From 9ff967199ab287465c04515c56d9c74c65c71625 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Sun, 18 Oct 2015 22:15:01 +0200
Subject: [PATCH] Improve numerical accuracy in LLT and triangular solve by
 using true scalar divisions (instead of x * (1/y)) (grafted from
 fe630c98739186c1dd3faf7a06b52a64baa5ea23 )

---
 Eigen/src/Cholesky/LLT.h                         | 2 +-
 Eigen/src/Core/products/TriangularSolverMatrix.h | 9 ++++++---
 2 files changed, 7 insertions(+), 4 deletions(-)

diff --git a/Eigen/src/Cholesky/LLT.h b/Eigen/src/Cholesky/LLT.h
index 59723a63d..7c11a2dc2 100644
--- a/Eigen/src/Cholesky/LLT.h
+++ b/Eigen/src/Cholesky/LLT.h
@@ -289,7 +289,7 @@ template<typename Scalar> struct llt_inplace<Scalar, Lower>
         return k;
       mat.coeffRef(k,k) = x = sqrt(x);
       if (k>0 && rs>0) A21.noalias() -= A20 * A10.adjoint();
-      if (rs>0) A21 *= RealScalar(1)/x;
+      if (rs>0) A21 /= x;
     }
     return -1;
   }
diff --git a/Eigen/src/Core/products/TriangularSolverMatrix.h b/Eigen/src/Core/products/TriangularSolverMatrix.h
index f103eae72..04240ab50 100644
--- a/Eigen/src/Core/products/TriangularSolverMatrix.h
+++ b/Eigen/src/Core/products/TriangularSolverMatrix.h
@@ -302,9 +302,12 @@ EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conj
                 for (Index i=0; i<actual_mc; ++i)
                   r[i] -= a[i] * b;
               }
-              Scalar b = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(rhs(j,j));
-              for (Index i=0; i<actual_mc; ++i)
-                r[i] *= b;
+              if((Mode & UnitDiag)==0)
+              {
+                Scalar b = conj(rhs(j,j));
+                for (Index i=0; i<actual_mc; ++i)
+                  r[i] /= b;
+              }
             }
 
             // pack the just computed part of lhs to A