From 2915e1fc5de1cd830eb1a4a723c41a7b14d87254 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Mon, 29 Aug 2016 14:14:18 +0200
Subject: [PATCH] Revert part of changeset
 5b3a6f51d353bb3b35f6d15f2455774b73d088e0  to keep accuracy of smallest
 eigenvalues.

---
 Eigen/src/Eigenvalues/RealSchur.h | 17 +++++------------
 1 file changed, 5 insertions(+), 12 deletions(-)

diff --git a/Eigen/src/Eigenvalues/RealSchur.h b/Eigen/src/Eigenvalues/RealSchur.h
index 9d9063004..d6a339f07 100644
--- a/Eigen/src/Eigenvalues/RealSchur.h
+++ b/Eigen/src/Eigenvalues/RealSchur.h
@@ -236,7 +236,7 @@ template<typename _MatrixType> class RealSchur
     typedef Matrix<Scalar,3,1> Vector3s;
 
     Scalar computeNormOfT();
-    Index findSmallSubdiagEntry(Index iu, const Scalar& maxDiagEntry);
+    Index findSmallSubdiagEntry(Index iu);
     void splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift);
     void computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo);
     void initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector);
@@ -293,18 +293,14 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa
 
   if(norm!=0)
   {
-    Scalar maxDiagEntry = m_matT.cwiseAbs().diagonal().maxCoeff();
-
     while (iu >= 0)
     {
-      Index il = findSmallSubdiagEntry(iu,maxDiagEntry);
+      Index il = findSmallSubdiagEntry(iu);
 
       // Check for convergence
       if (il == iu) // One root found
       {
         m_matT.coeffRef(iu,iu) = m_matT.coeff(iu,iu) + exshift;
-        // keep track of the largest diagonal coefficient
-        maxDiagEntry = numext::maxi<Scalar>(maxDiagEntry,abs(m_matT.coeffRef(iu,iu)));
         if (iu > 0)
           m_matT.coeffRef(iu, iu-1) = Scalar(0);
         iu--;
@@ -313,8 +309,6 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa
       else if (il == iu-1) // Two roots found
       {
         splitOffTwoRows(iu, computeU, exshift);
-        // keep track of the largest diagonal coefficient
-        maxDiagEntry = numext::maxi<Scalar>(maxDiagEntry,numext::maxi(abs(m_matT.coeff(iu,iu)), abs(m_matT.coeff(iu-1,iu-1))));
         iu -= 2;
         iter = 0;
       }
@@ -329,8 +323,6 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa
         Index im;
         initFrancisQRStep(il, iu, shiftInfo, im, firstHouseholderVector);
         performFrancisQRStep(il, im, iu, computeU, firstHouseholderVector, workspace);
-        // keep track of the largest diagonal coefficient
-        maxDiagEntry = numext::maxi(maxDiagEntry,m_matT.cwiseAbs().diagonal().segment(im,iu-im).maxCoeff());
       }
     }
   }
@@ -360,13 +352,14 @@ inline typename MatrixType::Scalar RealSchur<MatrixType>::computeNormOfT()
 
 /** \internal Look for single small sub-diagonal element and returns its index */
 template<typename MatrixType>
-inline Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu, const Scalar& maxDiagEntry)
+inline Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu)
 {
   using std::abs;
   Index res = iu;
   while (res > 0)
   {
-    if (abs(m_matT.coeff(res,res-1)) <= NumTraits<Scalar>::epsilon() * maxDiagEntry)
+    Scalar s = abs(m_matT.coeff(res-1,res-1)) + abs(m_matT.coeff(res,res));
+    if (abs(m_matT.coeff(res,res-1)) <= NumTraits<Scalar>::epsilon() * s)
       break;
     res--;
   }