1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
11#define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
12
13namespace Eigen {
14
15namespace internal {
16
17/**********************************************************************
18* This file implements a general A * B product while
19* evaluating only one triangular part of the product.
20* This is more general version of self adjoint product (C += A A^T)
21* as the level 3 SYRK Blas routine.
22**********************************************************************/
23
24// forward declarations (defined at the end of this file)
25template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
26struct tribb_kernel;
27
28/* Optimized matrix-matrix product evaluating only one triangular half */
29template <typename Index,
30          typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
31          typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
32                              int ResStorageOrder, int  UpLo, int Version = Specialized>
33struct general_matrix_matrix_triangular_product;
34
35// as usual if the result is row major => we transpose the product
36template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
37                          typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>
38struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>
39{
40  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
41  static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
42                                      const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, ResScalar alpha)
43  {
44    general_matrix_matrix_triangular_product<Index,
45        RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
46        LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
47        ColMajor, UpLo==Lower?Upper:Lower>
48      ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha);
49  }
50};
51
52template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
53                          typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int  UpLo, int Version>
54struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>
55{
56  typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar;
57  static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
58                                      const RhsScalar* _rhs, Index rhsStride, ResScalar* res, Index resStride, ResScalar alpha)
59  {
60    const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
61    const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
62
63    typedef gebp_traits<LhsScalar,RhsScalar> Traits;
64
65    Index kc = depth; // cache block size along the K direction
66    Index mc = size;  // cache block size along the M direction
67    Index nc = size;  // cache block size along the N direction
68    computeProductBlockingSizes<LhsScalar,RhsScalar>(kc, mc, nc);
69    // !!! mc must be a multiple of nr:
70    if(mc > Traits::nr)
71      mc = (mc/Traits::nr)*Traits::nr;
72
73    std::size_t sizeW = kc*Traits::WorkSpaceFactor;
74    std::size_t sizeB = sizeW + kc*size;
75    ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, kc*mc, 0);
76    ei_declare_aligned_stack_constructed_variable(RhsScalar, allocatedBlockB, sizeB, 0);
77    RhsScalar* blockB = allocatedBlockB + sizeW;
78
79    gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
80    gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs;
81    gebp_kernel <LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
82    tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb;
83
84    for(Index k2=0; k2<depth; k2+=kc)
85    {
86      const Index actual_kc = (std::min)(k2+kc,depth)-k2;
87
88      // note that the actual rhs is the transpose/adjoint of mat
89      pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, size);
90
91      for(Index i2=0; i2<size; i2+=mc)
92      {
93        const Index actual_mc = (std::min)(i2+mc,size)-i2;
94
95        pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
96
97        // the selected actual_mc * size panel of res is split into three different part:
98        //  1 - before the diagonal => processed with gebp or skipped
99        //  2 - the actual_mc x actual_mc symmetric block => processed with a special kernel
100        //  3 - after the diagonal => processed with gebp or skipped
101        if (UpLo==Lower)
102          gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, (std::min)(size,i2), alpha,
103               -1, -1, 0, 0, allocatedBlockB);
104
105        sybb(res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha, allocatedBlockB);
106
107        if (UpLo==Upper)
108        {
109          Index j2 = i2+actual_mc;
110          gebp(res+resStride*j2+i2, resStride, blockA, blockB+actual_kc*j2, actual_mc, actual_kc, (std::max)(Index(0), size-j2), alpha,
111               -1, -1, 0, 0, allocatedBlockB);
112        }
113      }
114    }
115  }
116};
117
118// Optimized packed Block * packed Block product kernel evaluating only one given triangular part
119// This kernel is built on top of the gebp kernel:
120// - the current destination block is processed per panel of actual_mc x BlockSize
121//   where BlockSize is set to the minimal value allowing gebp to be as fast as possible
122// - then, as usual, each panel is split into three parts along the diagonal,
123//   the sub blocks above and below the diagonal are processed as usual,
124//   while the triangular block overlapping the diagonal is evaluated into a
125//   small temporary buffer which is then accumulated into the result using a
126//   triangular traversal.
127template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
128struct tribb_kernel
129{
130  typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;
131  typedef typename Traits::ResScalar ResScalar;
132
133  enum {
134    BlockSize  = EIGEN_PLAIN_ENUM_MAX(mr,nr)
135  };
136  void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, ResScalar alpha, RhsScalar* workspace)
137  {
138    gebp_kernel<LhsScalar, RhsScalar, Index, mr, nr, ConjLhs, ConjRhs> gebp_kernel;
139    Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer;
140
141    // let's process the block per panel of actual_mc x BlockSize,
142    // again, each is split into three parts, etc.
143    for (Index j=0; j<size; j+=BlockSize)
144    {
145      Index actualBlockSize = std::min<Index>(BlockSize,size - j);
146      const RhsScalar* actual_b = blockB+j*depth;
147
148      if(UpLo==Upper)
149        gebp_kernel(res+j*resStride, resStride, blockA, actual_b, j, depth, actualBlockSize, alpha,
150                    -1, -1, 0, 0, workspace);
151
152      // selfadjoint micro block
153      {
154        Index i = j;
155        buffer.setZero();
156        // 1 - apply the kernel on the temporary buffer
157        gebp_kernel(buffer.data(), BlockSize, blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,
158                    -1, -1, 0, 0, workspace);
159        // 2 - triangular accumulation
160        for(Index j1=0; j1<actualBlockSize; ++j1)
161        {
162          ResScalar* r = res + (j+j1)*resStride + i;
163          for(Index i1=UpLo==Lower ? j1 : 0;
164              UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)
165            r[i1] += buffer(i1,j1);
166        }
167      }
168
169      if(UpLo==Lower)
170      {
171        Index i = j+actualBlockSize;
172        gebp_kernel(res+j*resStride+i, resStride, blockA+depth*i, actual_b, size-i, depth, actualBlockSize, alpha,
173                    -1, -1, 0, 0, workspace);
174      }
175    }
176  }
177};
178
179} // end namespace internal
180
181// high level API
182
183template<typename MatrixType, unsigned int UpLo>
184template<typename ProductDerived, typename _Lhs, typename _Rhs>
185TriangularView<MatrixType,UpLo>& TriangularView<MatrixType,UpLo>::assignProduct(const ProductBase<ProductDerived, _Lhs,_Rhs>& prod, const Scalar& alpha)
186{
187  typedef typename internal::remove_all<typename ProductDerived::LhsNested>::type Lhs;
188  typedef internal::blas_traits<Lhs> LhsBlasTraits;
189  typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
190  typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
191  typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
192
193  typedef typename internal::remove_all<typename ProductDerived::RhsNested>::type Rhs;
194  typedef internal::blas_traits<Rhs> RhsBlasTraits;
195  typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
196  typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
197  typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
198
199  typename ProductDerived::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
200
201  internal::general_matrix_matrix_triangular_product<Index,
202    typename Lhs::Scalar, _ActualLhs::Flags&RowMajorBit ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
203    typename Rhs::Scalar, _ActualRhs::Flags&RowMajorBit ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
204    MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo>
205    ::run(m_matrix.cols(), actualLhs.cols(),
206          &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(),
207          const_cast<Scalar*>(m_matrix.data()), m_matrix.outerStride(), actualAlpha);
208
209  return *this;
210}
211
212} // end namespace Eigen
213
214#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
215