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