From 90b3b6b5729d789224d2bf0a5a40ed2e3712ab51 Mon Sep 17 00:00:00 2001
From: jenswehner <jenswehner@gmail.com>
Date: Tue, 24 Aug 2021 14:09:20 +0200
Subject: [PATCH] added doxygen flowchart

---
 unsupported/Eigen/IterativeSolvers | 46 +++++++++++++++++++++++++++++-
 1 file changed, 45 insertions(+), 1 deletion(-)

diff --git a/unsupported/Eigen/IterativeSolvers b/unsupported/Eigen/IterativeSolvers
index a3f58d676..7a5b85c50 100644
--- a/unsupported/Eigen/IterativeSolvers
+++ b/unsupported/Eigen/IterativeSolvers
@@ -16,7 +16,7 @@
 
 
 /**
-  * \defgroup IterativeLinearSolvers_Module Iterative solvers module
+  * \defgroup IterativeLinearSolvers_Module (Iterative solvers module)
   * This module aims to provide various iterative linear and non linear solver algorithms.
   * It currently provides:
   *  - a constrained conjugate gradient
@@ -25,6 +25,50 @@
   *  - a DGMRES implementation
   *  - a MINRES implementation
   *
+  * Choosing the best solver for solving \c A \c x = \c b depends a lot on the preconditioner chosen as well as the properties of \c A. The following flowchart might help you.
+  * \dot width=50%
+  * digraph g {
+* node [ fontname=Arial, fontsize=11];
+* edge [ fontname=Helvetica, fontsize=10 ];
+*	A1[label="hermitian",shape="box"];
+* A2[label="positive definite",shape="box"];
+* CG[shape="plaintext"];
+* A3[label="ill conditioned",shape="box"];
+* A4[label="good preconditioner",shape="box"];
+* A5[label="flexible preconditioner",shape="box"];
+* A6[label="strongly indefinite",shape="box"];
+* A8[label="large imaginary eigenvalue",shape="box"];
+* A7[label="large imaginary eigenvalue",shape="box"];
+*
+* SYMMLQ[shape="plaintext"];
+* MINRES[shape="plaintext"];
+* GCR[shape="plaintext"];
+* GMRES[shape="plaintext"];
+* IDRSTABL[shape="plaintext"];
+* IDRS[shape="plaintext"];
+* BICGSTABL[shape="plaintext"];
+* BICGSTAB[shape="plaintext"];
+*	
+*	A1 -> A2 [label="yes"];
+*	A2 -> CG [label="yes"];
+*	A2 -> A3 [label="no"];
+*	A3 -> SYMMLQ [label="yes"];
+*	A3 -> MINRES [label="no"];
+*
+*	A1 -> A4 [label="no"];
+*	A4 -> A5 [label="yes"];
+*	A5 -> GCR [label="yes"];
+*	A5 -> GMRES [label="no"];
+*
+*	A4 -> A6 [label="no"];
+*	A6 -> A8 [label="yes"];
+*	A6 -> A7 [label="no"];
+*	A7 -> BICGSTABL [label="yes"];
+*	A7 -> BICGSTAB [label="no"];
+*	A8 -> IDRSTABL [label="yes"];
+*	A8 -> IDRS [label="no"];
+* }
+  * \enddot
   * \code
   * #include <unsupported/Eigen/IterativeSolvers>
   * \endcode