sync with mainline

10 files changed, 1479 insertions, 37 deletions

diff --git a/unsupported/Eigen/Complex b/unsupported/Eigen/Complex
new file mode 100644
index 000000000..e1c41ab38
--- /dev/null
+++ b/unsupported/Eigen/Complex
@@ -0,0 +1,182 @@
+#ifndef EIGEN_COMPLEX_H
+#define EIGEN_COMPLEX_H
+
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// 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/>.
+
+// Eigen::Complex reuses as much as possible from std::complex
+// and allows easy conversion to and from, even at the pointer level.
+
+
+#include <complex>
+
+namespace Eigen {
+
+template <typename _NativePtr,typename _PunnedPtr>
+struct castable_pointer
+{
+    castable_pointer(_NativePtr ptr) : _ptr(ptr) {}
+    operator _NativePtr ()  {return _ptr;}
+    operator _PunnedPtr ()  {return reinterpret_cast<_PunnedPtr>(_ptr);}
+    private: 
+    _NativePtr _ptr;
+};
+
+template <typename T>
+struct Complex
+{
+    typedef typename std::complex<T> StandardComplex;
+    typedef T value_type;
+
+    // constructors
+    Complex(const T& re = T(), const T& im = T()) : _re(re),_im(im) { }
+    Complex(const Complex&other ): _re(other.real()) ,_im(other.imag()) {}
+
+    template<class X> 
+    Complex(const Complex<X>&other): _re(other.real()) ,_im(other.imag()) {}
+    template<class X> 
+    Complex(const std::complex<X>&other): _re(other.real()) ,_im(other.imag()) {}
+
+
+    // allow binary access to the object as a std::complex
+    typedef castable_pointer< Complex<T>*, StandardComplex* > pointer_type;
+    typedef castable_pointer< const Complex<T>*, const StandardComplex* > const_pointer_type;
+    pointer_type operator & () {return pointer_type(this);}
+    const_pointer_type operator & () const {return const_pointer_type(this);}
+
+    operator StandardComplex () const {return std_type();}
+    operator StandardComplex & () {return std_type();}
+
+    StandardComplex std_type() const {return StandardComplex(real(),imag());}
+    StandardComplex & std_type() {return *reinterpret_cast<StandardComplex*>(this);}
+
+
+    // every sort of accessor and mutator that has ever been in fashion.
+    // For a brief history, search for "std::complex over-encapsulated"
+    // http://www.open-std.org/jtc1/sc22/wg21/docs/lwg-defects.html#387
+    const T & real() const {return _re;}
+    const T & imag() const {return _im;}
+    T & real() {return _re;}
+    T & imag() {return _im;}
+    T & real(const T & x) {return _re=x;}
+    T & imag(const T & x) {return _im=x;}
+    void set_real(const T & x) {_re = x;}
+    void set_imag(const T & x) {_im = x;}
+
+    // *** complex member functions: ***
+    Complex<T>& operator= (const T& val) { _re=val;_im=0;return *this;  }
+    Complex<T>& operator+= (const T& val) {_re+=val;return *this;}
+    Complex<T>& operator-= (const T& val) {_re-=val;return *this;}
+    Complex<T>& operator*= (const T& val) {_re*=val;_im*=val;return *this;  }
+    Complex<T>& operator/= (const T& val) {_re/=val;_im/=val;return *this;  }
+
+    Complex& operator= (const Complex& rhs) {_re=rhs._re;_im=rhs._im;return *this;}
+    Complex& operator= (const StandardComplex& rhs) {_re=rhs.real();_im=rhs.imag();return *this;}
+
+    template<class X> Complex<T>& operator= (const Complex<X>& rhs) { _re=rhs._re;_im=rhs._im;return *this;}
+    template<class X> Complex<T>& operator+= (const Complex<X>& rhs) { _re+=rhs._re;_im+=rhs._im;return *this;}
+    template<class X> Complex<T>& operator-= (const Complex<X>& rhs) { _re-=rhs._re;_im-=rhs._im;return *this;}
+    template<class X> Complex<T>& operator*= (const Complex<X>& rhs) { this->std_type() *= rhs.std_type(); return *this; }
+    template<class X> Complex<T>& operator/= (const Complex<X>& rhs) { this->std_type() /= rhs.std_type(); return *this; }
+
+    private:
+    T _re;
+    T _im;
+};
+
+template <typename T>
+T ei_to_std( const T & x) {return x;}
+
+template <typename T>
+std::complex<T> ei_to_std( const Complex<T> & x) {return x.std_type();}
+
+// 26.2.6 operators
+template<class T> Complex<T> operator+(const Complex<T>& rhs) {return rhs;}
+template<class T> Complex<T> operator-(const Complex<T>& rhs) {return -ei_to_std(rhs);}
+
+template<class T> Complex<T> operator+(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) + ei_to_std(rhs);}
+template<class T> Complex<T> operator-(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) - ei_to_std(rhs);}
+template<class T> Complex<T> operator*(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) * ei_to_std(rhs);}
+template<class T> Complex<T> operator/(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) / ei_to_std(rhs);}
+template<class T> bool operator==(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) == ei_to_std(rhs);}
+template<class T> bool operator!=(const Complex<T>& lhs, const Complex<T>& rhs) { return ei_to_std(lhs) != ei_to_std(rhs);}
+
+template<class T> Complex<T> operator+(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) + ei_to_std(rhs); }
+template<class T> Complex<T> operator-(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) - ei_to_std(rhs); }
+template<class T> Complex<T> operator*(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) * ei_to_std(rhs); }
+template<class T> Complex<T> operator/(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) / ei_to_std(rhs); }
+template<class T> bool operator==(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) == ei_to_std(rhs); }
+template<class T> bool operator!=(const Complex<T>& lhs, const T& rhs) {return ei_to_std(lhs) != ei_to_std(rhs); }
+
+template<class T> Complex<T> operator+(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) + ei_to_std(rhs); }
+template<class T> Complex<T> operator-(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) - ei_to_std(rhs); }
+template<class T> Complex<T> operator*(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) * ei_to_std(rhs); }
+template<class T> Complex<T> operator/(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) / ei_to_std(rhs); }
+template<class T> bool operator==(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) == ei_to_std(rhs); }
+template<class T> bool operator!=(const T& lhs, const Complex<T>& rhs) {return ei_to_std(lhs) != ei_to_std(rhs); }
+
+template<class T, class charT, class traits>
+std::basic_istream<charT,traits>&
+  operator>> (std::basic_istream<charT,traits>& istr, Complex<T>& rhs)
+{
+    return istr >> rhs.std_type();
+}
+
+template<class T, class charT, class traits>
+std::basic_ostream<charT,traits>&
+operator<< (std::basic_ostream<charT,traits>& ostr, const Complex<T>& rhs)
+{
+    return ostr << rhs.std_type();
+}
+
+ // 26.2.7 values:
+ template<class T> T real(const Complex<T>&x) {return real(ei_to_std(x));}
+ template<class T> T abs(const Complex<T>&x) {return abs(ei_to_std(x));}
+ template<class T> T arg(const Complex<T>&x) {return arg(ei_to_std(x));}
+ template<class T> T norm(const Complex<T>&x) {return norm(ei_to_std(x));}
+
+ template<class T> Complex<T> conj(const Complex<T>&x) { return conj(ei_to_std(x));}
+ template<class T> Complex<T> polar(const T& x, const T&y) {return polar(ei_to_std(x),ei_to_std(y));} 
+ // 26.2.8 transcendentals:
+ template<class T> Complex<T> cos (const  Complex<T>&x){return cos(ei_to_std(x));}
+ template<class T> Complex<T> cosh (const  Complex<T>&x){return cosh(ei_to_std(x));}
+ template<class T> Complex<T> exp (const  Complex<T>&x){return exp(ei_to_std(x));}
+ template<class T> Complex<T> log (const  Complex<T>&x){return log(ei_to_std(x));}
+ template<class T> Complex<T> log10 (const  Complex<T>&x){return log10(ei_to_std(x));}
+
+ template<class T> Complex<T> pow(const Complex<T>&x, int p) {return pow(ei_to_std(x),ei_to_std(p));}
+ template<class T> Complex<T> pow(const Complex<T>&x, const T&p) {return pow(ei_to_std(x),ei_to_std(p));}
+ template<class T> Complex<T> pow(const Complex<T>&x, const Complex<T>&p) {return pow(ei_to_std(x),ei_to_std(p));}
+ template<class T> Complex<T> pow(const T&x, const Complex<T>&p) {return pow(ei_to_std(x),ei_to_std(p));}
+
+ template<class T> Complex<T> sin (const  Complex<T>&x){return sin(ei_to_std(x));}
+ template<class T> Complex<T> sinh (const  Complex<T>&x){return sinh(ei_to_std(x));}
+ template<class T> Complex<T> sqrt (const  Complex<T>&x){return sqrt(ei_to_std(x));}
+ template<class T> Complex<T> tan (const  Complex<T>&x){return tan(ei_to_std(x));}
+ template<class T> Complex<T> tanh (const  Complex<T>&x){return tanh(ei_to_std(x));}
+}
+
+#endif
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */
+
diff --git a/unsupported/Eigen/FFT b/unsupported/Eigen/FFT
new file mode 100644
index 000000000..36afdde8d
--- /dev/null
+++ b/unsupported/Eigen/FFT
@@ -0,0 +1,135 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. 
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// 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_FFT_H
+#define EIGEN_FFT_H
+
+#include <complex>
+#include <vector>
+#include <map>
+
+#ifdef EIGEN_FFTW_DEFAULT
+// FFTW: faster, GPL -- incompatible with Eigen in LGPL form, bigger code size
+#  include <fftw3.h>
+   namespace Eigen {
+#    include "src/FFT/ei_fftw_impl.h"
+     //template <typename T> typedef struct ei_fftw_impl  default_fft_impl; this does not work
+     template <typename T> struct default_fft_impl : public ei_fftw_impl<T> {};
+   }
+#elif defined EIGEN_MKL_DEFAULT
+// TODO 
+// intel Math Kernel Library: fastest, commercial -- may be incompatible with Eigen in GPL form
+   namespace Eigen {
+#    include "src/FFT/ei_imklfft_impl.h"
+     template <typename T> struct default_fft_impl : public ei_imklfft_impl {};
+   }
+#else
+// ei_kissfft_impl:  small, free, reasonably efficient default, derived from kissfft
+//
+  namespace Eigen {
+#   include "src/FFT/ei_kissfft_impl.h"
+     template <typename T> 
+       struct default_fft_impl : public ei_kissfft_impl<T> {};
+  }
+#endif
+
+namespace Eigen {
+
+template <typename _Scalar,
+         typename _Impl=default_fft_impl<_Scalar> >
+class FFT
+{
+  public:
+    typedef _Impl impl_type;
+    typedef typename impl_type::Scalar Scalar;
+    typedef typename impl_type::Complex Complex;
+
+    FFT(const impl_type & impl=impl_type() ) :m_impl(impl) { }
+
+    template <typename _Input>
+    void fwd( Complex * dst, const _Input * src, int nfft)
+    {
+        m_impl.fwd(dst,src,nfft);
+    }
+
+    template <typename _Input>
+    void fwd( std::vector<Complex> & dst, const std::vector<_Input> & src) 
+    {
+        dst.resize( src.size() );
+        fwd( &dst[0],&src[0],src.size() );
+    }
+
+    template<typename InputDerived, typename ComplexDerived>
+    void fwd( MatrixBase<ComplexDerived> & dst, const MatrixBase<InputDerived> & src)
+    {
+        EIGEN_STATIC_ASSERT_VECTOR_ONLY(InputDerived)
+        EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
+        EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,InputDerived) // size at compile-time
+        EIGEN_STATIC_ASSERT((ei_is_same_type<typename ComplexDerived::Scalar, Complex>::ret),
+                            YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+        EIGEN_STATIC_ASSERT(int(InputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
+                            THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
+        dst.derived().resize( src.size() );
+        fwd( &dst[0],&src[0],src.size() );
+    }
+
+    template <typename _Output>
+    void inv( _Output * dst, const Complex * src, int nfft)
+    {
+        m_impl.inv( dst,src,nfft );
+    }
+
+    template <typename _Output>
+    void inv( std::vector<_Output> & dst, const std::vector<Complex> & src) 
+    {
+        dst.resize( src.size() );
+        inv( &dst[0],&src[0],src.size() );
+    }
+
+    template<typename OutputDerived, typename ComplexDerived>
+    void inv( MatrixBase<OutputDerived> & dst, const MatrixBase<ComplexDerived> & src)
+    {
+        EIGEN_STATIC_ASSERT_VECTOR_ONLY(OutputDerived)
+        EIGEN_STATIC_ASSERT_VECTOR_ONLY(ComplexDerived)
+        EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(ComplexDerived,OutputDerived) // size at compile-time
+        EIGEN_STATIC_ASSERT((ei_is_same_type<typename ComplexDerived::Scalar, Complex>::ret),
+                            YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
+        EIGEN_STATIC_ASSERT(int(OutputDerived::Flags)&int(ComplexDerived::Flags)&DirectAccessBit,
+                            THIS_METHOD_IS_ONLY_FOR_EXPRESSIONS_WITH_DIRECT_MEMORY_ACCESS_SUCH_AS_MAP_OR_PLAIN_MATRICES)
+        dst.derived().resize( src.size() );
+        inv( &dst[0],&src[0],src.size() );
+    }
+
+    // TODO: multi-dimensional FFTs
+    
+    // TODO: handle Eigen MatrixBase
+     // ---> i added fwd and inv specializations above + unit test, is this enough? (bjacob)
+
+    impl_type & impl() {return m_impl;}
+  private:
+    impl_type m_impl;
+};
+}
+#endif
+/* vim: set filetype=cpp et sw=2 ts=2 ai: */
diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h b/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h
index a5e881487..b3983f8a6 100644
--- a/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h
@@ -50,10 +50,12 @@ public:
   typedef typename Functor::InputType InputType;
   typedef typename Functor::ValueType ValueType;
   typedef typename Functor::JacobianType JacobianType;
+  typedef typename JacobianType::Scalar Scalar;
 
-  typedef Matrix<double,InputsAtCompileTime,1> DerivativeType;
+  typedef Matrix<Scalar,InputsAtCompileTime,1> DerivativeType;
   typedef AutoDiffScalar<DerivativeType> ActiveScalar;
 
+
   typedef Matrix<ActiveScalar, InputsAtCompileTime, 1> ActiveInput;
   typedef Matrix<ActiveScalar, ValuesAtCompileTime, 1> ActiveValue;
 
diff --git a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
index 888aa5c8c..2fb733a99 100644
--- a/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
+++ b/unsupported/Eigen/src/AutoDiff/AutoDiffScalar.h
@@ -42,9 +42,17 @@ void ei_make_coherent(const A& a, const B&b)
 /** \class AutoDiffScalar
   * \brief A scalar type replacement with automatic differentation capability
   *
-  * \param DerType the vector type used to store/represent the derivatives (e.g. Vector3f)
+  * \param _DerType the vector type used to store/represent the derivatives. The base scalar type
+  *                 as well as the number of derivatives to compute are determined from this type.
+  *                 Typical choices include, e.g., \c Vector4f for 4 derivatives, or \c VectorXf
+  *                 if the number of derivatives is not known at compile time, and/or, the number
+  *                 of derivatives is large.
+  *                 Note that _DerType can also be a reference (e.g., \c VectorXf&) to wrap a
+  *                 existing vector into an AutoDiffScalar.
+  *                 Finally, _DerType can also be any Eigen compatible expression.
   *
-  * This class represents a scalar value while tracking its respective derivatives.
+  * This class represents a scalar value while tracking its respective derivatives using Eigen's expression
+  * template mechanism.
   *
   * It supports the following list of global math function:
   *  - std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
@@ -56,10 +64,11 @@ void ei_make_coherent(const A& a, const B&b)
   * while derivatives are computed right away.
   *
   */
-template<typename DerType>
+template<typename _DerType>
 class AutoDiffScalar
 {
   public:
+    typedef typename ei_cleantype<_DerType>::type DerType;
     typedef typename ei_traits<DerType>::Scalar Scalar;
 
     inline AutoDiffScalar() {}
@@ -108,12 +117,28 @@ class AutoDiffScalar
     inline const DerType& derivatives() const { return m_derivatives; }
     inline DerType& derivatives() { return m_derivatives; }
 
+    inline const AutoDiffScalar<DerType&> operator+(const Scalar& other) const
+    {
+      return AutoDiffScalar<DerType>(m_value + other, m_derivatives);
+    }
+
+    friend inline const AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b)
+    {
+      return AutoDiffScalar<DerType>(a + b.value(), b.derivatives());
+    }
+
+    inline AutoDiffScalar& operator+=(const Scalar& other)
+    {
+      value() += other;
+      return *this;
+    }
+
     template<typename OtherDerType>
-    inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >
+    inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,typename ei_cleantype<OtherDerType>::type>::Type >
     operator+(const AutoDiffScalar<OtherDerType>& other) const
     {
       ei_make_coherent(m_derivatives, other.derivatives());
-      return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,OtherDerType> >(
+      return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,DerType,typename ei_cleantype<OtherDerType>::type>::Type >(
         m_value + other.value(),
         m_derivatives + other.derivatives());
     }
@@ -127,11 +152,11 @@ class AutoDiffScalar
     }
 
     template<typename OtherDerType>
-    inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >
+    inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,typename ei_cleantype<OtherDerType>::type>::Type >
     operator-(const AutoDiffScalar<OtherDerType>& other) const
     {
       ei_make_coherent(m_derivatives, other.derivatives());
-      return AutoDiffScalar<CwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,OtherDerType> >(
+      return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>, DerType,typename ei_cleantype<OtherDerType>::type>::Type >(
         m_value - other.value(),
         m_derivatives - other.derivatives());
     }
@@ -145,73 +170,73 @@ class AutoDiffScalar
     }
 
     template<typename OtherDerType>
-    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >
+    inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType>::Type >
     operator-() const
     {
-      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType> >(
+      return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_opposite_op<Scalar>, DerType>::Type >(
         -m_value,
         -m_derivatives);
     }
 
-    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
+    inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
     operator*(const Scalar& other) const
     {
-      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+      return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
         m_value * other,
         (m_derivatives * other));
     }
 
-    friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
+    friend inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
     operator*(const Scalar& other, const AutoDiffScalar& a)
     {
-      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+      return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
         a.value() * other,
         a.derivatives() * other);
     }
 
-    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
+    inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
     operator/(const Scalar& other) const
     {
-      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+      return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
         m_value / other,
         (m_derivatives * (Scalar(1)/other)));
     }
 
-    friend inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >
+    friend inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >
     operator/(const Scalar& other, const AutoDiffScalar& a)
     {
-      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+      return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
         other / a.value(),
         a.derivatives() * (-Scalar(1)/other));
     }
 
     template<typename OtherDerType>
-    inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
-        NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
-          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
-          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >
+    inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
+        typename MakeNestByValue<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,
+          typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
+          typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >::Type >::Type >
     operator/(const AutoDiffScalar<OtherDerType>& other) const
     {
       ei_make_coherent(m_derivatives, other.derivatives());
-      return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
-        NestByValue<CwiseBinaryOp<ei_scalar_difference_op<Scalar>,
-          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
-          NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > > > >(
+      return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>,
+        typename MakeNestByValue<typename MakeCwiseBinaryOp<ei_scalar_difference_op<Scalar>,
+          typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
+          typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >::Type >::Type >(
         m_value / other.value(),
           ((m_derivatives * other.value()).nestByValue() - (m_value * other.derivatives()).nestByValue()).nestByValue()
         * (Scalar(1)/(other.value()*other.value())));
     }
 
     template<typename OtherDerType>
-    inline const AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
-        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
-        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >
+    inline const AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,
+        typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
+        typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >
     operator*(const AutoDiffScalar<OtherDerType>& other) const
     {
       ei_make_coherent(m_derivatives, other.derivatives());
-      return AutoDiffScalar<CwiseBinaryOp<ei_scalar_sum_op<Scalar>,
-        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >,
-        NestByValue<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, OtherDerType> > > >(
+      return AutoDiffScalar<typename MakeCwiseBinaryOp<ei_scalar_sum_op<Scalar>,
+        typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type>::Type,
+        typename MakeNestByValue<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, typename ei_cleantype<OtherDerType>::type>::Type>::Type >::Type >(
         m_value * other.value(),
         (m_derivatives * other.value()).nestByValue() + (m_value * other.derivatives()).nestByValue());
     }
@@ -283,11 +308,11 @@ struct ei_make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRo
 
 #define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
   template<typename DerType> \
-  inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType> > \
+  inline const Eigen::AutoDiffScalar<typename Eigen::MakeCwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType>::Type > \
   FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
     using namespace Eigen; \
     typedef typename ei_traits<DerType>::Scalar Scalar; \
-    typedef AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> > ReturnType; \
+    typedef AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type > ReturnType; \
     CODE; \
   }
 
@@ -314,12 +339,12 @@ namespace std
     return ReturnType(std::log(x.value),x.derivatives() * (Scalar(1).x.value()));)
 
   template<typename DerType>
-  inline const Eigen::AutoDiffScalar<Eigen::CwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType> >
+  inline const Eigen::AutoDiffScalar<typename Eigen::MakeCwiseUnaryOp<Eigen::ei_scalar_multiple_op<typename Eigen::ei_traits<DerType>::Scalar>, DerType>::Type >
   pow(const Eigen::AutoDiffScalar<DerType>& x, typename Eigen::ei_traits<DerType>::Scalar y)
   {
     using namespace Eigen;
     typedef typename ei_traits<DerType>::Scalar Scalar;
-    return AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType> >(
+    return AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<Scalar>, DerType>::Type >(
       std::pow(x.value(),y),
       x.derivatives() * (y * std::pow(x.value(),y-1)));
   }
@@ -359,7 +384,7 @@ EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(ei_log,
   return ReturnType(ei_log(x.value),x.derivatives() * (Scalar(1).x.value()));)
 
 template<typename DerType>
-inline const AutoDiffScalar<CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType> >
+inline const AutoDiffScalar<typename MakeCwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<DerType>::Scalar>, DerType>::Type >
 ei_pow(const AutoDiffScalar<DerType>& x, typename ei_traits<DerType>::Scalar y)
 { return std::pow(x,y);}
 
diff --git a/unsupported/Eigen/src/FFT/ei_fftw_impl.h b/unsupported/Eigen/src/FFT/ei_fftw_impl.h
new file mode 100644
index 000000000..e1f67f334
--- /dev/null
+++ b/unsupported/Eigen/src/FFT/ei_fftw_impl.h
@@ -0,0 +1,224 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. 
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// 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/>.
+
+
+
+  // FFTW uses non-const arguments
+  // so we must use ugly const_cast calls for all the args it uses
+  //
+  // This should be safe as long as 
+  // 1. we use FFTW_ESTIMATE for all our planning
+  //       see the FFTW docs section 4.3.2 "Planner Flags"
+  // 2. fftw_complex is compatible with std::complex
+  //    This assumes std::complex<T> layout is array of size 2 with real,imag
+  template <typename T> 
+  inline 
+  T * ei_fftw_cast(const T* p) 
+  { 
+      return const_cast<T*>( p); 
+  }
+
+  inline 
+  fftw_complex * ei_fftw_cast( const std::complex<double> * p) 
+  {
+      return const_cast<fftw_complex*>( reinterpret_cast<const fftw_complex*>(p) ); 
+  }
+
+  inline 
+  fftwf_complex * ei_fftw_cast( const std::complex<float> * p) 
+  { 
+      return const_cast<fftwf_complex*>( reinterpret_cast<const fftwf_complex*>(p) ); 
+  }
+
+  inline 
+  fftwl_complex * ei_fftw_cast( const std::complex<long double> * p) 
+  { 
+      return const_cast<fftwl_complex*>( reinterpret_cast<const fftwl_complex*>(p) ); 
+  }
+
+  template <typename T> 
+  struct ei_fftw_plan {};
+
+  template <> 
+  struct ei_fftw_plan<float>
+  {
+      typedef float scalar_type;
+      typedef fftwf_complex complex_type;
+      fftwf_plan m_plan;
+      ei_fftw_plan() :m_plan(NULL) {}
+      ~ei_fftw_plan() {if (m_plan) fftwf_destroy_plan(m_plan);}
+
+      inline
+      void fwd(complex_type * dst,complex_type * src,int nfft) {
+          if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE);
+          fftwf_execute_dft( m_plan, src,dst);
+      }
+      inline
+      void inv(complex_type * dst,complex_type * src,int nfft) {
+          if (m_plan==NULL) m_plan = fftwf_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE);
+          fftwf_execute_dft( m_plan, src,dst);
+      }
+      inline
+      void fwd(complex_type * dst,scalar_type * src,int nfft) {
+          if (m_plan==NULL) m_plan = fftwf_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE);
+          fftwf_execute_dft_r2c( m_plan,src,dst);
+      }
+      inline
+      void inv(scalar_type * dst,complex_type * src,int nfft) {
+          if (m_plan==NULL)
+              m_plan = fftwf_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE);
+          fftwf_execute_dft_c2r( m_plan, src,dst);
+      }
+  };
+  template <> 
+  struct ei_fftw_plan<double>
+  {
+      typedef double scalar_type;
+      typedef fftw_complex complex_type;
+      fftw_plan m_plan;
+      ei_fftw_plan() :m_plan(NULL) {}
+      ~ei_fftw_plan() {if (m_plan) fftw_destroy_plan(m_plan);}
+
+      inline
+      void fwd(complex_type * dst,complex_type * src,int nfft) {
+          if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE);
+          fftw_execute_dft( m_plan, src,dst);
+      }
+      inline
+      void inv(complex_type * dst,complex_type * src,int nfft) {
+          if (m_plan==NULL) m_plan = fftw_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE);
+          fftw_execute_dft( m_plan, src,dst);
+      }
+      inline
+      void fwd(complex_type * dst,scalar_type * src,int nfft) {
+          if (m_plan==NULL) m_plan = fftw_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE);
+          fftw_execute_dft_r2c( m_plan,src,dst);
+      }
+      inline
+      void inv(scalar_type * dst,complex_type * src,int nfft) {
+          if (m_plan==NULL)
+              m_plan = fftw_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE);
+          fftw_execute_dft_c2r( m_plan, src,dst);
+      }
+  };
+  template <> 
+  struct ei_fftw_plan<long double>
+  {
+      typedef long double scalar_type;
+      typedef fftwl_complex complex_type;
+      fftwl_plan m_plan;
+      ei_fftw_plan() :m_plan(NULL) {}
+      ~ei_fftw_plan() {if (m_plan) fftwl_destroy_plan(m_plan);}
+
+      inline
+      void fwd(complex_type * dst,complex_type * src,int nfft) {
+          if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_FORWARD, FFTW_ESTIMATE);
+          fftwl_execute_dft( m_plan, src,dst);
+      }
+      inline
+      void inv(complex_type * dst,complex_type * src,int nfft) {
+          if (m_plan==NULL) m_plan = fftwl_plan_dft_1d(nfft,src,dst, FFTW_BACKWARD , FFTW_ESTIMATE);
+          fftwl_execute_dft( m_plan, src,dst);
+      }
+      inline
+      void fwd(complex_type * dst,scalar_type * src,int nfft) {
+          if (m_plan==NULL) m_plan = fftwl_plan_dft_r2c_1d(nfft,src,dst,FFTW_ESTIMATE);
+          fftwl_execute_dft_r2c( m_plan,src,dst);
+      }
+      inline
+      void inv(scalar_type * dst,complex_type * src,int nfft) {
+          if (m_plan==NULL)
+              m_plan = fftwl_plan_dft_c2r_1d(nfft,src,dst,FFTW_ESTIMATE);
+          fftwl_execute_dft_c2r( m_plan, src,dst);
+      }
+  };
+
+  template <typename _Scalar>
+  struct ei_fftw_impl
+  {
+      typedef _Scalar Scalar;
+      typedef std::complex<Scalar> Complex;
+
+      inline
+      void clear() 
+      {
+        m_plans.clear();
+      }
+
+      inline
+      void fwd( Complex * dst,const Complex *src,int nfft)
+      {
+        get_plan(nfft,false,dst,src).fwd(ei_fftw_cast(dst), ei_fftw_cast(src),nfft );
+      }
+
+      // real-to-complex forward FFT
+      inline
+      void fwd( Complex * dst,const Scalar * src,int nfft) 
+      {
+          get_plan(nfft,false,dst,src).fwd(ei_fftw_cast(dst), ei_fftw_cast(src) ,nfft);
+          int nhbins=(nfft>>1)+1;
+          for (int k=nhbins;k < nfft; ++k )
+              dst[k] = conj(dst[nfft-k]);
+      }
+
+      // inverse complex-to-complex
+      inline
+      void inv(Complex * dst,const Complex  *src,int nfft)
+      {
+        get_plan(nfft,true,dst,src).inv(ei_fftw_cast(dst), ei_fftw_cast(src),nfft );
+
+        //TODO move scaling to Eigen::FFT
+        // scaling
+        Scalar s = Scalar(1.)/nfft;
+        for (int k=0;k<nfft;++k)
+          dst[k] *= s;
+      }
+
+      // half-complex to scalar
+      inline
+      void inv( Scalar * dst,const Complex * src,int nfft) 
+      {
+        get_plan(nfft,true,dst,src).inv(ei_fftw_cast(dst), ei_fftw_cast(src),nfft );
+
+        //TODO move scaling to Eigen::FFT
+        Scalar s = Scalar(1.)/nfft;
+        for (int k=0;k<nfft;++k)
+          dst[k] *= s;
+      }
+
+  protected:
+      typedef ei_fftw_plan<Scalar> PlanData;
+      typedef std::map<int,PlanData> PlanMap;
+
+      PlanMap m_plans;
+
+      inline
+      PlanData & get_plan(int nfft,bool inverse,void * dst,const void * src)
+      {
+          bool inplace = (dst==src);
+          bool aligned = ( (reinterpret_cast<size_t>(src)&15) | (reinterpret_cast<size_t>(dst)&15) ) == 0;
+          int key = (nfft<<3 ) | (inverse<<2) | (inplace<<1) | aligned;
+          return m_plans[key];
+      }
+  };
diff --git a/unsupported/Eigen/src/FFT/ei_kissfft_impl.h b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
new file mode 100644
index 000000000..c068d8765
--- /dev/null
+++ b/unsupported/Eigen/src/FFT/ei_kissfft_impl.h
@@ -0,0 +1,414 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// 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/>.
+
+
+
+  // This FFT implementation was derived from kissfft http:sourceforge.net/projects/kissfft
+  // Copyright 2003-2009 Mark Borgerding
+
+  template <typename _Scalar>
+    struct ei_kiss_cpx_fft
+    {
+      typedef _Scalar Scalar;
+      typedef std::complex<Scalar> Complex;
+      std::vector<Complex> m_twiddles;
+      std::vector<int> m_stageRadix;
+      std::vector<int> m_stageRemainder;
+      std::vector<Complex> m_scratchBuf;
+      bool m_inverse;
+
+      void make_twiddles(int nfft,bool inverse)
+      {
+        m_inverse = inverse;
+        m_twiddles.resize(nfft);
+        Scalar phinc =  (inverse?2:-2)* acos( (Scalar) -1)  / nfft;
+        for (int i=0;i<nfft;++i)
+          m_twiddles[i] = exp( Complex(0,i*phinc) );
+      }
+
+      void factorize(int nfft)
+      {
+        //start factoring out 4's, then 2's, then 3,5,7,9,...
+        int n= nfft;
+        int p=4;
+        do {
+          while (n % p) {
+            switch (p) {
+              case 4: p = 2; break;
+              case 2: p = 3; break;
+              default: p += 2; break;
+            }
+            if (p*p>n)
+              p=n;// impossible to have a factor > sqrt(n)
+          }
+          n /= p;
+          m_stageRadix.push_back(p);
+          m_stageRemainder.push_back(n);
+          if ( p > 5 )
+              m_scratchBuf.resize(p); // scratchbuf will be needed in bfly_generic
+        }while(n>1);
+      }
+
+      template <typename _Src>
+        void work( int stage,Complex * xout, const _Src * xin, size_t fstride,size_t in_stride)
+        {
+          int p = m_stageRadix[stage];
+          int m = m_stageRemainder[stage];
+          Complex * Fout_beg = xout;
+          Complex * Fout_end = xout + p*m;
+
+          if (m>1) {
+            do{
+              // recursive call:
+              // DFT of size m*p performed by doing
+              // p instances of smaller DFTs of size m, 
+              // each one takes a decimated version of the input
+              work(stage+1, xout , xin, fstride*p,in_stride);
+              xin += fstride*in_stride;
+            }while( (xout += m) != Fout_end );
+          }else{
+            do{
+              *xout = *xin;
+              xin += fstride*in_stride;
+            }while(++xout != Fout_end );
+          }
+          xout=Fout_beg;
+
+          // recombine the p smaller DFTs 
+          switch (p) {
+            case 2: bfly2(xout,fstride,m); break;
+            case 3: bfly3(xout,fstride,m); break;
+            case 4: bfly4(xout,fstride,m); break;
+            case 5: bfly5(xout,fstride,m); break;
+            default: bfly_generic(xout,fstride,m,p); break;
+          }
+        }
+
+      inline
+      void bfly2( Complex * Fout, const size_t fstride, int m)
+      {
+        for (int k=0;k<m;++k) {
+          Complex t = Fout[m+k] * m_twiddles[k*fstride];
+          Fout[m+k] = Fout[k] - t;
+          Fout[k] += t;
+        }
+      }
+
+      inline
+      void bfly4( Complex * Fout, const size_t fstride, const size_t m)
+      {
+        Complex scratch[6];
+        int negative_if_inverse = m_inverse * -2 +1;
+        for (size_t k=0;k<m;++k) {
+          scratch[0] = Fout[k+m] * m_twiddles[k*fstride];
+          scratch[1] = Fout[k+2*m] * m_twiddles[k*fstride*2];
+          scratch[2] = Fout[k+3*m] * m_twiddles[k*fstride*3];
+          scratch[5] = Fout[k] - scratch[1];
+
+          Fout[k] += scratch[1];
+          scratch[3] = scratch[0] + scratch[2];
+          scratch[4] = scratch[0] - scratch[2];
+          scratch[4] = Complex( scratch[4].imag()*negative_if_inverse , -scratch[4].real()* negative_if_inverse );
+
+          Fout[k+2*m]  = Fout[k] - scratch[3];
+          Fout[k] += scratch[3];
+          Fout[k+m] = scratch[5] + scratch[4];
+          Fout[k+3*m] = scratch[5] - scratch[4];
+        }
+      }
+
+      inline
+      void bfly3( Complex * Fout, const size_t fstride, const size_t m)
+      {
+        size_t k=m;
+        const size_t m2 = 2*m;
+        Complex *tw1,*tw2;
+        Complex scratch[5];
+        Complex epi3;
+        epi3 = m_twiddles[fstride*m];
+
+        tw1=tw2=&m_twiddles[0];
+
+        do{
+          scratch[1]=Fout[m] * *tw1;
+          scratch[2]=Fout[m2] * *tw2;
+
+          scratch[3]=scratch[1]+scratch[2];
+          scratch[0]=scratch[1]-scratch[2];
+          tw1 += fstride;
+          tw2 += fstride*2;
+          Fout[m] = Complex( Fout->real() - .5*scratch[3].real() , Fout->imag() - .5*scratch[3].imag() );
+          scratch[0] *= epi3.imag();
+          *Fout += scratch[3];
+          Fout[m2] = Complex(  Fout[m].real() + scratch[0].imag() , Fout[m].imag() - scratch[0].real() );
+          Fout[m] += Complex( -scratch[0].imag(),scratch[0].real() );
+          ++Fout;
+        }while(--k);
+      }
+
+      inline
+      void bfly5( Complex * Fout, const size_t fstride, const size_t m)
+      {
+        Complex *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
+        size_t u;
+        Complex scratch[13];
+        Complex * twiddles = &m_twiddles[0];
+        Complex *tw;
+        Complex ya,yb;
+        ya = twiddles[fstride*m];
+        yb = twiddles[fstride*2*m];
+
+        Fout0=Fout;
+        Fout1=Fout0+m;
+        Fout2=Fout0+2*m;
+        Fout3=Fout0+3*m;
+        Fout4=Fout0+4*m;
+
+        tw=twiddles;
+        for ( u=0; u<m; ++u ) {
+          scratch[0] = *Fout0;
+
+          scratch[1]  = *Fout1 * tw[u*fstride];
+          scratch[2]  = *Fout2 * tw[2*u*fstride];
+          scratch[3]  = *Fout3 * tw[3*u*fstride];
+          scratch[4]  = *Fout4 * tw[4*u*fstride];
+
+          scratch[7] = scratch[1] + scratch[4];
+          scratch[10] = scratch[1] - scratch[4];
+          scratch[8] = scratch[2] + scratch[3];
+          scratch[9] = scratch[2] - scratch[3];
+
+          *Fout0 +=  scratch[7];
+          *Fout0 +=  scratch[8];
+
+          scratch[5] = scratch[0] + Complex(
+              (scratch[7].real()*ya.real() ) + (scratch[8].real() *yb.real() ),
+              (scratch[7].imag()*ya.real()) + (scratch[8].imag()*yb.real())
+              );
+
+          scratch[6] = Complex(
+              (scratch[10].imag()*ya.imag()) + (scratch[9].imag()*yb.imag()),
+              -(scratch[10].real()*ya.imag()) - (scratch[9].real()*yb.imag())
+              );
+
+          *Fout1 = scratch[5] - scratch[6];
+          *Fout4 = scratch[5] + scratch[6];
+
+          scratch[11] = scratch[0] +
+            Complex(
+                (scratch[7].real()*yb.real()) + (scratch[8].real()*ya.real()),
+                (scratch[7].imag()*yb.real()) + (scratch[8].imag()*ya.real())
+                );
+
+          scratch[12] = Complex(
+              -(scratch[10].imag()*yb.imag()) + (scratch[9].imag()*ya.imag()),
+              (scratch[10].real()*yb.imag()) - (scratch[9].real()*ya.imag())
+              );
+
+          *Fout2=scratch[11]+scratch[12];
+          *Fout3=scratch[11]-scratch[12];
+
+          ++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
+        }
+      }
+
+      /* perform the butterfly for one stage of a mixed radix FFT */
+      inline
+      void bfly_generic(
+          Complex * Fout,
+          const size_t fstride,
+          int m,
+          int p
+          )
+      {
+        int u,k,q1,q;
+        Complex * twiddles = &m_twiddles[0];
+        Complex t;
+        int Norig = m_twiddles.size();
+        Complex * scratchbuf = &m_scratchBuf[0];
+
+        for ( u=0; u<m; ++u ) {
+          k=u;
+          for ( q1=0 ; q1<p ; ++q1 ) {
+            scratchbuf[q1] = Fout[ k  ];
+            k += m;
+          }
+
+          k=u;
+          for ( q1=0 ; q1<p ; ++q1 ) {
+            int twidx=0;
+            Fout[ k ] = scratchbuf[0];
+            for (q=1;q<p;++q ) {
+              twidx += fstride * k;
+              if (twidx>=Norig) twidx-=Norig;
+              t=scratchbuf[q] * twiddles[twidx];
+              Fout[ k ] += t;
+            }
+            k += m;
+          }
+        }
+      }
+    };
+
+  template <typename _Scalar>
+    struct ei_kissfft_impl
+    {
+      typedef _Scalar Scalar;
+      typedef std::complex<Scalar> Complex;
+
+      void clear() 
+      {
+        m_plans.clear();
+        m_realTwiddles.clear();
+      }
+
+      template <typename _Src>
+      inline
+        void fwd( Complex * dst,const _Src *src,int nfft)
+        {
+          get_plan(nfft,false).work(0, dst, src, 1,1);
+        }
+
+      // real-to-complex forward FFT
+      // perform two FFTs of src even and src odd
+      // then twiddle to recombine them into the half-spectrum format
+      // then fill in the conjugate symmetric half
+      inline
+      void fwd( Complex * dst,const Scalar * src,int nfft) 
+      {
+        if ( nfft&3  ) {
+          // use generic mode for odd
+          get_plan(nfft,false).work(0, dst, src, 1,1);
+        }else{
+          int ncfft = nfft>>1;
+          int ncfft2 = nfft>>2;
+          Complex * rtw = real_twiddles(ncfft2);
+
+          // use optimized mode for even real
+          fwd( dst, reinterpret_cast<const Complex*> (src), ncfft);
+          Complex dc = dst[0].real() +  dst[0].imag();
+          Complex nyquist = dst[0].real() -  dst[0].imag();
+          int k;
+          for ( k=1;k <= ncfft2 ; ++k ) {
+            Complex fpk = dst[k];
+            Complex fpnk = conj(dst[ncfft-k]);
+            Complex f1k = fpk + fpnk;
+            Complex f2k = fpk - fpnk;
+            Complex tw= f2k * rtw[k-1];
+            dst[k] =  (f1k + tw) * Scalar(.5);
+            dst[ncfft-k] =  conj(f1k -tw)*Scalar(.5);
+          }
+
+          // place conjugate-symmetric half at the end for completeness
+          // TODO: make this configurable ( opt-out )
+          for ( k=1;k < ncfft ; ++k )
+            dst[nfft-k] = conj(dst[k]);
+          dst[0] = dc;
+          dst[ncfft] = nyquist;
+        }
+      }
+
+      // inverse complex-to-complex
+      inline
+      void inv(Complex * dst,const Complex  *src,int nfft)
+      {
+        get_plan(nfft,true).work(0, dst, src, 1,1);
+        scale(dst, nfft, Scalar(1)/nfft );
+      }
+
+      // half-complex to scalar
+      inline
+      void inv( Scalar * dst,const Complex * src,int nfft) 
+      {
+        if (nfft&3) {
+          m_tmpBuf.resize(nfft);
+          inv(&m_tmpBuf[0],src,nfft);
+          for (int k=0;k<nfft;++k)
+            dst[k] = m_tmpBuf[k].real();
+        }else{
+          // optimized version for multiple of 4
+          int ncfft = nfft>>1;
+          int ncfft2 = nfft>>2;
+          Complex * rtw = real_twiddles(ncfft2);
+          m_tmpBuf.resize(ncfft);
+          m_tmpBuf[0] = Complex( src[0].real() + src[ncfft].real(), src[0].real() - src[ncfft].real() );
+          for (int k = 1; k <= ncfft / 2; ++k) {
+            Complex fk = src[k];
+            Complex fnkc = conj(src[ncfft-k]);
+            Complex fek = fk + fnkc;
+            Complex tmp = fk - fnkc;
+            Complex fok = tmp * conj(rtw[k-1]);
+            m_tmpBuf[k] = fek + fok;
+            m_tmpBuf[ncfft-k] = conj(fek - fok);
+          }
+          scale(&m_tmpBuf[0], ncfft, Scalar(1)/nfft );
+          get_plan(ncfft,true).work(0, reinterpret_cast<Complex*>(dst), &m_tmpBuf[0], 1,1);
+        }
+      }
+
+      protected:
+      typedef ei_kiss_cpx_fft<Scalar> PlanData;
+      typedef std::map<int,PlanData> PlanMap;
+
+      PlanMap m_plans;
+      std::map<int, std::vector<Complex> > m_realTwiddles;
+      std::vector<Complex> m_tmpBuf;
+
+      inline
+      int PlanKey(int nfft,bool isinverse) const { return (nfft<<1) | isinverse; }
+
+      inline
+      PlanData & get_plan(int nfft,bool inverse)
+      {
+        // TODO look for PlanKey(nfft, ! inverse) and conjugate the twiddles
+        PlanData & pd = m_plans[ PlanKey(nfft,inverse) ];
+        if ( pd.m_twiddles.size() == 0 ) {
+          pd.make_twiddles(nfft,inverse);
+          pd.factorize(nfft);
+        }
+        return pd;
+      }
+
+      inline
+      Complex * real_twiddles(int ncfft2)
+      {
+        std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
+        if ( (int)twidref.size() != ncfft2 ) {
+          twidref.resize(ncfft2);
+          int ncfft= ncfft2<<1;
+          Scalar pi =  acos( Scalar(-1) );
+          for (int k=1;k<=ncfft2;++k) 
+            twidref[k-1] = exp( Complex(0,-pi * ((double) (k) / ncfft + .5) ) );
+        }
+        return &twidref[0];
+      }
+
+      // TODO move scaling up into Eigen::FFT
+      inline
+      void scale(Complex *dst,int n,Scalar s) 
+      {
+        for (int k=0;k<n;++k)
+          dst[k] *= s;
+      }
+    };
diff --git a/unsupported/doc/examples/FFT.cpp b/unsupported/doc/examples/FFT.cpp
new file mode 100644
index 000000000..55e29585a
--- /dev/null
+++ b/unsupported/doc/examples/FFT.cpp
@@ -0,0 +1,117 @@
+//  To use the simple FFT implementation
+//  g++ -o demofft -I.. -Wall -O3 FFT.cpp 
+
+//  To use the FFTW implementation
+//  g++ -o demofft -I.. -DUSE_FFTW -Wall -O3 FFT.cpp -lfftw3 -lfftw3f -lfftw3l
+
+#ifdef USE_FFTW
+#include <fftw3.h>
+#endif
+
+#include <vector>
+#include <complex>
+#include <algorithm>
+#include <iterator>
+#include <Eigen/Core>
+#include <unsupported/Eigen/FFT>
+
+using namespace std;
+using namespace Eigen;
+
+template <typename T>
+T mag2(T a)
+{
+    return a*a;
+}
+template <typename T>
+T mag2(std::complex<T> a)
+{
+    return norm(a);
+}
+
+template <typename T>
+T mag2(const std::vector<T> & vec)
+{
+    T out=0;
+    for (size_t k=0;k<vec.size();++k)
+        out += mag2(vec[k]);
+    return out;
+}
+
+template <typename T>
+T mag2(const std::vector<std::complex<T> > & vec)
+{
+    T out=0;
+    for (size_t k=0;k<vec.size();++k)
+        out += mag2(vec[k]);
+    return out;
+}
+
+template <typename T>
+vector<T> operator-(const vector<T> & a,const vector<T> & b )
+{
+    vector<T> c(a);
+    for (size_t k=0;k<b.size();++k) 
+        c[k] -= b[k];
+    return c;
+}
+
+template <typename T>
+void RandomFill(std::vector<T> & vec)
+{
+    for (size_t k=0;k<vec.size();++k)
+        vec[k] = T( rand() )/T(RAND_MAX) - .5;
+}
+
+template <typename T>
+void RandomFill(std::vector<std::complex<T> > & vec)
+{
+    for (size_t k=0;k<vec.size();++k)
+        vec[k] = std::complex<T> ( T( rand() )/T(RAND_MAX) - .5, T( rand() )/T(RAND_MAX) - .5);
+}
+
+template <typename T_time,typename T_freq>
+void fwd_inv(size_t nfft)
+{
+    typedef typename NumTraits<T_freq>::Real Scalar;
+    vector<T_time> timebuf(nfft);
+    RandomFill(timebuf);
+
+    vector<T_freq> freqbuf;
+    static FFT<Scalar> fft;
+    fft.fwd(freqbuf,timebuf);
+
+    vector<T_time> timebuf2;
+    fft.inv(timebuf2,freqbuf);
+
+    long double rmse = mag2(timebuf - timebuf2) / mag2(timebuf);
+    cout << "roundtrip rmse: " << rmse << endl;
+}
+
+template <typename T_scalar>
+void two_demos(int nfft)
+{
+    cout << "     scalar ";
+    fwd_inv<T_scalar,std::complex<T_scalar> >(nfft);
+    cout << "    complex ";
+    fwd_inv<std::complex<T_scalar>,std::complex<T_scalar> >(nfft);
+}
+
+void demo_all_types(int nfft)
+{
+    cout << "nfft=" << nfft << endl;
+    cout << "   float" << endl;
+    two_demos<float>(nfft);
+    cout << "   double" << endl;
+    two_demos<double>(nfft);
+    cout << "   long double" << endl;
+    two_demos<long double>(nfft);
+}
+
+int main()
+{
+    demo_all_types( 2*3*4*5*7 );
+    demo_all_types( 2*9*16*25 );
+    demo_all_types( 1024 );
+    return 0;
+}
diff --git a/unsupported/test/CMakeLists.txt b/unsupported/test/CMakeLists.txt
index abfbb0185..d182c9abf 100644
--- a/unsupported/test/CMakeLists.txt
+++ b/unsupported/test/CMakeLists.txt
@@ -19,3 +19,10 @@ ei_add_test(autodiff)
 ei_add_test(BVH)
 ei_add_test(matrixExponential)
 ei_add_test(alignedvector3)
+ei_add_test(FFT)
+
+find_package(FFTW)
+if(FFTW_FOUND)
+  ei_add_test(FFTW  "-DEIGEN_FFTW_DEFAULT " "-lfftw3 -lfftw3f -lfftw3l" )
+endif(FFTW_FOUND)
+
diff --git a/unsupported/test/FFT.cpp b/unsupported/test/FFT.cpp
new file mode 100644
index 000000000..cc68f3718
--- /dev/null
+++ b/unsupported/test/FFT.cpp
@@ -0,0 +1,200 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// 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/>.
+
+#include "main.h"
+#include <unsupported/Eigen/FFT>
+
+using namespace std;
+
+float norm(float x) {return x*x;}
+double norm(double x) {return x*x;}
+long double norm(long double x) {return x*x;}
+
+template < typename T>
+complex<long double>  promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
+
+complex<long double>  promote(float x) { return complex<long double>( x); }
+complex<long double>  promote(double x) { return complex<long double>( x); }
+complex<long double>  promote(long double x) { return complex<long double>( x); }
+    
+
+    template <typename VectorType1,typename VectorType2>
+    long double fft_rmse( const VectorType1 & fftbuf,const VectorType2 & timebuf)
+    {
+        long double totalpower=0;
+        long double difpower=0;
+        cerr <<"idx\ttruth\t\tvalue\t|dif|=\n";
+        for (size_t k0=0;k0<size_t(fftbuf.size());++k0) {
+            complex<long double> acc = 0;
+            long double phinc = -2.*k0* M_PIl / timebuf.size();
+            for (size_t k1=0;k1<size_t(timebuf.size());++k1) {
+                acc +=  promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
+            }
+            totalpower += norm(acc);
+            complex<long double> x = promote(fftbuf[k0]); 
+            complex<long double> dif = acc - x;
+            difpower += norm(dif);
+            cerr << k0 << "\t" << acc << "\t" <<  x << "\t" << sqrt(norm(dif)) << endl;
+        }
+        cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
+        return sqrt(difpower/totalpower);
+    }
+
+    template <typename VectorType1,typename VectorType2>
+    long double dif_rmse( const VectorType1& buf1,const VectorType2& buf2)
+    {
+        long double totalpower=0;
+        long double difpower=0;
+        size_t n = min( buf1.size(),buf2.size() );
+        for (size_t k=0;k<n;++k) {
+            totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.;
+            difpower += norm(buf1[k] - buf2[k]);
+        }
+        return sqrt(difpower/totalpower);
+    }
+
+enum { StdVectorContainer, EigenVectorContainer };
+
+template<int Container, typename Scalar> struct VectorType;
+
+template<typename Scalar> struct VectorType<StdVectorContainer,Scalar>
+{
+  typedef vector<Scalar> type;
+};
+
+template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar>
+{
+  typedef Matrix<Scalar,Dynamic,1> type;
+};
+
+template <int Container, typename T>
+void test_scalar_generic(int nfft)
+{
+    typedef typename FFT<T>::Complex Complex;
+    typedef typename FFT<T>::Scalar Scalar;
+    typedef typename VectorType<Container,Scalar>::type ScalarVector;
+    typedef typename VectorType<Container,Complex>::type ComplexVector;
+
+    FFT<T> fft;
+    ScalarVector inbuf(nfft);
+    ComplexVector outbuf;
+    for (int k=0;k<nfft;++k)
+        inbuf[k]= (T)(rand()/(double)RAND_MAX - .5);
+    fft.fwd( outbuf,inbuf);
+    VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>()  );// gross check
+
+    ScalarVector buf3;
+    fft.inv( buf3 , outbuf);
+    VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>()  );// gross check
+}
+
+template <typename T>
+void test_scalar(int nfft)
+{
+  test_scalar_generic<StdVectorContainer,T>(nfft);
+  test_scalar_generic<EigenVectorContainer,T>(nfft);
+}
+
+template <int Container, typename T>
+void test_complex_generic(int nfft)
+{
+    typedef typename FFT<T>::Complex Complex;
+    typedef typename VectorType<Container,Complex>::type ComplexVector;
+
+    FFT<T> fft;
+
+    ComplexVector inbuf(nfft);
+    ComplexVector outbuf;
+    ComplexVector buf3;
+    for (int k=0;k<nfft;++k)
+        inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
+    fft.fwd( outbuf , inbuf);
+
+    VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>()  );// gross check
+
+    fft.inv( buf3 , outbuf);
+
+    VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>()  );// gross check
+}
+
+template <typename T>
+void test_complex(int nfft)
+{
+  test_complex_generic<StdVectorContainer,T>(nfft);
+  test_complex_generic<EigenVectorContainer,T>(nfft);
+}
+
+void test_FFT()
+{
+
+  CALL_SUBTEST( test_complex<float>(32) );
+  CALL_SUBTEST( test_complex<double>(32) );
+  CALL_SUBTEST( test_complex<long double>(32) );
+  
+  CALL_SUBTEST( test_complex<float>(256) );
+  CALL_SUBTEST( test_complex<double>(256) );
+  CALL_SUBTEST( test_complex<long double>(256) );
+  
+  CALL_SUBTEST( test_complex<float>(3*8) );
+  CALL_SUBTEST( test_complex<double>(3*8) );
+  CALL_SUBTEST( test_complex<long double>(3*8) );
+  
+  CALL_SUBTEST( test_complex<float>(5*32) );
+  CALL_SUBTEST( test_complex<double>(5*32) );
+  CALL_SUBTEST( test_complex<long double>(5*32) );
+  
+  CALL_SUBTEST( test_complex<float>(2*3*4) );
+  CALL_SUBTEST( test_complex<double>(2*3*4) );
+  CALL_SUBTEST( test_complex<long double>(2*3*4) );
+  
+  CALL_SUBTEST( test_complex<float>(2*3*4*5) );
+  CALL_SUBTEST( test_complex<double>(2*3*4*5) );
+  CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
+  
+  CALL_SUBTEST( test_complex<float>(2*3*4*5*7) );
+  CALL_SUBTEST( test_complex<double>(2*3*4*5*7) );
+  CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
+
+
+
+  CALL_SUBTEST( test_scalar<float>(32) );
+  CALL_SUBTEST( test_scalar<double>(32) );
+  CALL_SUBTEST( test_scalar<long double>(32) );
+  
+  CALL_SUBTEST( test_scalar<float>(45) );
+  CALL_SUBTEST( test_scalar<double>(45) );
+  CALL_SUBTEST( test_scalar<long double>(45) );
+  
+  CALL_SUBTEST( test_scalar<float>(50) );
+  CALL_SUBTEST( test_scalar<double>(50) );
+  CALL_SUBTEST( test_scalar<long double>(50) );
+  
+  CALL_SUBTEST( test_scalar<float>(256) );
+  CALL_SUBTEST( test_scalar<double>(256) );
+  CALL_SUBTEST( test_scalar<long double>(256) );
+  
+  CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) );
+  CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) );
+  CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
+}
diff --git a/unsupported/test/FFTW.cpp b/unsupported/test/FFTW.cpp
new file mode 100644
index 000000000..cf7be75aa
--- /dev/null
+++ b/unsupported/test/FFTW.cpp
@@ -0,0 +1,136 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2009 Mark Borgerding mark a borgerding net
+//
+// 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/>.
+
+#include "main.h"
+#include <fftw3.h>
+#include <unsupported/Eigen/FFT>
+
+using namespace std;
+
+float norm(float x) {return x*x;}
+double norm(double x) {return x*x;}
+long double norm(long double x) {return x*x;}
+
+template < typename T>
+complex<long double>  promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
+
+complex<long double>  promote(float x) { return complex<long double>( x); }
+complex<long double>  promote(double x) { return complex<long double>( x); }
+complex<long double>  promote(long double x) { return complex<long double>( x); }
+    
+
+    template <typename T1,typename T2>
+    long double fft_rmse( const vector<T1> & fftbuf,const vector<T2> & timebuf)
+    {
+        long double totalpower=0;
+        long double difpower=0;
+        cerr <<"idx\ttruth\t\tvalue\t|dif|=\n";
+        for (size_t k0=0;k0<fftbuf.size();++k0) {
+            complex<long double> acc = 0;
+            long double phinc = -2.*k0* M_PIl / timebuf.size();
+            for (size_t k1=0;k1<timebuf.size();++k1) {
+                acc +=  promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
+            }
+            totalpower += norm(acc);
+            complex<long double> x = promote(fftbuf[k0]); 
+            complex<long double> dif = acc - x;
+            difpower += norm(dif);
+            cerr << k0 << "\t" << acc << "\t" <<  x << "\t" << sqrt(norm(dif)) << endl;
+        }
+        cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
+        return sqrt(difpower/totalpower);
+    }
+
+    template <typename T1,typename T2>
+    long double dif_rmse( const vector<T1> buf1,const vector<T2> buf2)
+    {
+        long double totalpower=0;
+        long double difpower=0;
+        size_t n = min( buf1.size(),buf2.size() );
+        for (size_t k=0;k<n;++k) {
+            totalpower += (norm( buf1[k] ) + norm(buf2[k]) )/2.;
+            difpower += norm(buf1[k] - buf2[k]);
+        }
+        return sqrt(difpower/totalpower);
+    }
+
+template <class T>
+void test_scalar(int nfft)
+{
+    typedef typename Eigen::FFT<T>::Complex Complex;
+    typedef typename Eigen::FFT<T>::Scalar Scalar;
+
+    FFT<T> fft;
+    vector<Scalar> inbuf(nfft);
+    vector<Complex> outbuf;
+    for (int k=0;k<nfft;++k)
+        inbuf[k]= (T)(rand()/(double)RAND_MAX - .5);
+    fft.fwd( outbuf,inbuf);
+    VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>()  );// gross check
+
+    vector<Scalar> buf3;
+    fft.inv( buf3 , outbuf);
+    VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>()  );// gross check
+}
+
+template <class T>
+void test_complex(int nfft)
+{
+    typedef typename Eigen::FFT<T>::Complex Complex;
+
+    FFT<T> fft;
+
+    vector<Complex> inbuf(nfft);
+    vector<Complex> outbuf;
+    vector<Complex> buf3;
+    for (int k=0;k<nfft;++k)
+        inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
+    fft.fwd( outbuf , inbuf);
+
+    VERIFY( fft_rmse(outbuf,inbuf) < test_precision<T>()  );// gross check
+
+    fft.inv( buf3 , outbuf);
+
+    VERIFY( dif_rmse(inbuf,buf3) < test_precision<T>()  );// gross check
+}
+
+void test_FFTW()
+{
+
+  CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) ); CALL_SUBTEST( test_complex<long double>(32) );
+  CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) ); CALL_SUBTEST( test_complex<long double>(256) );
+  CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) ); CALL_SUBTEST( test_complex<long double>(3*8) );
+  CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) ); CALL_SUBTEST( test_complex<long double>(5*32) );
+  CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) ); CALL_SUBTEST( test_complex<long double>(2*3*4) );
+  CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) ); CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
+  CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
+
+
+
+  CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) ); CALL_SUBTEST( test_scalar<long double>(32) );
+  CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) ); CALL_SUBTEST( test_scalar<long double>(45) );
+  CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) ); CALL_SUBTEST( test_scalar<long double>(50) );
+  CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) ); CALL_SUBTEST( test_scalar<long double>(256) );
+  CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
+}