New doc page on implementing a new expression class.

doc/examples/make_circulant.cpp

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+/*
+This program is presented in several fragments in the doc page.
+Every fragment is in its own file; this file simply combines them.
+*/
+
+#include "make_circulant.cpp.preamble"
+#include "make_circulant.cpp.traits"
+#include "make_circulant.cpp.expression"
+#include "make_circulant.cpp.evaluator"
+#include "make_circulant.cpp.entry"
+#include "make_circulant.cpp.main"

doc/examples/make_circulant.cpp.entry

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+template <class ArgType>
+Circulant<ArgType> makeCirculant(const Eigen::MatrixBase<ArgType>& arg)
+{
+  return Circulant<ArgType>(arg.derived());
+}

doc/examples/make_circulant.cpp.evaluator

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+namespace Eigen {
+  namespace internal {
+    template<typename ArgType>
+    struct evaluator<Circulant<ArgType> >
+      : evaluator_base<Circulant<ArgType> >
+    {
+      typedef Circulant<ArgType> XprType;
+      typedef typename nested_eval<ArgType, XprType::ColsAtCompileTime>::type ArgTypeNested;
+      typedef typename remove_all<ArgTypeNested>::type ArgTypeNestedCleaned;
+      typedef typename XprType::CoeffReturnType CoeffReturnType;
+      typedef typename XprType::Index Index;
+
+      enum { 
+        CoeffReadCost = evaluator<ArgTypeNestedCleaned>::CoeffReadCost,
+        Flags = Eigen::ColMajor 
+      };
+      
+      evaluator(const XprType& xpr)
+        : m_argImpl(xpr.m_arg), m_rows(xpr.rows())
+      { }
+
+      CoeffReturnType coeff(Index row, Index col) const
+      {
+        Index index = row - col;
+        if (index < 0) index += m_rows;
+        return m_argImpl.coeff(index);
+      }
+
+      typename evaluator<ArgTypeNestedCleaned>::nestedType m_argImpl;
+      const Index m_rows;
+    };
+  }
+}

doc/examples/make_circulant.cpp.expression

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+template <class ArgType>
+class Circulant : public Eigen::MatrixBase<Circulant<ArgType> >
+{
+public:
+  Circulant(const ArgType& arg)
+    : m_arg(arg)
+  { 
+    EIGEN_STATIC_ASSERT(ArgType::ColsAtCompileTime == 1,
+                        YOU_TRIED_CALLING_A_VECTOR_METHOD_ON_A_MATRIX);
+  }
+
+  typedef typename Eigen::internal::ref_selector<Circulant>::type Nested; 
+
+  typedef typename Eigen::internal::traits<Circulant>::Index Index;
+  Index rows() const { return m_arg.rows(); }
+  Index cols() const { return m_arg.rows(); }
+
+  typedef typename Eigen::internal::ref_selector<ArgType>::type ArgTypeNested;
+  ArgTypeNested m_arg;
+};

doc/examples/make_circulant.cpp.main

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+int main()
+{
+  Eigen::VectorXd vec(4);
+  vec << 1, 2, 4, 8;
+  Eigen::MatrixXd mat;
+  mat = makeCirculant(vec);
+  std::cout << mat << std::endl;
+}

doc/examples/make_circulant.cpp.preamble

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+#include <Eigen/Core>
+#include <iostream>
+
+template <class ArgType> class Circulant;

doc/examples/make_circulant.cpp.traits

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+namespace Eigen {
+  namespace internal {
+    template <class ArgType>
+    struct traits<Circulant<ArgType> > 
+    {
+      typedef Eigen::Dense StorageKind;
+      typedef Eigen::MatrixXpr XprKind;
+      typedef typename ArgType::Index Index;
+      typedef typename ArgType::Scalar Scalar;
+      enum { 
+        Flags = Eigen::ColMajor,
+        RowsAtCompileTime = ArgType::RowsAtCompileTime,
+        ColsAtCompileTime = ArgType::RowsAtCompileTime,
+        MaxRowsAtCompileTime = ArgType::MaxRowsAtCompileTime,
+        MaxColsAtCompileTime = ArgType::MaxRowsAtCompileTime
+      };
+    };
+  }
+}