GeneralMatrixMatrixTriangular.h
Go to the documentation of this file.
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>
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>
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 {
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  {
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 {
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  {
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 
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 {
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  {
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>
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 
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 
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 {
214  UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1,
215  UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1
216  };
217 
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 
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 
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 
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 
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>
270 {
272 
273  return *this;
274 }
275 
276 } // end namespace Eigen
277 
278 #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H
#define EIGEN_STRONG_INLINE
#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:104
static void run(MatrixType &mat, const ProductType &prod, const typename MatrixType::Scalar &alpha)
iterative scaling algorithm to equilibrate rows and column norms in matrices
Definition: matrix.hpp:471
void operator()(ResScalar *res, Index resStride, const LhsScalar *blockA, const RhsScalar *blockB, Index size, Index depth, const ResScalar &alpha, RhsScalar *workspace)
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:88
const unsigned int RowMajorBit
static void run(MatrixType &mat, const ProductType &prod, const typename MatrixType::Scalar &alpha)
EIGEN_STRONG_INLINE TriangularView & assignProduct(const ProductBase< ProductDerived, Lhs, Rhs > &prod, const Scalar &alpha)
internal::traits< TriangularView >::Scalar Scalar
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)
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)
gebp_traits< LhsScalar, RhsScalar, ConjLhs, ConjRhs > Traits
Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > & setZero(Index size)
void rhs(const real_t *x, real_t *f)
scalar_product_traits< LhsScalar, RhsScalar >::ReturnType ResScalar
Base class for triangular part in a matrix.
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:127
#define EIGEN_PLAIN_ENUM_MAX(a, b)


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:34:38