Fix bug #314:

- remove most of the metaprogramming kung fu in MathFunctions.h (only keep functions that differs from the std)
- remove the overloads for array expression that were in the std namespace

19 files changed, 88 insertions, 44 deletions

diff --git a/unsupported/Eigen/AlignedVector3 b/unsupported/Eigen/AlignedVector3
index 8ad0eb477..7236dddf4 100644
--- a/unsupported/Eigen/AlignedVector3
+++ b/unsupported/Eigen/AlignedVector3
@@ -167,7 +167,8 @@ template<typename _Scalar> class AlignedVector3
 
     inline Scalar norm() const
     {
-      return internal::sqrt(squaredNorm());
+      using std::sqrt;
+      return sqrt(squaredNorm());
     }
 
     inline AlignedVector3 cross(const AlignedVector3& other) const
diff --git a/unsupported/Eigen/src/FFT/ei_kissfft_impl.h b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
index 37f5af4c1..be51b4e6f 100644
--- a/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
+++ b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
@@ -28,6 +28,7 @@ struct kiss_cpx_fft
   inline
     void make_twiddles(int nfft,bool inverse)
     {
+      using std::acos;
       m_inverse = inverse;
       m_twiddles.resize(nfft);
       Scalar phinc =  (inverse?2:-2)* acos( (Scalar) -1)  / nfft;
@@ -399,6 +400,7 @@ struct kissfft_impl
   inline
     Complex * real_twiddles(int ncfft2)
     {
+      using std::acos;
       std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
       if ( (int)twidref.size() != ncfft2 ) {
         twidref.resize(ncfft2);
diff --git a/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h b/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
index 5bc41c0f8..746d29473 100644
--- a/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
+++ b/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
@@ -116,6 +116,7 @@ template<typename Scalar, int _UpLo, typename OrderingType>
 template<typename _MatrixType>
 void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType& mat)
 {
+  using std::sqrt;
   eigen_assert(m_analysisIsOk && "analyzePattern() should be called first"); 
   
   // FIXME Stability: We should probably compute the scaling factors and the shifts that are needed to ensure a succesful LLT factorization and an efficient preconditioner. 
@@ -182,7 +183,7 @@ void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType
        m_info = NumericalIssue; 
        return; 
      }
-     RealScalar rdiag = internal::sqrt(RealScalar(diag));
+     RealScalar rdiag = sqrt(RealScalar(diag));
      Scalar scal = Scalar(1)/rdiag; 
      vals[colPtr[j]] = rdiag;
      // Insert the largest p elements in the matrix and scale them meanwhile  
diff --git a/unsupported/Eigen/src/IterativeSolvers/IterationController.h b/unsupported/Eigen/src/IterativeSolvers/IterationController.h
index aaf46d544..ea86dfef4 100644
--- a/unsupported/Eigen/src/IterativeSolvers/IterationController.h
+++ b/unsupported/Eigen/src/IterativeSolvers/IterationController.h
@@ -129,7 +129,8 @@ class IterationController
     bool converged() const { return m_res <= m_rhsn * m_resmax; }
     bool converged(double nr)
     {
-      m_res = internal::abs(nr); 
+      using std::abs;
+      m_res = abs(nr); 
       m_resminreach = (std::min)(m_resminreach, m_res);
       return converged();
     }
diff --git a/unsupported/Eigen/src/IterativeSolvers/MINRES.h b/unsupported/Eigen/src/IterativeSolvers/MINRES.h
index 46d7bedc1..6bc1b8f5d 100644
--- a/unsupported/Eigen/src/IterativeSolvers/MINRES.h
+++ b/unsupported/Eigen/src/IterativeSolvers/MINRES.h
@@ -32,6 +32,7 @@ namespace Eigen {
                     const Preconditioner& precond, int& iters,
                     typename Dest::RealScalar& tol_error)
         {
+            using std::sqrt;
             typedef typename Dest::RealScalar RealScalar;
             typedef typename Dest::Scalar Scalar;
             typedef Matrix<Scalar,Dynamic,1> VectorType;
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
index e87a28f6c..7d426640c 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
@@ -235,6 +235,7 @@ void MatrixFunction<MatrixType,AtomicType,1>::computeSchurDecomposition()
 template <typename MatrixType, typename AtomicType>
 void MatrixFunction<MatrixType,AtomicType,1>::partitionEigenvalues()
 {
+  using std::abs;
   const Index rows = m_T.rows();
   VectorType diag = m_T.diagonal(); // contains eigenvalues of A
 
@@ -251,14 +252,14 @@ void MatrixFunction<MatrixType,AtomicType,1>::partitionEigenvalues()
 
     // Look for other element to add to the set
     for (Index j=i+1; j<rows; ++j) {
-      if (internal::abs(diag(j) - diag(i)) <= separation() && std::find(qi->begin(), qi->end(), diag(j)) == qi->end()) {
-	typename ListOfClusters::iterator qj = findCluster(diag(j));
-	if (qj == m_clusters.end()) {
-	  qi->push_back(diag(j));
-	} else {
-	  qi->insert(qi->end(), qj->begin(), qj->end());
-	  m_clusters.erase(qj);
-	}
+      if (abs(diag(j) - diag(i)) <= separation() && std::find(qi->begin(), qi->end(), diag(j)) == qi->end()) {
+        typename ListOfClusters::iterator qj = findCluster(diag(j));
+        if (qj == m_clusters.end()) {
+          qi->push_back(diag(j));
+        } else {
+          qi->insert(qi->end(), qj->begin(), qj->end());
+          m_clusters.erase(qj);
+        }
       }
     }
   }
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
index e1e5b770c..6ec870d3e 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
@@ -125,6 +125,7 @@ void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixTy
 template <typename MatrixType>
 void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixType& result)
 {
+  using std::pow;
   int numberOfSquareRoots = 0;
   int numberOfExtraSquareRoots = 0;
   int degree;
@@ -141,7 +142,7 @@ void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixTy
       degree = getPadeDegree(normTminusI);
       int degree2 = getPadeDegree(normTminusI / RealScalar(2));
       if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1)) 
-	break;
+        break;
       ++numberOfExtraSquareRoots;
     }
     MatrixType sqrtT;
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h b/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
index 3786510c0..abbf64096 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
@@ -99,11 +99,12 @@ template <typename MatrixType>
 void MatrixSquareRootQuasiTriangular<MatrixType>::computeDiagonalPartOfSqrt(MatrixType& sqrtT, 
 									  const MatrixType& T)
 {
+  using std::sqrt;
   const Index size = m_A.rows();
   for (Index i = 0; i < size; i++) {
     if (i == size - 1 || T.coeff(i+1, i) == 0) {
       eigen_assert(T(i,i) > 0);
-      sqrtT.coeffRef(i,i) = internal::sqrt(T.coeff(i,i));
+      sqrtT.coeffRef(i,i) = sqrt(T.coeff(i,i));
     }
     else {
       compute2x2diagonalBlock(sqrtT, T, i);
@@ -289,6 +290,7 @@ template <typename MatrixType>
 template <typename ResultType> 
 void MatrixSquareRootTriangular<MatrixType>::compute(ResultType &result)
 {
+  using std::sqrt;
   // Compute Schur decomposition of m_A
   const ComplexSchur<MatrixType> schurOfA(m_A);  
   const MatrixType& T = schurOfA.matrixT();
@@ -299,7 +301,7 @@ void MatrixSquareRootTriangular<MatrixType>::compute(ResultType &result)
   result.resize(m_A.rows(), m_A.cols());
   typedef typename MatrixType::Index Index;
   for (Index i = 0; i < m_A.rows(); i++) {
-    result.coeffRef(i,i) = internal::sqrt(T.coeff(i,i));
+    result.coeffRef(i,i) = sqrt(T.coeff(i,i));
   }
   for (Index j = 1; j < m_A.cols(); j++) {
     for (Index i = j-1; i >= 0; i--) {
diff --git a/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
index d9ce4eab6..b190827b3 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
@@ -52,7 +52,7 @@ public:
         Parameters()
             : factor(Scalar(100.))
             , maxfev(1000)
-            , xtol(internal::sqrt(NumTraits<Scalar>::epsilon()))
+            , xtol(std::sqrt(NumTraits<Scalar>::epsilon()))
             , nb_of_subdiagonals(-1)
             , nb_of_superdiagonals(-1)
             , epsfcn(Scalar(0.)) {}
@@ -70,7 +70,7 @@ public:
 
     HybridNonLinearSolverSpace::Status hybrj1(
             FVectorType  &x,
-            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     HybridNonLinearSolverSpace::Status solveInit(FVectorType  &x);
@@ -79,7 +79,7 @@ public:
 
     HybridNonLinearSolverSpace::Status hybrd1(
             FVectorType  &x,
-            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     HybridNonLinearSolverSpace::Status solveNumericalDiffInit(FVectorType  &x);
@@ -185,6 +185,8 @@ template<typename FunctorType, typename Scalar>
 HybridNonLinearSolverSpace::Status
 HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType  &x)
 {
+    using std::abs;
+    
     assert(x.size()==n); // check the caller is not cheating us
 
     Index j;
@@ -276,7 +278,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType  &x)
             ++ncsuc;
             if (ratio >= Scalar(.5) || ncsuc > 1)
                 delta = (std::max)(delta, pnorm / Scalar(.5));
-            if (internal::abs(ratio - 1.) <= Scalar(.1)) {
+            if (abs(ratio - 1.) <= Scalar(.1)) {
                 delta = pnorm / Scalar(.5);
             }
         }
@@ -423,6 +425,9 @@ template<typename FunctorType, typename Scalar>
 HybridNonLinearSolverSpace::Status
 HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType  &x)
 {
+    using std::sqrt;
+    using std::abs;
+    
     assert(x.size()==n); // check the caller is not cheating us
 
     Index j;
@@ -516,7 +521,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType
             ++ncsuc;
             if (ratio >= Scalar(.5) || ncsuc > 1)
                 delta = (std::max)(delta, pnorm / Scalar(.5));
-            if (internal::abs(ratio - 1.) <= Scalar(.1)) {
+            if (abs(ratio - 1.) <= Scalar(.1)) {
                 delta = pnorm / Scalar(.5);
             }
         }
diff --git a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
index 075faeeb0..4b1a2d0fb 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
@@ -55,8 +55,8 @@ public:
         Parameters()
             : factor(Scalar(100.))
             , maxfev(400)
-            , ftol(internal::sqrt(NumTraits<Scalar>::epsilon()))
-            , xtol(internal::sqrt(NumTraits<Scalar>::epsilon()))
+            , ftol(std::sqrt(NumTraits<Scalar>::epsilon()))
+            , xtol(std::sqrt(NumTraits<Scalar>::epsilon()))
             , gtol(Scalar(0.))
             , epsfcn(Scalar(0.)) {}
         Scalar factor;
@@ -72,7 +72,7 @@ public:
 
     LevenbergMarquardtSpace::Status lmder1(
             FVectorType &x,
-            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     LevenbergMarquardtSpace::Status minimize(FVectorType &x);
@@ -83,12 +83,12 @@ public:
             FunctorType &functor,
             FVectorType &x,
             Index *nfev,
-            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     LevenbergMarquardtSpace::Status lmstr1(
             FVectorType  &x,
-            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType  &x);
@@ -206,6 +206,9 @@ template<typename FunctorType, typename Scalar>
 LevenbergMarquardtSpace::Status
 LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
 {
+    using std::abs;
+    using std::sqrt;
+    
     assert(x.size()==n); // check the caller is not cheating us
 
     /* calculate the jacobian matrix. */
@@ -249,7 +252,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
     if (fnorm != 0.)
         for (Index j = 0; j < n; ++j)
             if (wa2[permutation.indices()[j]] != 0.)
-                gnorm = (std::max)(gnorm, internal::abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
+                gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
 
     /* test for convergence of the gradient norm. */
     if (gnorm <= parameters.gtol)
@@ -288,7 +291,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
         /* the scaled directional derivative. */
         wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1);
         temp1 = internal::abs2(wa3.stableNorm() / fnorm);
-        temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm);
+        temp2 = internal::abs2(sqrt(par) * pnorm / fnorm);
         prered = temp1 + temp2 / Scalar(.5);
         dirder = -(temp1 + temp2);
 
@@ -326,9 +329,9 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
         }
 
         /* tests for convergence. */
-        if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
+        if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
             return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
-        if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
+        if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
             return LevenbergMarquardtSpace::RelativeReductionTooSmall;
         if (delta <= parameters.xtol * xnorm)
             return LevenbergMarquardtSpace::RelativeErrorTooSmall;
@@ -336,7 +339,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
         /* tests for termination and stringent tolerances. */
         if (nfev >= parameters.maxfev)
             return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
-        if (internal::abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
+        if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
             return LevenbergMarquardtSpace::FtolTooSmall;
         if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
             return LevenbergMarquardtSpace::XtolTooSmall;
@@ -423,6 +426,9 @@ template<typename FunctorType, typename Scalar>
 LevenbergMarquardtSpace::Status
 LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorType  &x)
 {
+    using std::abs;
+    using std::sqrt;
+    
     assert(x.size()==n); // check the caller is not cheating us
 
     Index i, j;
@@ -496,7 +502,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
     if (fnorm != 0.)
         for (j = 0; j < n; ++j)
             if (wa2[permutation.indices()[j]] != 0.)
-                gnorm = (std::max)(gnorm, internal::abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
+                gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
 
     /* test for convergence of the gradient norm. */
     if (gnorm <= parameters.gtol)
@@ -535,7 +541,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
         /* the scaled directional derivative. */
         wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1);
         temp1 = internal::abs2(wa3.stableNorm() / fnorm);
-        temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm);
+        temp2 = internal::abs2(sqrt(par) * pnorm / fnorm);
         prered = temp1 + temp2 / Scalar(.5);
         dirder = -(temp1 + temp2);
 
@@ -573,9 +579,9 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
         }
 
         /* tests for convergence. */
-        if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
+        if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
             return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
-        if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
+        if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
             return LevenbergMarquardtSpace::RelativeReductionTooSmall;
         if (delta <= parameters.xtol * xnorm)
             return LevenbergMarquardtSpace::RelativeErrorTooSmall;
@@ -583,7 +589,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
         /* tests for termination and stringent tolerances. */
         if (nfev >= parameters.maxfev)
             return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
-        if (internal::abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
+        if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
             return LevenbergMarquardtSpace::FtolTooSmall;
         if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
             return LevenbergMarquardtSpace::XtolTooSmall;
diff --git a/unsupported/Eigen/src/NonLinearOptimization/chkder.h b/unsupported/Eigen/src/NonLinearOptimization/chkder.h
index ad37c5029..db8ff7d6e 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/chkder.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/chkder.h
@@ -16,6 +16,10 @@ void chkder(
         Matrix< Scalar, Dynamic, 1 >  &err
         )
 {
+    using std::sqrt;
+    using std::abs;
+    using std::log;
+    
     typedef DenseIndex Index;
 
     const Scalar eps = sqrt(NumTraits<Scalar>::epsilon());
diff --git a/unsupported/Eigen/src/NonLinearOptimization/covar.h b/unsupported/Eigen/src/NonLinearOptimization/covar.h
index c73a09645..c2fb79441 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/covar.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/covar.h
@@ -6,8 +6,9 @@ template <typename Scalar>
 void covar(
         Matrix< Scalar, Dynamic, Dynamic > &r,
         const VectorXi &ipvt,
-        Scalar tol = sqrt(NumTraits<Scalar>::epsilon()) )
+        Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )
 {
+    using std::abs;
     typedef DenseIndex Index;
 
     /* Local variables */
diff --git a/unsupported/Eigen/src/NonLinearOptimization/dogleg.h b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
index 4fbc98bfc..57dbc8bfb 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
@@ -10,6 +10,9 @@ void dogleg(
         Scalar delta,
         Matrix< Scalar, Dynamic, 1 >  &x)
 {
+    using std::abs;
+    using std::sqrt;
+    
     typedef DenseIndex Index;
 
     /* Local variables */
diff --git a/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
index 1cabe69ae..05947936e 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
@@ -11,6 +11,9 @@ DenseIndex fdjac1(
         DenseIndex ml, DenseIndex mu,
         Scalar epsfcn)
 {
+    using std::sqrt;
+    using std::abs;
+    
     typedef DenseIndex Index;
 
     /* Local variables */
diff --git a/unsupported/Eigen/src/NonLinearOptimization/lmpar.h b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
index 8aac5753b..834407c5a 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
@@ -12,6 +12,8 @@ void lmpar(
         Scalar &par,
         Matrix< Scalar, Dynamic, 1 >  &x)
 {
+    using std::abs;
+    using std::sqrt;
     typedef DenseIndex Index;
 
     /* Local variables */
@@ -168,6 +170,8 @@ void lmpar2(
         Matrix< Scalar, Dynamic, 1 >  &x)
 
 {
+    using std::sqrt;
+    using std::abs;
     typedef DenseIndex Index;
 
     /* Local variables */
diff --git a/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h b/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h
index d848cb407..7ee30e18c 100644
--- a/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h
+++ b/unsupported/Eigen/src/NumericalDiff/NumericalDiff.h
@@ -63,11 +63,13 @@ public:
      */
     int df(const InputType& _x, JacobianType &jac) const
     {
+        using std::sqrt;
+        using std::abs;
         /* Local variables */
         Scalar h;
         int nfev=0;
         const typename InputType::Index n = _x.size();
-        const Scalar eps = internal::sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
+        const Scalar eps = sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
         ValueType val1, val2;
         InputType x = _x;
         // TODO : we should do this only if the size is not already known
@@ -89,7 +91,7 @@ public:
 
         // Function Body
         for (int j = 0; j < n; ++j) {
-            h = eps * internal::abs(x[j]);
+            h = eps * abs(x[j]);
             if (h == 0.) {
                 h = eps;
             }
diff --git a/unsupported/Eigen/src/Polynomials/Companion.h b/unsupported/Eigen/src/Polynomials/Companion.h
index 4badd9d58..b515c2920 100644
--- a/unsupported/Eigen/src/Polynomials/Companion.h
+++ b/unsupported/Eigen/src/Polynomials/Companion.h
@@ -210,6 +210,7 @@ bool companion<_Scalar,_Deg>::balancedR( Scalar colNorm, Scalar rowNorm,
 template< typename _Scalar, int _Deg >
 void companion<_Scalar,_Deg>::balance()
 {
+  using std::abs;
   EIGEN_STATIC_ASSERT( Deg == Dynamic || 1 < Deg, YOU_MADE_A_PROGRAMMING_MISTAKE );
   const Index deg   = m_monic.size();
   const Index deg_1 = deg-1;
diff --git a/unsupported/Eigen/src/Polynomials/PolynomialSolver.h b/unsupported/Eigen/src/Polynomials/PolynomialSolver.h
index 70b873dbc..fba8fc910 100644
--- a/unsupported/Eigen/src/Polynomials/PolynomialSolver.h
+++ b/unsupported/Eigen/src/Polynomials/PolynomialSolver.h
@@ -69,10 +69,11 @@ class PolynomialSolverBase
     inline void realRoots( Stl_back_insertion_sequence& bi_seq,
         const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
     {
+      using std::abs;
       bi_seq.clear();
       for(Index i=0; i<m_roots.size(); ++i )
       {
-        if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold ){
+        if( abs( m_roots[i].imag() ) < absImaginaryThreshold ){
           bi_seq.push_back( m_roots[i].real() ); }
       }
     }
@@ -118,13 +119,14 @@ class PolynomialSolverBase
         bool& hasArealRoot,
         const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
     {
+      using std::abs;
       hasArealRoot = false;
       Index res=0;
       RealScalar abs2(0);
 
       for( Index i=0; i<m_roots.size(); ++i )
       {
-        if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold )
+        if( abs( m_roots[i].imag() ) < absImaginaryThreshold )
         {
           if( !hasArealRoot )
           {
@@ -144,7 +146,7 @@ class PolynomialSolverBase
         }
         else
         {
-          if( internal::abs( m_roots[i].imag() ) < internal::abs( m_roots[res].imag() ) ){
+          if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){
             res = i; }
         }
       }
@@ -158,13 +160,14 @@ class PolynomialSolverBase
         bool& hasArealRoot,
         const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
     {
+      using std::abs;
       hasArealRoot = false;
       Index res=0;
       RealScalar val(0);
 
       for( Index i=0; i<m_roots.size(); ++i )
       {
-        if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold )
+        if( abs( m_roots[i].imag() ) < absImaginaryThreshold )
         {
           if( !hasArealRoot )
           {
@@ -184,7 +187,7 @@ class PolynomialSolverBase
         }
         else
         {
-          if( internal::abs( m_roots[i].imag() ) < internal::abs( m_roots[res].imag() ) ){
+          if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){
             res = i; }
         }
       }
diff --git a/unsupported/Eigen/src/Polynomials/PolynomialUtils.h b/unsupported/Eigen/src/Polynomials/PolynomialUtils.h
index c23204c65..5a9ab110e 100644
--- a/unsupported/Eigen/src/Polynomials/PolynomialUtils.h
+++ b/unsupported/Eigen/src/Polynomials/PolynomialUtils.h
@@ -74,6 +74,7 @@ template <typename Polynomial>
 inline
 typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Polynomial& poly )
 {
+  using std::abs;
   typedef typename Polynomial::Scalar Scalar;
   typedef typename NumTraits<Scalar>::Real Real;
 
@@ -82,7 +83,7 @@ typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Po
   Real cb(0);
 
   for( DenseIndex i=0; i<poly.size()-1; ++i ){
-    cb += internal::abs(poly[i]*inv_leading_coeff); }
+    cb += abs(poly[i]*inv_leading_coeff); }
   return cb + Real(1);
 }
 
@@ -96,6 +97,7 @@ template <typename Polynomial>
 inline
 typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Polynomial& poly )
 {
+  using std::abs;
   typedef typename Polynomial::Scalar Scalar;
   typedef typename NumTraits<Scalar>::Real Real;
 
@@ -107,7 +109,7 @@ typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Po
   const Scalar inv_min_coeff = Scalar(1)/poly[i];
   Real cb(1);
   for( DenseIndex j=i+1; j<poly.size(); ++j ){
-    cb += internal::abs(poly[j]*inv_min_coeff); }
+    cb += abs(poly[j]*inv_min_coeff); }
   return Real(1)/cb;
 }