diff --git a/Eigen/src/Core/DenseBase.h b/Eigen/src/Core/DenseBase.h
index 53b427b17..8b994f35c 100644
--- a/Eigen/src/Core/DenseBase.h
+++ b/Eigen/src/Core/DenseBase.h
@@ -157,6 +157,11 @@ template<typename Derived> class DenseBase
           * we are dealing with a column-vector (if there is only one column) or with
           * a row-vector (if there is only one row). */
 
+      NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2,
+        /**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors, 
+         * and 2 for matrices.
+         */
+
       Flags = internal::traits<Derived>::Flags,
         /**< This stores expression \ref flags flags which may or may not be inherited by new expressions
           * constructed from this one. See the \ref flags "list of flags".
diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h
index 0903c3a6e..2603bd2f7 100644
--- a/Eigen/src/Core/GenericPacketMath.h
+++ b/Eigen/src/Core/GenericPacketMath.h
@@ -85,6 +85,8 @@ struct default_packet_traits
     HasI0e = 0,
     HasI1e = 0,
     HasIGamma = 0,
+    HasIGammaDerA = 0,
+    HasGammaSampleDerAlpha = 0,
     HasIGammac = 0,
     HasBetaInc = 0,
 
diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index 6beef5def..fe6d6585c 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -1293,17 +1293,17 @@ double exp(const double &x) { return ::exp(x); }
 
 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
 std::complex<float> exp(const std::complex<float>& x) {
-  auto com = ::expf(x.real());
-  auto res_real = com * ::cosf(x.imag());
-  auto res_imag = com * ::sinf(x.imag());
+  float com = ::expf(x.real());
+  float res_real = com * ::cosf(x.imag());
+  float res_imag = com * ::sinf(x.imag());
   return std::complex<float>(res_real, res_imag);
 }
 
 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
 std::complex<double> exp(const std::complex<double>& x) {
-  auto com = ::exp(x.real());
-  auto res_real = com * ::cos(x.imag());
-  auto res_imag = com * ::sin(x.imag());
+  double com = ::exp(x.real());
+  double res_real = com * ::cos(x.imag());
+  double res_imag = com * ::sin(x.imag());
   return std::complex<double>(res_real, res_imag);
 }
 #endif
diff --git a/Eigen/src/Core/ProductEvaluators.h b/Eigen/src/Core/ProductEvaluators.h
index cc75fbce3..e0868daf5 100644
--- a/Eigen/src/Core/ProductEvaluators.h
+++ b/Eigen/src/Core/ProductEvaluators.h
@@ -137,10 +137,14 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scal
   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type>
 {
   typedef Product<Lhs,Rhs,Options> SrcXprType;
+<<<<<<< local
   #if defined(EIGEN_HIPCC)
   EIGEN_DEVICE_FUNC
   #endif  
   static EIGEN_STRONG_INLINE
+=======
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+>>>>>>> other
   void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
   {
     Index dstRows = src.rows();
@@ -158,7 +162,7 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<
   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type>
 {
   typedef Product<Lhs,Rhs,Options> SrcXprType;
-  static EIGEN_STRONG_INLINE
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
   void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,Scalar> &)
   {
     eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
@@ -173,7 +177,7 @@ struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<
   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type>
 {
   typedef Product<Lhs,Rhs,Options> SrcXprType;
-  static EIGEN_STRONG_INLINE
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
   void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,Scalar> &)
   {
     eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
@@ -193,7 +197,7 @@ struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_product_op<ScalarBi
   typedef CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>,
                         const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>,
                         const Product<Lhs,Rhs,DefaultProduct> > SrcXprType;
-  static EIGEN_STRONG_INLINE
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
   void run(DstXprType &dst, const SrcXprType &src, const AssignFunc& func)
   {
     call_assignment_no_alias(dst, (src.lhs().functor().m_other * src.rhs().lhs())*src.rhs().rhs(), func);
@@ -220,7 +224,7 @@ template<typename DstXprType, typename OtherXpr, typename ProductType, typename
 struct assignment_from_xpr_op_product
 {
   template<typename SrcXprType, typename InitialFunc>
-  static EIGEN_STRONG_INLINE
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
   void run(DstXprType &dst, const SrcXprType &src, const InitialFunc& /*func*/)
   {
     call_assignment_no_alias(dst, src.lhs(), Func1());
@@ -249,19 +253,19 @@ template<typename Lhs, typename Rhs>
 struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,InnerProduct>
 {
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     dst.coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
   }
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     dst.coeffRef(0,0) += (lhs.transpose().cwiseProduct(rhs)).sum();
   }
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   { dst.coeffRef(0,0) -= (lhs.transpose().cwiseProduct(rhs)).sum(); }
 };
 
@@ -272,7 +276,7 @@ struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,InnerProduct>
 
 // Column major result
 template<typename Dst, typename Lhs, typename Rhs, typename Func>
-void outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const false_type&)
+void EIGEN_DEVICE_FUNC outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const false_type&)
 {
   evaluator<Rhs> rhsEval(rhs);
   typename nested_eval<Lhs,Rhs::SizeAtCompileTime>::type actual_lhs(lhs);
@@ -285,7 +289,7 @@ void outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const
 
 // Row major result
 template<typename Dst, typename Lhs, typename Rhs, typename Func>
-void outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const true_type&)
+void EIGEN_DEVICE_FUNC outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const true_type&)
 {
   evaluator<Lhs> lhsEval(lhs);
   typename nested_eval<Rhs,Lhs::SizeAtCompileTime>::type actual_rhs(rhs);
@@ -303,37 +307,37 @@ struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,OuterProduct>
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
   
   // TODO it would be nice to be able to exploit our *_assign_op functors for that purpose
-  struct set  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived()  = src; } };
-  struct add  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } };
-  struct sub  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() -= src; } };
+  struct set  { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived()  = src; } };
+  struct add  { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } };
+  struct sub  { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() -= src; } };
   struct adds {
     Scalar m_scale;
     explicit adds(const Scalar& s) : m_scale(s) {}
-    template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const {
+    template<typename Dst, typename Src> void EIGEN_DEVICE_FUNC operator()(const Dst& dst, const Src& src) const {
       dst.const_cast_derived() += m_scale * src;
     }
   };
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     internal::outer_product_selector_run(dst, lhs, rhs, set(), is_row_major<Dst>());
   }
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     internal::outer_product_selector_run(dst, lhs, rhs, add(), is_row_major<Dst>());
   }
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     internal::outer_product_selector_run(dst, lhs, rhs, sub(), is_row_major<Dst>());
   }
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
   {
     internal::outer_product_selector_run(dst, lhs, rhs, adds(alpha), is_row_major<Dst>());
   }
@@ -348,19 +352,19 @@ struct generic_product_impl_base
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   { dst.setZero(); scaleAndAddTo(dst, lhs, rhs, Scalar(1)); }
 
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   { scaleAndAddTo(dst,lhs, rhs, Scalar(1)); }
 
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   { scaleAndAddTo(dst, lhs, rhs, Scalar(-1)); }
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
   { Derived::scaleAndAddTo(dst,lhs,rhs,alpha); }
 
 };
@@ -376,7 +380,7 @@ struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemvProduct>
   typedef typename internal::remove_all<typename internal::conditional<int(Side)==OnTheRight,LhsNested,RhsNested>::type>::type MatrixType;
 
   template<typename Dest>
-  static EIGEN_STRONG_INLINE void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
   {
     LhsNested actual_lhs(lhs);
     RhsNested actual_rhs(rhs);
@@ -393,10 +397,14 @@ struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode>
   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
   
   template<typename Dst>
+<<<<<<< local
   #if defined(EIGEN_HIPCC)  
   EIGEN_DEVICE_FUNC
   #endif  
   static EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+=======
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+>>>>>>> other
   {
     // Same as: dst.noalias() = lhs.lazyProduct(rhs);
     // but easier on the compiler side
@@ -404,14 +412,14 @@ struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode>
   }
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     // dst.noalias() += lhs.lazyProduct(rhs);
     call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::add_assign_op<typename Dst::Scalar,Scalar>());
   }
   
   template<typename Dst>
-  static EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
+  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
   {
     // dst.noalias() -= lhs.lazyProduct(rhs);
     call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::sub_assign_op<typename Dst::Scalar,Scalar>());
diff --git a/Eigen/src/Core/SelfCwiseBinaryOp.h b/Eigen/src/Core/SelfCwiseBinaryOp.h
index 50099df82..7c89c2e23 100644
--- a/Eigen/src/Core/SelfCwiseBinaryOp.h
+++ b/Eigen/src/Core/SelfCwiseBinaryOp.h
@@ -17,7 +17,6 @@ namespace Eigen {
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator*=(const Scalar& other)
 {
-  typedef typename Derived::PlainObject PlainObject;
   internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::mul_assign_op<Scalar,Scalar>());
   return derived();
 }
@@ -25,7 +24,6 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator*=(co
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator+=(const Scalar& other)
 {
-  typedef typename Derived::PlainObject PlainObject;
   internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::add_assign_op<Scalar,Scalar>());
   return derived();
 }
@@ -33,7 +31,6 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator+=(co
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator-=(const Scalar& other)
 {
-  typedef typename Derived::PlainObject PlainObject;
   internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::sub_assign_op<Scalar,Scalar>());
   return derived();
 }
@@ -41,7 +38,6 @@ EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& ArrayBase<Derived>::operator-=(co
 template<typename Derived>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::operator/=(const Scalar& other)
 {
-  typedef typename Derived::PlainObject PlainObject;
   internal::call_assignment(this->derived(), PlainObject::Constant(rows(),cols(),other), internal::div_assign_op<Scalar,Scalar>());
   return derived();
 }
diff --git a/Eigen/src/Core/Solve.h b/Eigen/src/Core/Solve.h
index a8daea511..2bf940a26 100644
--- a/Eigen/src/Core/Solve.h
+++ b/Eigen/src/Core/Solve.h
@@ -181,7 +181,7 @@ struct Assignment<DstXprType, Solve<CwiseUnaryOp<internal::scalar_conjugate_op<t
   }
 };
 
-} // end namepsace internal
+} // end namespace internal
 
 } // end namespace Eigen
 
diff --git a/Eigen/src/Core/SolverBase.h b/Eigen/src/Core/SolverBase.h
index 8a4adc229..702a5485c 100644
--- a/Eigen/src/Core/SolverBase.h
+++ b/Eigen/src/Core/SolverBase.h
@@ -56,7 +56,8 @@ class SolverBase : public EigenBase<Derived>
       MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
                                                              internal::traits<Derived>::MaxColsAtCompileTime>::ret),
       IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1
-                           || internal::traits<Derived>::MaxColsAtCompileTime == 1
+                           || internal::traits<Derived>::MaxColsAtCompileTime == 1,
+      NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2
     };
 
     /** Default constructor */
diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
index 59aebd912..774e64981 100644
--- a/Eigen/src/Core/arch/AVX/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -318,9 +318,9 @@ template<> EIGEN_STRONG_INLINE void pstore1<Packet8i>(int* to, const int& a)
 }
 
 #ifndef EIGEN_VECTORIZE_AVX512
-template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
-template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
-template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
 #endif
 
 template<> EIGEN_STRONG_INLINE float  pfirst<Packet8f>(const Packet8f& a) {
diff --git a/Eigen/src/Core/arch/AVX512/PacketMath.h b/Eigen/src/Core/arch/AVX512/PacketMath.h
index eb5de43d4..4e2e916de 100644
--- a/Eigen/src/Core/arch/AVX512/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX512/PacketMath.h
@@ -604,9 +604,9 @@ EIGEN_STRONG_INLINE void pstore1<Packet16i>(int* to, const int& a) {
   pstore(to, pa);
 }
 
-template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
-template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
-template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
 
 template <>
 EIGEN_STRONG_INLINE float pfirst<Packet16f>(const Packet16f& a) {
diff --git a/Eigen/src/Core/arch/CUDA/PacketMath.h b/Eigen/src/Core/arch/CUDA/PacketMath.h
index 704a4e0d9..ab8e477f4 100644
--- a/Eigen/src/Core/arch/CUDA/PacketMath.h
+++ b/Eigen/src/Core/arch/CUDA/PacketMath.h
@@ -47,6 +47,8 @@ template<> struct packet_traits<float> : default_packet_traits
     HasI0e = 1,
     HasI1e = 1,
     HasIGamma = 1,
+    HasIGammaDerA = 1,
+    HasGammaSampleDerAlpha = 1,
     HasIGammac = 1,
     HasBetaInc = 1,
 
@@ -78,6 +80,8 @@ template<> struct packet_traits<double> : default_packet_traits
     HasI0e = 1,
     HasI1e = 1,
     HasIGamma = 1,
+    HasIGammaDerA = 1,
+    HasGammaSampleDerAlpha = 1,
     HasIGammac = 1,
     HasBetaInc = 1,
 
diff --git a/Eigen/src/Core/arch/SSE/Complex.h b/Eigen/src/Core/arch/SSE/Complex.h
index c618cfaaa..d075043ce 100644
--- a/Eigen/src/Core/arch/SSE/Complex.h
+++ b/Eigen/src/Core/arch/SSE/Complex.h
@@ -128,7 +128,7 @@ template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf
                                      _mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 3)));
 }
 
-template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
 
 template<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)
 {
@@ -324,7 +324,7 @@ template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<
 template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, Packet2d(from.v)); }
 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, Packet2d(from.v)); }
 
-template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
 
 template<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)
 {
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
index d1a7c65be..c944d2c0e 100755
--- a/Eigen/src/Core/arch/SSE/PacketMath.h
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -461,10 +461,16 @@ template<> EIGEN_STRONG_INLINE void pstore1<Packet2d>(double* to, const double&
   pstore(to, Packet2d(vec2d_swizzle1(pa,0,0)));
 }
 
+#if EIGEN_COMP_PGI
+typedef const void * SsePrefetchPtrType;
+#else
+typedef const char * SsePrefetchPtrType;
+#endif
+
 #ifndef EIGEN_VECTORIZE_AVX
-template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
-template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
-template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
 #endif
 
 #if EIGEN_COMP_MSVC_STRICT && EIGEN_OS_WIN64
diff --git a/Eigen/src/Core/products/Parallelizer.h b/Eigen/src/Core/products/Parallelizer.h
index e4d13103b..15b5c5f94 100644
--- a/Eigen/src/Core/products/Parallelizer.h
+++ b/Eigen/src/Core/products/Parallelizer.h
@@ -91,7 +91,7 @@ void parallelize_gemm(const Functor& func, Index rows, Index cols, Index depth,
   // FIXME the transpose variable is only needed to properly split
   // the matrix product when multithreading is enabled. This is a temporary
   // fix to support row-major destination matrices. This whole
-  // parallelizer mechanism has to be redisigned anyway.
+  // parallelizer mechanism has to be redesigned anyway.
   EIGEN_UNUSED_VARIABLE(depth);
   EIGEN_UNUSED_VARIABLE(transpose);
   func(0,rows, 0,cols);
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index c6e27f6af..64b7be423 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -702,7 +702,7 @@ namespace Eigen {
 // If the user explicitly disable vectorization, then we also disable alignment
 #if defined(EIGEN_DONT_VECTORIZE)
   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 0
-#elif defined(EIGEN_VECTORIZE_AVX512)
+#elif defined(__AVX512F__)
   // 64 bytes static alignment is preferred only if really required
   #define EIGEN_IDEAL_MAX_ALIGN_BYTES 64
 #elif defined(__AVX__)
@@ -1033,7 +1033,13 @@ namespace Eigen {
 #   define EIGEN_NOEXCEPT
 #   define EIGEN_NOEXCEPT_IF(x)
 #   define EIGEN_NO_THROW throw()
-#   define EIGEN_EXCEPTION_SPEC(X) throw(X)
+#   if EIGEN_COMP_MSVC
+      // MSVC does not support exception specifications (warning C4290),
+      // and they are deprecated in c++11 anyway.
+#     define EIGEN_EXCEPTION_SPEC(X) throw()
+#   else
+#     define EIGEN_EXCEPTION_SPEC(X) throw(X)
+#   endif
 #endif
 
 #endif // EIGEN_MACROS_H
diff --git a/Eigen/src/Core/util/Meta.h b/Eigen/src/Core/util/Meta.h
index ca6fa6ce9..7f78cc89c 100755
--- a/Eigen/src/Core/util/Meta.h
+++ b/Eigen/src/Core/util/Meta.h
@@ -587,23 +587,27 @@ T div_ceil(const T &a, const T &b)
 
 // The aim of the following functions is to bypass -Wfloat-equal warnings
 // when we really want a strict equality comparison on floating points.
-template<typename X, typename Y> EIGEN_STRONG_INLINE
+template<typename X, typename Y> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
 bool equal_strict(const X& x,const Y& y) { return x == y; }
 
-template<> EIGEN_STRONG_INLINE
+#if !defined(EIGEN_CUDA_ARCH)
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
 bool equal_strict(const float& x,const float& y) { return std::equal_to<float>()(x,y); }
 
-template<> EIGEN_STRONG_INLINE
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
 bool equal_strict(const double& x,const double& y) { return std::equal_to<double>()(x,y); }
+#endif
 
-template<typename X, typename Y> EIGEN_STRONG_INLINE
+template<typename X, typename Y> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
 bool not_equal_strict(const X& x,const Y& y) { return x != y; }
 
-template<> EIGEN_STRONG_INLINE
+#if !defined(EIGEN_CUDA_ARCH)
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
 bool not_equal_strict(const float& x,const float& y) { return std::not_equal_to<float>()(x,y); }
 
-template<> EIGEN_STRONG_INLINE
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC
 bool not_equal_strict(const double& x,const double& y) { return std::not_equal_to<double>()(x,y); }
+#endif
 
 } // end namespace numext
 
diff --git a/Eigen/src/Eigenvalues/RealSchur.h b/Eigen/src/Eigenvalues/RealSchur.h
index b72799e5b..4c53344bb 100644
--- a/Eigen/src/Eigenvalues/RealSchur.h
+++ b/Eigen/src/Eigenvalues/RealSchur.h
@@ -284,13 +284,13 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa
   using std::abs;
 
   m_matT = matrixH;
+  m_workspaceVector.resize(m_matT.cols());
   if(computeU)
-    m_matU = matrixQ;
+    matrixQ.evalTo(m_matU, m_workspaceVector);
   
   Index maxIters = m_maxIters;
   if (maxIters == -1)
     maxIters = m_maxIterationsPerRow * matrixH.rows();
-  m_workspaceVector.resize(m_matT.cols());
   Scalar* workspace = &m_workspaceVector.coeffRef(0);
 
   // The matrix m_matT is divided in three parts. 
diff --git a/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
index 0ace45177..79e1e4819 100644
--- a/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
+++ b/Eigen/src/IterativeLinearSolvers/SolveWithGuess.h
@@ -108,7 +108,7 @@ struct Assignment<DstXprType, SolveWithGuess<DecType,RhsType,GuessType>, interna
   }
 };
 
-} // end namepsace internal
+} // end namespace internal
 
 } // end namespace Eigen
 
diff --git a/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
index 84a1bf2bd..0aa92f8bc 100644
--- a/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
+++ b/Eigen/src/SparseCholesky/SimplicialCholesky_impl.h
@@ -5,7 +5,7 @@
 
 /*
 
-NOTE: thes functions vave been adapted from the LDL library:
+NOTE: these functions have been adapted from the LDL library:
 
 LDL Copyright (c) 2005 by Timothy A. Davis.  All Rights Reserved.
 
diff --git a/Eigen/src/SparseCore/SparseMatrixBase.h b/Eigen/src/SparseCore/SparseMatrixBase.h
index dac2d8c62..229449f02 100644
--- a/Eigen/src/SparseCore/SparseMatrixBase.h
+++ b/Eigen/src/SparseCore/SparseMatrixBase.h
@@ -87,6 +87,11 @@ template<typename Derived> class SparseMatrixBase
           * we are dealing with a column-vector (if there is only one column) or with
           * a row-vector (if there is only one row). */
 
+      NumDimensions = int(MaxSizeAtCompileTime) == 1 ? 0 : bool(IsVectorAtCompileTime) ? 1 : 2,
+        /**< This value is equal to Tensor::NumDimensions, i.e. 0 for scalars, 1 for vectors,
+         * and 2 for matrices.
+         */
+
       Flags = internal::traits<Derived>::Flags,
         /**< This stores expression \ref flags flags which may or may not be inherited by new expressions
           * constructed from this one. See the \ref flags "list of flags".
diff --git a/doc/examples/Cwise_lgamma.cpp b/doc/examples/Cwise_lgamma.cpp
index f1c4f503e..6bfaccbce 100644
--- a/doc/examples/Cwise_lgamma.cpp
+++ b/doc/examples/Cwise_lgamma.cpp
@@ -6,4 +6,4 @@ int main()
 {
   Array4d v(0.5,10,0,-1);
   std::cout << v.lgamma() << std::endl;
-}
\ No newline at end of file
+}
diff --git a/doc/examples/Tutorial_simple_example_dynamic_size.cpp b/doc/examples/Tutorial_simple_example_dynamic_size.cpp
index 0f0280e0e..defcb1ee4 100644
--- a/doc/examples/Tutorial_simple_example_dynamic_size.cpp
+++ b/doc/examples/Tutorial_simple_example_dynamic_size.cpp
@@ -10,7 +10,7 @@ int main()
     MatrixXi m(size,size+1);         // a (size)x(size+1)-matrix of int's
     for (int j=0; j<m.cols(); ++j)   // loop over columns
       for (int i=0; i<m.rows(); ++i) // loop over rows
-        m(i,j) = i+j*m.rows();       // to access matrix coefficients,
+        m(i,j) = i+j*size;           // to access matrix coefficients,
                                      // use operator()(int,int)
     std::cout << m << "\n\n";
   }
diff --git a/doc/examples/matrixfree_cg.cpp b/doc/examples/matrixfree_cg.cpp
index 6a205aea3..74699381c 100644
--- a/doc/examples/matrixfree_cg.cpp
+++ b/doc/examples/matrixfree_cg.cpp
@@ -67,6 +67,7 @@ namespace internal {
       // This method should implement "dst += alpha * lhs * rhs" inplace,
       // however, for iterative solvers, alpha is always equal to 1, so let's not bother about it.
       assert(alpha==Scalar(1) && "scaling is not implemented");
+      EIGEN_ONLY_USED_FOR_DEBUG(alpha);
 
       // Here we could simply call dst.noalias() += lhs.my_matrix() * rhs,
       // but let's do something fancier (and less efficient):
diff --git a/doc/special_examples/Tutorial_sparse_example.cpp b/doc/special_examples/Tutorial_sparse_example.cpp
index 89937b411..8850db052 100644
--- a/doc/special_examples/Tutorial_sparse_example.cpp
+++ b/doc/special_examples/Tutorial_sparse_example.cpp
@@ -1,5 +1,6 @@
 #include <Eigen/Sparse>
 #include <vector>
+#include <iostream>
 
 typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
 typedef Eigen::Triplet<double> T;
@@ -9,7 +10,10 @@ void saveAsBitmap(const Eigen::VectorXd& x, int n, const char* filename);
 
 int main(int argc, char** argv)
 {
-  assert(argc==2);
+  if(argc!=2) {
+    std::cerr << "Error: expected one and only one argument.\n";
+    return -1;
+  }
   
   int n = 300;  // size of the image
   int m = n*n;  // number of unknowns (=number of pixels)
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index 4a5c1d36d..f20df119a 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -47,7 +47,7 @@ set(EIGEN_TEST_MATRIX_DIR "" CACHE STRING "Enable testing of realword sparse mat
 if(EIGEN_TEST_MATRIX_DIR)
   if(NOT WIN32)
     message(STATUS "Test realworld sparse matrices: ${EIGEN_TEST_MATRIX_DIR}")
-    add_definitions( -DTEST_REAL_CASES=${EIGEN_TEST_MATRIX_DIR} )
+    add_definitions( -DTEST_REAL_CASES="${EIGEN_TEST_MATRIX_DIR}" )
   else(NOT WIN32)
     message(STATUS "REAL CASES CAN NOT BE CURRENTLY TESTED ON WIN32")
   endif(NOT WIN32)
@@ -292,6 +292,7 @@ ei_add_test(mpl2only)
 ei_add_test(inplace_decomposition)
 ei_add_test(half_float)
 ei_add_test(array_of_string)
+ei_add_test(num_dimensions)
 
 add_executable(bug1213 bug1213.cpp bug1213_main.cpp)
 
diff --git a/test/indexed_view.cpp b/test/indexed_view.cpp
index 033d8833f..551dc55b0 100644
--- a/test/indexed_view.cpp
+++ b/test/indexed_view.cpp
@@ -140,7 +140,7 @@ void check_indexed_view()
     "500  501  502  503  504  505  506  507  508  509")
   );
 
-  // takes the row numer 3, and repeat it 5 times
+  // take row number 3, and repeat it 5 times
   VERIFY( MATCH( A(seqN(3,5,0), all),
     "300  301  302  303  304  305  306  307  308  309\n"
     "300  301  302  303  304  305  306  307  308  309\n"
@@ -397,10 +397,6 @@ void test_indexed_view()
 //   }
 
   // static checks of some internals:
-
-  #define STATIC_CHECK( COND ) \
-    EIGEN_STATIC_ASSERT( (COND) , EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT )
-
   STATIC_CHECK(( internal::is_valid_index_type<int>::value ));
   STATIC_CHECK(( internal::is_valid_index_type<unsigned int>::value ));
   STATIC_CHECK(( internal::is_valid_index_type<short>::value ));
diff --git a/test/main.h b/test/main.h
index 79717a532..5691af52b 100644
--- a/test/main.h
+++ b/test/main.h
@@ -345,6 +345,8 @@ inline void verify_impl(bool condition, const char *testname, const char *file,
 
 #define VERIFY_IS_UNITARY(a) VERIFY(test_isUnitary(a))
 
+#define STATIC_CHECK(COND) EIGEN_STATIC_ASSERT( (COND) , EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT )
+
 #define CALL_SUBTEST(FUNC) do { \
     g_test_stack.push_back(EI_PP_MAKE_STRING(FUNC)); \
     FUNC; \
@@ -365,7 +367,7 @@ template<> inline long double test_precision<std::complex<long double> >() { ret
 inline bool test_isApprox(const short& a, const short& b)
 { return internal::isApprox(a, b, test_precision<short>()); }
 inline bool test_isApprox(const unsigned short& a, const unsigned short& b)
-{ return internal::isApprox(a, b, test_precision<unsigned long>()); }
+{ return internal::isApprox(a, b, test_precision<unsigned short>()); }
 inline bool test_isApprox(const unsigned int& a, const unsigned int& b)
 { return internal::isApprox(a, b, test_precision<unsigned int>()); }
 inline bool test_isApprox(const long& a, const long& b)
diff --git a/test/mapped_matrix.cpp b/test/mapped_matrix.cpp
index 6a84c5897..7b9e1fe52 100644
--- a/test/mapped_matrix.cpp
+++ b/test/mapped_matrix.cpp
@@ -205,7 +205,6 @@ void test_mapped_matrix()
     CALL_SUBTEST_8( map_static_methods(RowVector3d()) );
     CALL_SUBTEST_9( map_static_methods(VectorXcd(8)) );
     CALL_SUBTEST_10( map_static_methods(VectorXf(12)) );
-    
     CALL_SUBTEST_11( map_not_aligned_on_scalar<double>() );
   }
 }
diff --git a/test/num_dimensions.cpp b/test/num_dimensions.cpp
new file mode 100644
index 000000000..f5209283d
--- /dev/null
+++ b/test/num_dimensions.cpp
@@ -0,0 +1,90 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2018 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/SparseCore>
+
+template<int ExpectedDim,typename Xpr>
+void check_dim(const Xpr& ) {
+  STATIC_CHECK( Xpr::NumDimensions == ExpectedDim );
+}
+
+#if EIGEN_HAS_CXX11
+template<template <typename,int,int> class Object>
+void map_num_dimensions()
+{
+  typedef Object<double, 1, 1> ArrayScalarType;
+  typedef Object<double, 2, 1> ArrayVectorType;
+  typedef Object<double, 1, 2> TransposeArrayVectorType;
+  typedef Object<double, 2, 2> ArrayType;
+  typedef Object<double, Eigen::Dynamic, 1> DynamicArrayVectorType;
+  typedef Object<double, 1, Eigen::Dynamic> DynamicTransposeArrayVectorType;
+  typedef Object<double, Eigen::Dynamic, Eigen::Dynamic> DynamicArrayType;
+
+  STATIC_CHECK(ArrayScalarType::NumDimensions == 0);
+  STATIC_CHECK(ArrayVectorType::NumDimensions == 1);
+  STATIC_CHECK(TransposeArrayVectorType::NumDimensions == 1);
+  STATIC_CHECK(ArrayType::NumDimensions == 2);
+  STATIC_CHECK(DynamicArrayVectorType::NumDimensions == 1);
+  STATIC_CHECK(DynamicTransposeArrayVectorType::NumDimensions == 1);
+  STATIC_CHECK(DynamicArrayType::NumDimensions == 2);
+
+  typedef Eigen::Map<ArrayScalarType> ArrayScalarMap;
+  typedef Eigen::Map<ArrayVectorType> ArrayVectorMap;
+  typedef Eigen::Map<TransposeArrayVectorType> TransposeArrayVectorMap;
+  typedef Eigen::Map<ArrayType> ArrayMap;
+  typedef Eigen::Map<DynamicArrayVectorType> DynamicArrayVectorMap;
+  typedef Eigen::Map<DynamicTransposeArrayVectorType> DynamicTransposeArrayVectorMap;
+  typedef Eigen::Map<DynamicArrayType> DynamicArrayMap;
+
+  STATIC_CHECK(ArrayScalarMap::NumDimensions == 0);
+  STATIC_CHECK(ArrayVectorMap::NumDimensions == 1);
+  STATIC_CHECK(TransposeArrayVectorMap::NumDimensions == 1);
+  STATIC_CHECK(ArrayMap::NumDimensions == 2);
+  STATIC_CHECK(DynamicArrayVectorMap::NumDimensions == 1);
+  STATIC_CHECK(DynamicTransposeArrayVectorMap::NumDimensions == 1);
+  STATIC_CHECK(DynamicArrayMap::NumDimensions == 2);
+}
+
+template<typename Scalar, int Rows, int Cols>
+using TArray = Array<Scalar,Rows,Cols>;
+
+template<typename Scalar, int Rows, int Cols>
+using TMatrix = Matrix<Scalar,Rows,Cols>;
+
+#endif
+
+void test_num_dimensions()
+{
+  int n = 10;
+  ArrayXXd A(n,n);
+  CALL_SUBTEST( check_dim<2>(A) );
+  CALL_SUBTEST( check_dim<2>(A.block(1,1,2,2)) );
+  CALL_SUBTEST( check_dim<1>(A.col(1)) );
+  CALL_SUBTEST( check_dim<1>(A.row(1)) );
+
+  MatrixXd M(n,n);
+  CALL_SUBTEST( check_dim<0>(M.row(1)*M.col(1)) );
+
+  SparseMatrix<double> S(n,n);
+  CALL_SUBTEST( check_dim<2>(S) );
+  CALL_SUBTEST( check_dim<2>(S.block(1,1,2,2)) );
+  CALL_SUBTEST( check_dim<1>(S.col(1)) );
+  CALL_SUBTEST( check_dim<1>(S.row(1)) );
+
+  SparseVector<double> s(n);
+  CALL_SUBTEST( check_dim<1>(s) );
+  CALL_SUBTEST( check_dim<1>(s.head(2)) );
+  
+
+  #if EIGEN_HAS_CXX11
+  CALL_SUBTEST( map_num_dimensions<TArray>() );
+  CALL_SUBTEST( map_num_dimensions<TMatrix>() );
+  #endif
+}
diff --git a/unsupported/Eigen/CXX11/src/Tensor/README.md b/unsupported/Eigen/CXX11/src/Tensor/README.md
index 49cc33c5d..dfd7ab7c7 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/README.md
+++ b/unsupported/Eigen/CXX11/src/Tensor/README.md
@@ -581,7 +581,7 @@ is not initialized.
 
 Creates a tensor mapping an existing array of data. The data must not be freed
 until the TensorMap is discarded, and the size of the data must be large enough
-to accomodate of the coefficients of the tensor.
+to accommodate the coefficients of the tensor.
 
     float data[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
     Eigen::TensorMap<Tensor<float, 2>> a(data, 3, 4);
diff --git a/unsupported/Eigen/CXX11/src/Tensor/Tensor.h b/unsupported/Eigen/CXX11/src/Tensor/Tensor.h
index 1940a9692..4fd96448f 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/Tensor.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/Tensor.h
@@ -48,7 +48,7 @@ namespace Eigen {
   *
   * <dl>
   * <dt><b>Relation to other parts of Eigen:</b></dt>
-  * <dd>The midterm developement goal for this class is to have a similar hierarchy as Eigen uses for matrices, so that
+  * <dd>The midterm development goal for this class is to have a similar hierarchy as Eigen uses for matrices, so that
   * taking blocks or using tensors in expressions is easily possible, including an interface with the vector/matrix code
   * by providing .asMatrix() and .asVector() (or similar) methods for rank 2 and 1 tensors. However, currently, the %Tensor
   * class does not provide any of these features and is only available as a stand-alone class that just allows for
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
index a942c98dd..bdc1a17a7 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
@@ -20,7 +20,7 @@ namespace Eigen {
   * \brief The tensor base class.
   *
   * This class is the common parent of the Tensor and TensorMap class, thus
-  * making it possible to use either class interchangably in expressions.
+  * making it possible to use either class interchangeably in expressions.
   */
 
 template<typename Derived>
@@ -152,6 +152,20 @@ class TensorBase<Derived, ReadOnlyAccessors>
       return binaryExpr(other.derived(), internal::scalar_igamma_op<Scalar>());
     }
 
+    // igamma_der_a(a = this, x = other)
+    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+    const TensorCwiseBinaryOp<internal::scalar_igamma_der_a_op<Scalar>, const Derived, const OtherDerived>
+    igamma_der_a(const OtherDerived& other) const {
+      return binaryExpr(other.derived(), internal::scalar_igamma_der_a_op<Scalar>());
+    }
+
+    // gamma_sample_der_alpha(alpha = this, sample = other)
+    template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+    const TensorCwiseBinaryOp<internal::scalar_gamma_sample_der_alpha_op<Scalar>, const Derived, const OtherDerived>
+    gamma_sample_der_alpha(const OtherDerived& other) const {
+      return binaryExpr(other.derived(), internal::scalar_gamma_sample_der_alpha_op<Scalar>());
+    }
+
     // igammac(a = this, x = other)
     template<typename OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
     const TensorCwiseBinaryOp<internal::scalar_igammac_op<Scalar>, const Derived, const OtherDerived>
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorBroadcasting.h b/unsupported/Eigen/CXX11/src/Tensor/TensorBroadcasting.h
index b6c93aff9..9ab6b3565 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorBroadcasting.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorBroadcasting.h
@@ -105,6 +105,7 @@ struct TensorEvaluator<const TensorBroadcastingOp<Broadcast, ArgType>, Device>
   typedef typename XprType::CoeffReturnType CoeffReturnType;
   typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
   static const int PacketSize = internal::unpacket_traits<PacketReturnType>::size;
+  bool nByOne = false, oneByN = false;
 
   enum {
     IsAligned = true,
@@ -142,6 +143,24 @@ struct TensorEvaluator<const TensorBroadcastingOp<Broadcast, ArgType>, Device>
         m_outputStrides[i] = m_outputStrides[i+1] * m_dimensions[i+1];
       }
     }
+
+    if (input_dims[0] == 1) {
+      oneByN = true;
+      for (int i = 1; i < NumDims; ++i) {
+        if (broadcast[i] != 1) {
+          oneByN = false;
+          break;
+        }
+      }
+    } else if (input_dims[NumDims-1] == 1) {
+      nByOne = true;
+      for (int i = 0; i < NumDims-1; ++i) {
+        if (broadcast[i] != 1) {
+          nByOne = false;
+          break;
+        }
+      }
+    }
   }
 
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
@@ -237,9 +256,84 @@ struct TensorEvaluator<const TensorBroadcastingOp<Broadcast, ArgType>, Device>
     }
 
     if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
-      return packetColMajor<LoadMode>(index);
+      if (oneByN) {
+        return packetNByOne<LoadMode>(index);
+      } else if (nByOne) {
+        return packetOneByN<LoadMode>(index);
+      } else {
+        return packetColMajor<LoadMode>(index);
+      }
     } else {
-      return packetRowMajor<LoadMode>(index);
+      if (oneByN) {
+        return packetOneByN<LoadMode>(index);
+      } else if (nByOne) {
+        return packetNByOne<LoadMode>(index);
+      } else {
+        return packetRowMajor<LoadMode>(index);
+      }
+    }
+  }
+
+  template<int LoadMode>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetOneByN(Index index) const
+  {
+    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
+    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+    Index dim, inputIndex;
+
+    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+      dim = NumDims - 1;
+    } else {
+      dim = 0;
+    }
+
+    inputIndex = index % m_inputStrides[dim];
+    if (inputIndex + PacketSize <= m_inputStrides[dim]) {
+      return m_impl.template packet<Unaligned>(inputIndex);
+    } else {
+      EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];
+      for (int i = 0; i < PacketSize; ++i) {
+        if (inputIndex > m_inputStrides[dim]-1) {
+          inputIndex = 0;
+        }
+        values[i] = m_impl.coeff(inputIndex++);
+      }
+      return internal::pload<PacketReturnType>(values);
+    }
+  }
+
+  template<int LoadMode>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packetNByOne(Index index) const
+  {
+    EIGEN_STATIC_ASSERT((PacketSize > 1), YOU_MADE_A_PROGRAMMING_MISTAKE)
+    eigen_assert(index+PacketSize-1 < dimensions().TotalSize());
+
+    EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];
+    Index dim, inputIndex, outputOffset;
+
+    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
+      dim = 1;
+    } else {
+      dim = NumDims - 2;
+    }
+
+    inputIndex   = index / m_outputStrides[dim];
+    outputOffset = index % m_outputStrides[dim];
+    if (outputOffset + PacketSize <= m_outputStrides[dim]) {
+      values[0] = m_impl.coeff(inputIndex);
+      return internal::pload1<PacketReturnType>(values);
+    } else {
+      for (int i = 0, cur = 0; i < PacketSize; ++i, ++cur) {
+        if (outputOffset + cur < m_outputStrides[dim]) {
+          values[i] = m_impl.coeff(inputIndex);
+        } else {
+          values[i] = m_impl.coeff(++inputIndex);
+          outputOffset = 0;
+          cur = 0;
+        }
+      }
+      return internal::pload<PacketReturnType>(values);
     }
   }
 
@@ -290,7 +384,11 @@ struct TensorEvaluator<const TensorBroadcastingOp<Broadcast, ArgType>, Device>
       EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];
       values[0] = m_impl.coeff(inputIndex);
       for (int i = 1; i < PacketSize; ++i) {
-        values[i] = coeffColMajor(originalIndex+i);
+        if (innermostLoc + i < m_impl.dimensions()[0]) {
+          values[i] = m_impl.coeff(inputIndex+i);
+        } else {
+          values[i] = coeffColMajor(originalIndex+i);
+        }
       }
       PacketReturnType rslt = internal::pload<PacketReturnType>(values);
       return rslt;
@@ -342,7 +440,11 @@ struct TensorEvaluator<const TensorBroadcastingOp<Broadcast, ArgType>, Device>
       EIGEN_ALIGN_MAX typename internal::remove_const<CoeffReturnType>::type values[PacketSize];
       values[0] = m_impl.coeff(inputIndex);
       for (int i = 1; i < PacketSize; ++i) {
-        values[i] = coeffRowMajor(originalIndex+i);
+        if (innermostLoc + i < m_impl.dimensions()[NumDims-1]) {
+          values[i] = m_impl.coeff(inputIndex+i);
+        } else {
+          values[i] = coeffRowMajor(originalIndex+i);
+        }
       }
       PacketReturnType rslt = internal::pload<PacketReturnType>(values);
       return rslt;
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionBlocking.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionBlocking.h
index 4853dd37b..a1e292108 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionBlocking.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionBlocking.h
@@ -78,7 +78,7 @@ class TensorXsmmContractionBlocking {
       outer_n_ = outer_n_ != 0 ? outer_n_ : n;
     }
 #else
-    // Defaults, possibly overriden per-platform.
+    // Defaults, possibly overridden per-platform.
     copyA_ = true;
     copyB_ = false;
 
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
index d30cc96ab..3c007b183 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
@@ -350,7 +350,7 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
         // Normal number of notifications for k slice switch is
         // nm_ + nn_ + nm_ * nn_. However, first P - 1 slices will receive only
         // nm_ + nn_ notifications, because they will not receive notifications
-        // from preceeding kernels.
+        // from preceding kernels.
         state_switch_[x] =
             x == 0
                 ? 1
@@ -530,7 +530,7 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
 
     void kernel(Index m, Index n, Index k) {
       // Note: order of iteration matters here. Iteration over m is innermost
-      // because we want to reuse the same packed rhs in consequetive tasks
+      // because we want to reuse the same packed rhs in consecutive tasks
       // (rhs fits into L2$ while lhs only into L3$).
       const Index nend = n * gn_ + gn(n);
       const Index mend = m * gm_ + gm(m);
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorCostModel.h b/unsupported/Eigen/CXX11/src/Tensor/TensorCostModel.h
index b148dae39..bb63baee2 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorCostModel.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorCostModel.h
@@ -195,7 +195,7 @@ class TensorCostModel {
     // 11 is L2 cache latency on Haswell.
     // We don't know whether data is in L1, L2 or L3. But we are most interested
     // in single-threaded computational time around 100us-10ms (smaller time
-    // is too small for parallelization, larger time is not intersting
+    // is too small for parallelization, larger time is not interesting
     // either because we are probably using all available threads already).
     // And for the target time range, L2 seems to be what matters. Data set
     // fitting into L1 is too small to take noticeable time. Data set fitting
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceSycl.h b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceSycl.h
index 6158acbd9..e7beb2c82 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceSycl.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorDeviceSycl.h
@@ -286,7 +286,7 @@ m_queue(cl::sycl::queue(s, [&](cl::sycl::exception_list l) {
     tileSize =static_cast<Index>(m_queue.get_device(). template get_info<cl::sycl::info::device::max_work_group_size>());
     auto s=  m_queue.get_device().template get_info<cl::sycl::info::device::vendor>();
     std::transform(s.begin(), s.end(), s.begin(), ::tolower);
-    if(m_queue.get_device().is_cpu()){ // intel doesnot allow to use max workgroup size
+    if(m_queue.get_device().is_cpu()){ // intel doesn't allow to use max workgroup size
       tileSize=std::min(static_cast<Index>(256), static_cast<Index>(tileSize));
     }
     rng = n;
@@ -303,7 +303,7 @@ m_queue(cl::sycl::queue(s, [&](cl::sycl::exception_list l) {
   template<typename Index>
   EIGEN_STRONG_INLINE void parallel_for_setup(Index dim0, Index dim1, Index &tileSize0, Index &tileSize1, Index &rng0, Index &rng1, Index &GRange0, Index &GRange1)  const {
     Index max_workgroup_Size = static_cast<Index>(maxSyclThreadsPerBlock());
-    if(m_queue.get_device().is_cpu()){ // intel doesnot allow to use max workgroup size
+    if(m_queue.get_device().is_cpu()){ // intel doesn't allow to use max workgroup size
       max_workgroup_Size=std::min(static_cast<Index>(256), static_cast<Index>(max_workgroup_Size));
     }
     Index pow_of_2 = static_cast<Index>(std::log2(max_workgroup_Size));
@@ -331,7 +331,7 @@ m_queue(cl::sycl::queue(s, [&](cl::sycl::exception_list l) {
   template<typename Index>
   EIGEN_STRONG_INLINE void parallel_for_setup(Index dim0, Index dim1,Index dim2, Index &tileSize0, Index &tileSize1, Index &tileSize2, Index &rng0, Index &rng1, Index &rng2, Index &GRange0, Index &GRange1, Index &GRange2)  const {
     Index max_workgroup_Size = static_cast<Index>(maxSyclThreadsPerBlock());
-    if(m_queue.get_device().is_cpu()){ // intel doesnot allow to use max workgroup size
+    if(m_queue.get_device().is_cpu()){ // intel doesn't allow to use max workgroup size
       max_workgroup_Size=std::min(static_cast<Index>(256), static_cast<Index>(max_workgroup_Size));
     }
     Index pow_of_2 = static_cast<Index>(std::log2(max_workgroup_Size));
@@ -377,7 +377,7 @@ m_queue(cl::sycl::queue(s, [&](cl::sycl::exception_list l) {
   EIGEN_STRONG_INLINE int majorDeviceVersion() const { return 1; }
 
   EIGEN_STRONG_INLINE unsigned long maxSyclThreadsPerMultiProcessor() const {
-    // OpenCL doesnot have such concept
+    // OpenCL doesn't have such concept
     return 2;
   }
 
@@ -519,7 +519,7 @@ struct SyclDevice {
     return m_queue_stream->maxSyclThreadsPerBlock();
   }
   EIGEN_STRONG_INLINE unsigned long maxSyclThreadsPerMultiProcessor() const {
-    // OpenCL doesnot have such concept
+    // OpenCL doesn't have such concept
     return m_queue_stream->maxSyclThreadsPerMultiProcessor();
   //  return stream_->deviceProperties().maxThreadsPerMultiProcessor;
   }
@@ -544,7 +544,7 @@ struct SyclDevice {
 };
 // This is used as a distingushable device inside the kernel as the sycl device class is not Standard layout.
 // This is internal and must not be used by user. This dummy device allow us to specialise the tensor evaluator
-// inside the kenrel. So we can have two types of eval for host and device. This is required for TensorArgMax operation
+// inside the kernel. So we can have two types of eval for host and device. This is required for TensorArgMax operation
 struct SyclKernelDevice:DefaultDevice{};
 
 }  // end namespace Eigen
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h b/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h
index f81da318c..d6ab4d997 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h
@@ -274,7 +274,7 @@ struct TensorEvaluator<const TensorFFTOp<FFT, ArgType, FFTResultType, FFTDir>, D
           }
         }
 
-        // processs the line
+        // process the line
         if (is_power_of_two) {
           processDataLineCooleyTukey(line_buf, line_len, log_len);
         }
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h b/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h
index 354bbe8d1..6c237bac3 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorForwardDeclarations.h
@@ -12,7 +12,7 @@
 
 namespace Eigen {
 
-// MakePointer class is used as a container of the adress space of the pointer
+// MakePointer class is used as a container of the address space of the pointer
 // on the host and on the device. From the host side it generates the T* pointer
 // and when EIGEN_USE_SYCL is used it construct a buffer with a map_allocator to
 // T* m_data on the host. It is always called on the device.
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorImagePatch.h b/unsupported/Eigen/CXX11/src/Tensor/TensorImagePatch.h
index 91d4ead28..f0f7c7826 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorImagePatch.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorImagePatch.h
@@ -272,8 +272,8 @@ struct TensorEvaluator<const TensorImagePatchOp<Rows, Cols, ArgType>, Device>
           break;
         default:
           eigen_assert(false && "unexpected padding");
-          m_outputCols=0; // silence the uninitialised warnig;
-          m_outputRows=0; //// silence the uninitialised warnig;
+          m_outputCols=0; // silence the uninitialised warning;
+          m_outputRows=0; //// silence the uninitialised warning;
       }
     }
     eigen_assert(m_outputRows > 0);
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h b/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h
index bf5c532ff..25ba2001e 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h
@@ -167,7 +167,7 @@ struct TensorIntDivisor {
     shift2 = log_div > 1 ? log_div-1 : 0;
   }
 
-  // Must have 0 <= numerator. On platforms that dont support the __uint128_t
+  // Must have 0 <= numerator. On platforms that don't support the __uint128_t
   // type numerator should also be less than 2^32-1.
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T divide(const T numerator) const {
     eigen_assert(static_cast<typename UnsignedTraits<T>::type>(numerator) < NumTraits<UnsignedType>::highest()/2);
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionSycl.h b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionSycl.h
index 94899252b..a379f5a94 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorReductionSycl.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorReductionSycl.h
@@ -106,7 +106,7 @@ struct FullReducer<Self, Op, const Eigen::SyclDevice, Vectorizable> {
     /// if the shared memory is less than the GRange, we set shared_mem size to the TotalSize and in this case one kernel would be created for recursion to reduce all to one.
     if (GRange < outTileSize) outTileSize=GRange;
     /// creating the shared memory for calculating reduction.
-    /// This one is used to collect all the reduced value of shared memory as we dont have global barrier on GPU. Once it is saved we can
+    /// This one is used to collect all the reduced value of shared memory as we don't have global barrier on GPU. Once it is saved we can
     /// recursively apply reduction on it in order to reduce the whole.
     auto temp_global_buffer =cl::sycl::buffer<CoeffReturnType, 1>(cl::sycl::range<1>(GRange));
     typedef typename Eigen::internal::remove_all<decltype(self.xprDims())>::type Dims;
@@ -150,7 +150,7 @@ struct InnerReducer<Self, Op, const Eigen::SyclDevice> {
 
     // getting final out buffer at the moment the created buffer is true because there is no need for assign
     /// creating the shared memory for calculating reduction.
-    /// This one is used to collect all the reduced value of shared memory as we dont have global barrier on GPU. Once it is saved we can
+    /// This one is used to collect all the reduced value of shared memory as we don't have global barrier on GPU. Once it is saved we can
     /// recursively apply reduction on it in order to reduce the whole.
       dev.parallel_for_setup(num_coeffs_to_preserve, tileSize, range, GRange);
       dev.sycl_queue().submit([&](cl::sycl::handler &cgh) {
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorRef.h b/unsupported/Eigen/CXX11/src/Tensor/TensorRef.h
index 99245f778..b2b4fd8d3 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorRef.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorRef.h
@@ -31,7 +31,7 @@ class TensorLazyBaseEvaluator {
   int refCount() const { return m_refcount; }
 
  private:
-  // No copy, no assigment;
+  // No copy, no assignment;
   TensorLazyBaseEvaluator(const TensorLazyBaseEvaluator& other);
   TensorLazyBaseEvaluator& operator = (const TensorLazyBaseEvaluator& other);
 
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorSyclExtractFunctors.h b/unsupported/Eigen/CXX11/src/Tensor/TensorSyclExtractFunctors.h
index a7905706d..a248e303b 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorSyclExtractFunctors.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorSyclExtractFunctors.h
@@ -117,7 +117,7 @@ SYCLEXTRFUNCTERNARY()
 
 
 
-//TensorCustomOp must be specialised otherewise it will be captured by UnaryCategory while its action is different
+//TensorCustomOp must be specialised otherwise it will be captured by UnaryCategory while its action is different
 //from the UnaryCategory and it is similar to the general FunctorExtractor.
 /// specialisation of TensorCustomOp
 #define SYCLEXTRFUNCCUSTOMUNARYOP(CVQual)\
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorSyclFunctors.h b/unsupported/Eigen/CXX11/src/Tensor/TensorSyclFunctors.h
index e5b892f2e..a447c3f88 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorSyclFunctors.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorSyclFunctors.h
@@ -80,7 +80,7 @@ template < typename HostExpr, typename FunctorExpr, typename Tuple_of_Acc, typen
     typedef typename ConvertToDeviceExpression<const HostExpr>::Type DevExpr;
     auto device_expr = createDeviceExpression<DevExpr, PlaceHolderExpr>(functors, tuple_of_accessors);
     /// reduction cannot be captured automatically through our device conversion recursion. The reason is that reduction has two behaviour
-    /// the first behaviour is when it is used as a root to lauch the sub-kernel. The second one is when it is treated as a leafnode to pass the
+    /// the first behaviour is when it is used as a root to launch the sub-kernel. The second one is when it is treated as a leafnode to pass the
     /// calculated result to its parent kernel. While the latter is automatically detected through our device expression generator. The former is created here.
     const auto device_self_expr= Eigen::TensorReductionOp<Op, Dims, decltype(device_expr.expr) ,MakeGlobalPointer>(device_expr.expr, dims, functor);
     /// This is the evaluator for device_self_expr. This is exactly similar to the self which has been passed to run function. The difference is
@@ -121,7 +121,7 @@ class ReductionFunctor<HostExpr, FunctorExpr, Tuple_of_Acc, Dims, Eigen::interna
     typedef typename ConvertToDeviceExpression<const HostExpr>::Type DevExpr;
     auto device_expr = createDeviceExpression<DevExpr, PlaceHolderExpr>(functors, tuple_of_accessors);
     /// reduction cannot be captured automatically through our device conversion recursion. The reason is that reduction has two behaviour
-    /// the first behaviour is when it is used as a root to lauch the sub-kernel. The second one is when it is treated as a leafnode to pass the
+    /// the first behaviour is when it is used as a root to launch the sub-kernel. The second one is when it is treated as a leafnode to pass the
     /// calculated result to its parent kernel. While the latter is automatically detected through our device expression generator. The former is created here.
     const auto device_self_expr= Eigen::TensorReductionOp<Op, Dims, decltype(device_expr.expr) ,MakeGlobalPointer>(device_expr.expr, dims, functor);
     /// This is the evaluator for device_self_expr. This is exactly similar to the self which has been passed to run function. The difference is
@@ -168,7 +168,7 @@ public:
     typedef typename TensorSycl::internal::ConvertToDeviceExpression<const HostExpr>::Type DevExpr;
     auto device_expr = TensorSycl::internal::createDeviceExpression<DevExpr, PlaceHolderExpr>(functors, tuple_of_accessors);
     /// reduction cannot be captured automatically through our device conversion recursion. The reason is that reduction has two behaviour
-    /// the first behaviour is when it is used as a root to lauch the sub-kernel. The second one is when it is treated as a leafnode to pass the
+    /// the first behaviour is when it is used as a root to launch the sub-kernel. The second one is when it is treated as a leafnode to pass the
     /// calculated result to its parent kernel. While the latter is automatically detected through our device expression generator. The former is created here.
     const auto device_self_expr= Eigen::TensorReductionOp<Op, Dims, decltype(device_expr.expr) ,MakeGlobalPointer>(device_expr.expr, dims, op);
     /// This is the evaluator for device_self_expr. This is exactly similar to the self which has been passed to run function. The difference is
@@ -215,7 +215,7 @@ public:
     typedef typename TensorSycl::internal::ConvertToDeviceExpression<const HostExpr>::Type DevExpr;
     auto device_expr = TensorSycl::internal::createDeviceExpression<DevExpr, PlaceHolderExpr>(functors, tuple_of_accessors);
     /// reduction cannot be captured automatically through our device conversion recursion. The reason is that reduction has two behaviour
-    /// the first behaviour is when it is used as a root to lauch the sub-kernel. The second one is when it is treated as a leafnode to pass the
+    /// the first behaviour is when it is used as a root to launch the sub-kernel. The second one is when it is treated as a leafnode to pass the
     /// calculated result to its parent kernel. While the latter is automatically detected through our device expression generator. The former is created here.
     const auto device_self_expr= Eigen::TensorReductionOp<Op, Dims, decltype(device_expr.expr) ,MakeGlobalPointer>(device_expr.expr, dims, op);
     /// This is the evaluator for device_self_expr. This is exactly similar to the self which has been passed to run function. The difference is
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorSyclTuple.h b/unsupported/Eigen/CXX11/src/Tensor/TensorSyclTuple.h
index 58ab0f0d5..9e6c3e4fa 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorSyclTuple.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorSyclTuple.h
@@ -143,7 +143,7 @@ struct IndexList {};
 /// \brief Collects internal details for generating index ranges [MIN, MAX)
 /// Declare primary template for index range builder
 /// \tparam MIN is the starting index in the tuple
-/// \tparam N represents sizeof..(elemens)- sizeof...(Is)
+/// \tparam N represents sizeof..(elements)- sizeof...(Is)
 /// \tparam Is... are the list of generated index so far
 template <size_t MIN, size_t N, size_t... Is>
 struct RangeBuilder;
@@ -161,7 +161,7 @@ struct RangeBuilder<MIN, MIN, Is...> {
 /// in this case we are recursively subtracting N by one and adding one
 /// index to Is... list until MIN==N
 /// \tparam MIN is the starting index in the tuple
-/// \tparam N represents sizeof..(elemens)- sizeof...(Is)
+/// \tparam N represents sizeof..(elements)- sizeof...(Is)
 /// \tparam Is... are the list of generated index so far
 template <size_t MIN, size_t N, size_t... Is>
 struct RangeBuilder : public RangeBuilder<MIN, N - 1, N - 1, Is...> {};
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorVolumePatch.h b/unsupported/Eigen/CXX11/src/Tensor/TensorVolumePatch.h
index 51c099591..ef199bfb6 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorVolumePatch.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorVolumePatch.h
@@ -568,7 +568,7 @@ struct TensorEvaluator<const TensorVolumePatchOp<Planes, Rows, Cols, ArgType>, D
 
   Dimensions m_dimensions;
 
-  // Parameters passed to the costructor.
+  // Parameters passed to the constructor.
   Index m_plane_strides;
   Index m_row_strides;
   Index m_col_strides;
diff --git a/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h b/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h
index 0fe0b7c46..04d6d6b23 100644
--- a/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h
+++ b/unsupported/Eigen/CXX11/src/TensorSymmetry/util/TemplateGroupTheory.h
@@ -241,7 +241,7 @@ struct dimino_first_step_elements
   * multiplying all elements in the given subgroup with the new
   * coset representative. Note that the first element of the
   * subgroup is always the identity element, so the first element of
-  * ther result of this template is going to be the coset
+  * the result of this template is going to be the coset
   * representative itself.
   *
   * Note that this template accepts an additional boolean parameter
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/EventCount.h b/unsupported/Eigen/CXX11/src/ThreadPool/EventCount.h
index 71d55552d..0a7181102 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/EventCount.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/EventCount.h
@@ -33,10 +33,10 @@ namespace Eigen {
 //   ec.Notify(true);
 //
 // Notify is cheap if there are no waiting threads. Prewait/CommitWait are not
-// cheap, but they are executed only if the preceeding predicate check has
+// cheap, but they are executed only if the preceding predicate check has
 // failed.
 //
-// Algorihtm outline:
+// Algorithm outline:
 // There are two main variables: predicate (managed by user) and state_.
 // Operation closely resembles Dekker mutual algorithm:
 // https://en.wikipedia.org/wiki/Dekker%27s_algorithm
@@ -79,7 +79,7 @@ class EventCount {
     uint64_t state = state_.load(std::memory_order_seq_cst);
     for (;;) {
       if (int64_t((state & kEpochMask) - epoch) < 0) {
-        // The preceeding waiter has not decided on its fate. Wait until it
+        // The preceding waiter has not decided on its fate. Wait until it
         // calls either CancelWait or CommitWait, or is notified.
         EIGEN_THREAD_YIELD();
         state = state_.load(std::memory_order_seq_cst);
@@ -110,7 +110,7 @@ class EventCount {
     uint64_t state = state_.load(std::memory_order_relaxed);
     for (;;) {
       if (int64_t((state & kEpochMask) - epoch) < 0) {
-        // The preceeding waiter has not decided on its fate. Wait until it
+        // The preceding waiter has not decided on its fate. Wait until it
         // calls either CancelWait or CommitWait, or is notified.
         EIGEN_THREAD_YIELD();
         state = state_.load(std::memory_order_relaxed);
diff --git a/unsupported/Eigen/CXX11/src/ThreadPool/RunQueue.h b/unsupported/Eigen/CXX11/src/ThreadPool/RunQueue.h
index 49d0cdc36..cb3690a2e 100644
--- a/unsupported/Eigen/CXX11/src/ThreadPool/RunQueue.h
+++ b/unsupported/Eigen/CXX11/src/ThreadPool/RunQueue.h
@@ -198,7 +198,7 @@ class RunQueue {
   };
   std::mutex mutex_;
   // Low log(kSize) + 1 bits in front_ and back_ contain rolling index of
-  // front/back, repsectively. The remaining bits contain modification counters
+  // front/back, respectively. The remaining bits contain modification counters
   // that are incremented on Push operations. This allows us to (1) distinguish
   // between empty and full conditions (if we would use log(kSize) bits for
   // position, these conditions would be indistinguishable); (2) obtain
diff --git a/unsupported/Eigen/CXX11/src/util/EmulateArray.h b/unsupported/Eigen/CXX11/src/util/EmulateArray.h
index 18b76350b..5b01c5fb7 100644
--- a/unsupported/Eigen/CXX11/src/util/EmulateArray.h
+++ b/unsupported/Eigen/CXX11/src/util/EmulateArray.h
@@ -219,7 +219,7 @@ template<class T, std::size_t N> struct array_size<const array<T,N>& > {
 
 #else
 
-// The compiler supports c++11, and we're not targetting cuda: use std::array as Eigen::array
+// The compiler supports c++11, and we're not targeting cuda: use std::array as Eigen::array
 #include <array>
 namespace Eigen {
 
diff --git a/unsupported/Eigen/NonLinearOptimization b/unsupported/Eigen/NonLinearOptimization
index 600ab4c12..c22b89054 100644
--- a/unsupported/Eigen/NonLinearOptimization
+++ b/unsupported/Eigen/NonLinearOptimization
@@ -35,7 +35,7 @@
   * a zero for the system (Powell hybrid "dogleg" method).
   *
   * This code is a port of minpack (http://en.wikipedia.org/wiki/MINPACK).
-  * Minpack is a very famous, old, robust and well-reknown package, written in 
+  * Minpack is a very famous, old, robust and well renowned package, written in
   * fortran. Those implementations have been carefully tuned, tested, and used
   * for several decades.
   *
@@ -63,7 +63,7 @@
   * Other tests were added by myself at the very beginning of the 
   * process and check the results for levenberg-marquardt using the reference data 
   * on http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml. Since then i've 
-  * carefully checked that the same results were obtained when modifiying the 
+  * carefully checked that the same results were obtained when modifying the
   * code. Please note that we do not always get the exact same decimals as they do,
   * but this is ok : they use 128bits float, and we do the tests using the C type 'double',
   * which is 64 bits on most platforms (x86 and amd64, at least).
diff --git a/unsupported/Eigen/OpenGLSupport b/unsupported/Eigen/OpenGLSupport
index 87f50947d..11d99567e 100644
--- a/unsupported/Eigen/OpenGLSupport
+++ b/unsupported/Eigen/OpenGLSupport
@@ -25,7 +25,7 @@ namespace Eigen {
   *
   * This module provides wrapper functions for a couple of OpenGL functions
   * which simplify the way to pass Eigen's object to openGL.
-  * Here is an exmaple:
+  * Here is an example:
   * 
   * \code
   * // You need to add path_to_eigen/unsupported to your include path.
diff --git a/unsupported/Eigen/SpecialFunctions b/unsupported/Eigen/SpecialFunctions
index 482ec6e6f..9441ba8f5 100644
--- a/unsupported/Eigen/SpecialFunctions
+++ b/unsupported/Eigen/SpecialFunctions
@@ -29,6 +29,8 @@ namespace Eigen {
   * - erfc
   * - lgamma
   * - igamma
+  * - igamma_der_a
+  * - gamma_sample_der_alpha
   * - igammac
   * - digamma
   * - polygamma
diff --git a/unsupported/Eigen/src/BVH/KdBVH.h b/unsupported/Eigen/src/BVH/KdBVH.h
index 1b8d75865..13f792cd0 100644
--- a/unsupported/Eigen/src/BVH/KdBVH.h
+++ b/unsupported/Eigen/src/BVH/KdBVH.h
@@ -170,7 +170,7 @@ private:
   typedef internal::vector_int_pair<Scalar, Dim> VIPair;
   typedef std::vector<VIPair, aligned_allocator<VIPair> > VIPairList;
   typedef Matrix<Scalar, Dim, 1> VectorType;
-  struct VectorComparator //compares vectors, or, more specificall, VIPairs along a particular dimension
+  struct VectorComparator //compares vectors, or more specifically, VIPairs along a particular dimension
   {
     VectorComparator(int inDim) : dim(inDim) {}
     inline bool operator()(const VIPair &v1, const VIPair &v2) const { return v1.first[dim] < v2.first[dim]; }
diff --git a/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h b/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
index 866a8a460..9f7bff764 100644
--- a/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
+++ b/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
@@ -300,7 +300,7 @@ public:
 
   /** \brief Reports whether previous computation was successful.
    *
-   * \returns \c Success if computation was succesful, \c NoConvergence otherwise.
+   * \returns \c Success if computation was successful, \c NoConvergence otherwise.
    */
   ComputationInfo info() const
   {
diff --git a/unsupported/Eigen/src/EulerAngles/EulerSystem.h b/unsupported/Eigen/src/EulerAngles/EulerSystem.h
index 28f52da61..65c2e94c7 100644
--- a/unsupported/Eigen/src/EulerAngles/EulerSystem.h
+++ b/unsupported/Eigen/src/EulerAngles/EulerSystem.h
@@ -12,7 +12,7 @@
 
 namespace Eigen
 {
-  // Forward declerations
+  // Forward declarations
   template <typename _Scalar, class _System>
   class EulerAngles;
   
diff --git a/unsupported/Eigen/src/IterativeSolvers/ConstrainedConjGrad.h b/unsupported/Eigen/src/IterativeSolvers/ConstrainedConjGrad.h
index dc0093eb9..37d5b4c6c 100644
--- a/unsupported/Eigen/src/IterativeSolvers/ConstrainedConjGrad.h
+++ b/unsupported/Eigen/src/IterativeSolvers/ConstrainedConjGrad.h
@@ -99,7 +99,7 @@ void pseudo_inverse(const CMatrix &C, CINVMatrix &CINV)
 /** \ingroup IterativeSolvers_Module
   * Constrained conjugate gradient
   *
-  * Computes the minimum of \f$ 1/2((Ax).x) - bx \f$ under the contraint \f$ Cx \le f \f$
+  * Computes the minimum of \f$ 1/2((Ax).x) - bx \f$ under the constraint \f$ Cx \le f \f$
   */
 template<typename TMatrix, typename CMatrix,
          typename VectorX, typename VectorB, typename VectorF>
diff --git a/unsupported/Eigen/src/IterativeSolvers/DGMRES.h b/unsupported/Eigen/src/IterativeSolvers/DGMRES.h
index d603ba336..be039e07f 100644
--- a/unsupported/Eigen/src/IterativeSolvers/DGMRES.h
+++ b/unsupported/Eigen/src/IterativeSolvers/DGMRES.h
@@ -39,7 +39,6 @@ template <typename VectorType, typename IndexType>
 void sortWithPermutation (VectorType& vec, IndexType& perm, typename IndexType::Scalar& ncut)
 {
   eigen_assert(vec.size() == perm.size());
-  typedef typename IndexType::Scalar Index; 
   bool flag; 
   for (Index k  = 0; k < ncut; k++)
   {
@@ -112,7 +111,6 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >
     using Base::_solve_impl;
     typedef _MatrixType MatrixType;
     typedef typename MatrixType::Scalar Scalar;
-    typedef typename MatrixType::Index Index;
     typedef typename MatrixType::StorageIndex StorageIndex;
     typedef typename MatrixType::RealScalar RealScalar;
     typedef _Preconditioner Preconditioner;
@@ -146,7 +144,7 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >
   void _solve_with_guess_impl(const Rhs& b, Dest& x) const
   {    
     bool failed = false;
-    for(int j=0; j<b.cols(); ++j)
+    for(Index j=0; j<b.cols(); ++j)
     {
       m_iterations = Base::maxIterations();
       m_error = Base::m_tolerance;
@@ -170,17 +168,17 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >
   /** 
    * Get the restart value
     */
-  int restart() { return m_restart; }
+  Index restart() { return m_restart; }
   
   /** 
    * Set the restart value (default is 30)  
    */
-  void set_restart(const int restart) { m_restart=restart; }
+  void set_restart(const Index restart) { m_restart=restart; }
   
   /** 
    * Set the number of eigenvalues to deflate at each restart 
    */
-  void setEigenv(const int neig) 
+  void setEigenv(const Index neig) 
   {
     m_neig = neig;
     if (neig+1 > m_maxNeig) m_maxNeig = neig+1; // To allow for complex conjugates
@@ -189,12 +187,12 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >
   /** 
    * Get the size of the deflation subspace size
    */ 
-  int deflSize() {return m_r; }
+  Index deflSize() {return m_r; }
   
   /**
    * Set the maximum size of the deflation subspace
    */
-  void setMaxEigenv(const int maxNeig) { m_maxNeig = maxNeig; }
+  void setMaxEigenv(const Index maxNeig) { m_maxNeig = maxNeig; }
   
   protected:
     // DGMRES algorithm 
@@ -202,27 +200,27 @@ class DGMRES : public IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> >
     void dgmres(const MatrixType& mat,const Rhs& rhs, Dest& x, const Preconditioner& precond) const;
     // Perform one cycle of GMRES
     template<typename Dest>
-    int dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, int& nbIts) const; 
+    Index dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, Index& nbIts) const; 
     // Compute data to use for deflation 
-    int dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const;
+    Index dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const;
     // Apply deflation to a vector
     template<typename RhsType, typename DestType>
-    int dgmresApplyDeflation(const RhsType& In, DestType& Out) const; 
+    Index dgmresApplyDeflation(const RhsType& In, DestType& Out) const; 
     ComplexVector schurValues(const ComplexSchur<DenseMatrix>& schurofH) const;
     ComplexVector schurValues(const RealSchur<DenseMatrix>& schurofH) const;
     // Init data for deflation
     void dgmresInitDeflation(Index& rows) const; 
     mutable DenseMatrix m_V; // Krylov basis vectors
     mutable DenseMatrix m_H; // Hessenberg matrix 
-    mutable DenseMatrix m_Hes; // Initial hessenberg matrix wihout Givens rotations applied
+    mutable DenseMatrix m_Hes; // Initial hessenberg matrix without Givens rotations applied
     mutable Index m_restart; // Maximum size of the Krylov subspace
     mutable DenseMatrix m_U; // Vectors that form the basis of the invariant subspace 
     mutable DenseMatrix m_MU; // matrix operator applied to m_U (for next cycles)
     mutable DenseMatrix m_T; /* T=U^T*M^{-1}*A*U */
     mutable PartialPivLU<DenseMatrix> m_luT; // LU factorization of m_T
     mutable StorageIndex m_neig; //Number of eigenvalues to extract at each restart
-    mutable int m_r; // Current number of deflated eigenvalues, size of m_U
-    mutable int m_maxNeig; // Maximum number of eigenvalues to deflate
+    mutable Index m_r; // Current number of deflated eigenvalues, size of m_U
+    mutable Index m_maxNeig; // Maximum number of eigenvalues to deflate
     mutable RealScalar m_lambdaN; //Modulus of the largest eigenvalue of A
     mutable bool m_isDeflAllocated;
     mutable bool m_isDeflInitialized;
@@ -244,13 +242,13 @@ void DGMRES<_MatrixType, _Preconditioner>::dgmres(const MatrixType& mat,const Rh
               const Preconditioner& precond) const
 {
   //Initialization
-  int n = mat.rows(); 
+  Index n = mat.rows(); 
   DenseVector r0(n); 
-  int nbIts = 0; 
+  Index nbIts = 0; 
   m_H.resize(m_restart+1, m_restart);
   m_Hes.resize(m_restart, m_restart);
   m_V.resize(n,m_restart+1);
-  //Initial residual vector and intial norm
+  //Initial residual vector and initial norm
   x = precond.solve(x);
   r0 = rhs - mat * x; 
   RealScalar beta = r0.norm(); 
@@ -284,7 +282,7 @@ void DGMRES<_MatrixType, _Preconditioner>::dgmres(const MatrixType& mat,const Rh
  */
 template< typename _MatrixType, typename _Preconditioner>
 template<typename Dest>
-int DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, int& nbIts) const
+Index DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, const Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, const RealScalar& normRhs, Index& nbIts) const
 {
   //Initialization 
   DenseVector g(m_restart+1); // Right hand side of the least square problem
@@ -293,8 +291,8 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, con
   m_V.col(0) = r0/beta; 
   m_info = NoConvergence; 
   std::vector<JacobiRotation<Scalar> >gr(m_restart); // Givens rotations
-  int it = 0; // Number of inner iterations 
-  int n = mat.rows();
+  Index it = 0; // Number of inner iterations 
+  Index n = mat.rows();
   DenseVector tv1(n), tv2(n);  //Temporary vectors
   while (m_info == NoConvergence && it < m_restart && nbIts < m_iterations)
   {    
@@ -312,7 +310,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, con
    
     // Orthogonalize it with the previous basis in the basis using modified Gram-Schmidt
     Scalar coef; 
-    for (int i = 0; i <= it; ++i)
+    for (Index i = 0; i <= it; ++i)
     { 
       coef = tv1.dot(m_V.col(i));
       tv1 = tv1 - coef * m_V.col(i); 
@@ -328,7 +326,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresCycle(const MatrixType& mat, con
     // FIXME Check for happy breakdown 
     
     // Update Hessenberg matrix with Givens rotations
-    for (int i = 1; i <= it; ++i) 
+    for (Index i = 1; i <= it; ++i) 
     {
       m_H.col(it).applyOnTheLeft(i-1,i,gr[i-1].adjoint());
     }
@@ -418,7 +416,7 @@ inline typename DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_Matr
 }
 
 template< typename _MatrixType, typename _Preconditioner>
-int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const
+Index DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const MatrixType& mat, const Preconditioner& precond, const Index& it, StorageIndex& neig) const
 {
   // First, find the Schur form of the Hessenberg matrix H
   typename internal::conditional<NumTraits<Scalar>::IsComplex, ComplexSchur<DenseMatrix>, RealSchur<DenseMatrix> >::type schurofH; 
@@ -433,8 +431,8 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri
   
   // Reorder the absolute values of Schur values
   DenseRealVector modulEig(it); 
-  for (int j=0; j<it; ++j) modulEig(j) = std::abs(eig(j)); 
-  perm.setLinSpaced(it,0,it-1);
+  for (Index j=0; j<it; ++j) modulEig(j) = std::abs(eig(j)); 
+  perm.setLinSpaced(it,0,internal::convert_index<StorageIndex>(it-1));
   internal::sortWithPermutation(modulEig, perm, neig);
   
   if (!m_lambdaN)
@@ -442,7 +440,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri
     m_lambdaN = (std::max)(modulEig.maxCoeff(), m_lambdaN);
   }
   //Count the real number of extracted eigenvalues (with complex conjugates)
-  int nbrEig = 0; 
+  Index nbrEig = 0; 
   while (nbrEig < neig)
   {
     if(eig(perm(it-nbrEig-1)).imag() == RealScalar(0)) nbrEig++; 
@@ -451,7 +449,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri
   // Extract the  Schur vectors corresponding to the smallest Ritz values
   DenseMatrix Sr(it, nbrEig); 
   Sr.setZero();
-  for (int j = 0; j < nbrEig; j++)
+  for (Index j = 0; j < nbrEig; j++)
   {
     Sr.col(j) = schurofH.matrixU().col(perm(it-j-1));
   }
@@ -462,8 +460,8 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri
   if (m_r)
   {
    // Orthogonalize X against m_U using modified Gram-Schmidt
-   for (int j = 0; j < nbrEig; j++)
-     for (int k =0; k < m_r; k++)
+   for (Index j = 0; j < nbrEig; j++)
+     for (Index k =0; k < m_r; k++)
       X.col(j) = X.col(j) - (m_U.col(k).dot(X.col(j)))*m_U.col(k); 
   }
   
@@ -473,7 +471,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri
     dgmresInitDeflation(m); 
   DenseMatrix MX(m, nbrEig);
   DenseVector tv1(m);
-  for (int j = 0; j < nbrEig; j++)
+  for (Index j = 0; j < nbrEig; j++)
   {
     tv1 = mat * X.col(j);
     MX.col(j) = precond.solve(tv1);
@@ -488,8 +486,8 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri
   }
   
   // Save X into m_U and m_MX in m_MU
-  for (int j = 0; j < nbrEig; j++) m_U.col(m_r+j) = X.col(j);
-  for (int j = 0; j < nbrEig; j++) m_MU.col(m_r+j) = MX.col(j);
+  for (Index j = 0; j < nbrEig; j++) m_U.col(m_r+j) = X.col(j);
+  for (Index j = 0; j < nbrEig; j++) m_MU.col(m_r+j) = MX.col(j);
   // Increase the size of the invariant subspace
   m_r += nbrEig; 
   
@@ -502,7 +500,7 @@ int DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(const Matri
 }
 template<typename _MatrixType, typename _Preconditioner>
 template<typename RhsType, typename DestType>
-int DGMRES<_MatrixType, _Preconditioner>::dgmresApplyDeflation(const RhsType &x, DestType &y) const
+Index DGMRES<_MatrixType, _Preconditioner>::dgmresApplyDeflation(const RhsType &x, DestType &y) const
 {
   DenseVector x1 = m_U.leftCols(m_r).transpose() * x; 
   y = x + m_U.leftCols(m_r) * ( m_lambdaN * m_luT.solve(x1) - x1);
diff --git a/unsupported/Eigen/src/LevenbergMarquardt/LMqrsolv.h b/unsupported/Eigen/src/LevenbergMarquardt/LMqrsolv.h
index ae9d793b1..123485817 100644
--- a/unsupported/Eigen/src/LevenbergMarquardt/LMqrsolv.h
+++ b/unsupported/Eigen/src/LevenbergMarquardt/LMqrsolv.h
@@ -73,7 +73,7 @@ void lmqrsolv(
             qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
             wa[k] = temp;
 
-            /*           accumulate the tranformation in the row of s. */
+            /*           accumulate the transformation in the row of s. */
             for (i = k+1; i<n; ++i) {
                 temp = givens.c() * s(i,k) + givens.s() * sdiag[i];
                 sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];
diff --git a/unsupported/Eigen/src/LevenbergMarquardt/LevenbergMarquardt.h b/unsupported/Eigen/src/LevenbergMarquardt/LevenbergMarquardt.h
index 995427978..5f64501be 100644
--- a/unsupported/Eigen/src/LevenbergMarquardt/LevenbergMarquardt.h
+++ b/unsupported/Eigen/src/LevenbergMarquardt/LevenbergMarquardt.h
@@ -233,9 +233,9 @@ class LevenbergMarquardt : internal::no_assignment_operator
     
     /** 
      * \brief Reports whether the minimization was successful
-     * \returns \c Success if the minimization was succesful,
+     * \returns \c Success if the minimization was successful,
      *         \c NumericalIssue if a numerical problem arises during the 
-     *          minimization process, for exemple during the QR factorization
+     *          minimization process, for example during the QR factorization
      *         \c NoConvergence if the minimization did not converge after 
      *          the maximum number of function evaluation allowed
      *          \c InvalidInput if the input matrix is invalid
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
index 85ab3d97c..03356998b 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixExponential.h
@@ -313,7 +313,7 @@ struct matrix_exp_computeUV<MatrixType, long double>
       matrix_exp_pade17(A, U, V);
     }
   
-#elif LDBL_MANT_DIG <= 112  // quadruple precison
+#elif LDBL_MANT_DIG <= 112  // quadruple precision
   
     if (l1norm < 1.639394610288918690547467954466970e-005L) {
       matrix_exp_pade3(arg, U, V);
diff --git a/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h b/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h
index ebc433d89..33609aea9 100644
--- a/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h
+++ b/unsupported/Eigen/src/MatrixFunctions/MatrixPower.h
@@ -81,7 +81,7 @@ class MatrixPowerParenthesesReturnValue : public ReturnByValue< MatrixPowerParen
  *
  * \note Currently this class is only used by MatrixPower. One may
  * insist that this be nested into MatrixPower. This class is here to
- * faciliate future development of triangular matrix functions.
+ * facilitate future development of triangular matrix functions.
  */
 template<typename MatrixType>
 class MatrixPowerAtomic : internal::noncopyable
diff --git a/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
index feafd62a8..4f2f560b3 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
@@ -61,7 +61,7 @@ void qrsolv(
             qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
             wa[k] = temp;
 
-            /*           accumulate the tranformation in the row of s. */
+            /*           accumulate the transformation in the row of s. */
             for (i = k+1; i<n; ++i) {
                 temp = givens.c() * s(i,k) + givens.s() * sdiag[i];
                 sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];
diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1updt.h b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
index f28766061..09fc65255 100644
--- a/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
+++ b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
@@ -22,7 +22,7 @@ void r1updt(
     Scalar temp;
     JacobiRotation<Scalar> givens;
 
-    // r1updt had a broader usecase, but we dont use it here. And, more
+    // r1updt had a broader usecase, but we don't use it here. And, more
     // importantly, we can not test it.
     eigen_assert(m==n);
     eigen_assert(u.size()==m);
diff --git a/unsupported/Eigen/src/Polynomials/Companion.h b/unsupported/Eigen/src/Polynomials/Companion.h
index e0af6ebe4..41a4efc2f 100644
--- a/unsupported/Eigen/src/Polynomials/Companion.h
+++ b/unsupported/Eigen/src/Polynomials/Companion.h
@@ -104,7 +104,7 @@ class companion
     /** 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
+     * colB and rowB are respectively the multipliers for
      * the column and the row in order to balance them.
      * */
     bool balanced( RealScalar colNorm, RealScalar rowNorm,
@@ -113,7 +113,7 @@ class companion
     /** 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
+     * colB and rowB are respectively the multipliers for
      * the column and the row in order to balance them.
      * */
     bool balancedR( RealScalar colNorm, RealScalar rowNorm,
diff --git a/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h b/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h
index a1f54ed35..bda057a85 100644
--- a/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h
+++ b/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h
@@ -41,7 +41,7 @@ public:
 
     /** Sets the relative threshold value used to prune zero coefficients during the decomposition.
      *
-     * Setting a value greater than zero speeds up computation, and yields to an imcomplete
+     * Setting a value greater than zero speeds up computation, and yields to an incomplete
      * factorization with fewer non zero coefficients. Such approximate factors are especially
      * useful to initialize an iterative solver.
      *
diff --git a/unsupported/Eigen/src/Skyline/SkylineMatrix.h b/unsupported/Eigen/src/Skyline/SkylineMatrix.h
index a2a8933ca..f77d79a04 100644
--- a/unsupported/Eigen/src/Skyline/SkylineMatrix.h
+++ b/unsupported/Eigen/src/Skyline/SkylineMatrix.h
@@ -206,26 +206,26 @@ public:
             if (col > row) //upper matrix
             {
                 const Index minOuterIndex = inner - m_data.upperProfile(inner);
-                eigen_assert(outer >= minOuterIndex && "you try to acces a coeff that do not exist in the storage");
+                eigen_assert(outer >= minOuterIndex && "You tried to access a coeff that does not exist in the storage");
                 return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
             }
             if (col < row) //lower matrix
             {
                 const Index minInnerIndex = outer - m_data.lowerProfile(outer);
-                eigen_assert(inner >= minInnerIndex && "you try to acces a coeff that do not exist in the storage");
+                eigen_assert(inner >= minInnerIndex && "You tried to access a coeff that does not exist in the storage");
                 return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
             }
         } else {
             if (outer > inner) //upper matrix
             {
                 const Index maxOuterIndex = inner + m_data.upperProfile(inner);
-                eigen_assert(outer <= maxOuterIndex && "you try to acces a coeff that do not exist in the storage");
+                eigen_assert(outer <= maxOuterIndex && "You tried to access a coeff that does not exist in the storage");
                 return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
             }
             if (outer < inner) //lower matrix
             {
                 const Index maxInnerIndex = outer + m_data.lowerProfile(outer);
-                eigen_assert(inner <= maxInnerIndex && "you try to acces a coeff that do not exist in the storage");
+                eigen_assert(inner <= maxInnerIndex && "You tried to access a coeff that does not exist in the storage");
                 return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
             }
         }
@@ -300,11 +300,11 @@ public:
 
         if (IsRowMajor) {
             const Index minInnerIndex = outer - m_data.lowerProfile(outer);
-            eigen_assert(inner >= minInnerIndex && "you try to acces a coeff that do not exist in the storage");
+            eigen_assert(inner >= minInnerIndex && "You tried to access a coeff that does not exist in the storage");
             return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
         } else {
             const Index maxInnerIndex = outer + m_data.lowerProfile(outer);
-            eigen_assert(inner <= maxInnerIndex && "you try to acces a coeff that do not exist in the storage");
+            eigen_assert(inner <= maxInnerIndex && "You tried to access a coeff that does not exist in the storage");
             return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
         }
     }
@@ -336,11 +336,11 @@ public:
 
         if (IsRowMajor) {
             const Index minOuterIndex = inner - m_data.upperProfile(inner);
-            eigen_assert(outer >= minOuterIndex && "you try to acces a coeff that do not exist in the storage");
+            eigen_assert(outer >= minOuterIndex && "You tried to access a coeff that does not exist in the storage");
             return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
         } else {
             const Index maxOuterIndex = inner + m_data.upperProfile(inner);
-            eigen_assert(outer <= maxOuterIndex && "you try to acces a coeff that do not exist in the storage");
+            eigen_assert(outer <= maxOuterIndex && "You tried to access a coeff that does not exist in the storage");
             return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
         }
     }
diff --git a/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h b/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h
index 037a13f86..3f1ff14ad 100644
--- a/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h
+++ b/unsupported/Eigen/src/SparseExtra/DynamicSparseMatrix.h
@@ -187,7 +187,7 @@ template<typename _Scalar, int _Options, typename _StorageIndex>
     /** Does nothing: provided for compatibility with SparseMatrix */
     inline void finalize() {}
 
-    /** Suppress all nonzeros which are smaller than \a reference under the tolerence \a epsilon */
+    /** Suppress all nonzeros which are smaller than \a reference under the tolerance \a epsilon */
     void prune(Scalar reference, RealScalar epsilon = NumTraits<RealScalar>::dummy_precision())
     {
       for (Index j=0; j<outerSize(); ++j)
@@ -224,21 +224,21 @@ template<typename _Scalar, int _Options, typename _StorageIndex>
       }
     }
 
-    /** The class DynamicSparseMatrix is deprectaed */
+    /** The class DynamicSparseMatrix is deprecated */
     EIGEN_DEPRECATED inline DynamicSparseMatrix()
       : m_innerSize(0), m_data(0)
     {
       eigen_assert(innerSize()==0 && outerSize()==0);
     }
 
-    /** The class DynamicSparseMatrix is deprectaed */
+    /** The class DynamicSparseMatrix is deprecated */
     EIGEN_DEPRECATED inline DynamicSparseMatrix(Index rows, Index cols)
       : m_innerSize(0)
     {
       resize(rows, cols);
     }
 
-    /** The class DynamicSparseMatrix is deprectaed */
+    /** The class DynamicSparseMatrix is deprecated */
     template<typename OtherDerived>
     EIGEN_DEPRECATED explicit inline DynamicSparseMatrix(const SparseMatrixBase<OtherDerived>& other)
       : m_innerSize(0)
diff --git a/unsupported/Eigen/src/SparseExtra/MarketIO.h b/unsupported/Eigen/src/SparseExtra/MarketIO.h
index 6d57ab2e9..1618b09a8 100644
--- a/unsupported/Eigen/src/SparseExtra/MarketIO.h
+++ b/unsupported/Eigen/src/SparseExtra/MarketIO.h
@@ -104,7 +104,7 @@ namespace internal
     out << value.real << " " << value.imag()<< "\n"; 
   }
 
-} // end namepsace internal
+} // end namespace internal
 
 inline bool getMarketHeader(const std::string& filename, int& sym, bool& iscomplex, bool& isvector)
 {
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h
index b7a9d035b..30cdf4751 100644
--- a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsArrayAPI.h
@@ -33,6 +33,48 @@ igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerive
   );
 }
 
+/** \cpp11 \returns an expression of the coefficient-wise igamma_der_a(\a a, \a x) to the given arrays.
+  *
+  * This function computes the coefficient-wise derivative of the incomplete
+  * gamma function with respect to the parameter a.
+  *
+  * \note This function supports only float and double scalar types in c++11
+  * mode. To support other scalar types,
+  * or float/double in non c++11 mode, the user has to provide implementations
+  * of igamma_der_a(T,T) for any scalar
+  * type T to be supported.
+  *
+  * \sa Eigen::igamma(), Eigen::lgamma()
+  */
+template <typename Derived, typename ExponentDerived>
+inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_der_a_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
+igamma_der_a(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) {
+  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_der_a_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
+    a.derived(),
+    x.derived());
+}
+
+/** \cpp11 \returns an expression of the coefficient-wise gamma_sample_der_alpha(\a alpha, \a sample) to the given arrays.
+  *
+  * This function computes the coefficient-wise derivative of the sample
+  * of a Gamma(alpha, 1) random variable with respect to the parameter alpha.
+  *
+  * \note This function supports only float and double scalar types in c++11
+  * mode. To support other scalar types,
+  * or float/double in non c++11 mode, the user has to provide implementations
+  * of gamma_sample_der_alpha(T,T) for any scalar
+  * type T to be supported.
+  *
+  * \sa Eigen::igamma(), Eigen::lgamma()
+  */
+template <typename AlphaDerived, typename SampleDerived>
+inline const Eigen::CwiseBinaryOp<Eigen::internal::scalar_gamma_sample_der_alpha_op<typename AlphaDerived::Scalar>, const AlphaDerived, const SampleDerived>
+gamma_sample_der_alpha(const Eigen::ArrayBase<AlphaDerived>& alpha, const Eigen::ArrayBase<SampleDerived>& sample) {
+  return Eigen::CwiseBinaryOp<Eigen::internal::scalar_gamma_sample_der_alpha_op<typename AlphaDerived::Scalar>, const AlphaDerived, const SampleDerived>(
+      alpha.derived(),
+      sample.derived());
+}
+
 /** \cpp11 \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
   *
   * This function computes the coefficient-wise complementary incomplete gamma function.
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h
index 8420f0174..3a63dcdd6 100644
--- a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsFunctors.h
@@ -41,6 +41,60 @@ struct functor_traits<scalar_igamma_op<Scalar> > {
   };
 };
 
+/** \internal
+  * \brief Template functor to compute the derivative of the incomplete gamma
+  * function igamma_der_a(a, x)
+  *
+  * \sa class CwiseBinaryOp, Cwise::igamma_der_a
+  */
+template <typename Scalar>
+struct scalar_igamma_der_a_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_der_a_op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a, const Scalar& x) const {
+    using numext::igamma_der_a;
+    return igamma_der_a(a, x);
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const {
+    return internal::pigamma_der_a(a, x);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_igamma_der_a_op<Scalar> > {
+  enum {
+    // 2x the cost of igamma
+    Cost = 40 * NumTraits<Scalar>::MulCost + 20 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasIGammaDerA
+  };
+};
+
+/** \internal
+  * \brief Template functor to compute the derivative of the sample
+  * of a Gamma(alpha, 1) random variable with respect to the parameter alpha
+  * gamma_sample_der_alpha(alpha, sample)
+  *
+  * \sa class CwiseBinaryOp, Cwise::gamma_sample_der_alpha
+  */
+template <typename Scalar>
+struct scalar_gamma_sample_der_alpha_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_gamma_sample_der_alpha_op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& alpha, const Scalar& sample) const {
+    using numext::gamma_sample_der_alpha;
+    return gamma_sample_der_alpha(alpha, sample);
+  }
+  template <typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& alpha, const Packet& sample) const {
+    return internal::pgamma_sample_der_alpha(alpha, sample);
+  }
+};
+template <typename Scalar>
+struct functor_traits<scalar_gamma_sample_der_alpha_op<Scalar> > {
+  enum {
+    // 2x the cost of igamma, minus the lgamma cost (the lgamma cancels out)
+    Cost = 30 * NumTraits<Scalar>::MulCost + 15 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasGammaSampleDerAlpha
+  };
+};
 
 /** \internal
   * \brief Template functor to compute the complementary incomplete gamma function igammac(a, x)
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h
index c5867002e..fbdfd299e 100644
--- a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsHalf.h
@@ -33,6 +33,14 @@ template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erfc(const Eigen::h
 template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma(const Eigen::half& a, const Eigen::half& x) {
   return Eigen::half(Eigen::numext::igamma(static_cast<float>(a), static_cast<float>(x)));
 }
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma_der_a(const Eigen::half& a, const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::igamma_der_a(static_cast<float>(a), static_cast<float>(x)));
+}
+template <>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half gamma_sample_der_alpha(const Eigen::half& alpha, const Eigen::half& sample) {
+  return Eigen::half(Eigen::numext::gamma_sample_der_alpha(static_cast<float>(alpha), static_cast<float>(sample)));
+}
 template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igammac(const Eigen::half& a, const Eigen::half& x) {
   return Eigen::half(Eigen::numext::igammac(static_cast<float>(a), static_cast<float>(x)));
 }
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h
index 5ab67dc1f..9a719e3c0 100644
--- a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsImpl.h
@@ -521,6 +521,197 @@ struct cephes_helper<double> {
   }
 };
 
+enum IgammaComputationMode { VALUE, DERIVATIVE, SAMPLE_DERIVATIVE };
+
+template <typename Scalar, IgammaComputationMode mode>
+EIGEN_DEVICE_FUNC
+int igamma_num_iterations() {
+  /* Returns the maximum number of internal iterations for igamma computation.
+   */
+  if (mode == VALUE) {
+    return 2000;
+  }
+
+  if (internal::is_same<Scalar, float>::value) {
+    return 200;
+  } else if (internal::is_same<Scalar, double>::value) {
+    return 500;
+  } else {
+    return 2000;
+  }
+}
+
+template <typename Scalar, IgammaComputationMode mode>
+struct igammac_cf_impl {
+  /* Computes igamc(a, x) or derivative (depending on the mode)
+   * using the continued fraction expansion of the complementary
+   * incomplete Gamma function.
+   *
+   * Preconditions:
+   *   a > 0
+   *   x >= 1
+   *   x >= a
+   */
+  EIGEN_DEVICE_FUNC
+  static Scalar run(Scalar a, Scalar x) {
+    const Scalar zero = 0;
+    const Scalar one = 1;
+    const Scalar two = 2;
+    const Scalar machep = cephes_helper<Scalar>::machep();
+    const Scalar big = cephes_helper<Scalar>::big();
+    const Scalar biginv = cephes_helper<Scalar>::biginv();
+
+    if ((numext::isinf)(x)) {
+      return zero;
+    }
+
+    // continued fraction
+    Scalar y = one - a;
+    Scalar z = x + y + one;
+    Scalar c = zero;
+    Scalar pkm2 = one;
+    Scalar qkm2 = x;
+    Scalar pkm1 = x + one;
+    Scalar qkm1 = z * x;
+    Scalar ans = pkm1 / qkm1;
+
+    Scalar dpkm2_da = zero;
+    Scalar dqkm2_da = zero;
+    Scalar dpkm1_da = zero;
+    Scalar dqkm1_da = -x;
+    Scalar dans_da = (dpkm1_da - ans * dqkm1_da) / qkm1;
+
+    for (int i = 0; i < igamma_num_iterations<Scalar, mode>(); i++) {
+      c += one;
+      y += one;
+      z += two;
+
+      Scalar yc = y * c;
+      Scalar pk = pkm1 * z - pkm2 * yc;
+      Scalar qk = qkm1 * z - qkm2 * yc;
+
+      Scalar dpk_da = dpkm1_da * z - pkm1 - dpkm2_da * yc + pkm2 * c;
+      Scalar dqk_da = dqkm1_da * z - qkm1 - dqkm2_da * yc + qkm2 * c;
+
+      if (qk != zero) {
+        Scalar ans_prev = ans;
+        ans = pk / qk;
+
+        Scalar dans_da_prev = dans_da;
+        dans_da = (dpk_da - ans * dqk_da) / qk;
+
+        if (mode == VALUE) {
+          if (numext::abs(ans_prev - ans) <= machep * numext::abs(ans)) {
+            break;
+          }
+        } else {
+          if (numext::abs(dans_da - dans_da_prev) <= machep) {
+            break;
+          }
+        }
+      }
+
+      pkm2 = pkm1;
+      pkm1 = pk;
+      qkm2 = qkm1;
+      qkm1 = qk;
+
+      dpkm2_da = dpkm1_da;
+      dpkm1_da = dpk_da;
+      dqkm2_da = dqkm1_da;
+      dqkm1_da = dqk_da;
+
+      if (numext::abs(pk) > big) {
+        pkm2 *= biginv;
+        pkm1 *= biginv;
+        qkm2 *= biginv;
+        qkm1 *= biginv;
+
+        dpkm2_da *= biginv;
+        dpkm1_da *= biginv;
+        dqkm2_da *= biginv;
+        dqkm1_da *= biginv;
+      }
+    }
+
+    /* Compute  x**a * exp(-x) / gamma(a)  */
+    Scalar logax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);
+    Scalar dlogax_da = numext::log(x) - digamma_impl<Scalar>::run(a);
+    Scalar ax = numext::exp(logax);
+    Scalar dax_da = ax * dlogax_da;
+
+    switch (mode) {
+      case VALUE:
+        return ans * ax;
+      case DERIVATIVE:
+        return ans * dax_da + dans_da * ax;
+      case SAMPLE_DERIVATIVE:
+        return -(dans_da + ans * dlogax_da) * x;
+    }
+  }
+};
+
+template <typename Scalar, IgammaComputationMode mode>
+struct igamma_series_impl {
+  /* Computes igam(a, x) or its derivative (depending on the mode)
+   * using the series expansion of the incomplete Gamma function.
+   *
+   * Preconditions:
+   *   x > 0
+   *   a > 0
+   *   !(x > 1 && x > a)
+   */
+  EIGEN_DEVICE_FUNC
+  static Scalar run(Scalar a, Scalar x) {
+    const Scalar zero = 0;
+    const Scalar one = 1;
+    const Scalar machep = cephes_helper<Scalar>::machep();
+
+    /* power series */
+    Scalar r = a;
+    Scalar c = one;
+    Scalar ans = one;
+
+    Scalar dc_da = zero;
+    Scalar dans_da = zero;
+
+    for (int i = 0; i < igamma_num_iterations<Scalar, mode>(); i++) {
+      r += one;
+      Scalar term = x / r;
+      Scalar dterm_da = -x / (r * r);
+      dc_da = term * dc_da + dterm_da * c;
+      dans_da += dc_da;
+      c *= term;
+      ans += c;
+
+      if (mode == VALUE) {
+        if (c <= machep * ans) {
+          break;
+        }
+      } else {
+        if (numext::abs(dc_da) <= machep * numext::abs(dans_da)) {
+          break;
+        }
+      }
+    }
+
+    /* Compute  x**a * exp(-x) / gamma(a + 1)  */
+    Scalar logax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a + one);
+    Scalar dlogax_da = numext::log(x) - digamma_impl<Scalar>::run(a + one);
+    Scalar ax = numext::exp(logax);
+    Scalar dax_da = ax * dlogax_da;
+
+    switch (mode) {
+      case VALUE:
+        return ans * ax;
+      case DERIVATIVE:
+        return ans * dax_da + dans_da * ax;
+      case SAMPLE_DERIVATIVE:
+        return -(dans_da + ans * dlogax_da) * x / a;
+    }
+  }
+};
+
 #if !EIGEN_HAS_C99_MATH
 
 template <typename Scalar>
@@ -535,8 +726,6 @@ struct igammac_impl {
 
 #else
 
-template <typename Scalar> struct igamma_impl;  // predeclare igamma_impl
-
 template <typename Scalar>
 struct igammac_impl {
   EIGEN_DEVICE_FUNC
@@ -604,97 +793,15 @@ struct igammac_impl {
       return nan;
     }
 
-    if ((numext::isnan)(a) || (numext::isnan)(x)) { // propagate nans
+    if ((numext::isnan)(a) || (numext::isnan)(x)) {  // propagate nans
       return nan;
     }
 
     if ((x < one) || (x < a)) {
-      /* The checks above ensure that we meet the preconditions for
-       * igamma_impl::Impl(), so call it, rather than igamma_impl::Run().
-       * Calling Run() would also work, but in that case the compiler may not be
-       * able to prove that igammac_impl::Run and igamma_impl::Run are not
-       * mutually recursive.  This leads to worse code, particularly on
-       * platforms like nvptx, where recursion is allowed only begrudgingly.
-       */
-      return (one - igamma_impl<Scalar>::Impl(a, x));
+      return (one - igamma_series_impl<Scalar, VALUE>::run(a, x));
     }
 
-    return Impl(a, x);
-  }
-
- private:
-  /* igamma_impl calls igammac_impl::Impl. */
-  friend struct igamma_impl<Scalar>;
-
-  /* Actually computes igamc(a, x).
-   *
-   * Preconditions:
-   *   a > 0
-   *   x >= 1
-   *   x >= a
-   */
-  EIGEN_DEVICE_FUNC static Scalar Impl(Scalar a, Scalar x) {
-    const Scalar zero = 0;
-    const Scalar one = 1;
-    const Scalar two = 2;
-    const Scalar machep = cephes_helper<Scalar>::machep();
-    const Scalar maxlog = numext::log(NumTraits<Scalar>::highest());
-    const Scalar big = cephes_helper<Scalar>::big();
-    const Scalar biginv = cephes_helper<Scalar>::biginv();
-    const Scalar inf = NumTraits<Scalar>::infinity();
-
-    Scalar ans, ax, c, yc, r, t, y, z;
-    Scalar pk, pkm1, pkm2, qk, qkm1, qkm2;
-
-    if (x == inf) return zero;  // std::isinf crashes on CUDA
-
-    /* Compute  x**a * exp(-x) / gamma(a)  */
-    ax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);
-    if (ax < -maxlog) {  // underflow
-      return zero;
-    }
-    ax = numext::exp(ax);
-
-    // continued fraction
-    y = one - a;
-    z = x + y + one;
-    c = zero;
-    pkm2 = one;
-    qkm2 = x;
-    pkm1 = x + one;
-    qkm1 = z * x;
-    ans = pkm1 / qkm1;
-
-    for (int i = 0; i < 2000; i++) {
-      c += one;
-      y += one;
-      z += two;
-      yc = y * c;
-      pk = pkm1 * z - pkm2 * yc;
-      qk = qkm1 * z - qkm2 * yc;
-      if (qk != zero) {
-        r = pk / qk;
-        t = numext::abs((ans - r) / r);
-        ans = r;
-      } else {
-        t = one;
-      }
-      pkm2 = pkm1;
-      pkm1 = pk;
-      qkm2 = qkm1;
-      qkm1 = qk;
-      if (numext::abs(pk) > big) {
-        pkm2 *= biginv;
-        pkm1 *= biginv;
-        qkm2 *= biginv;
-        qkm1 *= biginv;
-      }
-      if (t <= machep) {
-        break;
-      }
-    }
-
-    return (ans * ax);
+    return igammac_cf_impl<Scalar, VALUE>::run(a, x);
   }
 };
 
@@ -704,15 +811,10 @@ struct igammac_impl {
  * Implementation of igamma (incomplete gamma integral), based on Cephes but requires C++11/C99 *
  ************************************************************************************************/
 
-template <typename Scalar>
-struct igamma_retval {
-  typedef Scalar type;
-};
-
 #if !EIGEN_HAS_C99_MATH
 
-template <typename Scalar>
-struct igamma_impl {
+template <typename Scalar, IgammaComputationMode mode>
+struct igamma_generic_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar x) {
     EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
@@ -723,69 +825,17 @@ struct igamma_impl {
 
 #else
 
-template <typename Scalar>
-struct igamma_impl {
+template <typename Scalar, IgammaComputationMode mode>
+struct igamma_generic_impl {
   EIGEN_DEVICE_FUNC
   static Scalar run(Scalar a, Scalar x) {
-    /*	igam()
-     *	Incomplete gamma integral
-     *
-     *
-     *
-     * SYNOPSIS:
-     *
-     * double a, x, y, igam();
-     *
-     * y = igam( a, x );
-     *
-     * DESCRIPTION:
-     *
-     * The function is defined by
-     *
-     *                           x
-     *                            -
-     *                   1       | |  -t  a-1
-     *  igam(a,x)  =   -----     |   e   t   dt.
-     *                  -      | |
-     *                 | (a)    -
-     *                           0
-     *
-     *
-     * In this implementation both arguments must be positive.
-     * The integral is evaluated by either a power series or
-     * continued fraction expansion, depending on the relative
-     * values of a and x.
-     *
-     * ACCURACY (double):
-     *
-     *                      Relative error:
-     * arithmetic   domain     # trials      peak         rms
-     *    IEEE      0,30       200000       3.6e-14     2.9e-15
-     *    IEEE      0,100      300000       9.9e-14     1.5e-14
-     *
-     *
-     * ACCURACY (float):
-     *
-     *                      Relative error:
-     * arithmetic   domain     # trials      peak         rms
-     *    IEEE      0,30        20000       7.8e-6      5.9e-7
-     *
-     */
-    /*
-      Cephes Math Library Release 2.2: June, 1992
-      Copyright 1985, 1987, 1992 by Stephen L. Moshier
-      Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-    */
-
-
-    /* left tail of incomplete gamma function:
-     *
-     *          inf.      k
-     *   a  -x   -       x
-     *  x  e     >   ----------
-     *           -     -
-     *          k=0   | (a+k+1)
+    /* Depending on the mode, returns
+     * - VALUE: incomplete Gamma function igamma(a, x)
+     * - DERIVATIVE: derivative of incomplete Gamma function d/da igamma(a, x)
+     * - SAMPLE_DERIVATIVE: implicit derivative of a Gamma random variable
+     * x ~ Gamma(x | a, 1), dx/da = -1 / Gamma(x | a, 1) * d igamma(a, x) / dx
      *
+     * Derivatives are implemented by forward-mode differentiation.
      */
     const Scalar zero = 0;
     const Scalar one = 1;
@@ -797,71 +847,167 @@ struct igamma_impl {
       return nan;
     }
 
-    if ((numext::isnan)(a) || (numext::isnan)(x)) { // propagate nans
+    if ((numext::isnan)(a) || (numext::isnan)(x)) {  // propagate nans
       return nan;
     }
 
     if ((x > one) && (x > a)) {
-      /* The checks above ensure that we meet the preconditions for
-       * igammac_impl::Impl(), so call it, rather than igammac_impl::Run().
-       * Calling Run() would also work, but in that case the compiler may not be
-       * able to prove that igammac_impl::Run and igamma_impl::Run are not
-       * mutually recursive.  This leads to worse code, particularly on
-       * platforms like nvptx, where recursion is allowed only begrudgingly.
-       */
-      return (one - igammac_impl<Scalar>::Impl(a, x));
-    }
-
-    return Impl(a, x);
-  }
-
- private:
-  /* igammac_impl calls igamma_impl::Impl. */
-  friend struct igammac_impl<Scalar>;
-
-  /* Actually computes igam(a, x).
-   *
-   * Preconditions:
-   *   x > 0
-   *   a > 0
-   *   !(x > 1 && x > a)
-   */
-  EIGEN_DEVICE_FUNC static Scalar Impl(Scalar a, Scalar x) {
-    const Scalar zero = 0;
-    const Scalar one = 1;
-    const Scalar machep = cephes_helper<Scalar>::machep();
-    const Scalar maxlog = numext::log(NumTraits<Scalar>::highest());
-
-    Scalar ans, ax, c, r;
-
-    /* Compute  x**a * exp(-x) / gamma(a)  */
-    ax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);
-    if (ax < -maxlog) {
-      // underflow
-      return zero;
-    }
-    ax = numext::exp(ax);
-
-    /* power series */
-    r = a;
-    c = one;
-    ans = one;
-
-    for (int i = 0; i < 2000; i++) {
-      r += one;
-      c *= x/r;
-      ans += c;
-      if (c/ans <= machep) {
-        break;
+      Scalar ret = igammac_cf_impl<Scalar, mode>::run(a, x);
+      if (mode == VALUE) {
+        return one - ret;
+      } else {
+        return -ret;
       }
     }
 
-    return (ans * ax / a);
+    return igamma_series_impl<Scalar, mode>::run(a, x);
   }
 };
 
 #endif  // EIGEN_HAS_C99_MATH
 
+template <typename Scalar>
+struct igamma_retval {
+  typedef Scalar type;
+};
+
+template <typename Scalar>
+struct igamma_impl : igamma_generic_impl<Scalar, VALUE> {
+  /* igam()
+   * Incomplete gamma integral.
+   *
+   * The CDF of Gamma(a, 1) random variable at the point x.
+   *
+   * Accuracy estimation. For each a in [10^-2, 10^-1...10^3] we sample
+   * 50 Gamma random variables x ~ Gamma(x | a, 1), a total of 300 points.
+   * The ground truth is computed by mpmath. Mean absolute error:
+   * float: 1.26713e-05
+   * double: 2.33606e-12
+   *
+   * Cephes documentation below.
+   *
+   * SYNOPSIS:
+   *
+   * double a, x, y, igam();
+   *
+   * y = igam( a, x );
+   *
+   * DESCRIPTION:
+   *
+   * The function is defined by
+   *
+   *                           x
+   *                            -
+   *                   1       | |  -t  a-1
+   *  igam(a,x)  =   -----     |   e   t   dt.
+   *                  -      | |
+   *                 | (a)    -
+   *                           0
+   *
+   *
+   * In this implementation both arguments must be positive.
+   * The integral is evaluated by either a power series or
+   * continued fraction expansion, depending on the relative
+   * values of a and x.
+   *
+   * ACCURACY (double):
+   *
+   *                      Relative error:
+   * arithmetic   domain     # trials      peak         rms
+   *    IEEE      0,30       200000       3.6e-14     2.9e-15
+   *    IEEE      0,100      300000       9.9e-14     1.5e-14
+   *
+   *
+   * ACCURACY (float):
+   *
+   *                      Relative error:
+   * arithmetic   domain     # trials      peak         rms
+   *    IEEE      0,30        20000       7.8e-6      5.9e-7
+   *
+   */
+  /*
+    Cephes Math Library Release 2.2: June, 1992
+    Copyright 1985, 1987, 1992 by Stephen L. Moshier
+    Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+  */
+
+  /* left tail of incomplete gamma function:
+   *
+   *          inf.      k
+   *   a  -x   -       x
+   *  x  e     >   ----------
+   *           -     -
+   *          k=0   | (a+k+1)
+   *
+   */
+};
+
+template <typename Scalar>
+struct igamma_der_a_retval : igamma_retval<Scalar> {};
+
+template <typename Scalar>
+struct igamma_der_a_impl : igamma_generic_impl<Scalar, DERIVATIVE> {
+  /* Derivative of the incomplete Gamma function with respect to a.
+   *
+   * Computes d/da igamma(a, x) by forward differentiation of the igamma code.
+   *
+   * Accuracy estimation. For each a in [10^-2, 10^-1...10^3] we sample
+   * 50 Gamma random variables x ~ Gamma(x | a, 1), a total of 300 points.
+   * The ground truth is computed by mpmath. Mean absolute error:
+   * float: 6.17992e-07
+   * double: 4.60453e-12
+   *
+   * Reference:
+   * R. Moore. "Algorithm AS 187: Derivatives of the incomplete gamma
+   * integral". Journal of the Royal Statistical Society. 1982
+   */
+};
+
+template <typename Scalar>
+struct gamma_sample_der_alpha_retval : igamma_retval<Scalar> {};
+
+template <typename Scalar>
+struct gamma_sample_der_alpha_impl
+    : igamma_generic_impl<Scalar, SAMPLE_DERIVATIVE> {
+  /* Derivative of a Gamma random variable sample with respect to alpha.
+   *
+   * Consider a sample of a Gamma random variable with the concentration
+   * parameter alpha: sample ~ Gamma(alpha, 1). The reparameterization
+   * derivative that we want to compute is dsample / dalpha =
+   * d igammainv(alpha, u) / dalpha, where u = igamma(alpha, sample).
+   * However, this formula is numerically unstable and expensive, so instead
+   * we use implicit differentiation:
+   *
+   * igamma(alpha, sample) = u, where u ~ Uniform(0, 1).
+   * Apply d / dalpha to both sides:
+   * d igamma(alpha, sample) / dalpha
+   *     + d igamma(alpha, sample) / dsample * dsample/dalpha  = 0
+   * d igamma(alpha, sample) / dalpha
+   *     + Gamma(sample | alpha, 1) dsample / dalpha = 0
+   * dsample/dalpha = - (d igamma(alpha, sample) / dalpha)
+   *                   / Gamma(sample | alpha, 1)
+   *
+   * Here Gamma(sample | alpha, 1) is the PDF of the Gamma distribution
+   * (note that the derivative of the CDF w.r.t. sample is the PDF).
+   * See the reference below for more details.
+   *
+   * The derivative of igamma(alpha, sample) is computed by forward
+   * differentiation of the igamma code. Division by the Gamma PDF is performed
+   * in the same code, increasing the accuracy and speed due to cancellation
+   * of some terms.
+   *
+   * Accuracy estimation. For each alpha in [10^-2, 10^-1...10^3] we sample
+   * 50 Gamma random variables sample ~ Gamma(sample | alpha, 1), a total of 300
+   * points. The ground truth is computed by mpmath. Mean absolute error:
+   * float: 2.1686e-06
+   * double: 1.4774e-12
+   *
+   * Reference:
+   * M. Figurnov, S. Mohamed, A. Mnih "Implicit Reparameterization Gradients".
+   * 2018
+   */
+};
+
 /*****************************************************************************
  * Implementation of Riemann zeta function of two arguments, based on Cephes *
  *****************************************************************************/
@@ -1574,6 +1720,8 @@ struct betainc_impl<double> {
   }
 };
 
+#endif  // EIGEN_HAS_C99_MATH
+
 /****************************************************************************
  * Implementation of Bessel function, based on Cephes                       *
  ****************************************************************************/
@@ -1902,8 +2050,6 @@ struct i1e_impl<double> {
   }
 };
 
-#endif  // EIGEN_HAS_C99_MATH
-
 }  // end namespace internal
 
 namespace numext {
@@ -1950,6 +2096,18 @@ EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igamma, Scalar)
   return EIGEN_MATHFUNC_IMPL(igamma, Scalar)::run(a, x);
 }
 
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igamma_der_a, Scalar)
+    igamma_der_a(const Scalar& a, const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(igamma_der_a, Scalar)::run(a, x);
+}
+
+template <typename Scalar>
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(gamma_sample_der_alpha, Scalar)
+    gamma_sample_der_alpha(const Scalar& a, const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(gamma_sample_der_alpha, Scalar)::run(a, x);
+}
+
 template <typename Scalar>
 EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igammac, Scalar)
     igammac(const Scalar& a, const Scalar& x) {
diff --git a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h
index 4c176716b..465f41d54 100644
--- a/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h
+++ b/unsupported/Eigen/src/SpecialFunctions/SpecialFunctionsPacketMath.h
@@ -42,6 +42,21 @@ Packet perfc(const Packet& a) { using numext::erfc; return erfc(a); }
 template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
 Packet pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); }
 
+/** \internal \returns the derivative of the incomplete gamma function
+ * igamma_der_a(\a a, \a x) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pigamma_der_a(const Packet& a, const Packet& x) {
+  using numext::igamma_der_a; return igamma_der_a(a, x);
+}
+
+/** \internal \returns compute the derivative of the sample
+  * of Gamma(alpha, 1) random variable with respect to the parameter a
+  * gamma_sample_der_alpha(\a alpha, \a sample) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pgamma_sample_der_alpha(const Packet& alpha, const Packet& sample) {
+  using numext::gamma_sample_der_alpha; return gamma_sample_der_alpha(alpha, sample);
+}
+
 /** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */
 template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
 Packet pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); }
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h
index c25fea0b3..020ac1b62 100644
--- a/unsupported/Eigen/src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/CUDA/CudaSpecialFunctions.h
@@ -120,6 +120,41 @@ double2 pigamma<double2>(const double2& a, const double2& x)
   return make_double2(igamma(a.x, x.x), igamma(a.y, x.y));
 }
 
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pigamma_der_a<float4>(
+    const float4& a, const float4& x) {
+  using numext::igamma_der_a;
+  return make_float4(igamma_der_a(a.x, x.x), igamma_der_a(a.y, x.y),
+                     igamma_der_a(a.z, x.z), igamma_der_a(a.w, x.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pigamma_der_a<double2>(const double2& a, const double2& x) {
+  using numext::igamma_der_a;
+  return make_double2(igamma_der_a(a.x, x.x), igamma_der_a(a.y, x.y));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pgamma_sample_der_alpha<float4>(
+    const float4& alpha, const float4& sample) {
+  using numext::gamma_sample_der_alpha;
+  return make_float4(
+      gamma_sample_der_alpha(alpha.x, sample.x),
+      gamma_sample_der_alpha(alpha.y, sample.y),
+      gamma_sample_der_alpha(alpha.z, sample.z),
+      gamma_sample_der_alpha(alpha.w, sample.w));
+}
+
+template <>
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
+pgamma_sample_der_alpha<double2>(const double2& alpha, const double2& sample) {
+  using numext::gamma_sample_der_alpha;
+  return make_double2(
+      gamma_sample_der_alpha(alpha.x, sample.x),
+      gamma_sample_der_alpha(alpha.y, sample.y));
+}
+
 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
 float4 pigammac<float4>(const float4& a, const float4& x)
 {
diff --git a/unsupported/Eigen/src/Splines/SplineFitting.h b/unsupported/Eigen/src/Splines/SplineFitting.h
index c761a9b3d..1a4b80a2f 100644
--- a/unsupported/Eigen/src/Splines/SplineFitting.h
+++ b/unsupported/Eigen/src/Splines/SplineFitting.h
@@ -181,7 +181,7 @@ namespace Eigen
    * \ingroup Splines_Module
    *
    * \param[in] pts The data points to which a spline should be fit.
-   * \param[out] chord_lengths The resulting chord lenggth vector.
+   * \param[out] chord_lengths The resulting chord length vector.
    *
    * \sa Les Piegl and Wayne Tiller, The NURBS book (2nd ed.), 1997, 9.2.1 Global Curve Interpolation to Point Data
    **/   
diff --git a/unsupported/README.txt b/unsupported/README.txt
index 83479ff0b..70793bf13 100644
--- a/unsupported/README.txt
+++ b/unsupported/README.txt
@@ -20,7 +20,7 @@ However, it:
  - must rely on Eigen,
  - must be highly related to math,
  - should have some general purpose in the sense that it could
-   potentially become an offical Eigen module (or be merged into another one).
+   potentially become an official Eigen module (or be merged into another one).
 
 In doubt feel free to contact us. For instance, if your addons is very too specific
 but it shows an interesting way of using Eigen, then it could be a nice demo.
diff --git a/unsupported/bench/bench_svd.cpp b/unsupported/bench/bench_svd.cpp
index 01d8231ae..e7028a2b9 100644
--- a/unsupported/bench/bench_svd.cpp
+++ b/unsupported/bench/bench_svd.cpp
@@ -70,7 +70,7 @@ void bench_svd(const MatrixType& a = MatrixType())
   std::cout<< std::endl;
   timerJacobi.reset();
   timerBDC.reset();
-  cout << " Computes rotaion matrix" <<endl;
+  cout << " Computes rotation matrix" <<endl;
   for (int k=1; k<=NUMBER_SAMPLE; ++k)
   {
     timerBDC.start();
diff --git a/unsupported/test/CMakeLists.txt b/unsupported/test/CMakeLists.txt
index c3dba5f2a..05b141e21 100644
--- a/unsupported/test/CMakeLists.txt
+++ b/unsupported/test/CMakeLists.txt
@@ -1,5 +1,5 @@
 # generate split test header file only if it does not yet exist
-# in order to prevent a rebuild everytime cmake is configured
+# in order to prevent a rebuild every time cmake is configured
 if(NOT EXISTS ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h)
   file(WRITE ${CMAKE_CURRENT_BINARY_DIR}/split_test_helper.h "")
   foreach(i RANGE 1 999)
diff --git a/unsupported/test/autodiff_scalar.cpp b/unsupported/test/autodiff_scalar.cpp
index a917ec344..1d4418203 100644
--- a/unsupported/test/autodiff_scalar.cpp
+++ b/unsupported/test/autodiff_scalar.cpp
@@ -81,7 +81,7 @@ void check_limits_specialization()
   typedef std::numeric_limits<AD> A;
   typedef std::numeric_limits<Scalar> B;
 
-  // workaround "unsed typedef" warning:
+  // workaround "unused typedef" warning:
   VERIFY(!bool(internal::is_same<B, A>::value));
 
 #if EIGEN_HAS_CXX11
diff --git a/unsupported/test/cxx11_tensor_broadcasting.cpp b/unsupported/test/cxx11_tensor_broadcasting.cpp
index 5c0ea5889..a9d268ea6 100644
--- a/unsupported/test/cxx11_tensor_broadcasting.cpp
+++ b/unsupported/test/cxx11_tensor_broadcasting.cpp
@@ -180,6 +180,64 @@ static void test_fixed_size_broadcasting()
 #endif
 }
 
+template <int DataLayout>
+static void test_simple_broadcasting_one_by_n()
+{
+  Tensor<float, 4, DataLayout> tensor(1,13,5,7);
+  tensor.setRandom();
+  array<ptrdiff_t, 4> broadcasts;
+  broadcasts[0] = 9;
+  broadcasts[1] = 1;
+  broadcasts[2] = 1;
+  broadcasts[3] = 1;
+  Tensor<float, 4, DataLayout> broadcast;
+  broadcast = tensor.broadcast(broadcasts);
+
+  VERIFY_IS_EQUAL(broadcast.dimension(0), 9);
+  VERIFY_IS_EQUAL(broadcast.dimension(1), 13);
+  VERIFY_IS_EQUAL(broadcast.dimension(2), 5);
+  VERIFY_IS_EQUAL(broadcast.dimension(3), 7);
+
+  for (int i = 0; i < 9; ++i) {
+    for (int j = 0; j < 13; ++j) {
+      for (int k = 0; k < 5; ++k) {
+        for (int l = 0; l < 7; ++l) {
+          VERIFY_IS_EQUAL(tensor(i%1,j%13,k%5,l%7), broadcast(i,j,k,l));
+        }
+      }
+    }
+  }
+}
+
+template <int DataLayout>
+static void test_simple_broadcasting_n_by_one()
+{
+  Tensor<float, 4, DataLayout> tensor(7,3,5,1);
+  tensor.setRandom();
+  array<ptrdiff_t, 4> broadcasts;
+  broadcasts[0] = 1;
+  broadcasts[1] = 1;
+  broadcasts[2] = 1;
+  broadcasts[3] = 19;
+  Tensor<float, 4, DataLayout> broadcast;
+  broadcast = tensor.broadcast(broadcasts);
+
+  VERIFY_IS_EQUAL(broadcast.dimension(0), 7);
+  VERIFY_IS_EQUAL(broadcast.dimension(1), 3);
+  VERIFY_IS_EQUAL(broadcast.dimension(2), 5);
+  VERIFY_IS_EQUAL(broadcast.dimension(3), 19);
+
+  for (int i = 0; i < 7; ++i) {
+    for (int j = 0; j < 3; ++j) {
+      for (int k = 0; k < 5; ++k) {
+        for (int l = 0; l < 19; ++l) {
+          VERIFY_IS_EQUAL(tensor(i%7,j%3,k%5,l%1), broadcast(i,j,k,l));
+        }
+      }
+    }
+  }
+}
+
 
 void test_cxx11_tensor_broadcasting()
 {
@@ -191,4 +249,8 @@ void test_cxx11_tensor_broadcasting()
   CALL_SUBTEST(test_static_broadcasting<RowMajor>());
   CALL_SUBTEST(test_fixed_size_broadcasting<ColMajor>());
   CALL_SUBTEST(test_fixed_size_broadcasting<RowMajor>());
+  CALL_SUBTEST(test_simple_broadcasting_one_by_n<RowMajor>());
+  CALL_SUBTEST(test_simple_broadcasting_n_by_one<RowMajor>());
+  CALL_SUBTEST(test_simple_broadcasting_one_by_n<ColMajor>());
+  CALL_SUBTEST(test_simple_broadcasting_n_by_one<ColMajor>());
 }
diff --git a/unsupported/test/cxx11_tensor_cuda.cu b/unsupported/test/cxx11_tensor_cuda.cu
index 63d0a345a..f238ed5be 100644
--- a/unsupported/test/cxx11_tensor_cuda.cu
+++ b/unsupported/test/cxx11_tensor_cuda.cu
@@ -1318,6 +1318,157 @@ void test_cuda_i1e()
   cudaFree(d_out);
 }
 
+template <typename Scalar>
+void test_cuda_igamma_der_a()
+{
+  Tensor<Scalar, 1> in_x(30);
+  Tensor<Scalar, 1> in_a(30);
+  Tensor<Scalar, 1> out(30);
+  Tensor<Scalar, 1> expected_out(30);
+  out.setZero();
+
+  Array<Scalar, 1, Dynamic> in_a_array(30);
+  Array<Scalar, 1, Dynamic> in_x_array(30);
+  Array<Scalar, 1, Dynamic> expected_out_array(30);
+
+  // See special_functions.cpp for the Python code that generates the test data.
+
+  in_a_array << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0,
+      1.0, 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0, 100.0,
+      100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0;
+
+  in_x_array << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05,
+      1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16, 0.0132865061065,
+      0.0200034203853, 6.29263709118e-17, 1.37160367764e-06, 0.333412038288,
+      1.18135687766, 0.580629033777, 0.170631439426, 0.786686768458,
+      7.63873279537, 13.1944344379, 11.896042354, 10.5830172417, 10.5020942233,
+      92.8918587747, 95.003720371, 86.3715926467, 96.0330217672, 82.6389930677,
+      968.702906754, 969.463546828, 1001.79726022, 955.047416547, 1044.27458568;
+
+  expected_out_array << -32.7256441441, -36.4394150514, -9.66467612263,
+      -36.4394150514, -36.4394150514, -1.0891900302, -2.66351229645,
+      -2.48666868596, -0.929700494428, -3.56327722764, -0.455320135314,
+      -0.391437214323, -0.491352055991, -0.350454834292, -0.471773162921,
+      -0.104084440522, -0.0723646747909, -0.0992828975532, -0.121638215446,
+      -0.122619605294, -0.0317670267286, -0.0359974812869, -0.0154359225363,
+      -0.0375775365921, -0.00794899153653, -0.00777303219211, -0.00796085782042,
+      -0.0125850719397, -0.00455500206958, -0.00476436993148;
+
+  for (int i = 0; i < 30; ++i) {
+    in_x(i) = in_x_array(i);
+    in_a(i) = in_a_array(i);
+    expected_out(i) = expected_out_array(i);
+  }
+
+  std::size_t bytes = in_x.size() * sizeof(Scalar);
+
+  Scalar* d_a;
+  Scalar* d_x;
+  Scalar* d_out;
+  cudaMalloc((void**)(&d_a), bytes);
+  cudaMalloc((void**)(&d_x), bytes);
+  cudaMalloc((void**)(&d_out), bytes);
+
+  cudaMemcpy(d_a, in_a.data(), bytes, cudaMemcpyHostToDevice);
+  cudaMemcpy(d_x, in_x.data(), bytes, cudaMemcpyHostToDevice);
+
+  Eigen::CudaStreamDevice stream;
+  Eigen::GpuDevice gpu_device(&stream);
+
+  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_a(d_a, 30);
+  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_x(d_x, 30);
+  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 30);
+
+  gpu_out.device(gpu_device) = gpu_a.igamma_der_a(gpu_x);
+
+  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost,
+                         gpu_device.stream()) == cudaSuccess);
+  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);
+
+  for (int i = 0; i < 30; ++i) {
+    VERIFY_IS_APPROX(out(i), expected_out(i));
+  }
+
+  cudaFree(d_a);
+  cudaFree(d_x);
+  cudaFree(d_out);
+}
+
+template <typename Scalar>
+void test_cuda_gamma_sample_der_alpha()
+{
+  Tensor<Scalar, 1> in_alpha(30);
+  Tensor<Scalar, 1> in_sample(30);
+  Tensor<Scalar, 1> out(30);
+  Tensor<Scalar, 1> expected_out(30);
+  out.setZero();
+
+  Array<Scalar, 1, Dynamic> in_alpha_array(30);
+  Array<Scalar, 1, Dynamic> in_sample_array(30);
+  Array<Scalar, 1, Dynamic> expected_out_array(30);
+
+  // See special_functions.cpp for the Python code that generates the test data.
+
+  in_alpha_array << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0,
+      1.0, 1.0, 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0,
+      100.0, 100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0;
+
+  in_sample_array << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05,
+      1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16, 0.0132865061065,
+      0.0200034203853, 6.29263709118e-17, 1.37160367764e-06, 0.333412038288,
+      1.18135687766, 0.580629033777, 0.170631439426, 0.786686768458,
+      7.63873279537, 13.1944344379, 11.896042354, 10.5830172417, 10.5020942233,
+      92.8918587747, 95.003720371, 86.3715926467, 96.0330217672, 82.6389930677,
+      968.702906754, 969.463546828, 1001.79726022, 955.047416547, 1044.27458568;
+
+  expected_out_array << 7.42424742367e-23, 1.02004297287e-34, 0.0130155240738,
+      1.02004297287e-34, 1.02004297287e-34, 1.96505168277e-13, 0.525575786243,
+      0.713903991771, 2.32077561808e-14, 0.000179348049886, 0.635500453302,
+      1.27561284917, 0.878125852156, 0.41565819538, 1.03606488534,
+      0.885964824887, 1.16424049334, 1.10764479598, 1.04590810812,
+      1.04193666963, 0.965193152414, 0.976217589464, 0.93008035061,
+      0.98153216096, 0.909196397698, 0.98434963993, 0.984738050206,
+      1.00106492525, 0.97734200649, 1.02198794179;
+
+  for (int i = 0; i < 30; ++i) {
+    in_alpha(i) = in_alpha_array(i);
+    in_sample(i) = in_sample_array(i);
+    expected_out(i) = expected_out_array(i);
+  }
+
+  std::size_t bytes = in_alpha.size() * sizeof(Scalar);
+
+  Scalar* d_alpha;
+  Scalar* d_sample;
+  Scalar* d_out;
+  cudaMalloc((void**)(&d_alpha), bytes);
+  cudaMalloc((void**)(&d_sample), bytes);
+  cudaMalloc((void**)(&d_out), bytes);
+
+  cudaMemcpy(d_alpha, in_alpha.data(), bytes, cudaMemcpyHostToDevice);
+  cudaMemcpy(d_sample, in_sample.data(), bytes, cudaMemcpyHostToDevice);
+
+  Eigen::CudaStreamDevice stream;
+  Eigen::GpuDevice gpu_device(&stream);
+
+  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_alpha(d_alpha, 30);
+  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_sample(d_sample, 30);
+  Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 30);
+
+  gpu_out.device(gpu_device) = gpu_alpha.gamma_sample_der_alpha(gpu_sample);
+
+  assert(cudaMemcpyAsync(out.data(), d_out, bytes, cudaMemcpyDeviceToHost,
+                         gpu_device.stream()) == cudaSuccess);
+  assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);
+
+  for (int i = 0; i < 30; ++i) {
+    VERIFY_IS_APPROX(out(i), expected_out(i));
+  }
+
+  cudaFree(d_alpha);
+  cudaFree(d_sample);
+  cudaFree(d_out);
+}
 
 void test_cxx11_tensor_cuda()
 {
@@ -1396,5 +1547,11 @@ void test_cxx11_tensor_cuda()
 
   CALL_SUBTEST_6(test_cuda_i1e<float>());
   CALL_SUBTEST_6(test_cuda_i1e<double>());
+
+  CALL_SUBTEST_6(test_cuda_igamma_der_a<float>());
+  CALL_SUBTEST_6(test_cuda_igamma_der_a<double>());
+
+  CALL_SUBTEST_6(test_cuda_gamma_sample_der_alpha<float>());
+  CALL_SUBTEST_6(test_cuda_gamma_sample_der_alpha<double>());
 #endif
 }
diff --git a/unsupported/test/cxx11_tensor_inflation_sycl.cpp b/unsupported/test/cxx11_tensor_inflation_sycl.cpp
index f2f87f7ed..cf3e29f4c 100644
--- a/unsupported/test/cxx11_tensor_inflation_sycl.cpp
+++ b/unsupported/test/cxx11_tensor_inflation_sycl.cpp
@@ -22,10 +22,10 @@
 
 using Eigen::Tensor;
 
-// Inflation Defenition for each dimention the inflated val would be
+// Inflation Definition for each dimension the inflated val would be
 //((dim-1)*strid[dim] +1)
 
-// for 1 dimnention vector of size 3 with value (4,4,4) with the inflated stride value of 3 would be changed to
+// for 1 dimension vector of size 3 with value (4,4,4) with the inflated stride value of 3 would be changed to
 // tensor of size (2*3) +1 = 7 with the value of
 // (4, 0, 0, 4, 0, 0, 4).
 
diff --git a/unsupported/test/cxx11_tensor_of_float16_cuda.cu b/unsupported/test/cxx11_tensor_of_float16_cuda.cu
index 167b75d25..7a751ff02 100644
--- a/unsupported/test/cxx11_tensor_of_float16_cuda.cu
+++ b/unsupported/test/cxx11_tensor_of_float16_cuda.cu
@@ -247,7 +247,7 @@ void test_cuda_trancendental() {
   }
   for (int i = 0; i < num_elem; ++i) {
     std::cout << "Checking elemwise log " << i << " input = " << input2(i) << " full = " << full_prec2(i) << " half = " << half_prec2(i) << std::endl;
-    if(std::abs(input2(i)-1.f)<0.05f) // log lacks accurary nearby 1
+    if(std::abs(input2(i)-1.f)<0.05f) // log lacks accuracy nearby 1
       VERIFY_IS_APPROX(full_prec2(i)+Eigen::half(0.1f), half_prec2(i)+Eigen::half(0.1f));
     else
       VERIFY_IS_APPROX(full_prec2(i), half_prec2(i));
diff --git a/unsupported/test/cxx11_tensor_random_cuda.cu b/unsupported/test/cxx11_tensor_random_cuda.cu
index fa1a46732..389c0a8c2 100644
--- a/unsupported/test/cxx11_tensor_random_cuda.cu
+++ b/unsupported/test/cxx11_tensor_random_cuda.cu
@@ -37,7 +37,7 @@ void test_cuda_random_uniform()
   assert(cudaMemcpyAsync(out.data(), d_out, out_bytes, cudaMemcpyDeviceToHost, gpu_device.stream()) == cudaSuccess);
   assert(cudaStreamSynchronize(gpu_device.stream()) == cudaSuccess);
 
-  // For now we just check thes code doesn't crash.
+  // For now we just check this code doesn't crash.
   // TODO: come up with a valid test of randomness
 }
 
diff --git a/unsupported/test/forward_adolc.cpp b/unsupported/test/forward_adolc.cpp
index 866db8e86..6d0ae738d 100644
--- a/unsupported/test/forward_adolc.cpp
+++ b/unsupported/test/forward_adolc.cpp
@@ -132,7 +132,7 @@ void test_forward_adolc()
   }
 
   {
-    // simple instanciation tests
+    // simple instantiation tests
     Matrix<adtl::adouble,2,1> x;
     foo(x);
     Matrix<adtl::adouble,Dynamic,Dynamic> A(4,4);;
diff --git a/unsupported/test/sparse_extra.cpp b/unsupported/test/sparse_extra.cpp
index 4f6723d6d..7cf4a77c3 100644
--- a/unsupported/test/sparse_extra.cpp
+++ b/unsupported/test/sparse_extra.cpp
@@ -8,7 +8,7 @@
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
 
-// import basic and product tests for deprectaed DynamicSparseMatrix
+// import basic and product tests for deprecated DynamicSparseMatrix
 #define EIGEN_NO_DEPRECATED_WARNING
 #include "sparse_basic.cpp"
 #include "sparse_product.cpp"
diff --git a/unsupported/test/special_functions.cpp b/unsupported/test/special_functions.cpp
index 48d0db95e..802e16150 100644
--- a/unsupported/test/special_functions.cpp
+++ b/unsupported/test/special_functions.cpp
@@ -335,6 +335,7 @@ template<typename ArrayType> void array_special_functions()
         ArrayType test = betainc(a, b + one, x) + eps;
         verify_component_wise(test, expected););
   }
+#endif  // EIGEN_HAS_C99_MATH
 
   // Test Bessel function i0e. Reference results obtained with SciPy.
   {
@@ -375,7 +376,100 @@ template<typename ArrayType> void array_special_functions()
     CALL_SUBTEST(res = i1e(x);
                  verify_component_wise(res, expected););
   }
-#endif
+
+  /* Code to generate the data for the following two test cases.
+    N = 5
+    np.random.seed(3)
+
+    a = np.logspace(-2, 3, 6)
+    a = np.ravel(np.tile(np.reshape(a, [-1, 1]), [1, N]))
+    x = np.random.gamma(a, 1.0)
+    x = np.maximum(x, np.finfo(np.float32).tiny)
+
+    def igamma(a, x):
+      return mpmath.gammainc(a, 0, x, regularized=True)
+
+    def igamma_der_a(a, x):
+      res = mpmath.diff(lambda a_prime: igamma(a_prime, x), a)
+      return np.float64(res)
+
+    def gamma_sample_der_alpha(a, x):
+      igamma_x = igamma(a, x)
+      def igammainv_of_igamma(a_prime):
+        return mpmath.findroot(lambda x_prime: igamma(a_prime, x_prime) -
+            igamma_x, x, solver='newton')
+      return np.float64(mpmath.diff(igammainv_of_igamma, a))
+
+    v_igamma_der_a = np.vectorize(igamma_der_a)(a, x)
+    v_gamma_sample_der_alpha = np.vectorize(gamma_sample_der_alpha)(a, x)
+  */
+
+#if EIGEN_HAS_C99_MATH
+  // Test igamma_der_a
+  {
+    ArrayType a(30);
+    ArrayType x(30);
+    ArrayType res(30);
+    ArrayType v(30);
+
+    a << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0, 1.0,
+        1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0, 100.0,
+        100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0;
+
+    x << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05,
+        1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16,
+        0.0132865061065, 0.0200034203853, 6.29263709118e-17, 1.37160367764e-06,
+        0.333412038288, 1.18135687766, 0.580629033777, 0.170631439426,
+        0.786686768458, 7.63873279537, 13.1944344379, 11.896042354,
+        10.5830172417, 10.5020942233, 92.8918587747, 95.003720371,
+        86.3715926467, 96.0330217672, 82.6389930677, 968.702906754,
+        969.463546828, 1001.79726022, 955.047416547, 1044.27458568;
+
+    v << -32.7256441441, -36.4394150514, -9.66467612263, -36.4394150514,
+        -36.4394150514, -1.0891900302, -2.66351229645, -2.48666868596,
+        -0.929700494428, -3.56327722764, -0.455320135314, -0.391437214323,
+        -0.491352055991, -0.350454834292, -0.471773162921, -0.104084440522,
+        -0.0723646747909, -0.0992828975532, -0.121638215446, -0.122619605294,
+        -0.0317670267286, -0.0359974812869, -0.0154359225363, -0.0375775365921,
+        -0.00794899153653, -0.00777303219211, -0.00796085782042,
+        -0.0125850719397, -0.00455500206958, -0.00476436993148;
+
+    CALL_SUBTEST(res = igamma_der_a(a, x); verify_component_wise(res, v););
+  }
+
+  // Test gamma_sample_der_alpha
+  {
+    ArrayType alpha(30);
+    ArrayType sample(30);
+    ArrayType res(30);
+    ArrayType v(30);
+
+    alpha << 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0,
+        1.0, 1.0, 1.0, 10.0, 10.0, 10.0, 10.0, 10.0, 100.0, 100.0, 100.0, 100.0,
+        100.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0;
+
+    sample << 1.25668890405e-26, 1.17549435082e-38, 1.20938905072e-05,
+        1.17549435082e-38, 1.17549435082e-38, 5.66572070696e-16,
+        0.0132865061065, 0.0200034203853, 6.29263709118e-17, 1.37160367764e-06,
+        0.333412038288, 1.18135687766, 0.580629033777, 0.170631439426,
+        0.786686768458, 7.63873279537, 13.1944344379, 11.896042354,
+        10.5830172417, 10.5020942233, 92.8918587747, 95.003720371,
+        86.3715926467, 96.0330217672, 82.6389930677, 968.702906754,
+        969.463546828, 1001.79726022, 955.047416547, 1044.27458568;
+
+    v << 7.42424742367e-23, 1.02004297287e-34, 0.0130155240738,
+        1.02004297287e-34, 1.02004297287e-34, 1.96505168277e-13, 0.525575786243,
+        0.713903991771, 2.32077561808e-14, 0.000179348049886, 0.635500453302,
+        1.27561284917, 0.878125852156, 0.41565819538, 1.03606488534,
+        0.885964824887, 1.16424049334, 1.10764479598, 1.04590810812,
+        1.04193666963, 0.965193152414, 0.976217589464, 0.93008035061,
+        0.98153216096, 0.909196397698, 0.98434963993, 0.984738050206,
+        1.00106492525, 0.97734200649, 1.02198794179;
+
+    CALL_SUBTEST(res = gamma_sample_der_alpha(alpha, sample);
+                 verify_component_wise(res, v););
+  }
+#endif  // EIGEN_HAS_C99_MATH
 }
 
 void test_special_functions()