text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
  #define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
  
  namespace Eigen { 
  
  template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
  struct selfadjoint_rank1_update;
  
  namespace internal {
  
  /**********************************************************************
  * This file implements a general A * B product while
  * evaluating only one triangular part of the product.
  * This is a more general version of self adjoint product (C += A A^T)
  * as the level 3 SYRK Blas routine.
  **********************************************************************/
  
  // forward declarations (defined at the end of this file)
  template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
  struct tribb_kernel;
    
  /* Optimized matrix-matrix product evaluating only one triangular half */
  template <typename Index,
            typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
            typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
                                int ResStorageOrder, int  UpLo, int Version = Specialized>
  struct general_matrix_matrix_triangular_product;
  
  // as usual if the result is row major => we transpose the product
  template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
                            typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>
  struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>
  {
    typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
    static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
                                        const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride,
                                        const ResScalar& alpha, level3_blocking<RhsScalar,LhsScalar>& blocking)
    {
      general_matrix_matrix_triangular_product<Index,
          RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
          LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
          ColMajor, UpLo==Lower?Upper:Lower>
        ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking);
    }
  };
  
  template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
                            typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>
  struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>
  {
    typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
    static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
                                        const RhsScalar* _rhs, Index rhsStride, ResScalar* _res, Index resStride,
                                        const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking)
    {
      typedef gebp_traits<LhsScalar,RhsScalar> Traits;
  
      typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper;
      typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper;
      typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;
      LhsMapper lhs(_lhs,lhsStride);
      RhsMapper rhs(_rhs,rhsStride);
      ResMapper res(_res, resStride);
  
      Index kc = blocking.kc();
      Index mc = (std::min)(size,blocking.mc());
  
      // !!! mc must be a multiple of nr:
      if(mc > Traits::nr)
        mc = (mc/Traits::nr)*Traits::nr;
  
      std::size_t sizeA = kc*mc;
      std::size_t sizeB = kc*size;
  
      ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
      ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
  
      gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
      gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
      gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
      tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb;
  
      for(Index k2=0; k2<depth; k2+=kc)
      {
        const Index actual_kc = (std::min)(k2+kc,depth)-k2;
  
        // note that the actual rhs is the transpose/adjoint of mat
        pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, size);
  
        for(Index i2=0; i2<size; i2+=mc)
        {
          const Index actual_mc = (std::min)(i2+mc,size)-i2;
  
          pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
  
          // the selected actual_mc * size panel of res is split into three different part:
          //  1 - before the diagonal => processed with gebp or skipped
          //  2 - the actual_mc x actual_mc symmetric block => processed with a special kernel
          //  3 - after the diagonal => processed with gebp or skipped
          if (UpLo==Lower)
            gebp(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc,
                 (std::min)(size,i2), alpha, -1, -1, 0, 0);
  
  
          sybb(_res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha);
  
          if (UpLo==Upper)
          {
            Index j2 = i2+actual_mc;
            gebp(res.getSubMapper(i2, j2), blockA, blockB+actual_kc*j2, actual_mc,
                 actual_kc, (std::max)(Index(0), size-j2), alpha, -1, -1, 0, 0);
          }
        }
      }
    }
  };
  
  // Optimized packed Block * packed Block product kernel evaluating only one given triangular part
  // This kernel is built on top of the gebp kernel:
  // - the current destination block is processed per panel of actual_mc x BlockSize
  //   where BlockSize is set to the minimal value allowing gebp to be as fast as possible
  // - then, as usual, each panel is split into three parts along the diagonal,
  //   the sub blocks above and below the diagonal are processed as usual,
  //   while the triangular block overlapping the diagonal is evaluated into a
  //   small temporary buffer which is then accumulated into the result using a
  //   triangular traversal.
  template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
  struct tribb_kernel
  {
    typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;
    typedef typename Traits::ResScalar ResScalar;
  
    enum {
      BlockSize  = meta_least_common_multiple<EIGEN_PLAIN_ENUM_MAX(mr,nr),EIGEN_PLAIN_ENUM_MIN(mr,nr)>::ret
    };
    void operator()(ResScalar* _res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha)
    {
      typedef blas_data_mapper<ResScalar, Index, ColMajor> ResMapper;
      ResMapper res(_res, resStride);
      gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel;
  
      Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer((internal::constructor_without_unaligned_array_assert()));
  
      // let's process the block per panel of actual_mc x BlockSize,
      // again, each is split into three parts, etc.
      for (Index j=0; j<size; j+=BlockSize)
      {
        Index actualBlockSize = std::min<Index>(BlockSize,size - j);
        const RhsScalar* actual_b = blockB+j*depth;
  
        if(UpLo==Upper)
          gebp_kernel(res.getSubMapper(0, j), blockA, actual_b, j, depth, actualBlockSize, alpha,
                      -1, -1, 0, 0);
  
        // selfadjoint micro block
        {
          Index i = j;
          buffer.setZero();
          // 1 - apply the kernel on the temporary buffer
          gebp_kernel(ResMapper(buffer.data(), BlockSize), blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,
                      -1, -1, 0, 0);
          // 2 - triangular accumulation
          for(Index j1=0; j1<actualBlockSize; ++j1)
          {
            ResScalar* r = &res(i, j + j1);
            for(Index i1=UpLo==Lower ? j1 : 0;
                UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)
              r[i1] += buffer(i1,j1);
          }
        }
  
        if(UpLo==Lower)
        {
          Index i = j+actualBlockSize;
          gebp_kernel(res.getSubMapper(i, j), blockA+depth*i, actual_b, size-i, 
                      depth, actualBlockSize, alpha, -1, -1, 0, 0);
        }
      }
    }
  };
  
  } // end namespace internal
  
  // high level API
  
  template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct>
  struct general_product_to_triangular_selector;
  
  
  template<typename MatrixType, typename ProductType, int UpLo>
  struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true>
  {
    static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta)
    {
      typedef typename MatrixType::Scalar Scalar;
      
      typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
      typedef internal::blas_traits<Lhs> LhsBlasTraits;
      typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
      typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
      typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
      
      typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
      typedef internal::blas_traits<Rhs> RhsBlasTraits;
      typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
      typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
      typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
  
      Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
  
      if(!beta)
        mat.template triangularView<UpLo>().setZero();
  
      enum {
        StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
        UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1,
        UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1
      };
      
      internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs;
      ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(),
        (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data()));
      if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs;
      
      internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs;
      ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(),
        (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data()));
      if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
      
      
      selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
                                LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
                                RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex>
            ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha);
    }
  };
  
  template<typename MatrixType, typename ProductType, int UpLo>
  struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
  {
    static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta)
    {
      typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
      typedef internal::blas_traits<Lhs> LhsBlasTraits;
      typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
      typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
      typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
      
      typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
      typedef internal::blas_traits<Rhs> RhsBlasTraits;
      typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
      typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
      typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
  
      typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
  
      if(!beta)
        mat.template triangularView<UpLo>().setZero();
  
      enum {
        IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0,
        LhsIsRowMajor = _ActualLhs::Flags&RowMajorBit ? 1 : 0,
        RhsIsRowMajor = _ActualRhs::Flags&RowMajorBit ? 1 : 0
      };
  
      Index size = mat.cols();
      Index depth = actualLhs.cols();
  
      typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,typename Lhs::Scalar,typename Rhs::Scalar,
            MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualRhs::MaxColsAtCompileTime> BlockingType;
  
      BlockingType blocking(size, size, depth, 1, false);
  
      internal::general_matrix_matrix_triangular_product<Index,
        typename Lhs::Scalar, LhsIsRowMajor ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
        typename Rhs::Scalar, RhsIsRowMajor ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
        IsRowMajor ? RowMajor : ColMajor, UpLo>
        ::run(size, depth,
              &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(),
              mat.data(), mat.outerStride(), actualAlpha, blocking);
    }
  };
  
  template<typename MatrixType, unsigned int UpLo>
  template<typename ProductType>
  TriangularView<MatrixType,UpLo>& TriangularViewImpl<MatrixType,UpLo,Dense>::_assignProduct(const ProductType& prod, const Scalar& alpha, bool beta)
  {
    eigen_assert(derived().nestedExpression().rows() == prod.rows() && derived().cols() == prod.cols());
    
    general_product_to_triangular_selector<MatrixType, ProductType, UpLo, internal::traits<ProductType>::InnerSize==1>::run(derived().nestedExpression().const_cast_derived(), prod, alpha, beta);
    
    return derived();
  }
  
  } // end namespace Eigen
  
  #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
  