest::ColXpr xj(x,j); + internal::minres(mp_matrix->template selfadjointView<UpLo>(), 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<typename Rhs,typename Dest> + void _solve(const Rhs& b, Dest& x) const + { + x.setZero(); + _solveWithGuess(b,x); + } + + protected: + + }; + + namespace internal { + + template<typename _MatrixType, int _UpLo, typename _Preconditioner, typename Rhs> + struct solve_retval<MINRES<_MatrixType,_UpLo,_Preconditioner>, Rhs> + : solve_retval_base<MINRES<_MatrixType,_UpLo,_Preconditioner>, Rhs> + { + typedef MINRES<_MatrixType,_UpLo,_Preconditioner> Dec; + EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) + + template<typename Dest> void evalTo(Dest& dst) const + { + dec()._solve(rhs(),dst); + } + }; + + } // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_MINRES_H + diff --git a/unsupported/test/CMakeLists.txt b/unsupported/test/CMakeLists.txt index ff0137ec6..1e8ba7240 100644 --- a/unsupported/test/CMakeLists.txt +++ b/unsupported/test/CMakeLists.txt @@ -85,4 +85,4 @@ ei_add_test(polynomialutils) ei_add_test(kronecker_product) ei_add_test(splines) ei_add_test(gmres) - +ei_add_test(minres) diff --git a/unsupported/test/minres.cpp b/unsupported/test/minres.cpp new file mode 100644 index 000000000..46946ca8b --- /dev/null +++ b/unsupported/test/minres.cpp @@ -0,0 +1,33 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2011 Gael Guennebaud <g.gael@free.fr> +// Copyright (C) 2012 Giacomo Po <gpo@ucla.edu> +// +// 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/. + +#include "../../test/sparse_solver.h" +#include <Eigen/IterativeSolvers> + +template<typename T> void test_minres_T() +{ + minres<SparseMatrix<T>, DiagonalPreconditioner<T> > minres_colmajor_diag; + minres<SparseMatrix<T>, IdentityPreconditioner > minres_colmajor_I; + minres<SparseMatrix<T>, IncompleteLUT<T> > minres_colmajor_ilut; + //minres<SparseMatrix<T>, SSORPreconditioner<T> > minres_colmajor_ssor; + + CALL_SUBTEST( check_sparse_square_solving(minres_colmajor_diag) ); +// CALL_SUBTEST( check_sparse_square_solving(minres_colmajor_I) ); + CALL_SUBTEST( check_sparse_square_solving(minres_colmajor_ilut) ); + //CALL_SUBTEST( check_sparse_square_solving(minres_colmajor_ssor) ); +} + +void test_minres() +{ + for(int i = 0; i < g_repeat; i++) { + CALL_SUBTEST_1(test_minres_T<double>()); + CALL_SUBTEST_2(test_minres_T<std::complex<double> >()); + } +} |