* merge with mainline

* adapt Eigenvalues module to the new rule that the RowMajorBit must have the proper value for vectors
* Fix RowMajorBit in ei_traits<ProductBase>
* Fix vectorizability logic in CoeffBasedProduct

11 files changed, 1184 insertions, 152 deletions

diff --git a/unsupported/Eigen/CMakeLists.txt b/unsupported/Eigen/CMakeLists.txt
index f9d79c51a..87cc4be1e 100644
--- a/unsupported/Eigen/CMakeLists.txt
+++ b/unsupported/Eigen/CMakeLists.txt
@@ -1,4 +1,4 @@
-set(Eigen_HEADERS AdolcForward BVH IterativeSolvers MatrixFunctions MoreVectorization AutoDiff AlignedVector3)
+set(Eigen_HEADERS AdolcForward BVH IterativeSolvers MatrixFunctions MoreVectorization AutoDiff AlignedVector3 Polynomials)
 
 install(FILES
   ${Eigen_HEADERS}
diff --git a/unsupported/Eigen/FFT b/unsupported/Eigen/FFT
index 045c44611..2a1e21007 100644
--- a/unsupported/Eigen/FFT
+++ b/unsupported/Eigen/FFT
@@ -320,7 +320,7 @@ class FFT
         // if the vector is strided, then we need to copy it to a packed temporary
         Matrix<src_type,1,Dynamic> tmp;
         if ( resize_input ) {
-          size_t ncopy = min(src.size(),src.size() + resize_input);
+          size_t ncopy = std::min(src.size(),src.size() + resize_input);
           tmp.setZero(src.size() + resize_input);
           if ( realfft && HasFlag(HalfSpectrum) ) {
             // pad at the Nyquist bin
diff --git a/unsupported/Eigen/MatrixFunctions b/unsupported/Eigen/MatrixFunctions
index 292357fda..e0bc4732c 100644
--- a/unsupported/Eigen/MatrixFunctions
+++ b/unsupported/Eigen/MatrixFunctions
@@ -40,6 +40,22 @@ namespace Eigen {
   * \brief This module aims to provide various methods for the computation of
   * matrix functions. 
   *
+  * To use this module, add 
+  * \code
+  * #include <unsupported/Eigen/MatrixFunctions>
+  * \endcode
+  * at the start of your source file.
+  *
+  * This module defines the following MatrixBase methods.
+  *  - \ref matrixbase_cos "MatrixBase::cos()", for computing the matrix cosine
+  *  - \ref matrixbase_cosh "MatrixBase::cosh()", for computing the matrix hyperbolic cosine
+  *  - \ref matrixbase_exp "MatrixBase::exp()", for computing the matrix exponential
+  *  - \ref matrixbase_matrixfunction "MatrixBase::matrixFunction()", for computing general matrix functions
+  *  - \ref matrixbase_sin "MatrixBase::sin()", for computing the matrix sine
+  *  - \ref matrixbase_sinh "MatrixBase::sinh()", for computing the matrix hyperbolic sine
+  *
+  * These methods are the main entry points to this module. 
+  *
   * %Matrix functions are defined as follows.  Suppose that \f$ f \f$
   * is an entire function (that is, a function on the complex plane
   * that is everywhere complex differentiable).  Then its Taylor
@@ -49,16 +65,205 @@ namespace Eigen {
   * function by the same series:
   * \f[ f(M) = f(0) + f'(0) M + \frac{f''(0)}{2} M^2 + \frac{f'''(0)}{3!} M^3 + \cdots \f]
   *
-  * \code
-  * #include <unsupported/Eigen/MatrixFunctions>
-  * \endcode
   */
 
 #include "src/MatrixFunctions/MatrixExponential.h"
 #include "src/MatrixFunctions/MatrixFunction.h"
 
-}
 
 
+/** 
+\page matrixbaseextra MatrixBase methods defined in the MatrixFunctions module
+\ingroup MatrixFunctions_Module
+
+The remainder of the page documents the following MatrixBase methods
+which are defined in the MatrixFunctions module.
+
+
+
+\section matrixbase_cos MatrixBase::cos()
+
+Compute the matrix cosine.
+
+\code
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
+\endcode
+
+\param[in]  M  a square matrix.
+\returns  expression representing \f$ \cos(M) \f$.
+
+This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cos().
+
+\sa \ref matrixbase_sin "sin()" for an example.
+
+
+
+\section matrixbase_cosh MatrixBase::cosh()
+
+Compute the matrix hyberbolic cosine.
+
+\code
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh() const
+\endcode
+
+\param[in]  M  a square matrix.
+\returns  expression representing \f$ \cosh(M) \f$
+
+This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cosh().
+
+\sa \ref matrixbase_sinh "sinh()" for an example.
+
+
+
+\section matrixbase_exp MatrixBase::exp()
+
+Compute the matrix exponential.
+
+\code
+const MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const
+\endcode
+
+\param[in]  M  matrix whose exponential is to be computed.
+\returns    expression representing the matrix exponential of \p M.
+
+The matrix exponential of \f$ M \f$ is defined by
+\f[ \exp(M) = \sum_{k=0}^\infty \frac{M^k}{k!}. \f]
+The matrix exponential can be used to solve linear ordinary
+differential equations: the solution of \f$ y' = My \f$ with the
+initial condition \f$ y(0) = y_0 \f$ is given by
+\f$ y(t) = \exp(M) y_0 \f$.
+
+The cost of the computation is approximately \f$ 20 n^3 \f$ for
+matrices of size \f$ n \f$. The number 20 depends weakly on the
+norm of the matrix.
+
+The matrix exponential is computed using the scaling-and-squaring
+method combined with Pad&eacute; approximation. The matrix is first
+rescaled, then the exponential of the reduced matrix is computed
+approximant, and then the rescaling is undone by repeated
+squaring. The degree of the Pad&eacute; approximant is chosen such
+that the approximation error is less than the round-off
+error. However, errors may accumulate during the squaring phase.
+
+Details of the algorithm can be found in: Nicholas J. Higham, "The
+scaling and squaring method for the matrix exponential revisited,"
+<em>SIAM J. %Matrix Anal. Applic.</em>, <b>26</b>:1179&ndash;1193,
+2005.
+
+Example: The following program checks that
+\f[ \exp \left[ \begin{array}{ccc}
+      0 & \frac14\pi & 0 \\
+      -\frac14\pi & 0 & 0 \\
+      0 & 0 & 0
+    \end{array} \right] = \left[ \begin{array}{ccc}
+      \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
+      \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
+      0 & 0 & 1
+    \end{array} \right]. \f]
+This corresponds to a rotation of \f$ \frac14\pi \f$ radians around
+the z-axis.
+
+\include MatrixExponential.cpp
+Output: \verbinclude MatrixExponential.out
+
+\note \p M has to be a matrix of \c float, \c double,
+\c complex<float> or \c complex<double> .
+
+
+
+\section matrixbase_matrixfunction MatrixBase::matrixFunction()
+
+Compute a matrix function.
+
+\code
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typename ei_stem_function<typename ei_traits<Derived>::Scalar>::type f) const
+\endcode
+
+\param[in]  M  argument of matrix function, should be a square matrix.
+\param[in]  f  an entire function; \c f(x,n) should compute the n-th
+derivative of f at x.
+\returns  expression representing \p f applied to \p M.
+
+Suppose that \p M is a matrix whose entries have type \c Scalar. 
+Then, the second argument, \p f, should be a function with prototype
+\code 
+ComplexScalar f(ComplexScalar, int) 
+\endcode
+where \c ComplexScalar = \c std::complex<Scalar> if \c Scalar is
+real (e.g., \c float or \c double) and \c ComplexScalar =
+\c Scalar if \c Scalar is complex. The return value of \c f(x,n)
+should be \f$ f^{(n)}(x) \f$, the n-th derivative of f at x.
+
+This routine uses the algorithm described in:
+Philip Davies and Nicholas J. Higham, 
+"A Schur-Parlett algorithm for computing matrix functions", 
+<em>SIAM J. %Matrix Anal. Applic.</em>, <b>25</b>:464&ndash;485, 2003.
+
+The actual work is done by the MatrixFunction class.
+
+Example: The following program checks that
+\f[ \exp \left[ \begin{array}{ccc} 
+      0 & \frac14\pi & 0 \\ 
+      -\frac14\pi & 0 & 0 \\
+      0 & 0 & 0 
+    \end{array} \right] = \left[ \begin{array}{ccc}
+      \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
+      \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
+      0 & 0 & 1
+    \end{array} \right]. \f]
+This corresponds to a rotation of \f$ \frac14\pi \f$ radians around
+the z-axis. This is the same example as used in the documentation
+of \ref matrixbase_exp "exp()".
+
+\include MatrixFunction.cpp
+Output: \verbinclude MatrixFunction.out
+
+Note that the function \c expfn is defined for complex numbers 
+\c x, even though the matrix \c A is over the reals. Instead of
+\c expfn, we could also have used StdStemFunctions::exp:
+\code
+A.matrixFunction(StdStemFunctions<std::complex<double> >::exp, &B);
+\endcode
+
+
+
+\section matrixbase_sin MatrixBase::sin()
+
+Compute the matrix sine.
+
+\code
+const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
+\endcode
+
+\param[in]  M  a square matrix.
+\returns  expression representing \f$ \sin(M) \f$.
+
+This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sin().
+
+Example: \include MatrixSine.cpp
+Output: \verbinclude MatrixSine.out
+
+
+
+\section matrixbase_sinh const MatrixBase::sinh()
+
+Compute the matrix hyperbolic sine.
+
+\code
+MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const
+\endcode
+
+\param[in]  M  a square matrix.
+\returns  expression representing \f$ \sinh(M) \f$
+
+This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sinh().
+
+Example: \include MatrixSinh.cpp
+Output: \verbinclude MatrixSinh.out
+
+*/
+
+}
+
 #endif // EIGEN_MATRIX_FUNCTIONS
 
diff --git a/unsupported/Eigen/Polynomials b/unsupported/Eigen/Polynomials
new file mode 100644
index 000000000..d69abb1be
--- /dev/null
+++ b/unsupported/Eigen/Polynomials
@@ -0,0 +1,137 @@
+#ifndef EIGEN_POLYNOMIALS_MODULE_H
+#define EIGEN_POLYNOMIALS_MODULE_H
+
+#include <Eigen/Core>
+
+#include <Eigen/src/Core/util/DisableMSVCWarnings.h>
+
+#include <Eigen/QR>
+
+// Note that EIGEN_HIDE_HEAVY_CODE has to be defined per module
+#if (defined EIGEN_EXTERN_INSTANTIATIONS) && (EIGEN_EXTERN_INSTANTIATIONS>=2)
+  #ifndef EIGEN_HIDE_HEAVY_CODE
+  #define EIGEN_HIDE_HEAVY_CODE
+  #endif
+#elif defined EIGEN_HIDE_HEAVY_CODE
+  #undef EIGEN_HIDE_HEAVY_CODE
+#endif
+
+namespace Eigen {
+
+/** \ingroup Unsupported_modules
+  * \defgroup Polynomials_Module Polynomials module
+  *
+  * \nonstableyet
+  *
+  * \brief This module provides a QR based polynomial solver.
+	*
+  * To use this module, add
+  * \code
+  * #include <unsupported/Eigen/Polynomials>
+  * \endcode
+	* at the start of your source file.
+  */
+
+#include "src/Polynomials/PolynomialUtils.h"
+#include "src/Polynomials/Companion.h"
+#include "src/Polynomials/PolynomialSolver.h"
+
+/**
+	\page polynomials Polynomials defines functions for dealing with polynomials
+	and a QR based polynomial solver.
+	\ingroup Polynomials_Module
+
+	The remainder of the page documents first the functions for evaluating, computing
+	polynomials, computing estimates about polynomials and next the QR based polynomial
+	solver.
+
+	\section polynomialUtils convenient functions to deal with polynomials
+	\subsection roots_to_monicPolynomial
+	The function
+	\code
+	void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly )
+	\endcode
+	computes the coefficients \f$ a_i \f$ of
+
+	\f$ p(x) = a_0 + a_{1}x + ... + a_{n-1}x^{n-1} + x^n \f$
+
+	where \f$ p \f$ is known through its roots i.e. \f$ p(x) = (x-r_1)(x-r_2)...(x-r_n) \f$.
+
+	\subsection poly_eval
+	The function
+	\code
+	T poly_eval( const Polynomials& poly, const T& x )
+	\endcode
+	evaluates a polynomial at a given point using stabilized H&ouml;rner method.
+
+	The following code: first computes the coefficients in the monomial basis of the monic polynomial that has the provided roots;
+	then, it evaluates the computed polynomial, using a stabilized H&ouml;rner method.
+
+	\include PolynomialUtils1.cpp
+  Output: \verbinclude PolynomialUtils1.out
+
+	\subsection Cauchy bounds
+	The function
+	\code
+	Real cauchy_max_bound( const Polynomial& poly )
+	\endcode
+	provides a maximum bound (the Cauchy one: \f$C(p)\f$) for the absolute value of a root of the given polynomial i.e.
+	\f$ \forall r_i \f$ root of \f$ p(x) = \sum_{k=0}^d a_k x^k \f$,
+	\f$ |r_i| \le C(p) = \sum_{k=0}^{d} \left | \frac{a_k}{a_d} \right | \f$
+	The leading coefficient \f$ p \f$: should be non zero \f$a_d \neq 0\f$.
+
+
+	The function
+	\code
+	Real cauchy_min_bound( const Polynomial& poly )
+	\endcode
+	provides a minimum bound (the Cauchy one: \f$c(p)\f$) for the absolute value of a non zero root of the given polynomial i.e.
+	\f$ \forall r_i \neq 0 \f$ root of \f$ p(x) = \sum_{k=0}^d a_k x^k \f$,
+	\f$ |r_i| \ge c(p) = \left( \sum_{k=0}^{d} \left | \frac{a_k}{a_0} \right | \right)^{-1} \f$
+
+
+
+
+	\section QR polynomial solver class
+	Computes the complex roots of a polynomial by computing the eigenvalues of the associated companion matrix with the QR algorithm.
+	
+	The roots of \f$ p(x) = a_0 + a_1 x + a_2 x^2 + a_{3} x^3 + x^4 \f$ are the eigenvalues of
+	\f$
+	\left [
+	\begin{array}{cccc}
+	0 & 0 &  0 & a_0 \\
+	1 & 0 &  0 & a_1 \\
+	0 & 1 &  0 & a_2 \\
+	0 & 0 &  1 & a_3
+	\end{array} \right ]
+	\f$
+
+	However, the QR algorithm is not guaranteed to converge when there are several eigenvalues with same modulus.
+
+	Therefore the current polynomial solver is guaranteed to provide a correct result only when the complex roots \f$r_1,r_2,...,r_d\f$ have distinct moduli i.e.
+	
+	\f$ \forall i,j \in [1;d],~ \| r_i \| \neq \| r_j \| \f$.
+
+	With 32bit (float) floating types this problem shows up frequently.
+  However, almost always, correct accuracy is reached even in these cases for 64bit
+  (double) floating types and small polynomial degree (<20).
+
+	\include PolynomialSolver1.cpp
+	
+	In the above example:
+	
+	-# a simple use of the polynomial solver is shown;
+	-# the accuracy problem with the QR algorithm is presented: a polynomial with almost conjugate roots is provided to the solver.
+	Those roots have almost same module therefore the QR algorithm failed to converge: the accuracy
+	of the last root is bad;
+	-# a simple way to circumvent the problem is shown: use doubles instead of floats.
+
+  Output: \verbinclude PolynomialSolver1.out
+*/
+
+} // namespace Eigen
+
+#include <Eigen/src/Core/util/EnableMSVCWarnings.h>
+
+#endif // EIGEN_POLYNOMIALS_MODULE_H
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */
diff --git a/unsupported/Eigen/src/CMakeLists.txt b/unsupported/Eigen/src/CMakeLists.txt
index a0870d3af..035a84ca8 100644
--- a/unsupported/Eigen/src/CMakeLists.txt
+++ b/unsupported/Eigen/src/CMakeLists.txt
@@ -5,3 +5,4 @@ ADD_SUBDIRECTORY(MoreVectorization)
 # ADD_SUBDIRECTORY(FFT)
 # ADD_SUBDIRECTORY(Skyline)
 ADD_SUBDIRECTORY(MatrixFunctions)
+ADD_SUBDIRECTORY(Polynomials)
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
index 3ef91a7b2..d7eb1b2fe 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
@@ -330,56 +330,6 @@ struct ei_traits<MatrixExponentialReturnValue<Derived> >
   typedef typename Derived::PlainObject ReturnType;
 };
 
-/** \ingroup MatrixFunctions_Module
- *
- * \brief Compute the matrix exponential.
- *
- * \param[in]  M  matrix whose exponential is to be computed.
- * \returns    expression representing the matrix exponential of \p M.
- *
- * The matrix exponential of \f$ M \f$ is defined by
- * \f[ \exp(M) = \sum_{k=0}^\infty \frac{M^k}{k!}. \f]
- * The matrix exponential can be used to solve linear ordinary
- * differential equations: the solution of \f$ y' = My \f$ with the
- * initial condition \f$ y(0) = y_0 \f$ is given by
- * \f$ y(t) = \exp(M) y_0 \f$.
- *
- * The cost of the computation is approximately \f$ 20 n^3 \f$ for
- * matrices of size \f$ n \f$. The number 20 depends weakly on the
- * norm of the matrix.
- *
- * The matrix exponential is computed using the scaling-and-squaring
- * method combined with Pad&eacute; approximation. The matrix is first
- * rescaled, then the exponential of the reduced matrix is computed
- * approximant, and then the rescaling is undone by repeated
- * squaring. The degree of the Pad&eacute; approximant is chosen such
- * that the approximation error is less than the round-off
- * error. However, errors may accumulate during the squaring phase.
- *
- * Details of the algorithm can be found in: Nicholas J. Higham, "The
- * scaling and squaring method for the matrix exponential revisited,"
- * <em>SIAM J. %Matrix Anal. Applic.</em>, <b>26</b>:1179&ndash;1193,
- * 2005.
- *
- * Example: The following program checks that
- * \f[ \exp \left[ \begin{array}{ccc}
- *       0 & \frac14\pi & 0 \\
- *       -\frac14\pi & 0 & 0 \\
- *       0 & 0 & 0
- *     \end{array} \right] = \left[ \begin{array}{ccc}
- *       \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
- *       \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
- *       0 & 0 & 1
- *     \end{array} \right]. \f]
- * This corresponds to a rotation of \f$ \frac14\pi \f$ radians around
- * the z-axis.
- *
- * \include MatrixExponential.cpp
- * Output: \verbinclude MatrixExponential.out
- *
- * \note \p M has to be a matrix of \c float, \c double,
- * \c complex<float> or \c complex<double> .
- */
 template <typename Derived>
 const MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp() const
 {
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
index 72e42aa7c..270d23b8b 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
@@ -536,56 +536,6 @@ struct ei_traits<MatrixFunctionReturnValue<Derived> >
 /********** MatrixBase methods **********/
 
 
-/** \ingroup MatrixFunctions_Module
-  *
-  * \brief Compute a matrix function.
-  *
-  * \param[in]  M  argument of matrix function, should be a square matrix.
-  * \param[in]  f  an entire function; \c f(x,n) should compute the n-th
-  * derivative of f at x.
-  * \returns  expression representing \p f applied to \p M.
-  *
-  * Suppose that \p M is a matrix whose entries have type \c Scalar. 
-  * Then, the second argument, \p f, should be a function with prototype
-  * \code 
-  * ComplexScalar f(ComplexScalar, int) 
-  * \endcode
-  * where \c ComplexScalar = \c std::complex<Scalar> if \c Scalar is
-  * real (e.g., \c float or \c double) and \c ComplexScalar =
-  * \c Scalar if \c Scalar is complex. The return value of \c f(x,n)
-  * should be \f$ f^{(n)}(x) \f$, the n-th derivative of f at x.
-  *
-  * This routine uses the algorithm described in:
-  * Philip Davies and Nicholas J. Higham, 
-  * "A Schur-Parlett algorithm for computing matrix functions", 
-  * <em>SIAM J. %Matrix Anal. Applic.</em>, <b>25</b>:464&ndash;485, 2003.
-  *
-  * The actual work is done by the MatrixFunction class.
-  *
-  * Example: The following program checks that
-  * \f[ \exp \left[ \begin{array}{ccc} 
-  *       0 & \frac14\pi & 0 \\ 
-  *       -\frac14\pi & 0 & 0 \\
-  *       0 & 0 & 0 
-  *     \end{array} \right] = \left[ \begin{array}{ccc}
-  *       \frac12\sqrt2 & -\frac12\sqrt2 & 0 \\
-  *       \frac12\sqrt2 & \frac12\sqrt2 & 0 \\
-  *       0 & 0 & 1
-  *     \end{array} \right]. \f]
-  * This corresponds to a rotation of \f$ \frac14\pi \f$ radians around
-  * the z-axis. This is the same example as used in the documentation
-  * of MatrixBase::exp().
-  *
-  * \include MatrixFunction.cpp
-  * Output: \verbinclude MatrixFunction.out
-  *
-  * Note that the function \c expfn is defined for complex numbers 
-  * \c x, even though the matrix \c A is over the reals. Instead of
-  * \c expfn, we could also have used StdStemFunctions::exp:
-  * \code
-  * A.matrixFunction(StdStemFunctions<std::complex<double> >::exp, &B);
-  * \endcode
-  */
 template <typename Derived>
 const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typename ei_stem_function<typename ei_traits<Derived>::Scalar>::type f) const
 {
@@ -593,18 +543,6 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(typ
   return MatrixFunctionReturnValue<Derived>(derived(), f);
 }
 
-/** \ingroup MatrixFunctions_Module
-  *
-  * \brief Compute the matrix sine.
-  *
-  * \param[in]  M  a square matrix.
-  * \returns  expression representing \f$ \sin(M) \f$.
-  * 
-  * This function calls matrixFunction() with StdStemFunctions::sin().
-  *
-  * \include MatrixSine.cpp
-  * Output: \verbinclude MatrixSine.out
-  */
 template <typename Derived>
 const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
 {
@@ -613,17 +551,6 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
   return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::sin);
 }
 
-/** \ingroup MatrixFunctions_Module
-  *
-  * \brief Compute the matrix cosine.
-  *
-  * \param[in]  M  a square matrix.
-  * \returns  expression representing \f$ \cos(M) \f$.
-  * 
-  * This function calls matrixFunction() with StdStemFunctions::cos().
-  *
-  * \sa ei_matrix_sin() for an example.
-  */
 template <typename Derived>
 const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
 {
@@ -632,18 +559,6 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
   return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::cos);
 }
 
-/** \ingroup MatrixFunctions_Module
-  *
-  * \brief Compute the matrix hyperbolic sine.
-  *
-  * \param[in]  M  a square matrix.
-  * \returns  expression representing \f$ \sinh(M) \f$
-  * 
-  * This function calls matrixFunction() with StdStemFunctions::sinh().
-  *
-  * \include MatrixSinh.cpp
-  * Output: \verbinclude MatrixSinh.out
-  */
 template <typename Derived>
 const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const
 {
@@ -652,17 +567,6 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh() const
   return MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::sinh);
 }
 
-/** \ingroup MatrixFunctions_Module
-  *
-  * \brief Compute the matrix hyberbolic cosine.
-  *
-  * \param[in]  M  a square matrix.
-  * \returns  expression representing \f$ \cosh(M) \f$
-  * 
-  * This function calls matrixFunction() with StdStemFunctions::cosh().
-  *
-  * \sa ei_matrix_sinh() for an example.
-  */
 template <typename Derived>
 const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh() const
 {
diff --git a/unsupported/Eigen/src/Polynomials/CMakeLists.txt b/unsupported/Eigen/src/Polynomials/CMakeLists.txt
new file mode 100644
index 000000000..51f13f3cb
--- /dev/null
+++ b/unsupported/Eigen/src/Polynomials/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Polynomials_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Polynomials_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/Polynomials COMPONENT Devel
+  )
diff --git a/unsupported/Eigen/src/Polynomials/Companion.h b/unsupported/Eigen/src/Polynomials/Companion.h
new file mode 100644
index 000000000..7c9e9c518
--- /dev/null
+++ b/unsupported/Eigen/src/Polynomials/Companion.h
@@ -0,0 +1,281 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_COMPANION_H
+#define EIGEN_COMPANION_H
+
+// This file requires the user to include
+// * Eigen/Core
+// * Eigen/src/PolynomialSolver.h
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+
+template <typename T>
+T ei_radix(){ return 2; }
+
+template <typename T>
+T ei_radix2(){ return ei_radix<T>()*ei_radix<T>(); }
+
+template<int Size>
+struct ei_decrement_if_fixed_size
+{
+  enum {
+    ret = (Size == Dynamic) ? Dynamic : Size-1 };
+};
+
+#endif
+
+template< typename _Scalar, int _Deg >
+class ei_companion
+{
+  public:
+    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg)
+
+    enum {
+      Deg = _Deg,
+      Deg_1=ei_decrement_if_fixed_size<Deg>::ret
+    };
+
+    typedef _Scalar                                Scalar;
+    typedef typename NumTraits<Scalar>::Real       RealScalar;
+    typedef Matrix<Scalar, Deg, 1>                 RightColumn;
+    //typedef DiagonalMatrix< Scalar, Deg_1, Deg_1 > BottomLeftDiagonal;
+    typedef Matrix<Scalar, Deg_1, 1>               BottomLeftDiagonal;
+
+    typedef Matrix<Scalar, Deg, Deg>               DenseCompanionMatrixType;
+    typedef Matrix< Scalar, _Deg, Deg_1 >          LeftBlock;
+    typedef Matrix< Scalar, Deg_1, Deg_1 >         BottomLeftBlock;
+    typedef Matrix< Scalar, 1, Deg_1 >             LeftBlockFirstRow;
+
+  public:
+    EIGEN_STRONG_INLINE const _Scalar operator()( int row, int col ) const
+    {
+      if( m_bl_diag.rows() > col )
+      {
+        if( 0 < row ){ return m_bl_diag[col]; }
+        else{ return 0; }
+      }
+      else{ return m_monic[row]; }
+    }
+
+  public:
+    template<typename VectorType>
+    void setPolynomial( const VectorType& poly )
+    {
+      const int deg = poly.size()-1;
+      m_monic = -1/poly[deg] * poly.head(deg);
+      //m_bl_diag.setIdentity( deg-1 );
+      m_bl_diag.setOnes(deg-1);
+    }
+
+    template<typename VectorType>
+    ei_companion( const VectorType& poly ){
+      setPolynomial( poly ); }
+
+  public:
+    DenseCompanionMatrixType denseMatrix() const
+    {
+      const int deg   = m_monic.size();
+      const int deg_1 = deg-1;
+      DenseCompanionMatrixType companion(deg,deg);
+      companion <<
+        ( LeftBlock(deg,deg_1)
+          << LeftBlockFirstRow::Zero(1,deg_1),
+          BottomLeftBlock::Identity(deg-1,deg-1)*m_bl_diag.asDiagonal() ).finished()
+        , m_monic;
+      return companion;
+    }
+
+
+
+  protected:
+    /** Helper function for the balancing algorithm.
+     * \returns true if the row and the column, having colNorm and rowNorm
+     * as norms, are balanced, false otherwise.
+     * colB and rowB are repectively the multipliers for
+     * the column and the row in order to balance them.
+     * */
+    bool balanced( Scalar colNorm, Scalar rowNorm,
+        bool& isBalanced, Scalar& colB, Scalar& rowB );
+
+    /** Helper function for the balancing algorithm.
+     * \returns true if the row and the column, having colNorm and rowNorm
+     * as norms, are balanced, false otherwise.
+     * colB and rowB are repectively the multipliers for
+     * the column and the row in order to balance them.
+     * */
+    bool balancedR( Scalar colNorm, Scalar rowNorm,
+        bool& isBalanced, Scalar& colB, Scalar& rowB );
+
+  public:
+    /**
+     * Balancing algorithm from B. N. PARLETT and C. REINSCH (1969)
+     * "Balancing a matrix for calculation of eigenvalues and eigenvectors"
+     * adapted to the case of companion matrices.
+     * A matrix with non zero row and non zero column is balanced
+     * for a certain norm if the i-th row and the i-th column
+     * have same norm for all i.
+     */
+    void balance();
+
+  protected:
+      RightColumn                m_monic;
+      BottomLeftDiagonal         m_bl_diag;
+};
+
+
+
+template< typename _Scalar, int _Deg >
+inline
+bool ei_companion<_Scalar,_Deg>::balanced( Scalar colNorm, Scalar rowNorm,
+    bool& isBalanced, Scalar& colB, Scalar& rowB )
+{
+  if( Scalar(0) == colNorm || Scalar(0) == rowNorm ){ return true; }
+  else
+  {
+    //To find the balancing coefficients, if the radix is 2,
+    //one finds \f$ \sigma \f$ such that
+    // \f$ 2^{2\sigma-1} < rowNorm / colNorm \le 2^{2\sigma+1} \f$
+    // then the balancing coefficient for the row is \f$ 1/2^{\sigma} \f$
+    // and the balancing coefficient for the column is \f$ 2^{\sigma} \f$
+    rowB = rowNorm / ei_radix<Scalar>();
+    colB = Scalar(1);
+    const Scalar s = colNorm + rowNorm;
+
+    while (colNorm < rowB)
+    {
+      colB *= ei_radix<Scalar>();
+      colNorm *= ei_radix2<Scalar>();
+    }
+
+    rowB = rowNorm * ei_radix<Scalar>();
+
+    while (colNorm >= rowB)
+    {
+      colB /= ei_radix<Scalar>();
+      colNorm /= ei_radix2<Scalar>();
+    }
+
+    //This line is used to avoid insubstantial balancing
+    if ((rowNorm + colNorm) < Scalar(0.95) * s * colB)
+    {
+      isBalanced = false;
+      rowB = Scalar(1) / colB;
+      return false;
+    }
+    else{
+      return true; }
+  }
+}
+
+template< typename _Scalar, int _Deg >
+inline
+bool ei_companion<_Scalar,_Deg>::balancedR( Scalar colNorm, Scalar rowNorm,
+    bool& isBalanced, Scalar& colB, Scalar& rowB )
+{
+  if( Scalar(0) == colNorm || Scalar(0) == rowNorm ){ return true; }
+  else
+  {
+    /**
+     * Set the norm of the column and the row to the geometric mean
+     * of the row and column norm
+     */
+    const _Scalar q = colNorm/rowNorm;
+    if( !ei_isApprox( q, _Scalar(1) ) )
+    {
+      rowB = ei_sqrt( colNorm/rowNorm );
+      colB = Scalar(1)/rowB;
+
+      isBalanced = false;
+      return false;
+    }
+    else{
+      return true; }
+  }
+}
+
+
+template< typename _Scalar, int _Deg >
+void ei_companion<_Scalar,_Deg>::balance()
+{
+  EIGEN_STATIC_ASSERT( 1 < Deg, YOU_MADE_A_PROGRAMMING_MISTAKE );
+  const int deg   = m_monic.size();
+  const int deg_1 = deg-1;
+
+  bool hasConverged=false;
+  while( !hasConverged )
+  {
+    hasConverged = true;
+    Scalar colNorm,rowNorm;
+    Scalar colB,rowB;
+
+    //First row, first column excluding the diagonal
+    //==============================================
+    colNorm = ei_abs(m_bl_diag[0]);
+    rowNorm = ei_abs(m_monic[0]);
+
+    //Compute balancing of the row and the column
+    if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )
+    {
+      m_bl_diag[0] *= colB;
+      m_monic[0] *= rowB;
+    }
+
+    //Middle rows and columns excluding the diagonal
+    //==============================================
+    for( int i=1; i<deg_1; ++i )
+    {
+      // column norm, excluding the diagonal
+      colNorm = ei_abs(m_bl_diag[i]);
+
+      // row norm, excluding the diagonal
+      rowNorm = ei_abs(m_bl_diag[i-1]) + ei_abs(m_monic[i]);
+
+      //Compute balancing of the row and the column
+      if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )
+      {
+        m_bl_diag[i]   *= colB;
+        m_bl_diag[i-1] *= rowB;
+        m_monic[i]     *= rowB;
+      }
+    }
+
+    //Last row, last column excluding the diagonal
+    //============================================
+    const int ebl = m_bl_diag.size()-1;
+    VectorBlock<RightColumn,Deg_1> headMonic( m_monic, 0, deg_1 );
+    colNorm = headMonic.array().abs().sum();
+    rowNorm = ei_abs( m_bl_diag[ebl] );
+
+    //Compute balancing of the row and the column
+    if( !balanced( colNorm, rowNorm, hasConverged, colB, rowB ) )
+    {
+      headMonic      *= colB;
+      m_bl_diag[ebl] *= rowB;
+    }
+  }
+}
+
+
+#endif // EIGEN_COMPANION_H
diff --git a/unsupported/Eigen/src/Polynomials/PolynomialSolver.h b/unsupported/Eigen/src/Polynomials/PolynomialSolver.h
new file mode 100644
index 000000000..49a5ffffa
--- /dev/null
+++ b/unsupported/Eigen/src/Polynomials/PolynomialSolver.h
@@ -0,0 +1,395 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_POLYNOMIAL_SOLVER_H
+#define EIGEN_POLYNOMIAL_SOLVER_H
+
+/** \ingroup Polynomials_Module
+ *  \class PolynomialSolverBase.
+ *
+ * \brief Defined to be inherited by polynomial solvers: it provides
+ * convenient methods such as
+ *  - real roots,
+ *  - greatest, smallest complex roots,
+ *  - real roots with greatest, smallest absolute real value,
+ *  - greatest, smallest real roots.
+ *
+ * It stores the set of roots as a vector of complexes.
+ *
+ */
+template< typename _Scalar, int _Deg >
+class PolynomialSolverBase
+{
+  public:
+    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg)
+
+    typedef _Scalar                             Scalar;
+    typedef typename NumTraits<Scalar>::Real    RealScalar;
+    typedef std::complex<RealScalar>            RootType;
+    typedef Matrix<RootType,_Deg,1>             RootsType;
+
+  protected:
+    template< typename OtherPolynomial >
+    inline void setPolynomial( const OtherPolynomial& poly ){
+      m_roots.resize(poly.size()); }
+
+  public:
+    template< typename OtherPolynomial >
+    inline PolynomialSolverBase( const OtherPolynomial& poly ){
+      setPolynomial( poly() ); }
+
+    inline PolynomialSolverBase(){}
+
+  public:
+    /** \returns the complex roots of the polynomial */
+    inline const RootsType& roots() const { return m_roots; }
+
+  public:
+    /** Clear and fills the back insertion sequence with the real roots of the polynomial
+     * i.e. the real part of the complex roots that have an imaginary part which
+     * absolute value is smaller than absImaginaryThreshold.
+     * absImaginaryThreshold takes the dummy_precision associated
+     * with the _Scalar template parameter of the PolynomialSolver class as the default value.
+     *
+     * \param[out] bi_seq : the back insertion sequence (stl concept)
+     * \param[in]  absImaginaryThreshold : the maximum bound of the imaginary part of a complex
+     *  number that is considered as real.
+     * */
+    template<typename Stl_back_insertion_sequence>
+    inline void realRoots( Stl_back_insertion_sequence& bi_seq,
+        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+    {
+      bi_seq.clear();
+      for( int i=0; i<m_roots.size(); ++i )
+      {
+        if( ei_abs( m_roots[i].imag() ) < absImaginaryThreshold ){
+          bi_seq.push_back( m_roots[i].real() ); }
+      }
+    }
+
+  protected:
+    template<typename squaredNormBinaryPredicate>
+    inline const RootType& selectComplexRoot_withRespectToNorm( squaredNormBinaryPredicate& pred ) const
+    {
+      int res=0;
+      RealScalar norm2 = ei_abs2( m_roots[0] );
+      for( int i=1; i<m_roots.size(); ++i )
+      {
+        const RealScalar currNorm2 = ei_abs2( m_roots[i] );
+        if( pred( currNorm2, norm2 ) ){
+          res=i; norm2=currNorm2; }
+      }
+      return m_roots[res];
+    }
+
+  public:
+    /**
+     * \returns the complex root with greatest norm.
+     */
+    inline const RootType& greatestRoot() const
+    {
+      std::greater<Scalar> greater;
+      return selectComplexRoot_withRespectToNorm( greater );
+    }
+
+    /**
+     * \returns the complex root with smallest norm.
+     */
+    inline const RootType& smallestRoot() const
+    {
+      std::less<Scalar> less;
+      return selectComplexRoot_withRespectToNorm( less );
+    }
+
+  protected:
+    template<typename squaredRealPartBinaryPredicate>
+    inline const RealScalar& selectRealRoot_withRespectToAbsRealPart(
+        squaredRealPartBinaryPredicate& pred,
+        bool& hasArealRoot,
+        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+    {
+      hasArealRoot = false;
+      int res=0;
+      RealScalar abs2;
+
+      for( int i=0; i<m_roots.size(); ++i )
+      {
+        if( ei_abs( m_roots[i].imag() ) < absImaginaryThreshold )
+        {
+          if( !hasArealRoot )
+          {
+            hasArealRoot = true;
+            res = i;
+            abs2 = m_roots[i].real() * m_roots[i].real();
+          }
+          else
+          {
+            const RealScalar currAbs2 = m_roots[i].real() * m_roots[i].real();
+            if( pred( currAbs2, abs2 ) )
+            {
+              abs2 = currAbs2;
+              res = i;
+            }
+          }
+        }
+        else
+        {
+          if( ei_abs( m_roots[i].imag() ) < ei_abs( m_roots[res].imag() ) ){
+            res = i; }
+        }
+      }
+      return m_roots[res].real();
+    }
+
+
+    template<typename RealPartBinaryPredicate>
+    inline const RealScalar& selectRealRoot_withRespectToRealPart(
+        RealPartBinaryPredicate& pred,
+        bool& hasArealRoot,
+        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+    {
+      hasArealRoot = false;
+      int res=0;
+      RealScalar val;
+
+      for( int i=0; i<m_roots.size(); ++i )
+      {
+        if( ei_abs( m_roots[i].imag() ) < absImaginaryThreshold )
+        {
+          if( !hasArealRoot )
+          {
+            hasArealRoot = true;
+            res = i;
+            val = m_roots[i].real();
+          }
+          else
+          {
+            const RealScalar curr = m_roots[i].real();
+            if( pred( curr, val ) )
+            {
+              val = curr;
+              res = i;
+            }
+          }
+        }
+        else
+        {
+          if( ei_abs( m_roots[i].imag() ) < ei_abs( m_roots[res].imag() ) ){
+            res = i; }
+        }
+      }
+      return m_roots[res].real();
+    }
+
+  public:
+    /**
+     * \returns a real root with greatest absolute magnitude.
+     * A real root is defined as the real part of a complex root with absolute imaginary
+     * part smallest than absImaginaryThreshold.
+     * absImaginaryThreshold takes the dummy_precision associated
+     * with the _Scalar template parameter of the PolynomialSolver class as the default value.
+     * If no real root is found the boolean hasArealRoot is set to false and the real part of
+     * the root with smallest absolute imaginary part is returned instead.
+     *
+     * \param[out] hasArealRoot : boolean true if a real root is found according to the
+     *  absImaginaryThreshold criterion, false otherwise.
+     * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide
+     *  whether or not a root is real.
+     */
+    inline const RealScalar& absGreatestRealRoot(
+        bool& hasArealRoot,
+        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+    {
+      std::greater<Scalar> greater;
+      return selectRealRoot_withRespectToAbsRealPart( greater, hasArealRoot, absImaginaryThreshold );
+    }
+
+
+    /**
+     * \returns a real root with smallest absolute magnitude.
+     * A real root is defined as the real part of a complex root with absolute imaginary
+     * part smallest than absImaginaryThreshold.
+     * absImaginaryThreshold takes the dummy_precision associated
+     * with the _Scalar template parameter of the PolynomialSolver class as the default value.
+     * If no real root is found the boolean hasArealRoot is set to false and the real part of
+     * the root with smallest absolute imaginary part is returned instead.
+     *
+     * \param[out] hasArealRoot : boolean true if a real root is found according to the
+     *  absImaginaryThreshold criterion, false otherwise.
+     * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide
+     *  whether or not a root is real.
+     */
+    inline const RealScalar& absSmallestRealRoot(
+        bool& hasArealRoot,
+        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+    {
+      std::less<Scalar> less;
+      return selectRealRoot_withRespectToAbsRealPart( less, hasArealRoot, absImaginaryThreshold );
+    }
+
+
+    /**
+     * \returns the real root with greatest value.
+     * A real root is defined as the real part of a complex root with absolute imaginary
+     * part smallest than absImaginaryThreshold.
+     * absImaginaryThreshold takes the dummy_precision associated
+     * with the _Scalar template parameter of the PolynomialSolver class as the default value.
+     * If no real root is found the boolean hasArealRoot is set to false and the real part of
+     * the root with smallest absolute imaginary part is returned instead.
+     *
+     * \param[out] hasArealRoot : boolean true if a real root is found according to the
+     *  absImaginaryThreshold criterion, false otherwise.
+     * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide
+     *  whether or not a root is real.
+     */
+    inline const RealScalar& greatestRealRoot(
+        bool& hasArealRoot,
+        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+    {
+      std::greater<Scalar> greater;
+      return selectRealRoot_withRespectToRealPart( greater, hasArealRoot, absImaginaryThreshold );
+    }
+
+
+    /**
+     * \returns the real root with smallest value.
+     * A real root is defined as the real part of a complex root with absolute imaginary
+     * part smallest than absImaginaryThreshold.
+     * absImaginaryThreshold takes the dummy_precision associated
+     * with the _Scalar template parameter of the PolynomialSolver class as the default value.
+     * If no real root is found the boolean hasArealRoot is set to false and the real part of
+     * the root with smallest absolute imaginary part is returned instead.
+     *
+     * \param[out] hasArealRoot : boolean true if a real root is found according to the
+     *  absImaginaryThreshold criterion, false otherwise.
+     * \param[in] absImaginaryThreshold : threshold on the absolute imaginary part to decide
+     *  whether or not a root is real.
+     */
+    inline const RealScalar& smallestRealRoot(
+        bool& hasArealRoot,
+        const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
+    {
+      std::less<Scalar> less;
+      return selectRealRoot_withRespectToRealPart( less, hasArealRoot, absImaginaryThreshold );
+    }
+
+  protected:
+    RootsType               m_roots;
+};
+
+#define EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( BASE )  \
+  typedef typename BASE::Scalar                 Scalar;       \
+  typedef typename BASE::RealScalar             RealScalar;   \
+  typedef typename BASE::RootType               RootType;     \
+  typedef typename BASE::RootsType              RootsType;
+
+
+
+/** \ingroup Polynomials_Module
+  *
+  * \class PolynomialSolver
+  *
+  * \brief A polynomial solver
+  *
+  * Computes the complex roots of a real polynomial.
+  *
+  * \param _Scalar the scalar type, i.e., the type of the polynomial coefficients
+  * \param _Deg the degree of the polynomial, can be a compile time value or Dynamic.
+  *             Notice that the number of polynomial coefficients is _Deg+1.
+  *
+  * This class implements a polynomial solver and provides convenient methods such as
+  * - real roots,
+  * - greatest, smallest complex roots,
+  * - real roots with greatest, smallest absolute real value.
+  * - greatest, smallest real roots.
+  *
+  * WARNING: this polynomial solver is experimental, part of the unsuported Eigen modules.
+  *
+  *
+  * Currently a QR algorithm is used to compute the eigenvalues of the companion matrix of
+  * the polynomial to compute its roots.
+  * This supposes that the complex moduli of the roots are all distinct: e.g. there should
+  * be no multiple roots or conjugate roots for instance.
+  * With 32bit (float) floating types this problem shows up frequently.
+  * However, almost always, correct accuracy is reached even in these cases for 64bit
+  * (double) floating types and small polynomial degree (<20).
+  */
+template< typename _Scalar, int _Deg >
+class PolynomialSolver : public PolynomialSolverBase<_Scalar,_Deg>
+{
+  public:
+    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Deg==Dynamic ? Dynamic : _Deg)
+
+    typedef PolynomialSolverBase<_Scalar,_Deg>    PS_Base;
+    EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base )
+
+    typedef Matrix<Scalar,_Deg,_Deg>                 CompanionMatrixType;
+    typedef EigenSolver<CompanionMatrixType>         EigenSolverType;
+
+  public:
+    /** Computes the complex roots of a new polynomial. */
+    template< typename OtherPolynomial >
+    void compute( const OtherPolynomial& poly )
+    {
+      assert( Scalar(0) != poly[poly.size()-1] );
+      ei_companion<Scalar,_Deg> companion( poly );
+      companion.balance();
+      m_eigenSolver.compute( companion.denseMatrix() );
+      m_roots = m_eigenSolver.eigenvalues();
+    }
+
+  public:
+    template< typename OtherPolynomial >
+    inline PolynomialSolver( const OtherPolynomial& poly ){
+      compute( poly ); }
+
+    inline PolynomialSolver(){}
+
+  protected:
+    using                   PS_Base::m_roots;
+    EigenSolverType         m_eigenSolver;
+};
+
+
+template< typename _Scalar >
+class PolynomialSolver<_Scalar,1> : public PolynomialSolverBase<_Scalar,1>
+{
+  public:
+    typedef PolynomialSolverBase<_Scalar,1>    PS_Base;
+    EIGEN_POLYNOMIAL_SOLVER_BASE_INHERITED_TYPES( PS_Base )
+
+  public:
+    /** Computes the complex roots of a new polynomial. */
+    template< typename OtherPolynomial >
+    void compute( const OtherPolynomial& poly )
+    {
+      assert( Scalar(0) != poly[poly.size()-1] );
+      m_roots[0] = -poly[0]/poly[poly.size()-1];
+    }
+
+  protected:
+    using                   PS_Base::m_roots;
+};
+
+#endif // EIGEN_POLYNOMIAL_SOLVER_H
diff --git a/unsupported/Eigen/src/Polynomials/PolynomialUtils.h b/unsupported/Eigen/src/Polynomials/PolynomialUtils.h
new file mode 100644
index 000000000..d78821f90
--- /dev/null
+++ b/unsupported/Eigen/src/Polynomials/PolynomialUtils.h
@@ -0,0 +1,153 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_POLYNOMIAL_UTILS_H
+#define EIGEN_POLYNOMIAL_UTILS_H
+
+/** \ingroup Polynomials_Module
+ * \returns the evaluation of the polynomial at x using Horner algorithm.
+ *
+ * \param[in] poly : the vector of coefficients of the polynomial ordered
+ *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ *  e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$.
+ * \param[in] x : the value to evaluate the polynomial at.
+ *
+ * <i><b>Note for stability:</b></i>
+ *  <dd> \f$ |x| \le 1 \f$ </dd>
+ */
+template <typename Polynomials, typename T>
+inline
+T poly_eval_horner( const Polynomials& poly, const T& x )
+{
+  T val=poly[poly.size()-1];
+  for( int i=poly.size()-2; i>=0; --i ){
+    val = val*x + poly[i]; }
+  return val;
+}
+
+/** \ingroup Polynomials_Module
+ * \returns the evaluation of the polynomial at x using stabilized Horner algorithm.
+ *
+ * \param[in] poly : the vector of coefficients of the polynomial ordered
+ *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ *  e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$.
+ * \param[in] x : the value to evaluate the polynomial at.
+ */
+template <typename Polynomials, typename T>
+inline
+T poly_eval( const Polynomials& poly, const T& x )
+{
+  typedef typename NumTraits<T>::Real Real;
+
+  if( ei_abs2( x ) <= Real(1) ){
+    return poly_eval_horner( poly, x ); }
+  else
+  {
+    T val=poly[0];
+    T inv_x = T(1)/x;
+    for( int i=1; i<poly.size(); ++i ){
+      val = val*inv_x + poly[i]; }
+
+    return std::pow(x,(T)(poly.size()-1)) * val;
+  }
+}
+
+/** \ingroup Polynomials_Module
+ * \returns a maximum bound for the absolute value of any root of the polynomial.
+ *
+ * \param[in] poly : the vector of coefficients of the polynomial ordered
+ *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ *  e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$.
+ *
+ *  <i><b>Precondition:</b></i>
+ *  <dd> the leading coefficient of the input polynomial poly must be non zero </dd>
+ */
+template <typename Polynomial>
+inline
+typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Polynomial& poly )
+{
+  typedef typename Polynomial::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real Real;
+
+  assert( Scalar(0) != poly[poly.size()-1] );
+  const Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1];
+  Real cb(0);
+
+  for( int i=0; i<poly.size()-1; ++i ){
+    cb += ei_abs(poly[i]*inv_leading_coeff); }
+  return cb + Real(1);
+}
+
+/** \ingroup Polynomials_Module
+ * \returns a minimum bound for the absolute value of any non zero root of the polynomial.
+ * \param[in] poly : the vector of coefficients of the polynomial ordered
+ *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ *  e.g. \f$ 1 + 3x^2 \f$ is stored as a vector \f$ [ 1, 0, 3 ] \f$.
+ */
+template <typename Polynomial>
+inline
+typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Polynomial& poly )
+{
+  typedef typename Polynomial::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real Real;
+
+  int i=0;
+  while( i<poly.size()-1 && Scalar(0) == poly(i) ){ ++i; }
+  if( poly.size()-1 == i ){
+    return Real(1); }
+
+  const Scalar inv_min_coeff = Scalar(1)/poly[i];
+  Real cb(1);
+  for( int j=i+1; j<poly.size(); ++j ){
+    cb += ei_abs(poly[j]*inv_min_coeff); }
+  return Real(1)/cb;
+}
+
+/** \ingroup Polynomials_Module
+ * Given the roots of a polynomial compute the coefficients in the
+ * monomial basis of the monic polynomial with same roots and minimal degree.
+ * If RootVector is a vector of complexes, Polynomial should also be a vector
+ * of complexes.
+ * \param[in] rv : a vector containing the roots of a polynomial.
+ * \param[out] poly : the vector of coefficients of the polynomial ordered
+ *  by degrees i.e. poly[i] is the coefficient of degree i of the polynomial
+ *  e.g. \f$ 3 + x^2 \f$ is stored as a vector \f$ [ 3, 0, 1 ] \f$.
+ */
+template <typename RootVector, typename Polynomial>
+void roots_to_monicPolynomial( const RootVector& rv, Polynomial& poly )
+{
+
+  typedef typename Polynomial::Scalar Scalar;
+
+  poly.setZero( rv.size()+1 );
+  poly[0] = -rv[0]; poly[1] = Scalar(1);
+  for( int i=1; i<(int)rv.size(); ++i )
+  {
+    for( int j=i+1; j>0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; }
+    poly[0] = -rv[i]*poly[0];
+  }
+}
+
+
+#endif // EIGEN_POLYNOMIAL_UTILS_H