bug #86 : use internal:: namespace instead of ei_ prefix

11 files changed, 93 insertions, 74 deletions

diff --git a/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
index 3308a4a34..a4863700e 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
@@ -65,7 +65,7 @@ public:
         Parameters()
             : factor(Scalar(100.))
             , maxfev(1000)
-            , xtol(ei_sqrt(NumTraits<Scalar>::epsilon()))
+            , xtol(internal::sqrt(NumTraits<Scalar>::epsilon()))
             , nb_of_subdiagonals(-1)
             , nb_of_superdiagonals(-1)
             , epsfcn(Scalar(0.)) {}
@@ -83,7 +83,7 @@ public:
 
     HybridNonLinearSolverSpace::Status hybrj1(
             FVectorType  &x,
-            const Scalar tol = ei_sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     HybridNonLinearSolverSpace::Status solveInit(FVectorType  &x);
@@ -92,7 +92,7 @@ public:
 
     HybridNonLinearSolverSpace::Status hybrd1(
             FVectorType  &x,
-            const Scalar tol = ei_sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     HybridNonLinearSolverSpace::Status solveNumericalDiffInit(FVectorType  &x);
@@ -246,7 +246,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType  &x)
 
     while (true) {
         /* determine the direction p. */
-        ei_dogleg<Scalar>(R, diag, qtf, delta, wa1);
+        internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);
 
         /* store the direction p and x + p. calculate the norm of p. */
         wa1 = -wa1;
@@ -266,14 +266,14 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType  &x)
         /* compute the scaled actual reduction. */
         actred = -1.;
         if (fnorm1 < fnorm) /* Computing 2nd power */
-            actred = 1. - ei_abs2(fnorm1 / fnorm);
+            actred = 1. - internal::abs2(fnorm1 / fnorm);
 
         /* compute the scaled predicted reduction. */
         wa3 = R.template triangularView<Upper>()*wa1 + qtf;
         temp = wa3.stableNorm();
         prered = 0.;
         if (temp < fnorm) /* Computing 2nd power */
-            prered = 1. - ei_abs2(temp / fnorm);
+            prered = 1. - internal::abs2(temp / fnorm);
 
         /* compute the ratio of the actual to the predicted reduction. */
         ratio = 0.;
@@ -290,7 +290,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType  &x)
             ++ncsuc;
             if (ratio >= Scalar(.5) || ncsuc > 1)
                 delta = std::max(delta, pnorm / Scalar(.5));
-            if (ei_abs(ratio - 1.) <= Scalar(.1)) {
+            if (internal::abs(ratio - 1.) <= Scalar(.1)) {
                 delta = pnorm / Scalar(.5);
             }
         }
@@ -342,9 +342,9 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType  &x)
         wa2 = (wa2-wa3)/pnorm;
 
         /* compute the qr factorization of the updated jacobian. */
-        ei_r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);
-        ei_r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);
-        ei_r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);
+        internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);
+        internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);
+        internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);
 
         jeval = false;
     }
@@ -447,7 +447,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType
     if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;
 
     /* calculate the jacobian matrix. */
-    if (ei_fdjac1(functor, x, fvec, fjac, parameters.nb_of_subdiagonals, parameters.nb_of_superdiagonals, parameters.epsfcn) <0)
+    if (internal::fdjac1(functor, x, fvec, fjac, parameters.nb_of_subdiagonals, parameters.nb_of_superdiagonals, parameters.epsfcn) <0)
         return HybridNonLinearSolverSpace::UserAksed;
     nfev += std::min(parameters.nb_of_subdiagonals+parameters.nb_of_superdiagonals+ 1, n);
 
@@ -487,7 +487,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType
 
     while (true) {
         /* determine the direction p. */
-        ei_dogleg<Scalar>(R, diag, qtf, delta, wa1);
+        internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);
 
         /* store the direction p and x + p. calculate the norm of p. */
         wa1 = -wa1;
@@ -507,14 +507,14 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType
         /* compute the scaled actual reduction. */
         actred = -1.;
         if (fnorm1 < fnorm) /* Computing 2nd power */
-            actred = 1. - ei_abs2(fnorm1 / fnorm);
+            actred = 1. - internal::abs2(fnorm1 / fnorm);
 
         /* compute the scaled predicted reduction. */
         wa3 = R.template triangularView<Upper>()*wa1 + qtf;
         temp = wa3.stableNorm();
         prered = 0.;
         if (temp < fnorm) /* Computing 2nd power */
-            prered = 1. - ei_abs2(temp / fnorm);
+            prered = 1. - internal::abs2(temp / fnorm);
 
         /* compute the ratio of the actual to the predicted reduction. */
         ratio = 0.;
@@ -531,7 +531,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType
             ++ncsuc;
             if (ratio >= Scalar(.5) || ncsuc > 1)
                 delta = std::max(delta, pnorm / Scalar(.5));
-            if (ei_abs(ratio - 1.) <= Scalar(.1)) {
+            if (internal::abs(ratio - 1.) <= Scalar(.1)) {
                 delta = pnorm / Scalar(.5);
             }
         }
@@ -583,9 +583,9 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType
         wa2 = (wa2-wa3)/pnorm;
 
         /* compute the qr factorization of the updated jacobian. */
-        ei_r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);
-        ei_r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);
-        ei_r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);
+        internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);
+        internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);
+        internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);
 
         jeval = false;
     }
diff --git a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
index a8f3f3e64..c43df3f7a 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
@@ -69,8 +69,8 @@ public:
         Parameters()
             : factor(Scalar(100.))
             , maxfev(400)
-            , ftol(ei_sqrt(NumTraits<Scalar>::epsilon()))
-            , xtol(ei_sqrt(NumTraits<Scalar>::epsilon()))
+            , ftol(internal::sqrt(NumTraits<Scalar>::epsilon()))
+            , xtol(internal::sqrt(NumTraits<Scalar>::epsilon()))
             , gtol(Scalar(0.))
             , epsfcn(Scalar(0.)) {}
         Scalar factor;
@@ -86,7 +86,7 @@ public:
 
     LevenbergMarquardtSpace::Status lmder1(
             FVectorType &x,
-            const Scalar tol = ei_sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     LevenbergMarquardtSpace::Status minimize(FVectorType &x);
@@ -97,12 +97,12 @@ public:
             FunctorType &functor,
             FVectorType &x,
             Index *nfev,
-            const Scalar tol = ei_sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     LevenbergMarquardtSpace::Status lmstr1(
             FVectorType  &x,
-            const Scalar tol = ei_sqrt(NumTraits<Scalar>::epsilon())
+            const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
             );
 
     LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType  &x);
@@ -263,7 +263,7 @@ 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, ei_abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
+                gnorm = std::max(gnorm, internal::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)
@@ -276,7 +276,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
     do {
 
         /* determine the levenberg-marquardt parameter. */
-        ei_lmpar2<Scalar>(qrfac, diag, qtf, delta, par, wa1);
+        internal::lmpar2<Scalar>(qrfac, diag, qtf, delta, par, wa1);
 
         /* store the direction p and x + p. calculate the norm of p. */
         wa1 = -wa1;
@@ -296,13 +296,13 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
         /* compute the scaled actual reduction. */
         actred = -1.;
         if (Scalar(.1) * fnorm1 < fnorm)
-            actred = 1. - ei_abs2(fnorm1 / fnorm);
+            actred = 1. - internal::abs2(fnorm1 / fnorm);
 
         /* compute the scaled predicted reduction and */
         /* the scaled directional derivative. */
         wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1);
-        temp1 = ei_abs2(wa3.stableNorm() / fnorm);
-        temp2 = ei_abs2(ei_sqrt(par) * pnorm / fnorm);
+        temp1 = internal::abs2(wa3.stableNorm() / fnorm);
+        temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm);
         prered = temp1 + temp2 / Scalar(.5);
         dirder = -(temp1 + temp2);
 
@@ -340,9 +340,9 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
         }
 
         /* tests for convergence. */
-        if (ei_abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
+        if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
             return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
-        if (ei_abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
+        if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
             return LevenbergMarquardtSpace::RelativeReductionTooSmall;
         if (delta <= parameters.xtol * xnorm)
             return LevenbergMarquardtSpace::RelativeErrorTooSmall;
@@ -350,7 +350,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType  &x)
         /* tests for termination and stringent tolerances. */
         if (nfev >= parameters.maxfev)
             return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
-        if (ei_abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
+        if (internal::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;
@@ -451,7 +451,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
     Index rownb = 2;
     for (i = 0; i < m; ++i) {
         if (functor.df(x, wa3, rownb) < 0) return LevenbergMarquardtSpace::UserAsked;
-        ei_rwupdt<Scalar>(fjac, wa3, qtf, fvec[i]);
+        internal::rwupdt<Scalar>(fjac, wa3, qtf, fvec[i]);
         ++rownb;
     }
     ++njev;
@@ -510,7 +510,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
     if (fnorm != 0.)
         for (j = 0; j < n; ++j)
             if (wa2[permutation.indices()[j]] != 0.)
-                gnorm = std::max(gnorm, ei_abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
+                gnorm = std::max(gnorm, internal::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)
@@ -523,7 +523,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
     do {
 
         /* determine the levenberg-marquardt parameter. */
-        ei_lmpar<Scalar>(fjac, permutation.indices(), diag, qtf, delta, par, wa1);
+        internal::lmpar<Scalar>(fjac, permutation.indices(), diag, qtf, delta, par, wa1);
 
         /* store the direction p and x + p. calculate the norm of p. */
         wa1 = -wa1;
@@ -543,13 +543,13 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
         /* compute the scaled actual reduction. */
         actred = -1.;
         if (Scalar(.1) * fnorm1 < fnorm)
-            actred = 1. - ei_abs2(fnorm1 / fnorm);
+            actred = 1. - internal::abs2(fnorm1 / fnorm);
 
         /* compute the scaled predicted reduction and */
         /* the scaled directional derivative. */
         wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1);
-        temp1 = ei_abs2(wa3.stableNorm() / fnorm);
-        temp2 = ei_abs2(ei_sqrt(par) * pnorm / fnorm);
+        temp1 = internal::abs2(wa3.stableNorm() / fnorm);
+        temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm);
         prered = temp1 + temp2 / Scalar(.5);
         dirder = -(temp1 + temp2);
 
@@ -587,9 +587,9 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
         }
 
         /* tests for convergence. */
-        if (ei_abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
+        if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
             return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
-        if (ei_abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
+        if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
             return LevenbergMarquardtSpace::RelativeReductionTooSmall;
         if (delta <= parameters.xtol * xnorm)
             return LevenbergMarquardtSpace::RelativeErrorTooSmall;
@@ -597,7 +597,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
         /* tests for termination and stringent tolerances. */
         if (nfev >= parameters.maxfev)
             return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
-        if (ei_abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
+        if (internal::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 4cb4fbdef..e2bdf923c 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/chkder.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/chkder.h
@@ -2,8 +2,10 @@
 #define chkder_log10e 0.43429448190325182765
 #define chkder_factor 100.
 
+namespace internal {
+
 template<typename Scalar>
-void ei_chkder(
+void chkder(
         const Matrix< Scalar, Dynamic, 1 >  &x,
         const Matrix< Scalar, Dynamic, 1 >  &fvec,
         const Matrix< Scalar, Dynamic, Dynamic > &fjac,
@@ -15,9 +17,9 @@ void ei_chkder(
 {
     typedef DenseIndex Index;
 
-    const Scalar eps = ei_sqrt(NumTraits<Scalar>::epsilon());
+    const Scalar eps = sqrt(NumTraits<Scalar>::epsilon());
     const Scalar epsf = chkder_factor * NumTraits<Scalar>::epsilon();
-    const Scalar epslog = chkder_log10e * ei_log(eps);
+    const Scalar epslog = chkder_log10e * log(eps);
     Scalar temp;
 
     const Index m = fvec.size(), n = x.size();
@@ -26,7 +28,7 @@ void ei_chkder(
         /* mode = 1. */
         xp.resize(n);
         for (Index j = 0; j < n; ++j) {
-            temp = eps * ei_abs(x[j]);
+            temp = eps * abs(x[j]);
             if (temp == 0.)
                 temp = eps;
             xp[j] = x[j] + temp;
@@ -36,21 +38,22 @@ void ei_chkder(
         /* mode = 2. */
         err.setZero(m); 
         for (Index j = 0; j < n; ++j) {
-            temp = ei_abs(x[j]);
+            temp = abs(x[j]);
             if (temp == 0.)
                 temp = 1.;
             err += temp * fjac.col(j);
         }
         for (Index i = 0; i < m; ++i) {
             temp = 1.;
-            if (fvec[i] != 0. && fvecp[i] != 0. && ei_abs(fvecp[i] - fvec[i]) >= epsf * ei_abs(fvec[i]))
-                temp = eps * ei_abs((fvecp[i] - fvec[i]) / eps - err[i]) / (ei_abs(fvec[i]) + ei_abs(fvecp[i]));
+            if (fvec[i] != 0. && fvecp[i] != 0. && abs(fvecp[i] - fvec[i]) >= epsf * abs(fvec[i]))
+                temp = eps * abs((fvecp[i] - fvec[i]) / eps - err[i]) / (abs(fvec[i]) + abs(fvecp[i]));
             err[i] = 1.;
             if (temp > NumTraits<Scalar>::epsilon() && temp < eps)
-                err[i] = (chkder_log10e * ei_log(temp) - epslog) / epslog;
+                err[i] = (chkder_log10e * log(temp) - epslog) / epslog;
             if (temp >= eps)
                 err[i] = 0.;
         }
     }
 }
 
+} // end namespace internal
\ No newline at end of file
diff --git a/unsupported/Eigen/src/NonLinearOptimization/covar.h b/unsupported/Eigen/src/NonLinearOptimization/covar.h
index 104898a30..6c77916f5 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/covar.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/covar.h
@@ -1,9 +1,10 @@
+namespace internal {
 
 template <typename Scalar>
-void ei_covar(
+void covar(
         Matrix< Scalar, Dynamic, Dynamic > &r,
         const VectorXi &ipvt,
-        Scalar tol = ei_sqrt(NumTraits<Scalar>::epsilon()) )
+        Scalar tol = sqrt(NumTraits<Scalar>::epsilon()) )
 {
     typedef DenseIndex Index;
 
@@ -14,14 +15,14 @@ void ei_covar(
 
     /* Function Body */
     const Index n = r.cols();
-    const Scalar tolr = tol * ei_abs(r(0,0));
+    const Scalar tolr = tol * abs(r(0,0));
     Matrix< Scalar, Dynamic, 1 > wa(n);
     assert(ipvt.size()==n);
 
     /* form the inverse of r in the full upper triangle of r. */
     l = -1;
     for (k = 0; k < n; ++k)
-        if (ei_abs(r(k,k)) > tolr) {
+        if (abs(r(k,k)) > tolr) {
             r(k,k) = 1. / r(k,k);
             for (j = 0; j <= k-1; ++j) {
                 temp = r(k,k) * r(j,k);
@@ -61,3 +62,4 @@ void ei_covar(
     r.diagonal() = wa;
 }
 
+} // end namespace internal
diff --git a/unsupported/Eigen/src/NonLinearOptimization/dogleg.h b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
index ab01d5c47..fffd9e0be 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
@@ -1,6 +1,7 @@
+namespace internal {
 
 template <typename Scalar>
-void ei_dogleg(
+void dogleg(
         const Matrix< Scalar, Dynamic, Dynamic >  &qrfac,
         const Matrix< Scalar, Dynamic, 1 >  &diag,
         const Matrix< Scalar, Dynamic, 1 >  &qtb,
@@ -86,8 +87,8 @@ void ei_dogleg(
     /* at which the quadratic is minimized. */
     bnorm = qtb.stableNorm();
     temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);
-    temp = temp - delta / qnorm * ei_abs2(sgnorm / delta) + ei_sqrt(ei_abs2(temp - delta / qnorm) + (1.-ei_abs2(delta / qnorm)) * (1.-ei_abs2(sgnorm / delta)));
-    alpha = delta / qnorm * (1. - ei_abs2(sgnorm / delta)) / temp;
+    temp = temp - delta / qnorm * abs2(sgnorm / delta) + sqrt(abs2(temp - delta / qnorm) + (1.-abs2(delta / qnorm)) * (1.-abs2(sgnorm / delta)));
+    alpha = delta / qnorm * (1. - abs2(sgnorm / delta)) / temp;
 algo_end:
 
     /* form appropriate convex combination of the gauss-newton */
@@ -96,3 +97,4 @@ algo_end:
     x = temp * wa1 + alpha * x;
 }
 
+} // end namespace internal
diff --git a/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
index 74cf53b90..887b76fa1 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
@@ -1,6 +1,7 @@
+namespace internal {
 
 template<typename FunctorType, typename Scalar>
-DenseIndex ei_fdjac1(
+DenseIndex fdjac1(
         const FunctorType &Functor,
         Matrix< Scalar, Dynamic, 1 >  &x,
         Matrix< Scalar, Dynamic, 1 >  &fvec,
@@ -25,13 +26,13 @@ DenseIndex ei_fdjac1(
     Matrix< Scalar, Dynamic, 1 >  wa1(n);
     Matrix< Scalar, Dynamic, 1 >  wa2(n);
 
-    eps = ei_sqrt(std::max(epsfcn,epsmch));
+    eps = sqrt(std::max(epsfcn,epsmch));
     msum = ml + mu + 1;
     if (msum >= n) {
         /* computation of dense approximate jacobian. */
         for (j = 0; j < n; ++j) {
             temp = x[j];
-            h = eps * ei_abs(temp);
+            h = eps * abs(temp);
             if (h == 0.)
                 h = eps;
             x[j] = temp + h;
@@ -47,7 +48,7 @@ DenseIndex ei_fdjac1(
         for (k = 0; k < msum; ++k) {
             for (j = k; (msum<0) ? (j>n): (j<n); j += msum) {
                 wa2[j] = x[j];
-                h = eps * ei_abs(wa2[j]);
+                h = eps * abs(wa2[j]);
                 if (h == 0.) h = eps;
                 x[j] = wa2[j] + h;
             }
@@ -56,7 +57,7 @@ DenseIndex ei_fdjac1(
                 return iflag;
             for (j = k; (msum<0) ? (j>n): (j<n); j += msum) {
                 x[j] = wa2[j];
-                h = eps * ei_abs(wa2[j]);
+                h = eps * abs(wa2[j]);
                 if (h == 0.) h = eps;
                 fjac.col(j).setZero();
                 start = std::max<Index>(0,j-mu);
@@ -68,3 +69,4 @@ DenseIndex ei_fdjac1(
     return 0;
 }
 
+} // end namespace internal
diff --git a/unsupported/Eigen/src/NonLinearOptimization/lmpar.h b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
index 27138de96..a6bbc50ba 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
@@ -1,6 +1,7 @@
+namespace internal {
 
 template <typename Scalar>
-void ei_lmpar(
+void lmpar(
         Matrix< Scalar, Dynamic, Dynamic > &r,
         const VectorXi &ipvt,
         const Matrix< Scalar, Dynamic, 1 >  &diag,
@@ -106,10 +107,10 @@ void ei_lmpar(
         /* evaluate the function at the current value of par. */
         if (par == 0.)
             par = std::max(dwarf,Scalar(.001) * paru); /* Computing MAX */
-        wa1 = ei_sqrt(par)* diag;
+        wa1 = sqrt(par)* diag;
 
         Matrix< Scalar, Dynamic, 1 > sdiag(n);
-        ei_qrsolv<Scalar>(r, ipvt, wa1, qtb, x, sdiag);
+        qrsolv<Scalar>(r, ipvt, wa1, qtb, x, sdiag);
 
         wa2 = diag.cwiseProduct(x);
         dxnorm = wa2.blueNorm();
@@ -119,7 +120,7 @@ void ei_lmpar(
         /* if the function is small enough, accept the current value */
         /* of par. also test for the exceptional cases where parl */
         /* is zero or the number of iterations has reached 10. */
-        if (ei_abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
+        if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
             break;
 
         /* compute the newton correction. */
@@ -156,7 +157,7 @@ void ei_lmpar(
 }
 
 template <typename Scalar>
-void ei_lmpar2(
+void lmpar2(
         const ColPivHouseholderQR<Matrix< Scalar, Dynamic, Dynamic> > &qr,
         const Matrix< Scalar, Dynamic, 1 >  &diag,
         const Matrix< Scalar, Dynamic, 1 >  &qtb,
@@ -243,10 +244,10 @@ void ei_lmpar2(
         /* evaluate the function at the current value of par. */
         if (par == 0.)
             par = std::max(dwarf,Scalar(.001) * paru); /* Computing MAX */
-        wa1 = ei_sqrt(par)* diag;
+        wa1 = sqrt(par)* diag;
 
         Matrix< Scalar, Dynamic, 1 > sdiag(n);
-        ei_qrsolv<Scalar>(s, qr.colsPermutation().indices(), wa1, qtb, x, sdiag);
+        qrsolv<Scalar>(s, qr.colsPermutation().indices(), wa1, qtb, x, sdiag);
 
         wa2 = diag.cwiseProduct(x);
         dxnorm = wa2.blueNorm();
@@ -256,7 +257,7 @@ void ei_lmpar2(
         /* if the function is small enough, accept the current value */
         /* of par. also test for the exceptional cases where parl */
         /* is zero or the number of iterations has reached 10. */
-        if (ei_abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
+        if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
             break;
 
         /* compute the newton correction. */
@@ -286,3 +287,4 @@ void ei_lmpar2(
     return;
 }
 
+} // end namespace internal
diff --git a/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
index 2a602fedf..cb1764a41 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
@@ -1,9 +1,10 @@
+namespace internal {
 
 // TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt
 template <typename Scalar>
-void ei_qrsolv(
+void qrsolv(
         Matrix< Scalar, Dynamic, Dynamic > &s,
-        // TODO : use a PermutationMatrix once ei_lmpar is no more:
+        // TODO : use a PermutationMatrix once lmpar is no more:
         const VectorXi &ipvt,
         const Matrix< Scalar, Dynamic, 1 >  &diag,
         const Matrix< Scalar, Dynamic, 1 >  &qtb,
@@ -83,3 +84,4 @@ void ei_qrsolv(
     for (j = 0; j < n; ++j) x[ipvt[j]] = wa[j];
 }
 
+} // end namespace internal
diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h b/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
index b2ea20d77..ffe505cd5 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
@@ -1,8 +1,9 @@
+namespace internal {
 
 // TODO : move this to GivensQR once there's such a thing in Eigen
 
 template <typename Scalar>
-void ei_r1mpyq(DenseIndex m, DenseIndex n, Scalar *a, const std::vector<JacobiRotation<Scalar> > &v_givens, const std::vector<JacobiRotation<Scalar> > &w_givens)
+void r1mpyq(DenseIndex m, DenseIndex n, Scalar *a, const std::vector<JacobiRotation<Scalar> > &v_givens, const std::vector<JacobiRotation<Scalar> > &w_givens)
 {
     typedef DenseIndex Index;
 
@@ -22,3 +23,4 @@ void ei_r1mpyq(DenseIndex m, DenseIndex n, Scalar *a, const std::vector<JacobiRo
         }
 }
 
+} // end namespace internal
diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1updt.h b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
index 881327af7..0b8ede119 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
@@ -1,6 +1,7 @@
+namespace internal {
 
 template <typename Scalar>
-void ei_r1updt(
+void r1updt(
         Matrix< Scalar, Dynamic, Dynamic > &s,
         const Matrix< Scalar, Dynamic, 1> &u,
         std::vector<JacobiRotation<Scalar> > &v_givens,
@@ -18,7 +19,7 @@ void ei_r1updt(
     Scalar temp;
     JacobiRotation<Scalar> givens;
 
-    // ei_r1updt had a broader usecase, but we dont use it here. And, more
+    // r1updt had a broader usecase, but we dont use it here. And, more
     // importantly, we can not test it.
     assert(m==n);
     assert(u.size()==m);
@@ -88,3 +89,4 @@ void ei_r1updt(
     return;
 }
 
+} // end namespace internal
diff --git a/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h b/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
index ec97b707a..96263f8c0 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
@@ -1,6 +1,7 @@
+namespace internal {
 
 template <typename Scalar>
-void ei_rwupdt(
+void rwupdt(
         Matrix< Scalar, Dynamic, Dynamic >  &r,
         const Matrix< Scalar, Dynamic, 1>  &w,
         Matrix< Scalar, Dynamic, 1>  &b,
@@ -44,3 +45,4 @@ void ei_rwupdt(
     }
 }
 
+} // end namespace internal
\ No newline at end of file