Move Eigen::all,last,lastp1,lastN to Eigen::placeholders::.

These names are so common, IMO they should not exist directly in the
`Eigen::` namespace.  This prevents us from using the `last` or `all`
names for any parameters or local variables, otherwise spitting out
warnings about shadowing or hiding the global values.  Many external
projects (and our own examples) also heavily use
```
using namespace Eigen;
```
which means these conflict with external libraries as well, e.g.
`std::fill(first,last,value)`.

It seems originally these were placed in a separate namespace
`Eigen::placeholders`, which has since been deprecated.  I propose
to un-deprecate this, and restore the original locations.

These symbols are also imported into `Eigen::indexing`, which
additionally imports `fix` and `seq`. An alternative is to remove the
`placeholders` namespace and stick with `indexing`.

NOTE: this is an API-breaking change.

Fixes #2321.

Eigen/src/Core/ArithmeticSequence.h

@@ -74,7 +74,7 @@ template<typename T> struct cleanup_seq_incr {
   typedef typename cleanup_index_type<T,DynamicIndex>::type type;
 };
 
-}
+}  // namespace internal
 
 //--------------------------------------------------------------------------------
 // seq(first,last,incr) and seqN(first,size,incr)
@@ -321,6 +321,7 @@ seq(const symbolic::BaseExpr<FirstTypeDerived> &f, const symbolic::BaseExpr<Last
 
 #endif // EIGEN_PARSED_BY_DOXYGEN
 
+namespace placeholders {
 
 #if EIGEN_HAS_CXX11 || defined(EIGEN_PARSED_BY_DOXYGEN)
 /** \cpp11
@@ -331,9 +332,9 @@ seq(const symbolic::BaseExpr<FirstTypeDerived> &f, const symbolic::BaseExpr<Last
   * \sa lastN(SizeType), seqN(FirstType,SizeType), seq(FirstType,LastType,IncrType) */
 template<typename SizeType,typename IncrType>
 auto lastN(SizeType size, IncrType incr)
--> decltype(seqN(Eigen::last-(size-fix<1>())*incr, size, incr))
+-> decltype(seqN(Eigen::placeholders::last-(size-fix<1>())*incr, size, incr))
 {
-  return seqN(Eigen::last-(size-fix<1>())*incr, size, incr);
+  return seqN(Eigen::placeholders::last-(size-fix<1>())*incr, size, incr);
 }
 
 /** \cpp11
@@ -344,12 +345,14 @@ auto lastN(SizeType size, IncrType incr)
   * \sa lastN(SizeType,IncrType, seqN(FirstType,SizeType), seq(FirstType,LastType) */
 template<typename SizeType>
 auto lastN(SizeType size)
--> decltype(seqN(Eigen::last+fix<1>()-size, size))
+-> decltype(seqN(Eigen::placeholders::last+fix<1>()-size, size))
 {
-  return seqN(Eigen::last+fix<1>()-size, size);
+  return seqN(Eigen::placeholders::last+fix<1>()-size, size);
 }
 #endif
 
+}  // namespace placeholders
+
 namespace internal {
 
 // Convert a symbolic span into a usable one (i.e., remove last/end "keywords")
@@ -389,25 +392,25 @@ struct get_compile_time_incr<ArithmeticSequence<FirstType,SizeType,IncrType> > {
   * \code using namespace Eigen::indexing; \endcode
   * is equivalent to:
   * \code
-  using Eigen::all;
+  using Eigen::fix;
   using Eigen::seq;
   using Eigen::seqN;
-  using Eigen::lastN; // c++11 only
-  using Eigen::last;
-  using Eigen::lastp1;
-  using Eigen::fix;
+  using Eigen::placeholders::all;
+  using Eigen::placeholders::last;
+  using Eigen::placeholders::lastN;  // c++11 only
+  using Eigen::placeholders::lastp1;
   \endcode
   */
 namespace indexing {
-  using Eigen::all;
+  using Eigen::fix;
   using Eigen::seq;
   using Eigen::seqN;
+  using Eigen::placeholders::all;
+  using Eigen::placeholders::last;
   #if EIGEN_HAS_CXX11
-  using Eigen::lastN;
+  using Eigen::placeholders::lastN;
   #endif
-  using Eigen::last;
-  using Eigen::lastp1;
-  using Eigen::fix;
+  using Eigen::placeholders::lastp1;
 }
 
 } // end namespace Eigen

Eigen/src/Core/IndexedView.h

@@ -98,7 +98,7 @@ class IndexedViewImpl;
   *  - decltype(ArrayXi::LinSpaced(...))
   *  - Any view/expressions of the previous types
   *  - Eigen::ArithmeticSequence
-  *  - Eigen::internal::AllRange      (helper for Eigen::all)
+  *  - Eigen::internal::AllRange     (helper for Eigen::placeholders::all)
   *  - Eigen::internal::SingleRange  (helper for single index)
   *  - etc.
   *

Eigen/src/Core/util/IndexedViewHelper.h

@@ -17,7 +17,11 @@ namespace Eigen {
 
 namespace internal {
 struct symbolic_last_tag {};
-}
+}  // namespace internal
+
+namespace placeholders {
+
+typedef symbolic::SymbolExpr<internal::symbolic_last_tag> last_t;
 
 /** \var last
   * \ingroup Core_Module
@@ -30,34 +34,16 @@ struct symbolic_last_tag {};
   * A typical usage example would be:
   * \code
   * using namespace Eigen;
-  * using Eigen::last;
+  * using Eigen::placeholders::last;
   * VectorXd v(n);
   * v(seq(2,last-2)).setOnes();
   * \endcode
   *
   * \sa end
   */
-static const symbolic::SymbolExpr<internal::symbolic_last_tag> last; // PLEASE use Eigen::last   instead of Eigen::placeholders::last
+static const last_t last;
 
-/** \var lastp1
-  * \ingroup Core_Module
-  *
-  * Can be used as a parameter to Eigen::seq and Eigen::seqN functions to symbolically
-  * reference the last+1 element/row/columns of the underlying vector or matrix once
-  * passed to DenseBase::operator()(const RowIndices&, const ColIndices&).
-  *
-  * This symbolic placeholder supports standard arithmetic operations.
-  * It is essentially an alias to last+fix<1>.
-  *
-  * \sa last
-  */
-#ifdef EIGEN_PARSED_BY_DOXYGEN
-static const auto lastp1 = last+fix<1>;
-#else
-// Using a FixedExpr<1> expression is important here to make sure the compiler
-// can fully optimize the computation starting indices with zero overhead.
-static const symbolic::AddExpr<symbolic::SymbolExpr<internal::symbolic_last_tag>,symbolic::ValueExpr<Eigen::internal::FixedInt<1> > > lastp1(last+fix<1>());
-#endif
+}  // namespace placeholders
 
 namespace internal {
 
@@ -70,7 +56,7 @@ FixedInt<N> eval_expr_given_size(FixedInt<N> x, Index /*size*/)   { return x; }
 template<typename Derived>
 Index eval_expr_given_size(const symbolic::BaseExpr<Derived> &x, Index size)
 {
-  return x.derived().eval(last=size-1);
+  return x.derived().eval(Eigen::placeholders::last=size-1);
 }
 
 // Extract increment/step at compile time
@@ -165,23 +151,44 @@ template<int Size> struct get_compile_time_incr<AllRange<Size> > {
 
 } // end namespace internal
 
+namespace placeholders {
+
+typedef symbolic::AddExpr<symbolic::SymbolExpr<internal::symbolic_last_tag>,symbolic::ValueExpr<Eigen::internal::FixedInt<1> > > lastp1_t;
+typedef Eigen::internal::all_t all_t;
+
+/** \var lastp1
+  * \ingroup Core_Module
+  *
+  * Can be used as a parameter to Eigen::seq and Eigen::seqN functions to symbolically
+  * reference the last+1 element/row/columns of the underlying vector or matrix once
+  * passed to DenseBase::operator()(const RowIndices&, const ColIndices&).
+  *
+  * This symbolic placeholder supports standard arithmetic operations.
+  * It is essentially an alias to last+fix<1>.
+  *
+  * \sa last
+  */
+#ifdef EIGEN_PARSED_BY_DOXYGEN
+static const auto lastp1 = last+fix<1>;
+#else
+// Using a FixedExpr<1> expression is important here to make sure the compiler
+// can fully optimize the computation starting indices with zero overhead.
+static const lastp1_t lastp1(last+fix<1>());
+#endif
+
+/** \var end
+  * \ingroup Core_Module
+  * \sa lastp1
+  */
+static const lastp1_t end = lastp1;
 
 /** \var all
   * \ingroup Core_Module
   * Can be used as a parameter to DenseBase::operator()(const RowIndices&, const ColIndices&) to index all rows or columns
   */
-static const Eigen::internal::all_t all; // PLEASE use Eigen::all instead of Eigen::placeholders::all
+static const Eigen::internal::all_t all;
 
-
-namespace placeholders {
-  typedef symbolic::SymbolExpr<internal::symbolic_last_tag> last_t;
-  typedef symbolic::AddExpr<symbolic::SymbolExpr<internal::symbolic_last_tag>,symbolic::ValueExpr<Eigen::internal::FixedInt<1> > > end_t;
-  typedef Eigen::internal::all_t all_t;
-
-  EIGEN_DEPRECATED static const all_t  all  = Eigen::all;    // PLEASE use Eigen::all    instead of Eigen::placeholders::all
-  EIGEN_DEPRECATED static const last_t last = Eigen::last;   // PLEASE use Eigen::last   instead of Eigen::placeholders::last
-  EIGEN_DEPRECATED static const end_t  end  = Eigen::lastp1; // PLEASE use Eigen::lastp1 instead of Eigen::placeholders::end
-}
+} // namespace placeholders
 
 } // end namespace Eigen
 

Eigen/src/Core/util/SymbolicIndex.h

@@ -37,7 +37,9 @@ namespace Eigen {
   * std::cout << expr98.eval(x=6) << "\n";
   * \endcode
   *
-  * It is currently only used internally to define and manipulate the Eigen::last and Eigen::lastp1 symbols in Eigen::seq and Eigen::seqN.
+  * It is currently only used internally to define and manipulate the
+  * Eigen::placeholders::last and Eigen::placeholders::lastp1 symbols in
+  * Eigen::seq and Eigen::seqN.
   *
   */
 namespace symbolic {

Eigen/src/plugins/IndexedViewMethods.h

@@ -218,7 +218,7 @@ operator()(const IndicesT (&indices)[IndicesN]) EIGEN_INDEXED_VIEW_METHOD_CONST
   *
   * Each parameter must either be:
   *  - An integer indexing a single row or column
-  *  - Eigen::all indexing the full set of respective rows or columns in increasing order
+  *  - Eigen::placeholders::all indexing the full set of respective rows or columns in increasing order
   *  - An ArithmeticSequence as returned by the Eigen::seq and Eigen::seqN functions
   *  - Any %Eigen's vector/array of integers or expressions
   *  - Plain C arrays: \c int[N]
@@ -235,7 +235,7 @@ operator()(const IndicesT (&indices)[IndicesN]) EIGEN_INDEXED_VIEW_METHOD_CONST
   * method will returns a Block object after extraction of the relevant information from the passed arguments. This is the case
   * when all arguments are either:
   *  - An integer
-  *  - Eigen::all
+  *  - Eigen::placeholders::all
   *  - An ArithmeticSequence with compile-time increment strictly equal to 1, as returned by Eigen::seq(a,b), and Eigen::seqN(a,N).
   *
   * Otherwise a more general IndexedView<Derived,RowIndices',ColIndices'> object will be returned, after conversion of the inputs

doc/TutorialSlicingIndexing.dox

@@ -15,7 +15,7 @@ All the aforementioned operations are handled through the generic DenseBase::ope
 Each argument can be:
   - An integer indexing a single row or column, including symbolic indices.
   - The symbol Eigen::all representing the whole set of respective rows or columns in increasing order.
-  - An ArithmeticSequence as constructed by the Eigen::seq, Eigen::seqN, or Eigen::lastN functions.
+  - An ArithmeticSequence as constructed by the Eigen::seq, Eigen::seqN, or Eigen::placeholders::lastN functions.
   - Any 1D vector/array of integers including %Eigen's vector/array, expressions, std::vector, std::array, as well as plain C arrays: `int[N]`.
 
 More generally, it can accepts any object exposing the following two member functions:
@@ -114,7 +114,8 @@ Here are some examples for a 2D array/matrix \c A and a 1D array/vector \c v.
 
 As seen in the last exemple, referencing the <i> last n </i> elements (or rows/columns) is a bit cumbersome to write.
 This becomes even more tricky and error prone with a non-default increment.
-Here comes \link Eigen::lastN(SizeType) Eigen::lastN(size) \endlink, and \link Eigen::lastN(SizeType,IncrType) Eigen::lastN(size,incr) \endlink:
+Here comes \link Eigen::placeholders::lastN(SizeType) Eigen::placeholders::lastN(size) \endlink, and
+\link Eigen::placeholders::lastN(SizeType,IncrType) Eigen::placeholders::lastN(size,incr) \endlink:
 
 <table class="manual">
 <tr>

test/indexed_view.cpp

@@ -36,7 +36,12 @@
 #include <vector>
 #include "main.h"
 
+using Eigen::placeholders::all;
+using Eigen::placeholders::last;
+using Eigen::placeholders::lastp1;
+
 #if EIGEN_HAS_CXX11
+using Eigen::placeholders::lastN;
 #include <array>
 #endif
 

test/reshape.cpp

@@ -10,6 +10,9 @@
 
 #include "main.h"
 
+using Eigen::placeholders::last;
+using Eigen::placeholders::all;
+
 template<typename T1,typename T2>
 typename internal::enable_if<internal::is_same<T1,T2>::value,bool>::type
 is_same_eq(const T1& a, const T2& b)

test/stl_iterators.cpp

@@ -133,6 +133,7 @@ void test_stl_iterators(int rows=Rows, int cols=Cols)
   ColMatrixType A = ColMatrixType::Random(rows,cols);
   const ColMatrixType& cA(A);
   RowMatrixType B = RowMatrixType::Random(rows,cols);
+  using Eigen::placeholders::last;
   
   Index i, j;
 

test/symbolic_index.cpp

@@ -19,6 +19,10 @@
 
 #include "main.h"
 
+using Eigen::placeholders::last;
+using Eigen::placeholders::lastp1;
+using Eigen::placeholders::all;
+
 template<typename T1,typename T2>
 bool is_same_symb(const T1& a, const T2& b, Index size)
 {