Add sub/super-diagonal expression (read/write) as a trivial extension of

DiagonalCoeffs. The current API is simply:
  m.diagonal<1>() => 1st super diagonal
  m.diagonal<-2>() => the 2nd sub diagonal
I'll add a code snippet once we agree on this API.

Eigen/src/Core/DiagonalCoeffs.h

@@ -39,16 +39,17 @@
   *
   * \sa MatrixBase::diagonal()
   */
-template<typename MatrixType>
-struct ei_traits<DiagonalCoeffs<MatrixType> >
+template<typename MatrixType, int DiagId>
+struct ei_traits<DiagonalCoeffs<MatrixType,DiagId> >
 {
   typedef typename MatrixType::Scalar Scalar;
   typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
   typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
   enum {
+    AbsDiagId = DiagId<0 ? -DiagId : DiagId,
     RowsAtCompileTime = int(MatrixType::SizeAtCompileTime) == Dynamic ? Dynamic
                       : EIGEN_ENUM_MIN(MatrixType::RowsAtCompileTime,
-                                       MatrixType::ColsAtCompileTime),
+                                       MatrixType::ColsAtCompileTime) - AbsDiagId,
     ColsAtCompileTime = 1,
     MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
                             : EIGEN_ENUM_MIN(MatrixType::MaxRowsAtCompileTime,
@@ -59,9 +60,14 @@ struct ei_traits<DiagonalCoeffs<MatrixType> >
   };
 };
 
-template<typename MatrixType> class DiagonalCoeffs
-   : public MatrixBase<DiagonalCoeffs<MatrixType> >
+template<typename MatrixType, int DiagId> class DiagonalCoeffs
+   : public MatrixBase<DiagonalCoeffs<MatrixType, DiagId> >
 {
+    enum {
+      AbsDiagId = DiagId<0 ? -DiagId : DiagId,
+      OffsetRow = DiagId<0 ? -DiagId : 0,
+      OffsetCol = DiagId<0 ? 0 : DiagId
+    };
   public:
 
     EIGEN_GENERIC_PUBLIC_INTERFACE(DiagonalCoeffs)
@@ -70,27 +76,27 @@ template<typename MatrixType> class DiagonalCoeffs
 
     EIGEN_INHERIT_ASSIGNMENT_OPERATORS(DiagonalCoeffs)
 
-    inline int rows() const { return std::min(m_matrix.rows(), m_matrix.cols()); }
+    inline int rows() const { return std::min(m_matrix.rows(), m_matrix.cols()) - AbsDiagId; }
     inline int cols() const { return 1; }
 
     inline Scalar& coeffRef(int row, int)
     {
-      return m_matrix.const_cast_derived().coeffRef(row, row);
+      return m_matrix.const_cast_derived().coeffRef(row+OffsetRow, row+OffsetCol);
     }
 
     inline const Scalar coeff(int row, int) const
     {
-      return m_matrix.coeff(row, row);
+      return m_matrix.coeff(row+OffsetRow, row+OffsetCol);
     }
 
     inline Scalar& coeffRef(int index)
     {
-      return m_matrix.const_cast_derived().coeffRef(index, index);
+      return m_matrix.const_cast_derived().coeffRef(index+OffsetRow, index+OffsetCol);
     }
 
     inline const Scalar coeff(int index) const
     {
-      return m_matrix.coeff(index, index);
+      return m_matrix.coeff(index+OffsetRow, index+OffsetCol);
     }
 
   protected:
@@ -121,4 +127,29 @@ MatrixBase<Derived>::diagonal() const
   return DiagonalCoeffs<Derived>(derived());
 }
 
+/** \returns an expression of the \a Id-th sub or super diagonal of the matrix \c *this
+  *
+  * \c *this is not required to be square.
+  *
+  * The template parameter \a Id represent a super diagonal if \a Id > 0
+  * and a sub diagonal otherwise. \a Id == 0 is equivalent to the main diagonal.
+  *
+  * \sa class DiagonalCoeffs */
+template<typename Derived>
+template<int Id>
+inline DiagonalCoeffs<Derived,Id>
+MatrixBase<Derived>::diagonal()
+{
+  return DiagonalCoeffs<Derived,Id>(derived());
+}
+
+/** This is the const version of diagonal<int>(). */
+template<typename Derived>
+template<int Id>
+inline const DiagonalCoeffs<Derived,Id>
+MatrixBase<Derived>::diagonal() const
+{
+  return DiagonalCoeffs<Derived,Id>(derived());
+}
+
 #endif // EIGEN_DIAGONALCOEFFS_H

Eigen/src/Core/MatrixBase.h

@@ -408,6 +408,9 @@ template<typename Derived> class MatrixBase
     DiagonalCoeffs<Derived> diagonal();
     const DiagonalCoeffs<Derived> diagonal() const;
 
+    template<int Id> DiagonalCoeffs<Derived,Id> diagonal();
+    template<int Id> const DiagonalCoeffs<Derived,Id> diagonal() const;
+
     template<unsigned int Mode> Part<Derived, Mode> part();
     template<unsigned int Mode> const Part<Derived, Mode> part() const;
 

Eigen/src/Core/util/ForwardDeclarations.h

@@ -48,7 +48,7 @@ template<typename Lhs, typename Rhs, int ProductMode> class Product;
 template<typename CoeffsVectorType, typename Derived> class DiagonalMatrixBase;
 template<typename CoeffsVectorType> class DiagonalMatrixWrapper;
 template<typename _Scalar, int _Size> class DiagonalMatrix;
-template<typename MatrixType> class DiagonalCoeffs;
+template<typename MatrixType, int DiagId=0> class DiagonalCoeffs;
 template<typename MatrixType, int PacketAccess = AsRequested> class Map;
 template<typename MatrixType, unsigned int Mode> class Part;
 template<typename MatrixType, unsigned int Mode> class Extract;

Eigen/src/Core/util/Macros.h

@@ -41,7 +41,7 @@
 // because extra memory must be allocated for bookkeeping).
 // if the compiler is not GNUC, just cross fingers that the architecture isn't too exotic, because we don't want
 // to keep track of all the different preprocessor symbols for all compilers.
-#if !defined(__GNUC__) || defined(__i386__) || defined(__x86_64__) || defined(__ppc__) || defined(__ia64__)
+#if (!defined(__GNUC__)) || defined(__i386__) || defined(__x86_64__) || defined(__ppc__) || defined(__ia64__)
   #define EIGEN_ARCH_WANTS_ALIGNMENT 1
 #else
   #ifdef EIGEN_VECTORIZE

test/submatrices.cpp

@@ -138,6 +138,20 @@ template<typename MatrixType> void submatrices(const MatrixType& m)
     VERIFY_IS_APPROX(v1.template end<2>(), v1.template segment<2>(i));
     i = ei_random(0,rows-2);
     VERIFY_IS_APPROX(v1.segment(i,2), v1.template segment<2>(i));
+
+    enum {
+      N1 = MatrixType::RowsAtCompileTime>1 ?  1 : 0,
+      N2 = MatrixType::RowsAtCompileTime>2 ? -2 : 0
+    };
+
+    // check sub/super diagonal
+    m2.template diagonal<N1>() = 2 * m1.template diagonal<N1>();
+    m2.template diagonal<N1>()[0] *= 3;
+    VERIFY_IS_APPROX(m2.template diagonal<N1>()[0], static_cast<Scalar>(6) * m1.template diagonal<N1>()[0]);
+
+    m2.template diagonal<N2>() = 2 * m1.template diagonal<N2>();
+    m2.template diagonal<N2>()[0] *= 3;
+    VERIFY_IS_APPROX(m2.template diagonal<N2>()[0], static_cast<Scalar>(6) * m1.template diagonal<N2>()[0]);
   }
 
   // stress some basic stuffs with block matrices