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-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2011-2014 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_CONJUGATE_GRADIENT_H
-#define EIGEN_CONJUGATE_GRADIENT_H
-
-namespace Eigen {
-
-namespace internal {
-
-/** \internal Low-level conjugate gradient 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<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
-EIGEN_DONT_INLINE
-void conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
- const Preconditioner& precond, Index& iters,
- typename Dest::RealScalar& tol_error)
-{
- using std::sqrt;
- using std::abs;
- typedef typename Dest::RealScalar RealScalar;
- typedef typename Dest::Scalar Scalar;
- typedef Matrix<Scalar,Dynamic,1> VectorType;
-
- RealScalar tol = tol_error;
- Index maxIters = iters;
-
- Index n = mat.cols();
-
- VectorType residual = rhs - mat * x; //initial residual
-
- RealScalar rhsNorm2 = rhs.squaredNorm();
- if(rhsNorm2 == 0)
- {
- x.setZero();
- iters = 0;
- tol_error = 0;
- return;
- }
- RealScalar threshold = tol*tol*rhsNorm2;
- RealScalar residualNorm2 = residual.squaredNorm();
- if (residualNorm2 < threshold)
- {
- iters = 0;
- tol_error = sqrt(residualNorm2 / rhsNorm2);
- return;
- }
-
- VectorType p(n);
- p = precond.solve(residual); // initial search direction
-
- VectorType z(n), tmp(n);
- RealScalar absNew = numext::real(residual.dot(p)); // the square of the absolute value of r scaled by invM
- Index i = 0;
- while(i < maxIters)
- {
- tmp.noalias() = mat * p; // the bottleneck of the algorithm
-
- Scalar alpha = absNew / p.dot(tmp); // the amount we travel on dir
- x += alpha * p; // update solution
- residual -= alpha * tmp; // update residual
-
- residualNorm2 = residual.squaredNorm();
- if(residualNorm2 < threshold)
- break;
-
- z = precond.solve(residual); // approximately solve for "A z = residual"
-
- RealScalar absOld = absNew;
- absNew = numext::real(residual.dot(z)); // update the absolute value of r
- RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction
- p = z + beta * p; // update search direction
- i++;
- }
- tol_error = sqrt(residualNorm2 / rhsNorm2);
- iters = i;
-}
-
-}
-
-template< typename _MatrixType, int _UpLo=Lower,
- typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> >
-class ConjugateGradient;
-
-namespace internal {
-
-template< typename _MatrixType, int _UpLo, typename _Preconditioner>
-struct traits<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
-{
- typedef _MatrixType MatrixType;
- typedef _Preconditioner Preconditioner;
-};
-
-}
-
-/** \ingroup IterativeLinearSolvers_Module
- * \brief A conjugate gradient solver for sparse (or dense) self-adjoint problems
- *
- * This class allows to solve for A.x = b linear problems using an iterative conjugate gradient algorithm.
- * The matrix A must be selfadjoint. The matrix A and the vectors x and b can be either dense or sparse.
- *
- * \tparam _MatrixType the type of the 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,
- * \c Upper, or \c Lower|Upper in which the full matrix entries will be considered.
- * Default is \c Lower, best performance is \c Lower|Upper.
- * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner
- *
- * \implsparsesolverconcept
- *
- * 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.
- *
- * The tolerance corresponds to the relative residual error: |Ax-b|/|b|
- *
- * \b Performance: Even though the default value of \c _UpLo is \c Lower, significantly higher performance is
- * achieved when using a complete matrix and \b Lower|Upper as the \a _UpLo template parameter. Moreover, in this
- * case multi-threading can be exploited if the user code is compiled with OpenMP enabled.
- * See \ref TopicMultiThreading for details.
- *
- * 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
- ConjugateGradient<SparseMatrix<double>, Lower|Upper> cg;
- cg.compute(A);
- x = cg.solve(b);
- std::cout << "#iterations: " << cg.iterations() << std::endl;
- std::cout << "estimated error: " << cg.error() << std::endl;
- // update b, and solve again
- x = cg.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.
- *
- * ConjugateGradient can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
- *
- * \sa class LeastSquaresConjugateGradient, class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
- */
-template< typename _MatrixType, int _UpLo, typename _Preconditioner>
-class ConjugateGradient : public IterativeSolverBase<ConjugateGradient<_MatrixType,_UpLo,_Preconditioner> >
-{
- typedef IterativeSolverBase<ConjugateGradient> Base;
- using Base::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::RealScalar RealScalar;
- typedef _Preconditioner Preconditioner;
-
- enum {
- UpLo = _UpLo
- };
-
-public:
-
- /** Default constructor. */
- ConjugateGradient() : 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.
- */
- template<typename MatrixDerived>
- explicit ConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
-
- ~ConjugateGradient() {}
-
- /** \internal */
- template<typename Rhs,typename Dest>
- void _solve_with_guess_impl(const Rhs& b, Dest& x) const
- {
- typedef typename Base::MatrixWrapper MatrixWrapper;
- typedef typename Base::ActualMatrixType ActualMatrixType;
- enum {
- TransposeInput = (!MatrixWrapper::MatrixFree)
- && (UpLo==(Lower|Upper))
- && (!MatrixType::IsRowMajor)
- && (!NumTraits<Scalar>::IsComplex)
- };
- typedef typename internal::conditional<TransposeInput,Transpose<const ActualMatrixType>, ActualMatrixType const&>::type RowMajorWrapper;
- EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(MatrixWrapper::MatrixFree,UpLo==(Lower|Upper)),MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY);
- typedef typename internal::conditional<UpLo==(Lower|Upper),
- RowMajorWrapper,
- typename MatrixWrapper::template ConstSelfAdjointViewReturnType<UpLo>::Type
- >::type SelfAdjointWrapper;
- m_iterations = Base::maxIterations();
- m_error = Base::m_tolerance;
-
- for(Index j=0; j<b.cols(); ++j)
- {
- m_iterations = Base::maxIterations();
- m_error = Base::m_tolerance;
-
- typename Dest::ColXpr xj(x,j);
- RowMajorWrapper row_mat(matrix());
- internal::conjugate_gradient(SelfAdjointWrapper(row_mat), b.col(j), xj, Base::m_preconditioner, m_iterations, m_error);
- }
-
- m_isInitialized = true;
- m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
- }
-
- /** \internal */
- using Base::_solve_impl;
- template<typename Rhs,typename Dest>
- void _solve_impl(const MatrixBase<Rhs>& b, Dest& x) const
- {
- x.setZero();
- _solve_with_guess_impl(b.derived(),x);
- }
-
-protected:
-
-};
-
-} // end namespace Eigen
-
-#endif // EIGEN_CONJUGATE_GRADIENT_H