Eigen  3.3.0
 
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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
13namespace Eigen {
14
15template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs>
16struct selfadjoint_rank1_update;
17
18namespace internal {
19
20/**********************************************************************
21* This file implements a general A * B product while
22* evaluating only one triangular part of the product.
23* This is a more general version of self adjoint product (C += A A^T)
24* as the level 3 SYRK Blas routine.
25**********************************************************************/
26
27// forward declarations (defined at the end of this file)
28template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
29struct tribb_kernel;
30
31/* Optimized matrix-matrix product evaluating only one triangular half */
32template <typename Index,
33 typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
34 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs,
35 int ResStorageOrder, int UpLo, int Version = Specialized>
36struct general_matrix_matrix_triangular_product;
37
38// as usual if the result is row major => we transpose the product
39template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
40 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
41struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version>
42{
43 typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
44 static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride,
45 const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride,
46 const ResScalar& alpha, level3_blocking<RhsScalar,LhsScalar>& blocking)
47 {
48 general_matrix_matrix_triangular_product<Index,
49 RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
50 LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
52 ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking);
53 }
54};
55
56template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
57 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version>
58struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version>
59{
60 typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar;
61 static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride,
62 const RhsScalar* _rhs, Index rhsStride, ResScalar* _res, Index resStride,
63 const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking)
64 {
65 typedef gebp_traits<LhsScalar,RhsScalar> Traits;
66
67 typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper;
68 typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper;
69 typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;
70 LhsMapper lhs(_lhs,lhsStride);
71 RhsMapper rhs(_rhs,rhsStride);
72 ResMapper res(_res, resStride);
73
74 Index kc = blocking.kc();
75 Index mc = (std::min)(size,blocking.mc());
76
77 // !!! mc must be a multiple of nr:
78 if(mc > Traits::nr)
79 mc = (mc/Traits::nr)*Traits::nr;
80
81 std::size_t sizeA = kc*mc;
82 std::size_t sizeB = kc*size;
83
84 ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
85 ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
86
87 gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
88 gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs;
89 gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp;
90 tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb;
91
92 for(Index k2=0; k2<depth; k2+=kc)
93 {
94 const Index actual_kc = (std::min)(k2+kc,depth)-k2;
95
96 // note that the actual rhs is the transpose/adjoint of mat
97 pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, size);
98
99 for(Index i2=0; i2<size; i2+=mc)
100 {
101 const Index actual_mc = (std::min)(i2+mc,size)-i2;
102
103 pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
104
105 // the selected actual_mc * size panel of res is split into three different part:
106 // 1 - before the diagonal => processed with gebp or skipped
107 // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel
108 // 3 - after the diagonal => processed with gebp or skipped
109 if (UpLo==Lower)
110 gebp(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc,
111 (std::min)(size,i2), alpha, -1, -1, 0, 0);
112
113
114 sybb(_res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha);
115
116 if (UpLo==Upper)
117 {
118 Index j2 = i2+actual_mc;
119 gebp(res.getSubMapper(i2, j2), blockA, blockB+actual_kc*j2, actual_mc,
120 actual_kc, (std::max)(Index(0), size-j2), alpha, -1, -1, 0, 0);
121 }
122 }
123 }
124 }
125};
126
127// Optimized packed Block * packed Block product kernel evaluating only one given triangular part
128// This kernel is built on top of the gebp kernel:
129// - the current destination block is processed per panel of actual_mc x BlockSize
130// where BlockSize is set to the minimal value allowing gebp to be as fast as possible
131// - then, as usual, each panel is split into three parts along the diagonal,
132// the sub blocks above and below the diagonal are processed as usual,
133// while the triangular block overlapping the diagonal is evaluated into a
134// small temporary buffer which is then accumulated into the result using a
135// triangular traversal.
136template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo>
137struct tribb_kernel
138{
139 typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits;
140 typedef typename Traits::ResScalar ResScalar;
141
142 enum {
143 BlockSize = meta_least_common_multiple<EIGEN_PLAIN_ENUM_MAX(mr,nr),EIGEN_PLAIN_ENUM_MIN(mr,nr)>::ret
144 };
145 void operator()(ResScalar* _res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha)
146 {
147 typedef blas_data_mapper<ResScalar, Index, ColMajor> ResMapper;
148 ResMapper res(_res, resStride);
149 gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel;
150
151 Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer;
152
153 // let's process the block per panel of actual_mc x BlockSize,
154 // again, each is split into three parts, etc.
155 for (Index j=0; j<size; j+=BlockSize)
156 {
157 Index actualBlockSize = std::min<Index>(BlockSize,size - j);
158 const RhsScalar* actual_b = blockB+j*depth;
159
160 if(UpLo==Upper)
161 gebp_kernel(res.getSubMapper(0, j), blockA, actual_b, j, depth, actualBlockSize, alpha,
162 -1, -1, 0, 0);
163
164 // selfadjoint micro block
165 {
166 Index i = j;
167 buffer.setZero();
168 // 1 - apply the kernel on the temporary buffer
169 gebp_kernel(ResMapper(buffer.data(), BlockSize), blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha,
170 -1, -1, 0, 0);
171 // 2 - triangular accumulation
172 for(Index j1=0; j1<actualBlockSize; ++j1)
173 {
174 ResScalar* r = &res(i, j + j1);
175 for(Index i1=UpLo==Lower ? j1 : 0;
176 UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1)
177 r[i1] += buffer(i1,j1);
178 }
179 }
180
181 if(UpLo==Lower)
182 {
183 Index i = j+actualBlockSize;
184 gebp_kernel(res.getSubMapper(i, j), blockA+depth*i, actual_b, size-i,
185 depth, actualBlockSize, alpha, -1, -1, 0, 0);
186 }
187 }
188 }
189};
190
191} // end namespace internal
192
193// high level API
194
195template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct>
196struct general_product_to_triangular_selector;
197
198
199template<typename MatrixType, typename ProductType, int UpLo>
200struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true>
201{
202 static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
203 {
204 typedef typename MatrixType::Scalar Scalar;
205
206 typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
207 typedef internal::blas_traits<Lhs> LhsBlasTraits;
208 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
209 typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
210 typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
211
212 typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
213 typedef internal::blas_traits<Rhs> RhsBlasTraits;
214 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
215 typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
216 typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
217
218 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
219
220 enum {
221 StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor,
222 UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1,
223 UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1
224 };
225
226 internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs;
227 ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(),
228 (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data()));
229 if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs;
230
231 internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs;
232 ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(),
233 (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data()));
234 if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
235
236
237 selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo,
238 LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex,
239 RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex>
240 ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha);
241 }
242};
243
244template<typename MatrixType, typename ProductType, int UpLo>
245struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false>
246{
247 static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha)
248 {
249 typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs;
250 typedef internal::blas_traits<Lhs> LhsBlasTraits;
251 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs;
252 typedef typename internal::remove_all<ActualLhs>::type _ActualLhs;
253 typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
254
255 typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs;
256 typedef internal::blas_traits<Rhs> RhsBlasTraits;
257 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs;
258 typedef typename internal::remove_all<ActualRhs>::type _ActualRhs;
259 typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
260
261 typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived());
262
263 enum {
264 IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0,
265 LhsIsRowMajor = _ActualLhs::Flags&RowMajorBit ? 1 : 0,
266 RhsIsRowMajor = _ActualRhs::Flags&RowMajorBit ? 1 : 0
267 };
268
269 Index size = mat.cols();
270 Index depth = actualLhs.cols();
271
272 typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,typename Lhs::Scalar,typename Rhs::Scalar,
273 MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualRhs::MaxColsAtCompileTime> BlockingType;
274
275 BlockingType blocking(size, size, depth, 1, false);
276
277 internal::general_matrix_matrix_triangular_product<Index,
278 typename Lhs::Scalar, LhsIsRowMajor ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
279 typename Rhs::Scalar, RhsIsRowMajor ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
280 IsRowMajor ? RowMajor : ColMajor, UpLo>
281 ::run(size, depth,
282 &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(),
283 mat.data(), mat.outerStride(), actualAlpha, blocking);
284 }
285};
286
287template<typename MatrixType, unsigned int UpLo>
288template<typename ProductType>
289TriangularView<MatrixType,UpLo>& TriangularViewImpl<MatrixType,UpLo,Dense>::_assignProduct(const ProductType& prod, const Scalar& alpha)
290{
291 eigen_assert(derived().nestedExpression().rows() == prod.rows() && derived().cols() == prod.cols());
292
293 general_product_to_triangular_selector<MatrixType, ProductType, UpLo, internal::traits<ProductType>::InnerSize==1>::run(derived().nestedExpression().const_cast_derived(), prod, alpha);
294
295 return derived();
296}
297
298} // end namespace Eigen
299
300#endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
@ Lower
Definition: Constants.h:204
@ Upper
Definition: Constants.h:206
@ ColMajor
Definition: Constants.h:320
@ RowMajor
Definition: Constants.h:322
const unsigned int RowMajorBit
Definition: Constants.h:61
Namespace containing all symbols from the Eigen library.
Definition: Core:287
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33