Made AutoDiffJacobian more intuitive to use and updated for C++11

Changes:
* Removed unnecessary types from the Functor by inferring from its types
* Removed inputs() function reference, replaced with .rows()
* Updated the forward constructor to use variadic templates
* Added optional parameters to the Fuctor for passing parameters,
  control signals, etc
* Has been tested with fixed size and dynamic matricies

Ammendment by chtz: overload operator() for compatibility with not fully conforming compilers

unsupported/Eigen/src/AutoDiff/AutoDiffJacobian.h

@@ -20,37 +20,60 @@ public:
   AutoDiffJacobian(const Functor& f) : Functor(f) {}
 
   // forward constructors
+#if EIGEN_HAS_VARIADIC_TEMPLATES
+  template<typename... T>
+  AutoDiffJacobian(const T& ...Values) : Functor(Values...) {}
+#else
   template<typename T0>
   AutoDiffJacobian(const T0& a0) : Functor(a0) {}
   template<typename T0, typename T1>
   AutoDiffJacobian(const T0& a0, const T1& a1) : Functor(a0, a1) {}
   template<typename T0, typename T1, typename T2>
   AutoDiffJacobian(const T0& a0, const T1& a1, const T2& a2) : Functor(a0, a1, a2) {}
-
-  enum {
-    InputsAtCompileTime = Functor::InputsAtCompileTime,
-    ValuesAtCompileTime = Functor::ValuesAtCompileTime
-  };
+#endif
 
   typedef typename Functor::InputType InputType;
   typedef typename Functor::ValueType ValueType;
-  typedef typename Functor::JacobianType JacobianType;
-  typedef typename JacobianType::Scalar Scalar;
+  typedef typename ValueType::Scalar Scalar;
+
+  enum {
+    InputsAtCompileTime = InputType::RowsAtCompileTime,
+    ValuesAtCompileTime = ValueType::RowsAtCompileTime
+  };
+
+  typedef Matrix<Scalar, ValuesAtCompileTime, InputsAtCompileTime> JacobianType;
   typedef typename JacobianType::Index Index;
 
-  typedef Matrix<Scalar,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;
 
+#if EIGEN_HAS_VARIADIC_TEMPLATES
+  // Some compilers don't accept variadic parameters after a default parameter,
+  // i.e., we can't just write _jac=0 but we need to overload operator():
+  EIGEN_STRONG_INLINE
+  void operator() (const InputType& x, ValueType* v) const
+  {
+      this->operator()(x, v, 0);
+  }
+  template<typename... ParamsType>
+  void operator() (const InputType& x, ValueType* v, JacobianType* _jac,
+                   const ParamsType&... Params) const
+#else
   void operator() (const InputType& x, ValueType* v, JacobianType* _jac=0) const
+#endif
   {
     eigen_assert(v!=0);
+
     if (!_jac)
     {
+#if EIGEN_HAS_VARIADIC_TEMPLATES
+      Functor::operator()(x, v, Params...);
+#else
       Functor::operator()(x, v);
+#endif
       return;
     }
 
@@ -61,12 +84,16 @@ public:
 
     if(InputsAtCompileTime==Dynamic)
       for (Index j=0; j<jac.rows(); j++)
-        av[j].derivatives().resize(this->inputs());
+        av[j].derivatives().resize(x.rows());
 
     for (Index i=0; i<jac.cols(); i++)
-      ax[i].derivatives() = DerivativeType::Unit(this->inputs(),i);
+      ax[i].derivatives() = DerivativeType::Unit(x.rows(),i);
 
+#if EIGEN_HAS_VARIADIC_TEMPLATES
+    Functor::operator()(ax, &av, Params...);
+#else
     Functor::operator()(ax, &av);
+#endif
 
     for (Index i=0; i<jac.rows(); i++)
     {
@@ -74,8 +101,6 @@ public:
       jac.row(i) = av[i].derivatives();
     }
   }
-protected:
-
 };
 
 }

unsupported/test/autodiff.cpp

@@ -105,6 +105,89 @@ struct TestFunc1
   }
 };
 
+
+#if EIGEN_HAS_VARIADIC_TEMPLATES
+/* Test functor for the C++11 features. */
+template <typename Scalar>
+struct integratorFunctor
+{
+    typedef Matrix<Scalar, 2, 1> InputType;
+    typedef Matrix<Scalar, 2, 1> ValueType;
+
+    /*
+     * Implementation starts here.
+     */
+    integratorFunctor(const Scalar gain) : _gain(gain) {}
+    integratorFunctor(const integratorFunctor& f) : _gain(f._gain) {}
+    const Scalar _gain;
+
+    template <typename T1, typename T2>
+    void operator() (const T1 &input, T2 *output, const Scalar dt) const
+    {
+        T2 &o = *output;
+
+        /* Integrator to test the AD. */
+        o[0] = input[0] + input[1] * dt * _gain;
+        o[1] = input[1] * _gain;
+    }
+
+    /* Only needed for the test */
+    template <typename T1, typename T2, typename T3>
+    void operator() (const T1 &input, T2 *output, T3 *jacobian, const Scalar dt) const
+    {
+        T2 &o = *output;
+
+        /* Integrator to test the AD. */
+        o[0] = input[0] + input[1] * dt * _gain;
+        o[1] = input[1] * _gain;
+
+        if (jacobian)
+        {
+            T3 &j = *jacobian;
+
+            j(0, 0) = 1;
+            j(0, 1) = dt * _gain;
+            j(1, 0) = 0;
+            j(1, 1) = _gain;
+        }
+    }
+
+};
+
+template<typename Func> void forward_jacobian_cpp11(const Func& f)
+{
+    typedef typename Func::ValueType::Scalar Scalar;
+    typedef typename Func::ValueType ValueType;
+    typedef typename Func::InputType InputType;
+    typedef typename AutoDiffJacobian<Func>::JacobianType JacobianType;
+
+    InputType x = InputType::Random(InputType::RowsAtCompileTime);
+    ValueType y, yref;
+    JacobianType j, jref;
+
+    const Scalar dt = internal::random<double>();
+
+    jref.setZero();
+    yref.setZero();
+    f(x, &yref, &jref, dt);
+
+    //std::cerr << "y, yref, jref: " << "\n";
+    //std::cerr << y.transpose() << "\n\n";
+    //std::cerr << yref << "\n\n";
+    //std::cerr << jref << "\n\n";
+
+    AutoDiffJacobian<Func> autoj(f);
+    autoj(x, &y, &j, dt);
+
+    //std::cerr << "y j (via autodiff): " << "\n";
+    //std::cerr << y.transpose() << "\n\n";
+    //std::cerr << j << "\n\n";
+
+    VERIFY_IS_APPROX(y, yref);
+    VERIFY_IS_APPROX(j, jref);
+}
+#endif
+
 template<typename Func> void forward_jacobian(const Func& f)
 {
     typename Func::InputType x = Func::InputType::Random(f.inputs());
@@ -128,7 +211,6 @@ template<typename Func> void forward_jacobian(const Func& f)
     VERIFY_IS_APPROX(j, jref);
 }
 
-
 // TODO also check actual derivatives!
 template <int>
 void test_autodiff_scalar()
@@ -141,6 +223,7 @@ void test_autodiff_scalar()
   VERIFY_IS_APPROX(res.value(), foo(p.x(),p.y()));
 }
 
+
 // TODO also check actual derivatives!
 template <int>
 void test_autodiff_vector()
@@ -151,7 +234,7 @@ void test_autodiff_vector()
   VectorAD ap = p.cast<AD>();
   ap.x().derivatives() = Vector2f::UnitX();
   ap.y().derivatives() = Vector2f::UnitY();
-  
+
   AD res = foo<VectorAD>(ap);
   VERIFY_IS_APPROX(res.value(), foo(p));
 }
@@ -164,6 +247,9 @@ void test_autodiff_jacobian()
   CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,2>()) ));
   CALL_SUBTEST(( forward_jacobian(TestFunc1<double,3,3>()) ));
   CALL_SUBTEST(( forward_jacobian(TestFunc1<double>(3,3)) ));
+#if EIGEN_HAS_VARIADIC_TEMPLATES
+  CALL_SUBTEST(( forward_jacobian_cpp11(integratorFunctor<double>(10)) ));
+#endif
 }