text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.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
  
  namespace Eigen { 
  
  namespace internal {
  
  // template<typename Scalar, int mr, int StorageOrder, bool Conjugate, int Mode>
  // struct gemm_pack_lhs_triangular
  // {
  //   Matrix<Scalar,mr,mr,
  //   void operator()(Scalar* blockA, const EIGEN_RESTRICT Scalar* _lhs, int lhsStride, int depth, int rows)
  //   {
  //     conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
  //     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 triangular matrix * matrix (_TRMM++) product built on top of
   * the general matrix matrix product.
   */
  template <typename Scalar, typename Index,
            int Mode, bool LhsIsTriangular,
            int LhsStorageOrder, bool ConjugateLhs,
            int RhsStorageOrder, bool ConjugateRhs,
            int ResStorageOrder, int Version = Specialized>
  struct product_triangular_matrix_matrix;
  
  template <typename Scalar, typename Index,
            int Mode, bool LhsIsTriangular,
            int LhsStorageOrder, bool ConjugateLhs,
            int RhsStorageOrder, bool ConjugateRhs, int Version>
  struct product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular,
                                             LhsStorageOrder,ConjugateLhs,
                                             RhsStorageOrder,ConjugateRhs,RowMajor,Version>
  {
    static EIGEN_STRONG_INLINE void run(
      Index rows, Index cols, Index depth,
      const Scalar* lhs, Index lhsStride,
      const Scalar* rhs, Index rhsStride,
      Scalar* res,       Index resStride,
      Scalar alpha)
    {
      product_triangular_matrix_matrix<Scalar, Index,
        (Mode&(UnitDiag|ZeroDiag)) | ((Mode&Upper) ? Lower : Upper),
        (!LhsIsTriangular),
        RhsStorageOrder==RowMajor ? ColMajor : RowMajor,
        ConjugateRhs,
        LhsStorageOrder==RowMajor ? ColMajor : RowMajor,
        ConjugateLhs,
        ColMajor>
        ::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha);
    }
  };
  
  // implements col-major += alpha * op(triangular) * op(general)
  template <typename Scalar, typename Index, int Mode,
            int LhsStorageOrder, bool ConjugateLhs,
            int RhsStorageOrder, bool ConjugateRhs, int Version>
  struct product_triangular_matrix_matrix<Scalar,Index,Mode,true,
                                             LhsStorageOrder,ConjugateLhs,
                                             RhsStorageOrder,ConjugateRhs,ColMajor,Version>
  {
    
    typedef gebp_traits<Scalar,Scalar> Traits;
    enum {
      SmallPanelWidth   = 2 * EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
      IsLower = (Mode&Lower) == Lower,
      SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
    };
  
    static EIGEN_DONT_INLINE void run(
      Index _rows, Index _cols, Index _depth,
      const Scalar* _lhs, Index lhsStride,
      const Scalar* _rhs, Index rhsStride,
      Scalar* res,        Index resStride,
      Scalar alpha)
    {
      // strip zeros
      Index diagSize  = (std::min)(_rows,_depth);
      Index rows      = IsLower ? _rows : diagSize;
      Index depth     = IsLower ? diagSize : _depth;
      Index cols      = _cols;
      
      const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
      const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
  
      Index kc = depth; // cache block size along the K direction
      Index mc = rows;  // cache block size along the M direction
      Index nc = cols;  // cache block size along the N direction
      computeProductBlockingSizes<Scalar,Scalar,4>(kc, mc, nc);
      std::size_t sizeW = kc*Traits::WorkSpaceFactor;
      std::size_t sizeB = sizeW + kc*cols;
      ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
      ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);    
      Scalar* blockB = allocatedBlockB + sizeW;
  
      Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
      triangularBuffer.setZero();
      if((Mode&ZeroDiag)==ZeroDiag)
        triangularBuffer.diagonal().setZero();
      else
        triangularBuffer.diagonal().setOnes();
  
      gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
      gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
      gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
  
      for(Index k2=IsLower ? depth : 0;
          IsLower ? k2>0 : k2<depth;
          IsLower ? k2-=kc : k2+=kc)
      {
        Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);
        Index actual_k2 = IsLower ? k2-actual_kc : k2;
  
        // align blocks with the end of the triangular part for trapezoidal lhs
        if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
        {
          actual_kc = rows-k2;
          k2 = k2+actual_kc-kc;
        }
  
        pack_rhs(blockB, &rhs(actual_k2,0), rhsStride, actual_kc, cols);
  
        // the selected lhs's panel has to be split in three different parts:
        //  1 - the part which is zero => skip it
        //  2 - the diagonal block => special kernel
        //  3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
  
        // the block diagonal, if any:
        if(IsLower || actual_k2<rows)
        {
          // for each small vertical panels of lhs
          for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
          {
            Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
            Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
            Index startBlock   = actual_k2+k1;
            Index 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 a small temporary buffer
            for (Index k=0;k<actualPanelWidth;++k)
            {
              if (SetDiag)
                triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
              for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)
                triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
            }
            pack_lhs(blockA, triangularBuffer.data(), triangularBuffer.outerStride(), actualPanelWidth, actualPanelWidth);
  
            gebp_kernel(res+startBlock, resStride, blockA, blockB, actualPanelWidth, actualPanelWidth, cols, alpha,
                        actualPanelWidth, actual_kc, 0, blockBOffset);
  
            // GEBP with remaining micro panel
            if (lengthTarget>0)
            {
              Index startTarget  = IsLower ? 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, alpha,
                          actualPanelWidth, actual_kc, 0, blockBOffset);
            }
          }
        }
        // the part below (lower case) or above (upper case) the diagonal => GEPP
        {
          Index start = IsLower ? k2 : 0;
          Index end   = IsLower ? rows : (std::min)(actual_k2,rows);
          for(Index i2=start; i2<end; i2+=mc)
          {
            const Index actual_mc = (std::min)(i2+mc,end)-i2;
            gemm_pack_lhs<Scalar, Index, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
              (blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
  
            gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
          }
        }
      }
    }
  };
  
  // implements col-major += alpha * op(general) * op(triangular)
  template <typename Scalar, typename Index, int Mode,
            int LhsStorageOrder, bool ConjugateLhs,
            int RhsStorageOrder, bool ConjugateRhs, int Version>
  struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
                                             LhsStorageOrder,ConjugateLhs,
                                             RhsStorageOrder,ConjugateRhs,ColMajor,Version>
  {
    typedef gebp_traits<Scalar,Scalar> Traits;
    enum {
      SmallPanelWidth   = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
      IsLower = (Mode&Lower) == Lower,
      SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
    };
  
    static EIGEN_DONT_INLINE void run(
      Index _rows, Index _cols, Index _depth,
      const Scalar* _lhs, Index lhsStride,
      const Scalar* _rhs, Index rhsStride,
      Scalar* res,        Index resStride,
      Scalar alpha)
    {
      // strip zeros
      Index diagSize  = (std::min)(_cols,_depth);
      Index rows      = _rows;
      Index depth     = IsLower ? _depth : diagSize;
      Index cols      = IsLower ? diagSize : _cols;
      
      const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
      const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
  
      Index kc = depth; // cache block size along the K direction
      Index mc = rows;  // cache block size along the M direction
      Index nc = cols;  // cache block size along the N direction
      computeProductBlockingSizes<Scalar,Scalar,4>(kc, mc, nc);
  
      std::size_t sizeW = kc*Traits::WorkSpaceFactor;
      std::size_t sizeB = sizeW + kc*cols;
      ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
      ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
      Scalar* blockB = allocatedBlockB + sizeW;
  
      Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
      triangularBuffer.setZero();
      if((Mode&ZeroDiag)==ZeroDiag)
        triangularBuffer.diagonal().setZero();
      else
        triangularBuffer.diagonal().setOnes();
  
      gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
      gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
      gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
      gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
  
      for(Index k2=IsLower ? 0 : depth;
          IsLower ? k2<depth  : k2>0;
          IsLower ? k2+=kc   : k2-=kc)
      {
        Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);
        Index actual_k2 = IsLower ? k2 : k2-actual_kc;
  
        // align blocks with the end of the triangular part for trapezoidal rhs
        if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
        {
          actual_kc = cols-k2;
          k2 = actual_k2 + actual_kc - kc;
        }
  
        // remaining size
        Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;
        // size of the triangular part
        Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
  
        Scalar* geb = blockB+ts*ts;
  
        pack_rhs(geb, &rhs(actual_k2,IsLower ? 0 : k2), rhsStride, actual_kc, rs);
  
        // pack the triangular part of the rhs padding the unrolled blocks with zeros
        if(ts>0)
        {
          for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
          {
            Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
            Index actual_j2 = actual_k2 + j2;
            Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
            Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
            // general part
            pack_rhs_panel(blockB+j2*actual_kc,
                           &rhs(actual_k2+panelOffset, actual_j2), rhsStride,
                           panelLength, actualPanelWidth,
                           actual_kc, panelOffset);
  
            // append the triangular part via a temporary buffer
            for (Index j=0;j<actualPanelWidth;++j)
            {
              if (SetDiag)
                triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
              for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)
                triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
            }
  
            pack_rhs_panel(blockB+j2*actual_kc,
                           triangularBuffer.data(), triangularBuffer.outerStride(),
                           actualPanelWidth, actualPanelWidth,
                           actual_kc, j2);
          }
        }
  
        for (Index i2=0; i2<rows; i2+=mc)
        {
          const Index actual_mc = (std::min)(mc,rows-i2);
          pack_lhs(blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
  
          // triangular kernel
          if(ts>0)
          {
            for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
            {
              Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
              Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;
              Index blockOffset = IsLower ? j2 : 0;
  
              gebp_kernel(res+i2+(actual_k2+j2)*resStride, resStride,
                          blockA, blockB+j2*actual_kc,
                          actual_mc, panelLength, actualPanelWidth,
                          alpha,
                          actual_kc, actual_kc,  // strides
                          blockOffset, blockOffset,// offsets
                          allocatedBlockB); // workspace
            }
          }
          gebp_kernel(res+i2+(IsLower ? 0 : k2)*resStride, resStride,
                      blockA, geb, actual_mc, actual_kc, rs,
                      alpha,
                      -1, -1, 0, 0, allocatedBlockB);
        }
      }
    }
  };
  
  /***************************************************************************
  * Wrapper to product_triangular_matrix_matrix
  ***************************************************************************/
  
  template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
  struct traits<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false> >
    : traits<ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs> >
  {};
  
  } // end namespace internal
  
  template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
  struct TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
    : public ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs >
  {
    EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
  
    TriangularProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
  
    template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
    {
      typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
      typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
  
      Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
                                 * RhsBlasTraits::extractScalarFactor(m_rhs);
  
      internal::product_triangular_matrix_matrix<Scalar, Index,
        Mode, LhsIsTriangular,
        (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
        (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
        (internal::traits<Dest          >::Flags&RowMajorBit) ? RowMajor : ColMajor>
        ::run(
          lhs.rows(), rhs.cols(), lhs.cols(),// LhsIsTriangular ? rhs.cols() : lhs.rows(),           // sizes
          &lhs.coeffRef(0,0),    lhs.outerStride(), // lhs info
          &rhs.coeffRef(0,0),    rhs.outerStride(), // rhs info
          &dst.coeffRef(0,0), dst.outerStride(), // result info
          actualAlpha                            // alpha
        );
    }
  };
  
  } // end namespace Eigen
  
  #endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H
  