* added a pseudo expression Array giving access to:

- matrix-scalar addition/subtraction operators, e.g.:
       m.array() += 0.5;
   - matrix/matrix comparison operators, e.g.:
      if (m1.array() < m2.array()) {}
* fix compilation issues with Transform and gcc < 4.1

Eigen/Array

@@ -10,6 +10,7 @@ namespace Eigen {
 #include "src/Array/AllAndAny.h"
 #include "src/Array/PartialRedux.h"
 #include "src/Array/Random.h"
+#include "src/Array/Array.h"
 
 } // namespace Eigen
 

Eigen/src/Array/Array.h

@@ -0,0 +1,152 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ARRAY_H
+#define EIGEN_ARRAY_H
+
+/** \class Array
+  *
+  * \brief Pseudo expression offering additional features to an expression
+  *
+  * \param ExpressionType the type of the object of which we want array related features
+  *
+  * This class represents an expression with additional, array related, features.
+  * It is the return type of MatrixBase::array()
+  * and most of the time this is the only way it is used.
+  *
+  * \sa MatrixBase::array()
+  */
+template<typename ExpressionType> class Array
+{
+  public:
+
+    typedef typename ei_traits<ExpressionType>::Scalar Scalar;
+    typedef typename ei_meta_if<ei_must_nest_by_value<ExpressionType>::ret,
+        ExpressionType, const ExpressionType&>::ret ExpressionTypeNested;
+//     typedef NestByValue<typename ExpressionType::ConstantReturnType> ConstantReturnType;
+    typedef CwiseUnaryOp<ei_scalar_add_op<Scalar>, ExpressionType> ScalarAddReturnType;
+
+    inline Array(const ExpressionType& matrix) : m_matrix(matrix) {}
+
+    /** \internal */
+    inline const ExpressionType& _expression() const { return m_matrix; }
+
+    const ScalarAddReturnType
+    operator+(const Scalar& scalar) const;
+
+    /** \relates Array */
+    friend const ScalarAddReturnType
+    operator+(const Scalar& scalar, const Array& mat)
+    { return mat + scalar; }
+
+    ExpressionType& operator+=(const Scalar& scalar);
+
+    const ScalarAddReturnType
+    operator-(const Scalar& scalar) const;
+
+    ExpressionType& operator-=(const Scalar& scalar);
+
+    /** \returns true if each coeff of \c *this is less than its respective coeff of \a other */
+    template<typename OtherDerived> bool operator<(const Array<OtherDerived>& other) const
+    { return m_matrix.cwiseLessThan(other._expression()).all(); }
+
+    /** \returns true if each coeff of \c *this is less or equal to its respective coeff of \a other */
+    template<typename OtherDerived> bool operator<=(const Array<OtherDerived>& other) const
+    { return m_matrix.cwiseLessEqual(other._expression()).all(); }
+
+    /** \returns true if each coeff of \c *this is greater to its respective coeff of \a other */
+    template<typename OtherDerived>
+    bool operator>(const Array<OtherDerived>& other) const
+    { return m_matrix.cwiseGreaterThan(other._expression()).all(); }
+
+    /** \returns true if each coeff of \c *this is greater or equal to its respective coeff of \a other */
+    template<typename OtherDerived>
+    bool operator>=(const Array<OtherDerived>& other) const
+    { return m_matrix.cwiseGreaterEqual(other._expression()).all(); }
+
+  protected:
+    ExpressionTypeNested m_matrix;
+};
+
+/** \returns an expression of \c *this with each coeff incremented by the constant \a scalar */
+template<typename ExpressionType>
+const typename Array<ExpressionType>::ScalarAddReturnType
+Array<ExpressionType>::operator+(const Scalar& scalar) const
+{
+  return CwiseUnaryOp<ei_scalar_add_op<Scalar>, ExpressionType>(m_matrix, ei_scalar_add_op<Scalar>(scalar));
+}
+
+/** \see operator+ */
+template<typename ExpressionType>
+ExpressionType& Array<ExpressionType>::operator+=(const Scalar& scalar)
+{
+  m_matrix.const_cast_derived() = *this + scalar;
+  return m_matrix.const_cast_derived();
+}
+
+/** \returns an expression of \c *this with each coeff decremented by the constant \a scalar */
+template<typename ExpressionType>
+const typename Array<ExpressionType>::ScalarAddReturnType
+Array<ExpressionType>::operator-(const Scalar& scalar) const
+{
+  return *this + (-scalar);
+}
+
+/** \see operator- */
+template<typename ExpressionType>
+ExpressionType& Array<ExpressionType>::operator-=(const Scalar& scalar)
+{
+  m_matrix.const_cast_derived() = *this - scalar;
+  return m_matrix.const_cast_derived();
+}
+
+/** \array_module
+  *
+  * \returns an Array expression of *this providing additional,
+  * array related, features.
+  *
+  * \sa class Array
+  */
+template<typename Derived>
+inline const Array<Derived>
+MatrixBase<Derived>::array() const
+{
+  return derived();
+}
+
+/** \array_module
+  *
+  * \returns an Array expression of *this providing additional,
+  * array related, features.
+  *
+  * \sa class Array
+  */
+template<typename Derived>
+inline Array<Derived>
+MatrixBase<Derived>::array()
+{
+  return derived();
+}
+
+#endif // EIGEN_FLAGGED_H

Eigen/src/Array/Functors.h

@@ -25,10 +25,38 @@
 #ifndef EIGEN_ARRAY_FUNCTORS_H
 #define EIGEN_ARRAY_FUNCTORS_H
 
+/** \internal
+  * \array_module
+  *
+  * \brief Template functor to add a scalar to a fixed other one
+  *
+  * \sa class CwiseUnaryOp, Array::operator+
+  */
+template<typename Scalar, bool PacketAccess = (int(ei_packet_traits<Scalar>::size)>1?true:false) > struct ei_scalar_add_op;
+
+template<typename Scalar>
+struct ei_scalar_add_op<Scalar,true> {
+  typedef typename ei_packet_traits<Scalar>::type PacketScalar;
+  inline ei_scalar_add_op(const Scalar& other) : m_other(ei_pset1(other)) { }
+  inline Scalar operator() (const Scalar& a) const { return a + ei_pfirst(m_other); }
+  inline const PacketScalar packetOp(const PacketScalar& a) const
+  { return ei_padd(a, m_other); }
+  const PacketScalar m_other;
+};
+template<typename Scalar>
+struct ei_scalar_add_op<Scalar,false> {
+  inline ei_scalar_add_op(const Scalar& other) : m_other(other) { }
+  inline Scalar operator() (const Scalar& a) const { return a + m_other; }
+  const Scalar m_other;
+};
+template<typename Scalar>
+struct ei_functor_traits<ei_scalar_add_op<Scalar> >
+{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = ei_packet_traits<Scalar>::size>1 }; };
+
 /** \internal
   *
   * \array_module
-  * 
+  *
   * \brief Template functor to compute the square root of a scalar
   *
   * \sa class CwiseUnaryOp, MatrixBase::cwiseSqrt()
@@ -43,7 +71,7 @@ struct ei_functor_traits<ei_scalar_sqrt_op<Scalar> >
 /** \internal
   *
   * \array_module
-  * 
+  *
   * \brief Template functor to compute the exponential of a scalar
   *
   * \sa class CwiseUnaryOp, MatrixBase::cwiseExp()
@@ -58,7 +86,7 @@ struct ei_functor_traits<ei_scalar_exp_op<Scalar> >
 /** \internal
   *
   * \array_module
-  * 
+  *
   * \brief Template functor to compute the logarithm of a scalar
   *
   * \sa class CwiseUnaryOp, MatrixBase::cwiseLog()
@@ -73,7 +101,7 @@ struct ei_functor_traits<ei_scalar_log_op<Scalar> >
 /** \internal
   *
   * \array_module
-  * 
+  *
   * \brief Template functor to compute the cosine of a scalar
   *
   * \sa class CwiseUnaryOp, MatrixBase::cwiseCos()
@@ -88,7 +116,7 @@ struct ei_functor_traits<ei_scalar_cos_op<Scalar> >
 /** \internal
   *
   * \array_module
-  * 
+  *
   * \brief Template functor to compute the sine of a scalar
   *
   * \sa class CwiseUnaryOp, MatrixBase::cwiseSin()
@@ -103,7 +131,7 @@ struct ei_functor_traits<ei_scalar_sin_op<Scalar> >
 /** \internal
   *
   * \array_module
-  * 
+  *
   * \brief Template functor to raise a scalar to a power
   *
   * \sa class CwiseUnaryOp, MatrixBase::cwisePow
@@ -121,7 +149,7 @@ struct ei_functor_traits<ei_scalar_pow_op<Scalar> >
 /** \internal
   *
   * \array_module
-  * 
+  *
   * \brief Template functor to compute the reciprocal of a scalar
   *
   * \sa class CwiseUnaryOp, MatrixBase::cwiseInverse

Eigen/src/Core/MatrixBase.h

@@ -482,6 +482,9 @@ template<typename Derived> class MatrixBase
 
 /////////// Array module ///////////
 
+    const Array<Derived> array() const;
+    Array<Derived> array();
+
     const CwiseUnaryOp<ei_scalar_sqrt_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseSqrt() const;
     const CwiseUnaryOp<ei_scalar_exp_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseExp() const;
     const CwiseUnaryOp<ei_scalar_log_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseLog() const;

Eigen/src/Core/util/ForwardDeclarations.h

@@ -55,7 +55,7 @@ template<typename MatrixType> class Map;
 template<int Direction, typename UnaryOp, typename MatrixType> class PartialRedux;
 template<typename MatrixType, unsigned int Mode> class Part;
 template<typename MatrixType, unsigned int Mode> class Extract;
-template<typename Derived, bool HasArrayFlag = int(ei_traits<Derived>::Flags) & ArrayBit> class ArrayBase {};
+template<typename MatrixType> class Array;
 template<typename Lhs, typename Rhs> class Cross;
 template<typename Scalar> class Quaternion;
 template<typename Scalar> class Rotation2D;

Eigen/src/Geometry/Transform.h

@@ -25,6 +25,16 @@
 #ifndef EIGEN_TRANSFORM_H
 #define EIGEN_TRANSFORM_H
 
+// Note that we have to pass Dim and HDim because it is not allowed to use a template
+// parameter to define a template specialization. To be more precise, in the following
+// specializations, it is not allowed to use Dim+1 instead of HDim.
+template< typename Other,
+          int Dim,
+          int HDim,
+          int OtherRows=Other::RowsAtCompileTime,
+          int OtherCols=Other::ColsAtCompileTime>
+struct ei_transform_product_impl;
+
 /** \class Transform
   *
   * \brief Represents an homogeneous transformation in a N dimensional space
@@ -57,52 +67,6 @@ protected:
 
   MatrixType m_matrix;
 
-  template<typename Other,
-  int OtherRows=Other::RowsAtCompileTime,
-  int OtherCols=Other::ColsAtCompileTime>
-  struct ei_transform_product_impl;
-
-  // FIXME these specializations of ei_transform_product_impl does not work with gcc 3.3 and 3.4 because
-  // Dim depends on a template parameter. Replacing Dim by 3 (for the 3D case) works.
-
-  // note that these specializations have to be defined here,
-  // otherwise some compilers (at least ICC and NVCC) complain about
-  // the use of Dim in the specialization parameters.
-  template<typename Other>
-  struct ei_transform_product_impl<Other,Dim+1,Dim+1>
-  {
-    typedef typename Transform<Scalar,Dim>::MatrixType MatrixType;
-    typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
-    static ResultType run(const Transform<Scalar,Dim>& tr, const Other& other)
-    { return tr.matrix() * other; }
-  };
-
-  template<typename Other>
-  struct ei_transform_product_impl<Other,Dim+1,1>
-  {
-    typedef typename Transform<Scalar,Dim>::MatrixType MatrixType;
-    typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
-    static ResultType run(const Transform<Scalar,Dim>& tr, const Other& other)
-    { return tr.matrix() * other; }
-  };
-
-  template<typename Other>
-  struct ei_transform_product_impl<Other,Dim,1>
-  {
-    typedef typename Transform<Scalar,Dim>::AffineMatrixRef MatrixType;
-    typedef const CwiseUnaryOp<
-        ei_scalar_multiple_op<Scalar>,
-        NestByValue<CwiseBinaryOp<
-          ei_scalar_sum_op<Scalar>,
-          NestByValue<typename ProductReturnType<NestByValue<MatrixType>,Other>::Type >,
-          NestByValue<typename Transform<Scalar,Dim>::VectorRef> > >
-        > ResultType;
-    // FIXME shall we offer an optimized version when the last row is know to be 0,0...,0,1 ?
-    static ResultType run(const Transform<Scalar,Dim>& tr, const Other& other)
-    { return ((tr.affine().nestByValue() * other).nestByValue() + tr.translation().nestByValue()).nestByValue()
-            * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
-  };
-
 public:
 
   /** Default constructor without initialization of the coefficients. */
@@ -144,7 +108,7 @@ public:
   inline VectorRef translation() { return m_matrix.template block<Dim,1>(0,Dim); }
 
   template<typename OtherDerived>
-  const typename ei_transform_product_impl<OtherDerived>::ResultType
+  const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
   operator * (const MatrixBase<OtherDerived> &other) const;
 
   /** Contatenates two transformations */
@@ -225,12 +189,17 @@ QMatrix Transform<Scalar,Dim>::toQMatrix(void) const
 }
 #endif
 
+/** \returns an expression of the product between the transform \c *this and a matrix expression \a other
+  *
+  * The right hand side \a other might be a vector of size Dim, an homogeneous vector of size Dim+1
+  * or a transformation matrix of size Dim+1 x Dim+1.
+  */
 template<typename Scalar, int Dim>
 template<typename OtherDerived>
-const typename Transform<Scalar,Dim>::template ei_transform_product_impl<OtherDerived>::ResultType
+const typename ei_transform_product_impl<OtherDerived,Dim,Dim+1>::ResultType
 Transform<Scalar,Dim>::operator*(const MatrixBase<OtherDerived> &other) const
 {
-  return ei_transform_product_impl<OtherDerived>::run(*this,other.derived());
+  return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived());
 }
 
 /** Applies on the right the non uniform scale transformation represented
@@ -408,4 +377,47 @@ Transform<Scalar,Dim>::fromPositionOrientationScale(const MatrixBase<PositionDer
   return *this;
 }
 
+/***********************************
+*** Specializations of operator* ***
+***********************************/
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim>
+{
+  typedef Transform<typename Other::Scalar,Dim> Transform;
+  typedef typename Transform::MatrixType MatrixType;
+  typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
+  static ResultType run(const Transform& tr, const Other& other)
+  { return tr.matrix() * other; }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, HDim,1>
+{
+  typedef Transform<typename Other::Scalar,Dim> Transform;
+  typedef typename Transform::MatrixType MatrixType;
+  typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
+  static ResultType run(const Transform& tr, const Other& other)
+  { return tr.matrix() * other; }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
+{
+  typedef typename Other::Scalar Scalar;
+  typedef Transform<Scalar,Dim> Transform;
+  typedef typename Transform::AffineMatrixRef MatrixType;
+  typedef const CwiseUnaryOp<
+      ei_scalar_multiple_op<Scalar>,
+      NestByValue<CwiseBinaryOp<
+        ei_scalar_sum_op<Scalar>,
+        NestByValue<typename ProductReturnType<NestByValue<MatrixType>,Other>::Type >,
+        NestByValue<typename Transform::VectorRef> > >
+      > ResultType;
+  // FIXME shall we offer an optimized version when the last row is known to be 0,0...,0,1 ?
+  static ResultType run(const Transform& tr, const Other& other)
+  { return ((tr.affine().nestByValue() * other).nestByValue() + tr.translation().nestByValue()).nestByValue()
+          * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
+};
+
 #endif // EIGEN_TRANSFORM_H

test/CMakeLists.txt

@@ -86,6 +86,7 @@ EI_ADD_TEST(submatrices)
 EI_ADD_TEST(miscmatrices)
 EI_ADD_TEST(smallvectors)
 EI_ADD_TEST(map)
+EI_ADD_TEST(array)
 EI_ADD_TEST(triangular)
 EI_ADD_TEST(cholesky)
 # EI_ADD_TEST(determinant)

test/linearstructure.cpp

@@ -94,6 +94,7 @@ void test_linearstructure()
 {
   for(int i = 0; i < g_repeat; i++) {
     CALL_SUBTEST( linearStructure(Matrix<float, 1, 1>()) );
+    CALL_SUBTEST( linearStructure(Matrix2f()) );
     CALL_SUBTEST( linearStructure(Matrix4d()) );
     CALL_SUBTEST( linearStructure(MatrixXcf(3, 3)) );
     CALL_SUBTEST( linearStructure(MatrixXf(8, 12)) );