* split Product to a DiagonalProduct template specialization

  to optimize matrix-diag and diag-matrix products without
  making Product over complicated.
* compilation fixes in Tridiagonalization and HessenbergDecomposition
  in the case of 2x2 matrices.
* added an Orientation2D small class with similar interface than Quaternion
  (used by Transform to handle 2D and 3D orientations seamlessly)
* added a couple of features in Transform.

1 files changed, 108 insertions, 0 deletions

diff --git a/Eigen/src/Core/DiagonalProduct.h b/Eigen/src/Core/DiagonalProduct.h
new file mode 100644
index 000000000..5663942ff
--- /dev/null
+++ b/Eigen/src/Core/DiagonalProduct.h
@@ -0,0 +1,108 @@
+// 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>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.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_DIAGONALPRODUCT_H
+#define EIGEN_DIAGONALPRODUCT_H
+
+template<typename Lhs, typename Rhs>
+struct ei_traits<Product<Lhs, Rhs, DiagonalProduct> >
+{
+  typedef typename Lhs::Scalar Scalar;
+  typedef typename ei_nested<Lhs>::type LhsNested;
+  typedef typename ei_nested<Rhs>::type RhsNested;
+  typedef typename ei_unref<LhsNested>::type _LhsNested;
+  typedef typename ei_unref<RhsNested>::type _RhsNested;
+  enum {
+    LhsFlags = _LhsNested::Flags,
+    RhsFlags = _RhsNested::Flags,
+    RowsAtCompileTime = Lhs::RowsAtCompileTime,
+    ColsAtCompileTime = Rhs::ColsAtCompileTime,
+    MaxRowsAtCompileTime = Lhs::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = Rhs::MaxColsAtCompileTime,
+    _RhsVectorizable =  (RhsFlags & RowMajorBit) && (RhsFlags & VectorizableBit)
+                     && (ColsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
+    _LhsVectorizable =  (!(LhsFlags & RowMajorBit)) && (LhsFlags & VectorizableBit)
+                     && (RowsAtCompileTime % ei_packet_traits<Scalar>::size == 0),
+    _LostBits = ~(((RhsFlags & RowMajorBit) && (!_LhsVectorizable) ? 0 : RowMajorBit)
+                | ((RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic) ? 0 : LargeBit)),
+    Flags = ((unsigned int)(LhsFlags | RhsFlags) & HereditaryBits & _LostBits)
+          | (_LhsVectorizable || _RhsVectorizable ? VectorizableBit : 0),
+    CoeffReadCost = NumTraits<Scalar>::MulCost + _LhsNested::CoeffReadCost + _RhsNested::CoeffReadCost
+  };
+};
+
+template<typename Lhs, typename Rhs> class Product<Lhs, Rhs, DiagonalProduct> : ei_no_assignment_operator,
+  public MatrixBase<Product<Lhs, Rhs, DiagonalProduct> >
+{
+  public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
+    typedef typename ei_traits<Product>::LhsNested LhsNested;
+    typedef typename ei_traits<Product>::RhsNested RhsNested;
+    typedef typename ei_traits<Product>::_LhsNested _LhsNested;
+    typedef typename ei_traits<Product>::_RhsNested _RhsNested;
+
+    enum {
+      PacketSize = ei_packet_traits<Scalar>::size
+    };
+
+    inline Product(const Lhs& lhs, const Rhs& rhs)
+      : m_lhs(lhs), m_rhs(rhs)
+    {
+      ei_assert(lhs.cols() == rhs.rows());
+    }
+
+  private:
+
+    inline int _rows() const { return m_lhs.rows(); }
+    inline int _cols() const { return m_rhs.cols(); }
+
+    const Scalar _coeff(int row, int col) const
+    {
+      int unique = ((Rhs::Flags&Diagonal)==Diagonal) ? col : row;
+      return m_lhs.coeff(row, unique) * m_rhs.coeff(unique, col);
+    }
+
+    template<int LoadMode>
+    const PacketScalar _packetCoeff(int row, int col) const
+    {
+      if ((Rhs::Flags&Diagonal)==Diagonal)
+      {
+        ei_assert((_LhsNested::Flags&RowMajorBit)==0);
+        return ei_pmul(m_lhs.template packetCoeff<LoadMode>(row, col), ei_pset1(m_rhs.coeff(col, col)));
+      }
+      else
+      {
+        ei_assert(_RhsNested::Flags&RowMajorBit);
+        return ei_pmul(ei_pset1(m_lhs.coeff(row, row)), m_rhs.template packetCoeff<LoadMode>(row, col));
+      }
+    }
+
+  protected:
+    const LhsNested m_lhs;
+    const RhsNested m_rhs;
+};
+
+#endif // EIGEN_DIAGONALPRODUCT_H