* add a Make* expression type builder to allow the

  construction of generic expressions working
  for both dense and sparse matrix. A nicer solution
  would be to use CwiseBinaryOp for any kind of matrix.
  To this end we either need to change the overall design
  so that the base class(es) depends on the kind of matrix,
  or we could add a template parameter to each expression
  type (e.g., int Kind = ei_traits<MatrixType>::Kind)
  allowing to specialize each expression for each kind of matrix.
* Extend AutoDiffScalar to work with sparse vector expression
  for the derivatives.

2 files changed, 50 insertions, 39 deletions

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 fc5e237ab..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 +117,12 @@ 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
+    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)
+    friend inline const AutoDiffScalar<DerType&> operator+(const Scalar& a, const AutoDiffScalar& b)
     {
       return AutoDiffScalar<DerType>(a + b.value(), b.derivatives());
     }
@@ -125,11 +134,11 @@ class AutoDiffScalar
     }
 
     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());
     }
@@ -143,11 +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());
     }
@@ -161,73 +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());
     }
@@ -299,11 +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; \
   }
 
@@ -330,12 +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)));
   }
@@ -375,7 +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);}