From e546ee315aba04e4429bd71fc7fab35611134693 Mon Sep 17 00:00:00 2001
From: Jitse Niesen <jitse@maths.leeds.ac.uk>
Date: Sun, 22 Jul 2012 22:03:23 +0100
Subject: [PATCH] Use EISPACK's strategy re max number of iters in Schur
 decomposition (bug #479).

---
 Eigen/src/Eigenvalues/ComplexSchur.h |  8 +++++---
 Eigen/src/Eigenvalues/RealSchur.h    | 10 ++++++----
 2 files changed, 11 insertions(+), 7 deletions(-)

diff --git a/Eigen/src/Eigenvalues/ComplexSchur.h b/Eigen/src/Eigenvalues/ComplexSchur.h
index 16a9a03d2..55aeedb90 100644
--- a/Eigen/src/Eigenvalues/ComplexSchur.h
+++ b/Eigen/src/Eigenvalues/ComplexSchur.h
@@ -336,6 +336,7 @@ void ComplexSchur<MatrixType>::reduceToTriangularForm(bool computeU)
   Index iu = m_matT.cols() - 1;
   Index il;
   Index iter = 0; // number of iterations we are working on the (iu,iu) element
+  Index totalIter = 0; // number of iterations for whole matrix
 
   while(true)
   {
@@ -350,9 +351,10 @@ void ComplexSchur<MatrixType>::reduceToTriangularForm(bool computeU)
     // if iu is zero then we are done; the whole matrix is triangularized
     if(iu==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 * m_matT.cols()) break;
+    totalIter++;
+    if(totalIter > m_maxIterations * m_matT.cols()) break;
 
     // find il, the top row of the active submatrix
     il = iu-1;
@@ -382,7 +384,7 @@ void ComplexSchur<MatrixType>::reduceToTriangularForm(bool computeU)
     }
   }
 
-  if(iter <= m_maxIterations * m_matT.cols()) 
+  if(totalIter <= m_maxIterations * m_matT.cols())
     m_info = Success;
   else
     m_info = NoConvergence;
diff --git a/Eigen/src/Eigenvalues/RealSchur.h b/Eigen/src/Eigenvalues/RealSchur.h
index 781692ecc..d1949b83c 100644
--- a/Eigen/src/Eigenvalues/RealSchur.h
+++ b/Eigen/src/Eigenvalues/RealSchur.h
@@ -220,8 +220,9 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::compute(const MatrixType& matrix,
   // Rows il,...,iu is the part we are working on (the active window).
   // Rows iu+1,...,end are already brought in triangular form.
   Index iu = m_matT.cols() - 1;
-  Index iter = 0; // iteration count
-  Scalar exshift(0); // sum of exceptional shifts
+  Index iter = 0;      // iteration count for current eigenvalue
+  Index totalIter = 0; // iteration count for whole matrix
+  Scalar exshift(0);   // sum of exceptional shifts
   Scalar norm = computeNormOfT();
 
   if(norm!=0)
@@ -251,14 +252,15 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::compute(const MatrixType& matrix,
         Vector3s firstHouseholderVector(0,0,0), shiftInfo;
         computeShift(iu, iter, exshift, shiftInfo);
         iter = iter + 1;
-        if (iter > m_maxIterations * m_matT.cols()) break;
+        totalIter = totalIter + 1;
+        if (totalIter > m_maxIterations * matrix.cols()) break;
         Index im;
         initFrancisQRStep(il, iu, shiftInfo, im, firstHouseholderVector);
         performFrancisQRStep(il, im, iu, computeU, firstHouseholderVector, workspace);
       }
     }
   }
-  if(iter <= m_maxIterations * m_matT.cols()) 
+  if(totalIter <= m_maxIterations * matrix.cols()) 
     m_info = Success;
   else
     m_info = NoConvergence;