Rasmus Munk LarsenandRasmus Munk Larsen
2e20f3533b
libeigen/eigen!2663 Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>
124 lines
4.8 KiB
Plaintext
124 lines
4.8 KiB
Plaintext
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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// SPDX-FileCopyrightText: The Eigen Authors
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// SPDX-License-Identifier: MPL-2.0
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#ifndef EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
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#define EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
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#include "SparseCore"
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#include "OrderingMethods"
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#include "Jacobi"
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#include "Householder"
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#include "QR"
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#include "LU"
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#include "src/Core/util/DisableStupidWarnings.h"
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/**
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* \defgroup IterativeLinearSolvers_Module IterativeLinearSolvers module
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*
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* This module provides iterative methods to solve problems of the form \c A \c x = \c b, where \c A is a
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squared matrix, usually very large and sparse.
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* Those solvers are accessible via the following classes:
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* - ConjugateGradient for selfadjoint (hermitian) matrices,
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* - LeastSquaresConjugateGradient for rectangular least-square problems,
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* - LSMR for rectangular least-square problems (Golub-Kahan bidiagonalization, optionally damped),
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* - BiCGSTAB for general square matrices,
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* - GMRES - a Householder GMRES implementation,
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* - DGMRES - a deflated GMRES implementation,
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* - MINRES for symmetric indefinite matrices,
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* - IDRS - an IDR(s) implementation,
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* - BiCGSTABL - a BiCGSTAB(L) implementation,
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* - IDRSTABL - an IDR(s)STAB(L) implementation.
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*
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* These iterative solvers are associated with some preconditioners:
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* - IdentityPreconditioner - not really useful
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* - DiagonalPreconditioner - also called Jacobi preconditioner, work very well on diagonal dominant matrices.
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* - IncompleteLUT - incomplete LU factorization with dual thresholding
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* - IncompleteLU - incomplete LU factorization without fill-in
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*
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* The IterScaling class can be used as a preprocessing step to equilibrate the row and column norms of a matrix.
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*
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* Choosing the best solver for solving \c A \c x = \c b depends a lot on the preconditioner chosen as well as the
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* properties of \c A. The following flowchart might help you.
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* \dot width=50%
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* digraph g {
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* node [ fontname=Arial, fontsize=11];
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* edge [ fontname=Helvetica, fontsize=10 ];
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* A1[label="hermitian", shape="box"];
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* A2[label="positive definite", shape="box"];
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* CG[shape="plaintext"];
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* A3[label="ill conditioned", shape="box"];
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* A4[label="good preconditioner", shape="box"];
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* A5[label="flexible preconditioner", shape="box"];
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* A6[label="strongly indefinite", shape="box"];
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* A8[label="large imaginary eigenvalue", shape="box"];
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* A7[label="large imaginary eigenvalue",shape="box"];
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*
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* SYMMLQ[shape="plaintext"];
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* MINRES[shape="plaintext"];
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* GCR[shape="plaintext"];
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* GMRES[shape="plaintext"];
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* IDRSTABL[shape="plaintext"];
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* IDRS[shape="plaintext"];
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* BICGSTABL[shape="plaintext"];
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* BICGSTAB[shape="plaintext"];
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*
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* A1 -> A2 [label="yes"];
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* A2 -> CG [label="yes"];
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* A2 -> A3 [label="no"];
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* A3 -> SYMMLQ [label="yes"];
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* A3 -> MINRES [label="no"];
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*
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* A1 -> A4 [label="no"];
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* A4 -> A5 [label="yes"];
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* A5 -> GCR [label="yes"];
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* A5 -> GMRES [label="no"];
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*
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* A4 -> A6 [label="no"];
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* A6 -> A8 [label="yes"];
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* A6 -> A7 [label="no"];
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* A7 -> BICGSTABL [label="yes"];
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* A7 -> BICGSTAB [label="no"];
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* A8 -> IDRSTABL [label="yes"];
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* A8 -> IDRS [label="no"];
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* }
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* \enddot
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*
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* Such problems can also be solved using the direct sparse decomposition modules: SparseCholesky, CholmodSupport,
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UmfPackSupport, SuperLUSupport, AccelerateSupport.
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*
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\code
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#include <Eigen/IterativeLinearSolvers>
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\endcode
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*/
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// IWYU pragma: begin_exports
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#include "src/IterativeLinearSolvers/SolveWithGuess.h"
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#include "src/IterativeLinearSolvers/IterativeSolverBase.h"
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#include "src/IterativeLinearSolvers/BasicPreconditioners.h"
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#include "src/IterativeLinearSolvers/ConjugateGradient.h"
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#include "src/IterativeLinearSolvers/LeastSquareConjugateGradient.h"
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#include "src/IterativeLinearSolvers/LSMR.h"
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#include "src/IterativeLinearSolvers/BiCGSTAB.h"
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#include "src/IterativeLinearSolvers/IncompleteLUT.h"
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#include "src/IterativeLinearSolvers/IncompleteCholesky.h"
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#include "src/IterativeLinearSolvers/Scaling.h"
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#include "src/IterativeLinearSolvers/IncompleteLU.h"
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#include "src/IterativeLinearSolvers/GMRES.h"
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#include "src/IterativeLinearSolvers/DGMRES.h"
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#include "src/IterativeLinearSolvers/MINRES.h"
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#include "src/IterativeLinearSolvers/IDRS.h"
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#include "src/IterativeLinearSolvers/BiCGSTABL.h"
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#include "src/IterativeLinearSolvers/IDRSTABL.h"
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// IWYU pragma: end_exports
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#include "src/Core/util/ReenableStupidWarnings.h"
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#endif // EIGEN_ITERATIVELINEARSOLVERS_MODULE_H
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