trmm is now fully working and available via TriangularView::operator*

3 files changed, 501 insertions, 30 deletions

diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h
index d2f1e6c28..861b738cb 100644
--- a/Eigen/src/Core/TriangularMatrix.h
+++ b/Eigen/src/Core/TriangularMatrix.h
@@ -142,8 +142,10 @@ struct ei_traits<TriangularView<MatrixType, _Mode> > : ei_traits<MatrixType>
   };
 };
 
-template<typename Lhs,typename Rhs>
-struct ei_triangular_vector_product_returntype;
+template<int Mode, bool LhsIsTriangular,
+         typename Lhs, bool LhsIsVector,
+         typename Rhs, bool RhsIsVector>
+struct ei_triangular_product_returntype;
 
 template<typename _MatrixType, unsigned int _Mode> class TriangularView
   : public TriangularBase<TriangularView<_MatrixType, _Mode> >
@@ -247,11 +249,24 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
       return res;
     }
 
+    /** Efficient triangular matrix times vector/matrix product */
     template<typename OtherDerived>
-    ei_triangular_vector_product_returntype<TriangularView,OtherDerived>
+    ei_triangular_product_returntype<Mode,true,MatrixType,false,OtherDerived,OtherDerived::IsVectorAtCompileTime>
     operator*(const MatrixBase<OtherDerived>& rhs) const
     {
-      return ei_triangular_vector_product_returntype<TriangularView,OtherDerived>(*this, rhs.derived(), 1);
+      return ei_triangular_product_returntype
+              <Mode,true,MatrixType,false,OtherDerived,OtherDerived::IsVectorAtCompileTime>
+              (m_matrix, rhs.derived());
+    }
+
+    /** Efficient vector/matrix times triangular matrix product */
+    template<typename OtherDerived> friend
+    ei_triangular_product_returntype<Mode,false,OtherDerived,OtherDerived::IsVectorAtCompileTime,MatrixType,false>
+    operator*(const MatrixBase<OtherDerived>& lhs, const TriangularView& rhs)
+    {
+      return ei_triangular_product_returntype
+              <Mode,false,OtherDerived,OtherDerived::IsVectorAtCompileTime,MatrixType,false>
+              (lhs.derived(),rhs.m_matrix);
     }
 
     template<typename OtherDerived>
diff --git a/Eigen/src/Core/products/TriangularMatrixMatrix.h b/Eigen/src/Core/products/TriangularMatrixMatrix.h
new file mode 100644
index 000000000..43a4c3d18
--- /dev/null
+++ b/Eigen/src/Core/products/TriangularMatrixMatrix.h
@@ -0,0 +1,392 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 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_TRIANGULAR_MATRIX_MATRIX_H
+#define EIGEN_TRIANGULAR_MATRIX_MATRIX_H
+
+// template<typename Scalar, int mr, int StorageOrder, bool Conjugate, int Mode>
+// struct ei_gemm_pack_lhs_triangular
+// {
+//   Matrix<Scalar,mr,mr,
+//   void operator()(Scalar* blockA, const EIGEN_RESTRICT Scalar* _lhs, int lhsStride, int depth, int rows)
+//   {
+//     ei_conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
+//     ei_const_blas_data_mapper<Scalar, StorageOrder> lhs(_lhs,lhsStride);
+//     int count = 0;
+//     const int peeled_mc = (rows/mr)*mr;
+//     for(int i=0; i<peeled_mc; i+=mr)
+//     {
+//       for(int k=0; k<depth; k++)
+//         for(int w=0; w<mr; w++)
+//           blockA[count++] = cj(lhs(i+w, k));
+//     }
+//     for(int i=peeled_mc; i<rows; i++)
+//     {
+//       for(int k=0; k<depth; k++)
+//         blockA[count++] = cj(lhs(i, k));
+//     }
+//   }
+// };
+
+/* Optimized selfadjoint matrix * matrix (_SYMM) product built on top of
+ * the general matrix matrix product.
+ */
+template <typename Scalar,
+          int Mode, bool LhsIsTriangular,
+          int LhsStorageOrder, bool ConjugateLhs,
+          int RhsStorageOrder, bool ConjugateRhs,
+          int ResStorageOrder>
+struct ei_product_triangular_matrix_matrix;
+
+template <typename Scalar,
+          int Mode, bool LhsIsTriangular,
+          int LhsStorageOrder, bool ConjugateLhs,
+          int RhsStorageOrder, bool ConjugateRhs>
+struct ei_product_triangular_matrix_matrix<Scalar,Mode,LhsIsTriangular,
+                                           LhsStorageOrder,ConjugateLhs,
+                                           RhsStorageOrder,ConjugateRhs,RowMajor>
+{
+  static EIGEN_STRONG_INLINE void run(
+    int size, int otherSize,
+    const Scalar* lhs, int lhsStride,
+    const Scalar* rhs, int rhsStride,
+    Scalar* res,       int resStride,
+    Scalar alpha)
+  {
+    ei_product_triangular_matrix_matrix<Scalar,
+      (Mode&UnitDiagBit) | (Mode&UpperTriangular) ? LowerTriangular : UpperTriangular,
+      (!LhsIsTriangular),
+      RhsStorageOrder==RowMajor ? ColMajor : RowMajor,
+      ConjugateRhs,
+      LhsStorageOrder==RowMajor ? ColMajor : RowMajor,
+      ConjugateLhs,
+      ColMajor>
+      ::run(size, otherSize, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha);
+  }
+};
+
+// implements col-major += alpha * op(triangular) * op(general)
+template <typename Scalar, int Mode,
+          int LhsStorageOrder, bool ConjugateLhs,
+          int RhsStorageOrder, bool ConjugateRhs>
+struct ei_product_triangular_matrix_matrix<Scalar,Mode,true,
+                                           LhsStorageOrder,ConjugateLhs,
+                                           RhsStorageOrder,ConjugateRhs,ColMajor>
+{
+
+  static EIGEN_DONT_INLINE void run(
+    int size, int cols,
+    const Scalar* _lhs, int lhsStride,
+    const Scalar* _rhs, int rhsStride,
+    Scalar* res,        int resStride,
+    Scalar alpha)
+  {
+    int rows = size;
+    
+    ei_const_blas_data_mapper<Scalar, LhsStorageOrder> lhs(_lhs,lhsStride);
+    ei_const_blas_data_mapper<Scalar, RhsStorageOrder> rhs(_rhs,rhsStride);
+
+    if (ConjugateRhs)
+      alpha = ei_conj(alpha);
+
+    typedef ei_product_blocking_traits<Scalar> Blocking;
+    enum {
+      SmallPanelWidth   = EIGEN_ENUM_MAX(Blocking::mr,Blocking::nr),
+      IsLowerTriangular = (Mode&LowerTriangular) == LowerTriangular
+    };
+
+    int kc = std::min<int>(Blocking::Max_kc/4,size); // cache block size along the K direction
+    int mc = std::min<int>(Blocking::Max_mc,rows);   // cache block size along the M direction
+
+    Scalar* blockA = ei_aligned_stack_new(Scalar, kc*mc);
+    Scalar* blockB = ei_aligned_stack_new(Scalar, kc*cols*Blocking::PacketSize);
+
+    Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
+    triangularBuffer.setZero();
+    triangularBuffer.diagonal().setOnes();
+
+    ei_gebp_kernel<Scalar, Blocking::mr, Blocking::nr, ei_conj_helper<ConjugateLhs,ConjugateRhs> > gebp_kernel;
+    ei_gemm_pack_lhs<Scalar,Blocking::mr,LhsStorageOrder> pack_lhs;
+    ei_gemm_pack_rhs<Scalar,Blocking::nr,RhsStorageOrder> pack_rhs;
+
+    for(int k2=IsLowerTriangular ? size : 0;
+        IsLowerTriangular ? k2>0 : k2<size;
+        IsLowerTriangular ? k2-=kc : k2+=kc)
+    {
+      const int actual_kc = std::min(IsLowerTriangular ? k2 : size-k2, kc);
+      int actual_k2 = IsLowerTriangular ? k2-actual_kc : k2;
+
+      pack_rhs(blockB, &rhs(actual_k2,0), rhsStride, alpha, actual_kc, cols);
+
+      // the selected lhs's panel has to be split in three different parts:
+      //  1 - the part which is above the diagonal block => skip it
+      //  2 - the diagonal block => special kernel
+      //  3 - the panel below the diagonal block => GEPP
+      // the block diagonal
+      {
+        // for each small vertical panels of lhs
+        for (int k1=0; k1<actual_kc; k1+=SmallPanelWidth)
+        {
+          int actualPanelWidth = std::min<int>(actual_kc-k1, SmallPanelWidth);
+          int lengthTarget = IsLowerTriangular ? actual_kc-k1-actualPanelWidth : k1;
+          int startBlock   = actual_k2+k1;
+          int blockBOffset = k1;
+          
+          // => GEBP with the micro triangular block
+          // The trick is to pack this micro block while filling the opposite triangular part with zeros.
+          // To this end we do an extra triangular copy to small temporary buffer
+          for (int k=0;k<actualPanelWidth;++k)
+          {
+            if (!(Mode&UnitDiagBit))
+              triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
+            for (int i=IsLowerTriangular ? k+1 : 0; IsLowerTriangular ? i<actualPanelWidth : i<k; ++i)
+              triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
+          }
+          pack_lhs(blockA, triangularBuffer.data(), triangularBuffer.stride(), actualPanelWidth, actualPanelWidth);
+
+          gebp_kernel(res+startBlock, resStride, blockA, blockB, actualPanelWidth, actualPanelWidth, cols,
+                      actualPanelWidth, actual_kc, 0, blockBOffset*Blocking::PacketSize);
+
+          // GEBP with remaining micro panel
+          if (lengthTarget>0)
+          {
+            int startTarget  = IsLowerTriangular ? actual_k2+k1+actualPanelWidth : actual_k2;
+
+            pack_lhs(blockA, &lhs(startTarget,startBlock), lhsStride, actualPanelWidth, lengthTarget);
+
+            gebp_kernel(res+startTarget, resStride, blockA, blockB, lengthTarget, actualPanelWidth, cols,
+                        actualPanelWidth, actual_kc, 0, blockBOffset*Blocking::PacketSize);
+          }
+        }
+      }
+      // the part below the diagonal => GEPP
+      {
+        int start = IsLowerTriangular ? k2 : 0;
+        int end   = IsLowerTriangular ? size : actual_k2;
+        for(int i2=start; i2<end; i2+=mc)
+        {
+          const int actual_mc = std::min(i2+mc,end)-i2;
+          ei_gemm_pack_lhs<Scalar,Blocking::mr,LhsStorageOrder,false>()
+            (blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
+
+          gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols);
+        }
+      }
+    }
+
+    ei_aligned_stack_delete(Scalar, blockA, kc*mc);
+    ei_aligned_stack_delete(Scalar, blockB, kc*cols*Blocking::PacketSize);
+  }
+};
+
+// implements col-major += alpha * op(general) * op(triangular)
+template <typename Scalar, int Mode,
+          int LhsStorageOrder, bool ConjugateLhs,
+          int RhsStorageOrder, bool ConjugateRhs>
+struct ei_product_triangular_matrix_matrix<Scalar,Mode,false,
+                                           LhsStorageOrder,ConjugateLhs,
+                                           RhsStorageOrder,ConjugateRhs,ColMajor>
+{
+
+  static EIGEN_DONT_INLINE void run(
+    int size, int rows,
+    const Scalar* _lhs, int lhsStride,
+    const Scalar* _rhs, int rhsStride,
+    Scalar* res,        int resStride,
+    Scalar alpha)
+  {
+    int cols = size;
+
+    ei_const_blas_data_mapper<Scalar, LhsStorageOrder> lhs(_lhs,lhsStride);
+    ei_const_blas_data_mapper<Scalar, RhsStorageOrder> rhs(_rhs,rhsStride);
+
+    if (ConjugateRhs)
+      alpha = ei_conj(alpha);
+
+    typedef ei_product_blocking_traits<Scalar> Blocking;
+    enum {
+      SmallPanelWidth   = EIGEN_ENUM_MAX(Blocking::mr,Blocking::nr),
+      IsLowerTriangular = (Mode&LowerTriangular) == LowerTriangular
+    };
+
+    int kc = std::min<int>(Blocking::Max_kc/4,size); // cache block size along the K direction
+    int mc = std::min<int>(Blocking::Max_mc,rows);   // cache block size along the M direction
+
+    Scalar* blockA = ei_aligned_stack_new(Scalar, kc*mc);
+    Scalar* blockB = ei_aligned_stack_new(Scalar, kc*cols*Blocking::PacketSize);
+
+    Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
+    triangularBuffer.setZero();
+    triangularBuffer.diagonal().setOnes();
+
+    ei_gebp_kernel<Scalar, Blocking::mr, Blocking::nr, ei_conj_helper<ConjugateLhs,ConjugateRhs> > gebp_kernel;
+    ei_gemm_pack_lhs<Scalar,Blocking::mr,LhsStorageOrder> pack_lhs;
+    ei_gemm_pack_rhs<Scalar,Blocking::nr,RhsStorageOrder> pack_rhs;
+    ei_gemm_pack_rhs<Scalar,Blocking::nr,RhsStorageOrder,true> pack_rhs_panel;
+
+    for(int k2=IsLowerTriangular ? 0 : size;
+        IsLowerTriangular ? k2<size  : k2>0;
+        IsLowerTriangular ? k2+=kc   : k2-=kc)
+    {
+      const int actual_kc = std::min(IsLowerTriangular ? size-k2 : k2, kc);
+      int actual_k2 = IsLowerTriangular ? k2 : k2-actual_kc;
+      int rs = IsLowerTriangular ? actual_k2 : size - k2;
+      Scalar* geb = blockB+actual_kc*actual_kc*Blocking::PacketSize;
+
+      pack_rhs(geb, &rhs(actual_k2,IsLowerTriangular ? 0 : k2), rhsStride, alpha, actual_kc, rs);
+
+      // pack the triangular part of the rhs padding the unrolled blocks with zeros
+      {
+        for (int j2=0; j2<actual_kc; j2+=SmallPanelWidth)
+        {
+          int actualPanelWidth = std::min<int>(actual_kc-j2, SmallPanelWidth);
+          int actual_j2 = actual_k2 + j2;
+          int panelOffset = IsLowerTriangular ? j2+actualPanelWidth : 0;
+          int panelLength = IsLowerTriangular ? actual_kc-j2-actualPanelWidth : j2;
+          // general part
+          pack_rhs_panel(blockB+j2*actual_kc*Blocking::PacketSize,
+                         &rhs(actual_k2+panelOffset, actual_j2), rhsStride, alpha,
+                         panelLength, actualPanelWidth,
+                         actual_kc, panelOffset);
+          
+          // append the triangular part via a temporary buffer
+          for (int j=0;j<actualPanelWidth;++j)
+          {
+            if (!(Mode&UnitDiagBit))
+              triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
+            for (int k=IsLowerTriangular ? j+1 : 0; IsLowerTriangular ? k<actualPanelWidth : k<j; ++k)
+              triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
+          }
+
+          pack_rhs_panel(blockB+j2*actual_kc*Blocking::PacketSize,
+                         triangularBuffer.data(), triangularBuffer.stride(), alpha,
+                         actualPanelWidth, actualPanelWidth,
+                         actual_kc, j2);
+        }
+      }
+
+      for (int i2=0; i2<rows; i2+=mc)
+      {
+        const int actual_mc = std::min(mc,rows-i2);
+        pack_lhs(blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
+
+        // triangular kernel
+        {
+          for (int j2=0; j2<actual_kc; j2+=SmallPanelWidth)
+          {
+            int actualPanelWidth = std::min<int>(actual_kc-j2, SmallPanelWidth);
+            int panelLength = IsLowerTriangular ? actual_kc-j2 : j2+actualPanelWidth;
+            int blockOffset = IsLowerTriangular ? j2 : 0;
+
+            gebp_kernel(res+i2+(actual_k2+j2)*resStride, resStride,
+                        blockA, blockB+j2*actual_kc*Blocking::PacketSize,
+                        actual_mc, panelLength, actualPanelWidth,
+                        actual_kc, actual_kc,  // strides
+                        blockOffset, blockOffset*Blocking::PacketSize);// offsets
+          }
+        }
+        gebp_kernel(res+i2+(IsLowerTriangular ? 0 : k2)*resStride, resStride,
+                    blockA, geb, actual_mc, actual_kc, rs);
+      }
+    }
+
+    ei_aligned_stack_delete(Scalar, blockA, kc*mc);
+    ei_aligned_stack_delete(Scalar, blockB, kc*cols*Blocking::PacketSize);
+  }
+};
+
+/***************************************************************************
+* Wrapper to ei_product_triangular_matrix_matrix
+***************************************************************************/
+
+template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
+struct ei_triangular_product_returntype<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
+  : public ReturnByValue<ei_triangular_product_returntype<Mode,LhsIsTriangular,Lhs,false,Rhs,false>,
+                         Matrix<typename ei_traits<Rhs>::Scalar,
+                                Lhs::RowsAtCompileTime,Rhs::ColsAtCompileTime> >
+{
+  ei_triangular_product_returntype(const Lhs& lhs, const Rhs& rhs)
+    : m_lhs(lhs), m_rhs(rhs)
+  {}
+
+  typedef typename Lhs::Scalar Scalar;
+
+  typedef typename Lhs::Nested LhsNested;
+  typedef typename ei_cleantype<LhsNested>::type _LhsNested;
+  typedef ei_blas_traits<_LhsNested> LhsBlasTraits;
+  typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+  typedef typename ei_cleantype<ActualLhsType>::type _ActualLhsType;
+
+  typedef typename Rhs::Nested RhsNested;
+  typedef typename ei_cleantype<RhsNested>::type _RhsNested;
+  typedef ei_blas_traits<_RhsNested> RhsBlasTraits;
+  typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+  typedef typename ei_cleantype<ActualRhsType>::type _ActualRhsType;
+
+//   enum {
+//     LhsUpLo = LhsMode&(UpperTriangularBit|LowerTriangularBit),
+//     LhsIsTriangular = (LhsMode&SelfAdjointBit)==SelfAdjointBit,
+//     RhsUpLo = RhsMode&(UpperTriangularBit|LowerTriangularBit),
+//     RhsIsSelfAdjoint = (RhsMode&SelfAdjointBit)==SelfAdjointBit
+//   };
+
+  template<typename Dest> inline void _addTo(Dest& dst) const
+  { evalTo(dst,1); }
+  template<typename Dest> inline void _subTo(Dest& dst) const
+  { evalTo(dst,-1); }
+
+  template<typename Dest> void evalTo(Dest& dst) const
+  {
+    dst.resize(m_lhs.rows(), m_rhs.cols());
+    dst.setZero();
+    evalTo(dst,1);
+  }
+
+  template<typename Dest> void evalTo(Dest& dst, Scalar alpha) const
+  {
+    const ActualLhsType lhs = LhsBlasTraits::extract(m_lhs);
+    const ActualRhsType rhs = RhsBlasTraits::extract(m_rhs);
+
+    Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
+                               * RhsBlasTraits::extractScalarFactor(m_rhs);
+
+    ei_product_triangular_matrix_matrix<Scalar,
+      Mode, LhsIsTriangular,
+      (ei_traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
+      (ei_traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
+      (ei_traits<Dest          >::Flags&RowMajorBit) ? RowMajor : ColMajor>
+      ::run(
+        lhs.rows(), LhsIsTriangular ? rhs.cols() : lhs.rows(),           // sizes
+        &lhs.coeff(0,0),    lhs.stride(), // lhs info
+        &rhs.coeff(0,0),    rhs.stride(), // rhs info
+        &dst.coeffRef(0,0), dst.stride(), // result info
+        actualAlpha                       // alpha
+      );
+  }
+
+  const LhsNested m_lhs;
+  const RhsNested m_rhs;
+};
+
+#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H
diff --git a/Eigen/src/Core/products/TriangularMatrixVector.h b/Eigen/src/Core/products/TriangularMatrixVector.h
index 533aad170..0fbbb50d2 100644
--- a/Eigen/src/Core/products/TriangularMatrixVector.h
+++ b/Eigen/src/Core/products/TriangularMatrixVector.h
@@ -113,49 +113,113 @@ struct ei_product_triangular_vector_selector<Lhs,Rhs,Result,Mode,ConjLhs,ConjRhs
   }
 };
 
-template<typename Lhs,typename Rhs>
-struct ei_triangular_vector_product_returntype
-  : public ReturnByValue<ei_triangular_vector_product_returntype<Lhs,Rhs>,
+// template<typename Lhs,typename Rhs>
+// struct ei_triangular_vector_product_returntype
+//   : public ReturnByValue<ei_triangular_vector_product_returntype<Lhs,Rhs>,
+//                          Matrix<typename ei_traits<Rhs>::Scalar,
+//                                 Rhs::RowsAtCompileTime,Rhs::ColsAtCompileTime> >
+// {
+//   typedef typename Lhs::Scalar Scalar;
+//   typedef typename ei_cleantype<typename Rhs::Nested>::type RhsNested;
+//   ei_triangular_vector_product_returntype(const Lhs& lhs, const Rhs& rhs, Scalar alpha)
+//     : m_lhs(lhs), m_rhs(rhs), m_alpha(alpha)
+//   {}
+// 
+//   template<typename Dest> void evalTo(Dest& dst) const
+//   {
+//     typedef typename Lhs::MatrixType MatrixType;
+//     
+//     typedef ei_blas_traits<MatrixType> LhsBlasTraits;
+//     typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+//     typedef typename ei_cleantype<ActualLhsType>::type _ActualLhsType;
+//     const ActualLhsType actualLhs = LhsBlasTraits::extract(m_lhs._expression());
+// 
+//     typedef ei_blas_traits<Rhs> RhsBlasTraits;
+//     typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+//     typedef typename ei_cleantype<ActualRhsType>::type _ActualRhsType;
+//     const ActualRhsType actualRhs = RhsBlasTraits::extract(m_rhs);
+// 
+//     Scalar actualAlpha = m_alpha * LhsBlasTraits::extractScalarFactor(m_lhs._expression())
+//                                  * RhsBlasTraits::extractScalarFactor(m_rhs);
+//                              
+//     dst.resize(m_rhs.rows(), m_rhs.cols());
+//     dst.setZero();
+//     ei_product_triangular_vector_selector
+//       <_ActualLhsType,_ActualRhsType,Dest,
+//        ei_traits<Lhs>::Mode,
+//        LhsBlasTraits::NeedToConjugate,
+//        RhsBlasTraits::NeedToConjugate,
+//        ei_traits<Lhs>::Flags&RowMajorBit>
+//       ::run(actualLhs,actualRhs,dst,actualAlpha);
+//   }
+// 
+//   const Lhs m_lhs;
+//   const typename Rhs::Nested m_rhs;
+//   const Scalar m_alpha;
+// };
+
+
+/***************************************************************************
+* Wrapper to ei_product_triangular_vector
+***************************************************************************/
+
+template<int Mode, /*bool LhsIsTriangular, */typename Lhs, typename Rhs>
+struct ei_triangular_product_returntype<Mode,true,Lhs,false,Rhs,true>
+  : public ReturnByValue<ei_triangular_product_returntype<Mode,true,Lhs,false,Rhs,true>,
                          Matrix<typename ei_traits<Rhs>::Scalar,
                                 Rhs::RowsAtCompileTime,Rhs::ColsAtCompileTime> >
 {
   typedef typename Lhs::Scalar Scalar;
-  typedef typename ei_cleantype<typename Rhs::Nested>::type RhsNested;
-  ei_triangular_vector_product_returntype(const Lhs& lhs, const Rhs& rhs, Scalar alpha)
-    : m_lhs(lhs), m_rhs(rhs), m_alpha(alpha)
+
+  typedef typename Lhs::Nested LhsNested;
+  typedef typename ei_cleantype<LhsNested>::type _LhsNested;
+  typedef ei_blas_traits<_LhsNested> LhsBlasTraits;
+  typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
+  typedef typename ei_cleantype<ActualLhsType>::type _ActualLhsType;
+
+  typedef typename Rhs::Nested RhsNested;
+  typedef typename ei_cleantype<RhsNested>::type _RhsNested;
+  typedef ei_blas_traits<_RhsNested> RhsBlasTraits;
+  typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
+  typedef typename ei_cleantype<ActualRhsType>::type _ActualRhsType;
+
+  ei_triangular_product_returntype(const Lhs& lhs, const Rhs& rhs)
+    : m_lhs(lhs), m_rhs(rhs)
   {}
 
+  template<typename Dest> inline void _addTo(Dest& dst) const
+  { evalTo(dst,1); }
+  template<typename Dest> inline void _subTo(Dest& dst) const
+  { evalTo(dst,-1); }
+
   template<typename Dest> void evalTo(Dest& dst) const
   {
-    typedef typename Lhs::MatrixType MatrixType;
-    
-    typedef ei_blas_traits<MatrixType> LhsBlasTraits;
-    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
-    typedef typename ei_cleantype<ActualLhsType>::type _ActualLhsType;
-    const ActualLhsType actualLhs = LhsBlasTraits::extract(m_lhs._expression());
-
-    typedef ei_blas_traits<Rhs> RhsBlasTraits;
-    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
-    typedef typename ei_cleantype<ActualRhsType>::type _ActualRhsType;
-    const ActualRhsType actualRhs = RhsBlasTraits::extract(m_rhs);
-
-    Scalar actualAlpha = m_alpha * LhsBlasTraits::extractScalarFactor(m_lhs._expression())
-                                 * RhsBlasTraits::extractScalarFactor(m_rhs);
-                             
+    dst.resize(m_lhs.rows(), m_rhs.cols());
+    dst.setZero();
+    evalTo(dst,1);
+  }
+
+  template<typename Dest> void evalTo(Dest& dst, Scalar alpha) const
+  {
+    const ActualLhsType lhs = LhsBlasTraits::extract(m_lhs);
+    const ActualRhsType rhs = RhsBlasTraits::extract(m_rhs);
+
+    Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
+                               * RhsBlasTraits::extractScalarFactor(m_rhs);
+
     dst.resize(m_rhs.rows(), m_rhs.cols());
     dst.setZero();
     ei_product_triangular_vector_selector
       <_ActualLhsType,_ActualRhsType,Dest,
-       ei_traits<Lhs>::Mode,
+       Mode,
        LhsBlasTraits::NeedToConjugate,
        RhsBlasTraits::NeedToConjugate,
        ei_traits<Lhs>::Flags&RowMajorBit>
-      ::run(actualLhs,actualRhs,dst,actualAlpha);
+      ::run(lhs,rhs,dst,actualAlpha);
   }
 
-  const Lhs m_lhs;
-  const typename Rhs::Nested m_rhs;
-  const Scalar m_alpha;
+  const LhsNested m_lhs;
+  const RhsNested m_rhs;
 };
 
 #endif // EIGEN_TRIANGULARMATRIXVECTOR_H