From a594ac3966541f46e88b785c56d82bfaf71fd302 Mon Sep 17 00:00:00 2001
From: Jitse Niesen <jitse@maths.leeds.ac.uk>
Date: Wed, 2 Nov 2011 14:18:20 +0000
Subject: Allow for more iterations in SelfAdjointEigenSolver (bug #354). Add
 an assert to guard against using eigenvalues that have not converged. Add
 call to info() in tutorial example to cover non-convergence.

---
 Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h        | 16 ++++++++++------
 doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp |  3 ++-
 2 files changed, 12 insertions(+), 7 deletions(-)

diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
index 84be9bce1..e748f03b0 100644
--- a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
+++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
@@ -242,6 +242,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
     const MatrixType& eigenvectors() const
     {
       eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+      eigen_assert(info() == Success && "Eigenvalue computation did not converge.");
       eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
       return m_eivec;
     }
@@ -264,6 +265,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
     const RealVectorType& eigenvalues() const
     {
       eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+      eigen_assert(info() == Success && "Eigenvalue computation did not converge.");
       return m_eivalues;
     }
 
@@ -288,6 +290,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
     MatrixType operatorSqrt() const
     {
       eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+      eigen_assert(info() == Success && "Eigenvalue computation did not converge.");
       eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
       return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();
     }
@@ -313,6 +316,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
     MatrixType operatorInverseSqrt() const
     {
       eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
+      eigen_assert(info() == Success && "Eigenvalue computation did not converge.");
       eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
       return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();
     }
@@ -329,7 +333,8 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
 
     /** \brief Maximum number of iterations.
       *
-      * Maximum number of iterations allowed for an eigenvalue to converge.
+      * The algorithm terminates if it does not converge within m_maxIterations * n iterations, where n
+      * denotes the size of the matrix. This value is currently set to 30 (copied from LAPACK).
       */
     static const int m_maxIterations = 30;
 
@@ -429,7 +434,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
   
   Index end = n-1;
   Index start = 0;
-  Index iter = 0; // number of iterations we are working on one element
+  Index iter = 0; // total number of iterations
 
   while (end>0)
   {
@@ -440,15 +445,14 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
     // find the largest unreduced block
     while (end>0 && m_subdiag[end-1]==0)
     {
-      iter = 0;
       end--;
     }
     if (end<=0)
       break;
 
-    // if we spent too many iterations on the current element, we give up
+    // if we spent too many iterations, we give up
     iter++;
-    if(iter > m_maxIterations) break;
+    if(iter > m_maxIterations * n) break;
 
     start = end - 1;
     while (start>0 && m_subdiag[start-1]!=0)
@@ -457,7 +461,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
     internal::tridiagonal_qr_step<MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor>(diag.data(), m_subdiag.data(), start, end, computeEigenvectors ? m_eivec.data() : (Scalar*)0, n);
   }
 
-  if (iter <= m_maxIterations)
+  if (iter <= m_maxIterations * n)
     m_info = Success;
   else
     m_info = NoConvergence;
diff --git a/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp b/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp
index e98444347..8d1d1ed65 100644
--- a/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp
+++ b/doc/examples/TutorialLinAlgSelfAdjointEigenSolver.cpp
@@ -10,8 +10,9 @@ int main()
    A << 1, 2, 2, 3;
    cout << "Here is the matrix A:\n" << A << endl;
    SelfAdjointEigenSolver<Matrix2f> eigensolver(A);
+   if (eigensolver.info() != Success) abort();
    cout << "The eigenvalues of A are:\n" << eigensolver.eigenvalues() << endl;
-   cout << "Here's a matrix whose columns are eigenvectors of A "
+   cout << "Here's a matrix whose columns are eigenvectors of A \n"
         << "corresponding to these eigenvalues:\n"
         << eigensolver.eigenvectors() << endl;
 }
-- 
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