GeneralMatrixMatrixTriangular.h
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 
13 namespace Eigen {
14 
15 namespace 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)
25 template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
26 struct tribb_kernel;
27 
28 /* Optimized matrix-matrix product evaluating only one triangular half */
29 template <typename Index,
30  typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
31  typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
32  int ResStorageOrder, int UpLo, int Version = Specialized>
33 struct general_matrix_matrix_triangular_product;
34 
35 // as usual if the result is row major => we transpose the product
36 template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
37  typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
38 struct 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 
52 template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
53  typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
54 struct 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.
127 template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
128 struct 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 
183 template<typename MatrixType, unsigned int UpLo>
184 template<typename ProductDerived, typename _Lhs, typename _Rhs>
185 TriangularView<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