xref: /aosp_15_r20/external/eigen/unsupported/Eigen/CXX11/src/Tensor/TensorContraction.h (revision bf2c37156dfe67e5dfebd6d394bad8b2ab5804d4)
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2014 Benoit Steiner <[email protected]>
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_CXX11_TENSOR_TENSOR_CONTRACTION_H
11 #define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H
12 
13 namespace Eigen {
14 
15 /** \class TensorContraction
16   * \ingroup CXX11_Tensor_Module
17   *
18   * \brief Tensor contraction class.
19   *
20   *
21   */
22 namespace internal {
23 
24 template<typename Dimensions, typename LhsXprType, typename RhsXprType, typename OutputKernelType>
25 struct traits<TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType> >
26 {
27   // Type promotion to handle the case where the types of the lhs and the rhs are different.
28   typedef typename gebp_traits<typename remove_const<typename LhsXprType::Scalar>::type,
29                                typename remove_const<typename RhsXprType::Scalar>::type>::ResScalar Scalar;
30 
31   typedef typename promote_storage_type<typename traits<LhsXprType>::StorageKind,
32                                         typename traits<RhsXprType>::StorageKind>::ret StorageKind;
33   typedef typename promote_index_type<typename traits<LhsXprType>::Index,
34                                       typename traits<RhsXprType>::Index>::type Index;
35   typedef typename LhsXprType::Nested LhsNested;
36   typedef typename RhsXprType::Nested RhsNested;
37   typedef typename remove_reference<LhsNested>::type _LhsNested;
38   typedef typename remove_reference<RhsNested>::type _RhsNested;
39 
40   // From NumDims below.
41   static const int NumDimensions = traits<LhsXprType>::NumDimensions + traits<RhsXprType>::NumDimensions - 2 * array_size<Dimensions>::value;
42   static const int Layout = traits<LhsXprType>::Layout;
43   typedef typename conditional<Pointer_type_promotion<typename LhsXprType::Scalar, Scalar>::val,
44                                typename traits<LhsXprType>::PointerType,
45                                typename traits<RhsXprType>::PointerType>::type
46       PointerType;
47 
48   enum {
49     Flags = 0
50   };
51 };
52 
53 template<typename Dimensions, typename LhsXprType, typename RhsXprType, typename OutputKernelType>
54 struct eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType>, Eigen::Dense>
55 {
56   typedef const TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType>& type;
57 };
58 
59 template<typename Dimensions, typename LhsXprType, typename RhsXprType, typename OutputKernelType>
60 struct nested<TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType>, 1, typename eval<TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType> >::type>
61 {
62   typedef TensorContractionOp<Dimensions, LhsXprType, RhsXprType, OutputKernelType> type;
63 };
64 
65 template<typename Indices_, typename LeftArgType_, typename RightArgType_, typename OutputKernelType_, typename Device_>
66 struct traits<TensorEvaluator<const TensorContractionOp<Indices_, LeftArgType_, RightArgType_, OutputKernelType_>, Device_> > {
67   typedef Indices_ Indices;
68   typedef LeftArgType_ LeftArgType;
69   typedef RightArgType_ RightArgType;
70   typedef OutputKernelType_ OutputKernelType;
71   typedef Device_ Device;
72 
73   // From NumDims below.
74   static const int NumDimensions = traits<LeftArgType_>::NumDimensions + traits<RightArgType_>::NumDimensions - 2 * array_size<Indices_>::value;
75 };
76 
77 // Helper class to allocate and deallocate temporary memory for packed buffers.
78 template <typename LhsScalar, typename RhsScalar>
79 struct TensorContractionBlockMemAllocator {
80   typedef void* BlockMemHandle;
81 
82   template <typename Device>
83   EIGEN_DEVICE_FUNC static BlockMemHandle allocate(Device& d, const Index bm,
84                                                    const Index bk,
85                                                    const Index bn,
86                                                    LhsScalar** lhs_block,
87                                                    RhsScalar** rhs_block) {
88     eigen_assert(lhs_block);
89     eigen_assert(rhs_block);
90     BlockSizes sz = ComputeLhsRhsBlockSizes(bm, bk, bn);
91     char* block_mem = static_cast<char*>(d.allocate(sz.lhs_size + sz.rhs_size));
92     eigen_assert(block_mem);
93     *lhs_block = reinterpret_cast<LhsScalar*>(block_mem);
94     *rhs_block = reinterpret_cast<RhsScalar*>(block_mem + sz.lhs_size);
95     return block_mem;
96   }
97 
98   template <typename Device>
99   EIGEN_DEVICE_FUNC static BlockMemHandle allocateSlices(
100       Device& d, const Index bm, const Index bk, const Index bn,
101       const Index num_lhs, const Index num_rhs, const Index num_slices,
102       std::vector<LhsScalar*>* lhs_blocks,
103       std::vector<RhsScalar*>* rhs_blocks) {
104     eigen_assert(num_slices > 0);
105     eigen_assert(num_lhs >= 0 && num_rhs >= 0);
106     eigen_assert(num_lhs == 0 || lhs_blocks);
107     eigen_assert(num_rhs == 0 || rhs_blocks);
108     BlockSizes sz = ComputeLhsRhsBlockSizes(bm, bk, bn);
109     void* block_mem = d.allocate(
110         (num_lhs * sz.lhs_size + num_rhs * sz.rhs_size) * num_slices);
111     eigen_assert(block_mem);
112     char* mem = static_cast<char*>(block_mem);
113 
114     for (Index x = 0; x < num_slices; x++) {
115       if (num_lhs > 0) lhs_blocks[x].resize(num_lhs);
116       for (Index m = 0; m < num_lhs; m++) {
117         lhs_blocks[x][m] = reinterpret_cast<LhsScalar*>(mem);
118         mem += sz.lhs_size;
119       }
120       if (num_rhs > 0) rhs_blocks[x].resize(num_rhs);
121       for (Index n = 0; n < num_rhs; n++) {
122         rhs_blocks[x][n] = reinterpret_cast<RhsScalar*>(mem);
123         mem += sz.rhs_size;
124       }
125     }
126 
127     return block_mem;
128   }
129 
130   template <typename Device>
131   EIGEN_DEVICE_FUNC static void deallocate(Device& d, BlockMemHandle handle) {
132     d.deallocate(handle);
133   }
134 
135  private:
136   struct BlockSizes {
137     Index lhs_size;
138     Index rhs_size;
139   };
140   EIGEN_DEVICE_FUNC static BlockSizes ComputeLhsRhsBlockSizes(const Index bm,
141                                                               const Index bk,
142                                                               const Index bn) {
143     Index align = numext::maxi(EIGEN_MAX_ALIGN_BYTES, 1);
144     BlockSizes sz;
145     sz.lhs_size = divup<Index>(bm * bk * sizeof(LhsScalar), align) * align;
146     sz.rhs_size = divup<Index>(bn * bk * sizeof(RhsScalar), align) * align;
147     return sz;
148   }
149 };
150 
151 // WARNING: In this code we assume that Lhs and Rhs tensor expressions are in
152 // ColMajor storage order. This property is guaranteed by the
153 // TensorContractionOp evaluator. TensorContractionKernel specifies how we pack
154 // blocks of Lhs and Rhs tensor expressions, and how we invoke matrix
155 // multiplication for these blocks. Default tensor contraction uses
156 // gemm_pack_rhs, gemm_pack_lhs and gebp_kernel from Eigen Core (see
157 // GeneralBlocPanelKernel.h for details).
158 //
159 // By specializing contraction kernels we can use other low level libraries to
160 // perform matrix multiplication, and still rely on Eigen contraction evaluator.
161 // This also includes full support in TensorContractionThreadPool, assuming that
162 // underlying gemm do not use it's own threading.
163 //
164 // - ResScalar/LhsScalar/RhsScalar - scalar type for the result of
165 //   multiplication, lhs tensor and rhs tensor respectively.
166 //
167 // - StorageIndex - index type for the tensor expressions. In practice almost
168 //   always is Eigen::Index.
169 //
170 // - OutputMapper provides access to the memory of the output matrix. In
171 //   practice it's always column major blas_data_mapper (it must be of ResScalar
172 //   type).
173 //
174 // - LhsMapper/RhsMapper similarly to blas_data_mapper provide a two dimensional
175 //   view into the Lhs/Rhs tensor expressions. In practice it's
176 //   TensorContractionInputMapper, or some specialization of it based on the
177 //   type of tensor expression (e.g. TensorImagePatchOp has optimized input
178 //   mapper).
179 template <typename ResScalar, typename LhsScalar, typename RhsScalar,
180     typename StorageIndex, typename OutputMapper, typename LhsMapper,
181     typename RhsMapper>
182 struct TensorContractionKernel {
183   // True if `invoke()` supports `beta` in `C <- alpha * A * B + beta * C`
184   // (otherwise beta should be always equal to 1).
185   enum { HasBeta = false };
186 
187   EIGEN_DEVICE_FUNC
188   TensorContractionKernel(StorageIndex m_, StorageIndex k_, StorageIndex n_,
189                           StorageIndex bm_, StorageIndex bk_, StorageIndex bn_)
190       : m(m_), k(k_), n(n_), bm(bm_), bk(bk_), bn(bn_) {}
191 
192   // Pack blocks of Lhs and Rhs into contiguous blocks in memory.
193   typedef LhsScalar* LhsBlock;
194   typedef RhsScalar* RhsBlock;
195 
196   // Packed Lhs/Rhs block memory allocator.
197   typedef TensorContractionBlockMemAllocator<LhsScalar, RhsScalar>
198       BlockMemAllocator;
199   typedef typename BlockMemAllocator::BlockMemHandle BlockMemHandle;
200 
201   typedef typename internal::gebp_traits<LhsScalar, RhsScalar> Traits;
202 
203   typedef internal::gemm_pack_lhs<
204       LhsScalar, StorageIndex, typename LhsMapper::SubMapper, Traits::mr,
205       Traits::LhsProgress, typename Traits::LhsPacket4Packing, ColMajor>
206       LhsPacker;
207 
208   typedef internal::gemm_pack_rhs<RhsScalar, StorageIndex,
209                                   typename RhsMapper::SubMapper, Traits::nr,
210                                   ColMajor>
211       RhsPacker;
212 
213   typedef internal::gebp_kernel<LhsScalar, RhsScalar, StorageIndex,
214                                 OutputMapper, Traits::mr, Traits::nr,
215       /*ConjugateLhs*/ false, /*ConjugateRhs*/ false>
216       GebpKernel;
217 
218   template <typename Device>
219   EIGEN_DEVICE_FUNC BlockMemHandle allocate(Device& d, LhsBlock* lhs_block,
220                                             RhsBlock* rhs_block) {
221     return BlockMemAllocator::allocate(d, bm, bk, bn, lhs_block, rhs_block);
222   }
223 
224   template <typename Device>
225   EIGEN_DEVICE_FUNC BlockMemHandle allocateSlices(
226       Device& d, const StorageIndex num_lhs, const StorageIndex num_rhs,
227       const StorageIndex num_slices, std::vector<LhsBlock>* lhs_blocks,
228       std::vector<RhsBlock>* rhs_blocks) {
229     return BlockMemAllocator::allocateSlices(
230         d, bm, bk, bn, num_lhs, num_rhs, num_slices, lhs_blocks, rhs_blocks);
231   }
232 
233   template <typename Device>
234   EIGEN_DEVICE_FUNC static void deallocate(Device& d, BlockMemHandle handle) {
235     BlockMemAllocator::deallocate(d, handle);
236   }
237 
238   EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE void packLhs(
239       LhsBlock* lhsBlock, const typename LhsMapper::SubMapper& data_mapper,
240       const StorageIndex depth, const StorageIndex rows) {
241     LhsPacker()(*lhsBlock, data_mapper, depth, rows, /*stride*/ 0,
242         /*offset*/ 0);
243   }
244 
245   EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE void packRhs(
246       RhsBlock* rhsBlock, const typename RhsMapper::SubMapper& data_mapper,
247       const StorageIndex depth, const StorageIndex cols) {
248     RhsPacker()(*rhsBlock, data_mapper, depth, cols);
249   }
250 
251   EIGEN_DEVICE_FUNC EIGEN_DONT_INLINE void invoke(
252       const OutputMapper& output_mapper, const LhsBlock& lhsBlock,
253       const RhsBlock& rhsBlock, const StorageIndex rows,
254       const StorageIndex depth, const StorageIndex cols,
255       const ResScalar alpha, const ResScalar beta) {
256     // Default GEBP kernel does not support beta.
257     eigen_assert(beta == ResScalar(1));
258     static const int kComputeStrideFromBlockDimensions = -1;
259     GebpKernel()(output_mapper, lhsBlock, rhsBlock, rows, depth, cols, alpha,
260         /*strideA*/ kComputeStrideFromBlockDimensions,
261         /*strideB*/ kComputeStrideFromBlockDimensions,
262         /*offsetA*/ 0, /*offsetB*/ 0);
263   }
264 
265  private:
266   // These are dimensions of the original Tensors, and selected block sizes. The
267   // actual block sizes passed to all function above might be smaller because of
268   // the partial blocks at the end.
269   const StorageIndex m;
270   const StorageIndex k;
271   const StorageIndex n;
272   const StorageIndex bm;
273   const StorageIndex bk;
274   const StorageIndex bn;
275 };
276 
277 }  // end namespace internal
278 
279 // Tensor contraction params that should enable to get from output matrix
280 // 2-dimensional coordinates to the output tensor dimensions.
281 struct TensorContractionParams {
282   // TensorContraction evaluator assumes that both tensors are in ColMajor
283   // layout, if tensors are in RowMajor evaluator swap lhs with rhs.
284   bool swapped_arguments;
285 };
286 
287 // Output kernel allows to fuse operations into the tensor contraction.
288 //
289 // Examples:
290 //   1. Elementwise Relu transformation following Conv2D.
291 //   2. AddBias to the Conv2D output channels dimension.
292 //
293 // The NoOpOutputKernel implements an output kernel that does absolutely nothing.
294 struct NoOpOutputKernel {
295   /**
296    * Tensor contraction evaluator calls this kernel after finishing each block
297    * of output matrix. Output blocks belong to the 2-dimensional output tensor.
298    *
299    * TensorContractionParams contains contraction dimensions information
300    * required to map output 2-d space into the expected output tensor space
301    * (potentially higher dimensional).
302    *
303    * \param[in] output_mapper Access to output tensor memory
304    * \param[in] params   Tensor contraction parameters
305    * \param[in] i        Index of a first row available through output_mapper
306    * \param[in] j        Index of a first column available through output_mapper
307    * \param[in] num_rows Number of available rows
308    * \param[in] num_cols Number of available columns
309    */
310   template <typename Index, typename Scalar>
311   EIGEN_ALWAYS_INLINE void operator()(
312       const internal::blas_data_mapper<Scalar, Index, ColMajor>& output_mapper,
313       const TensorContractionParams& params, Index i,
314       Index j, Index num_rows, Index num_cols) const {
315     EIGEN_UNUSED_VARIABLE(output_mapper);
316     EIGEN_UNUSED_VARIABLE(params);
317     EIGEN_UNUSED_VARIABLE(i);
318     EIGEN_UNUSED_VARIABLE(j);
319     EIGEN_UNUSED_VARIABLE(num_rows);
320     EIGEN_UNUSED_VARIABLE(num_cols);
321   }
322 };
323 
324 template<typename Indices, typename LhsXprType, typename RhsXprType, typename OutputKernelType = const NoOpOutputKernel>
325 class TensorContractionOp : public TensorBase<TensorContractionOp<Indices, LhsXprType, RhsXprType, OutputKernelType>, ReadOnlyAccessors>
326 {
327   public:
328   typedef typename Eigen::internal::traits<TensorContractionOp>::Scalar Scalar;
329   typedef typename internal::gebp_traits<typename LhsXprType::CoeffReturnType,
330                                          typename RhsXprType::CoeffReturnType>::ResScalar CoeffReturnType;
331   typedef typename Eigen::internal::nested<TensorContractionOp>::type Nested;
332   typedef typename Eigen::internal::traits<TensorContractionOp>::StorageKind StorageKind;
333   typedef typename Eigen::internal::traits<TensorContractionOp>::Index Index;
334 
335   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorContractionOp(
336       const LhsXprType& lhs, const RhsXprType& rhs, const Indices& dims,
337       const OutputKernelType& output_kernel = OutputKernelType())
338       : m_lhs_xpr(lhs), m_rhs_xpr(rhs), m_indices(dims),
339         m_output_kernel(output_kernel) {}
340 
341   EIGEN_DEVICE_FUNC
342   const Indices& indices() const { return m_indices; }
343 
344   /** \returns the nested expressions */
345   EIGEN_DEVICE_FUNC
346   const typename internal::remove_all<typename LhsXprType::Nested>::type&
347   lhsExpression() const { return m_lhs_xpr; }
348 
349   EIGEN_DEVICE_FUNC
350   const typename internal::remove_all<typename RhsXprType::Nested>::type&
351   rhsExpression() const { return m_rhs_xpr; }
352 
353   EIGEN_DEVICE_FUNC
354   const OutputKernelType& outputKernel() const { return m_output_kernel; }
355 
356   protected:
357     typename LhsXprType::Nested m_lhs_xpr;
358     typename RhsXprType::Nested m_rhs_xpr;
359     const Indices m_indices;
360     const OutputKernelType m_output_kernel;
361 };
362 
363 
364 template<typename Derived>
365 struct TensorContractionEvaluatorBase : internal::no_assignment_operator
366 {
367   typedef typename internal::traits<Derived>::Indices Indices;
368   typedef typename internal::traits<Derived>::LeftArgType LeftArgType;
369   typedef typename internal::traits<Derived>::RightArgType RightArgType;
370   typedef typename internal::traits<Derived>::OutputKernelType OutputKernelType;
371   typedef typename internal::traits<Derived>::Device Device;
372 
373   typedef TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType> XprType;
374   typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;
375   typedef typename XprType::Index Index;
376   typedef typename XprType::CoeffReturnType CoeffReturnType;
377   typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
378   typedef StorageMemory<Scalar, Device> Storage;
379   typedef typename Storage::Type EvaluatorPointerType;
380 
381   enum {
382     IsAligned         = true,
383     PacketAccess      = (PacketType<CoeffReturnType, Device>::size > 1),
384     BlockAccess       = false,
385     PreferBlockAccess = false,
386     Layout            = TensorEvaluator<LeftArgType, Device>::Layout,
387     CoordAccess       = false,  // to be implemented
388     RawAccess         = true
389   };
390 
391   //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
392   typedef internal::TensorBlockNotImplemented TensorBlock;
393   //===--------------------------------------------------------------------===//
394 
395   // Most of the code is assuming that both input tensors are ColMajor. If the
396   // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS:
397   // If we want to compute A * B = C, where A is LHS and B is RHS, the code
398   // will pretend B is LHS and A is RHS.
399   typedef typename internal::conditional<
400     static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType;
401   typedef typename internal::conditional<
402     static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType;
403 
404   typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluatorType;
405   typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluatorType;
406 
407   static const int LDims =
408       internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;
409   static const int RDims =
410       internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;
411   static const int ContractDims = internal::array_size<Indices>::value;
412   static const int NumDims = LDims + RDims - 2 * ContractDims;
413 
414   typedef array<Index, ContractDims> contract_t;
415   typedef array<Index, LDims - ContractDims> left_nocontract_t;
416   typedef array<Index, RDims - ContractDims> right_nocontract_t;
417 
418   typedef DSizes<Index, NumDims> Dimensions;
419 
420   EIGEN_STRONG_INLINE
421   TensorContractionEvaluatorBase(const XprType& op, const Device& device)
422       : m_leftImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(),
423                           op.lhsExpression(), op.rhsExpression()), device),
424         m_rightImpl(choose(Cond<static_cast<int>(Layout) == static_cast<int>(ColMajor)>(),
425                            op.rhsExpression(), op.lhsExpression()), device),
426         m_device(device),
427         m_output_kernel(op.outputKernel()),
428         m_result(NULL) {
429     EIGEN_STATIC_ASSERT((static_cast<int>(TensorEvaluator<LeftArgType, Device>::Layout) ==
430          static_cast<int>(TensorEvaluator<RightArgType, Device>::Layout)),
431                         YOU_MADE_A_PROGRAMMING_MISTAKE);
432 
433 
434     DSizes<Index, LDims> eval_left_dims;
435     DSizes<Index, RDims> eval_right_dims;
436     array<IndexPair<Index>, ContractDims> eval_op_indices;
437     if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
438       // For ColMajor, we keep using the existing dimensions
439       for (int i = 0; i < LDims; i++) {
440         eval_left_dims[i] = m_leftImpl.dimensions()[i];
441       }
442       for (int i = 0; i < RDims; i++) {
443         eval_right_dims[i] = m_rightImpl.dimensions()[i];
444       }
445       // We keep the pairs of contracting indices.
446       for (int i = 0; i < ContractDims; i++) {
447         eval_op_indices[i].first = op.indices()[i].first;
448         eval_op_indices[i].second = op.indices()[i].second;
449       }
450     } else {
451       // For RowMajor, we need to reverse the existing dimensions
452       for (int i = 0; i < LDims; i++) {
453         eval_left_dims[i] = m_leftImpl.dimensions()[LDims - i - 1];
454       }
455       for (int i = 0; i < RDims; i++) {
456         eval_right_dims[i] = m_rightImpl.dimensions()[RDims - i - 1];
457       }
458       // We need to flip all the pairs of contracting indices as well as
459       // reversing the dimensions.
460       for (int i = 0; i < ContractDims; i++) {
461         eval_op_indices[i].first = LDims - 1 - op.indices()[ContractDims - 1 - i].second;
462         eval_op_indices[i].second = RDims - 1 - op.indices()[ContractDims - 1 - i].first;
463       }
464     }
465 
466     // Check for duplicate axes and make sure the first index in eval_op_indices
467     // is increasing. Using O(n^2) sorting is OK since ContractDims is small
468     for (int i = 0; i < ContractDims; i++) {
469       for (int j = i + 1; j < ContractDims; j++) {
470         eigen_assert(eval_op_indices[j].first != eval_op_indices[i].first &&
471                      eval_op_indices[j].second != eval_op_indices[i].second &&
472                      "contraction axes should be unique");
473         if (eval_op_indices[j].first < eval_op_indices[i].first) {
474           numext::swap(eval_op_indices[j], eval_op_indices[i]);
475         }
476       }
477     }
478 
479     array<Index, LDims> lhs_strides;
480     lhs_strides[0] = 1;
481     for (int i = 0; i < LDims-1; ++i) {
482       lhs_strides[i+1] = lhs_strides[i] * eval_left_dims[i];
483     }
484 
485     array<Index, RDims> rhs_strides;
486     rhs_strides[0] = 1;
487     for (int i = 0; i < RDims-1; ++i) {
488       rhs_strides[i+1] = rhs_strides[i] * eval_right_dims[i];
489     }
490 
491     if (m_i_strides.size() > 0) m_i_strides[0] = 1;
492     if (m_j_strides.size() > 0) m_j_strides[0] = 1;
493     if (m_k_strides.size() > 0) m_k_strides[0] = 1;
494 
495     m_i_size = 1;
496     m_j_size = 1;
497     m_k_size = 1;
498 
499     // To compute the dimension, we simply concatenate the non-contracting
500     // dimensions of the left and then the right tensor. Additionally, we also
501     // compute the strides corresponding to the left non-contracting
502     // dimensions and right non-contracting dimensions.
503     m_lhs_inner_dim_contiguous = true;
504     int dim_idx = 0;
505     Index nocontract_idx = 0;
506 
507     for (int i = 0; i < LDims; i++) {
508       // find if we are contracting on index i of left tensor
509       bool contracting = false;
510       for (int j = 0; j < ContractDims; j++) {
511         if (eval_op_indices[j].first == i) {
512           contracting = true;
513           break;
514         }
515       }
516       if (!contracting) {
517         // add dimension size to output dimensions
518         m_dimensions[dim_idx] = eval_left_dims[i];
519         m_left_nocontract_strides[nocontract_idx] = lhs_strides[i];
520         if (dim_idx != i) {
521           m_lhs_inner_dim_contiguous = false;
522         }
523         if (nocontract_idx+1 < internal::array_size<left_nocontract_t>::value) {
524           m_i_strides[nocontract_idx+1] =
525               m_i_strides[nocontract_idx] * eval_left_dims[i];
526         } else {
527           m_i_size = m_i_strides[nocontract_idx] * eval_left_dims[i];
528         }
529         dim_idx++;
530         nocontract_idx++;
531       }
532     }
533 
534     nocontract_idx = 0;
535     for (int i = 0; i < RDims; i++) {
536       bool contracting = false;
537       // find if we are contracting on index i of right tensor
538       for (int j = 0; j < ContractDims; j++) {
539         if (eval_op_indices[j].second == i) {
540           contracting = true;
541           break;
542         }
543       }
544       if (!contracting) {
545         m_dimensions[dim_idx] = eval_right_dims[i];
546         if (nocontract_idx+1 < internal::array_size<right_nocontract_t>::value) {
547           m_j_strides[nocontract_idx+1] =
548               m_j_strides[nocontract_idx] * eval_right_dims[i];
549         } else {
550           m_j_size = m_j_strides[nocontract_idx] * eval_right_dims[i];
551         }
552         m_right_nocontract_strides[nocontract_idx] = rhs_strides[i];
553         dim_idx++;
554         nocontract_idx++;
555       }
556     }
557 
558     // Now compute the strides corresponding to the contracting dimensions. We
559     // assumed above that non-contracting axes are represented in the same order
560     // in the matrix as they are in the tensor. This is not the case for
561     // contracting axes. As the contracting axes must be of the same size in
562     // each tensor, we'll only look at the first tensor here.
563     m_rhs_inner_dim_contiguous = true;
564     m_rhs_inner_dim_reordered = false;
565     for (int i = 0; i < ContractDims; i++) {
566       Index left = eval_op_indices[i].first;
567       Index right = eval_op_indices[i].second;
568 
569       Index size = eval_left_dims[left];
570       eigen_assert(size == eval_right_dims[right] &&
571                    "Contraction axes must be same size");
572 
573       if (i+1 < static_cast<int>(internal::array_size<contract_t>::value)) {
574         m_k_strides[i+1] = m_k_strides[i] * size;
575       } else {
576         m_k_size = m_k_strides[i] * size;
577       }
578       m_left_contracting_strides[i] = lhs_strides[left];
579       m_right_contracting_strides[i] = rhs_strides[right];
580 
581       if (i > 0 && right < eval_op_indices[i-1].second) {
582         m_rhs_inner_dim_reordered = true;
583       }
584       if (right != i) {
585         m_rhs_inner_dim_contiguous = false;
586       }
587     }
588 
589     // If the layout is RowMajor, we need to reverse the m_dimensions
590     if (static_cast<int>(Layout) == static_cast<int>(RowMajor)) {
591       for (int i = 0, j = NumDims - 1; i < j; i++, j--) {
592         numext::swap(m_dimensions[i], m_dimensions[j]);
593       }
594     }
595 
596     // A set of parameters that will allow output kernel to get from output
597     // tensor dimensions (i, j) into the original tensor dimensions.
598     // TODO(ezhulenev): Add parameters required to infer output tensor index for
599     // more complex contractions than 2x2 on internal dimension.
600     m_tensor_contraction_params.swapped_arguments = static_cast<int>(Layout) == RowMajor;
601   }
602 
603   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
604 
605   EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
606     m_leftImpl.evalSubExprsIfNeeded(NULL);
607     m_rightImpl.evalSubExprsIfNeeded(NULL);
608     if (data) {
609       evalTo(data);
610       return false;
611     } else {
612       m_result = static_cast<EvaluatorPointerType>(m_device.allocate(dimensions().TotalSize() * sizeof(Scalar)));
613       evalTo(m_result);
614       return true;
615     }
616   }
617 
618 #ifdef EIGEN_USE_THREADS
619   template <typename EvalSubExprsCallback>
620   EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(
621       EvaluatorPointerType dest, EvalSubExprsCallback done) {
622     m_leftImpl.evalSubExprsIfNeededAsync(nullptr, [this, done, dest](bool) {
623       m_rightImpl.evalSubExprsIfNeededAsync(nullptr, [this, done, dest](bool) {
624         if (dest) {
625           evalToAsync(dest, [done]() { done(false); });
626         } else {
627           m_result = static_cast<EvaluatorPointerType>(
628               m_device.allocate(dimensions().TotalSize() * sizeof(Scalar)));
629           evalToAsync(m_result, [done]() { done(true); });
630         }
631       });
632     });
633   }
634 #endif  // EIGEN_USE_THREADS
635 
636 #ifndef TENSOR_CONTRACTION_DISPATCH
637 #define TENSOR_CONTRACTION_DISPATCH(METHOD, ALIGNMENT, ARGS) \
638   if (this->m_lhs_inner_dim_contiguous) {                    \
639     if (this->m_rhs_inner_dim_contiguous) {                  \
640       if (this->m_rhs_inner_dim_reordered) {                 \
641         METHOD<true, true, true, ALIGNMENT> ARGS;            \
642       } else {                                               \
643         METHOD<true, true, false, ALIGNMENT> ARGS;           \
644       }                                                      \
645     } else {                                                 \
646       if (this->m_rhs_inner_dim_reordered) {                 \
647         METHOD<true, false, true, ALIGNMENT> ARGS;           \
648       } else {                                               \
649         METHOD<true, false, false, ALIGNMENT> ARGS;          \
650       }                                                      \
651     }                                                        \
652   } else {                                                   \
653     if (this->m_rhs_inner_dim_contiguous) {                  \
654       if (this->m_rhs_inner_dim_reordered) {                 \
655         METHOD<false, true, true, ALIGNMENT> ARGS;           \
656       } else {                                               \
657         METHOD<false, true, false, ALIGNMENT> ARGS;          \
658       }                                                      \
659     } else {                                                 \
660       if (this->m_rhs_inner_dim_reordered) {                 \
661         METHOD<false, false, true, ALIGNMENT> ARGS;          \
662       } else {                                               \
663         METHOD<false, false, false, ALIGNMENT> ARGS;         \
664       }                                                      \
665     }                                                        \
666   }
667 #endif
668 
669 #ifndef TENSOR_CONTRACTION_ASYNC_DISPATCH
670 #define TENSOR_CONTRACTION_ASYNC_DISPATCH(METHOD, DONE, ALIGNMENT, ARGS, FN) \
671   if (this->m_lhs_inner_dim_contiguous) {                                    \
672     if (this->m_rhs_inner_dim_contiguous) {                                  \
673       if (this->m_rhs_inner_dim_reordered) {                                 \
674         (new METHOD<DONE, true, true, true, ALIGNMENT> ARGS)->FN;            \
675       } else {                                                               \
676         (new METHOD<DONE, true, true, false, ALIGNMENT> ARGS)->FN;           \
677       }                                                                      \
678     } else {                                                                 \
679       if (this->m_rhs_inner_dim_reordered) {                                 \
680         (new METHOD<DONE, true, false, true, ALIGNMENT> ARGS)->FN;           \
681       } else {                                                               \
682         (new METHOD<DONE, true, false, false, ALIGNMENT> ARGS)->FN;          \
683       }                                                                      \
684     }                                                                        \
685   } else {                                                                   \
686     if (this->m_rhs_inner_dim_contiguous) {                                  \
687       if (this->m_rhs_inner_dim_reordered) {                                 \
688         (new METHOD<DONE, false, true, true, ALIGNMENT> ARGS)->FN;           \
689       } else {                                                               \
690         (new METHOD<DONE, false, true, false, ALIGNMENT> ARGS)->FN;          \
691       }                                                                      \
692     } else {                                                                 \
693       if (this->m_rhs_inner_dim_reordered) {                                 \
694         (new METHOD<DONE, false, false, true, ALIGNMENT> ARGS)->FN;          \
695       } else {                                                               \
696         (new METHOD<DONE, false, false, false, ALIGNMENT> ARGS)->FN;         \
697       }                                                                      \
698     }                                                                        \
699   }
700 #endif
701 
702   EIGEN_DEVICE_FUNC void evalTo(Scalar* buffer) const {
703    static_cast<const Derived*>(this)->template evalProduct<Unaligned>(buffer);
704   }
705 
706 #ifdef EIGEN_USE_THREADS
707   template <typename EvalToCallback>
708   void evalToAsync(Scalar* buffer, EvalToCallback done) const {
709     static_cast<const Derived*>(this)
710         ->template evalProductAsync<EvalToCallback, Unaligned>(buffer,
711                                                                std::move(done));
712   }
713 #endif  // EIGEN_USE_THREADS
714 
715   template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous,
716             bool rhs_inner_dim_reordered, int Alignment>
717   void evalProductSequential(Scalar* buffer) const {
718     if (this->m_j_size == 1) {
719       this->template evalGemv<lhs_inner_dim_contiguous,
720                               rhs_inner_dim_contiguous, rhs_inner_dim_reordered,
721                               Alignment>(buffer);
722     } else {
723       this->template evalGemm<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous,
724                               rhs_inner_dim_reordered, Alignment>(buffer);
725     }
726   }
727 
728   template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
729   #if !defined(EIGEN_HIPCC)
730   EIGEN_DEVICE_FUNC
731   #endif
732   void evalGemv(Scalar* buffer) const {
733     const Index rows = m_i_size;
734     const Index cols = m_k_size;
735 
736     typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;
737     typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;
738     typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;
739     typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;
740     const Index lhs_packet_size = internal::unpacket_traits<typename LeftEvaluator::PacketReturnType>::size;
741     const Index rhs_packet_size = internal::unpacket_traits<typename RightEvaluator::PacketReturnType>::size;
742     const int lhs_alignment = LeftEvaluator::IsAligned ? Aligned : Unaligned;
743     const int rhs_alignment = RightEvaluator::IsAligned ? Aligned : Unaligned;
744     typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,
745                                                    LeftEvaluator, left_nocontract_t,
746                                                    contract_t, lhs_packet_size,
747                                                    lhs_inner_dim_contiguous,
748                                                    false, lhs_alignment> LhsMapper;
749 
750     typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,
751                                                    RightEvaluator, right_nocontract_t,
752                                                    contract_t, rhs_packet_size,
753                                                    rhs_inner_dim_contiguous,
754                                                    rhs_inner_dim_reordered, rhs_alignment> RhsMapper;
755 
756     LhsMapper lhs(m_leftImpl, m_left_nocontract_strides, m_i_strides,
757                   m_left_contracting_strides, m_k_strides);
758     RhsMapper rhs(m_rightImpl, m_right_nocontract_strides, m_j_strides,
759                   m_right_contracting_strides, m_k_strides);
760 
761     const Scalar alpha(1);
762     const Index resIncr(1);
763 
764     // zero out the result buffer (which must be of size at least rows * sizeof(Scalar)
765     m_device.memset(buffer, 0, rows * sizeof(Scalar));
766 
767     internal::general_matrix_vector_product<Index,LhsScalar,LhsMapper,ColMajor,false,RhsScalar,RhsMapper,false>::run(
768         rows, cols, lhs, rhs,
769         buffer, resIncr, alpha);
770 
771     typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;
772     m_output_kernel(OutputMapper(buffer, rows), m_tensor_contraction_params,
773                     static_cast<Index>(0), static_cast<Index>(0), rows,
774                     static_cast<Index>(1));
775   }
776 
777   template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
778   #if !defined(EIGEN_HIPCC)
779   EIGEN_DEVICE_FUNC
780   #endif
781   void evalGemm(Scalar* buffer) const {
782     // columns in left side, rows in right side
783     const Index k = this->m_k_size;
784     this->template evalGemmPartial<lhs_inner_dim_contiguous,
785                                    rhs_inner_dim_contiguous,
786                                    rhs_inner_dim_reordered,
787                                    Alignment, true>(buffer, 0, k, 1);
788   }
789 
790   template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous,
791       bool rhs_inner_dim_reordered, int Alignment>
792   EIGEN_DEVICE_FUNC void evalGemmPartialWithoutOutputKernel(
793       Scalar* buffer, Index k_start, Index k_end, int num_threads) const {
794     evalGemmPartial<lhs_inner_dim_contiguous, rhs_inner_dim_contiguous,
795                     rhs_inner_dim_reordered, Alignment,
796         /*use_output_kernel*/ false>(buffer, k_start, k_end,
797                                      num_threads);
798   }
799 
800   template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment, bool use_output_kernel>
801   EIGEN_DEVICE_FUNC void evalGemmPartial(Scalar* buffer, Index k_start, Index k_end, int num_threads) const {
802     eigen_assert(k_end >= k_start && k_start >= 0 && k_end <= this->m_k_size);
803     // columns in slice on left side, rows on right side
804     const Index k_slice = k_end - k_start;
805 
806     // rows in left side
807     const Index m = this->m_i_size;
808 
809     // columns in right side
810     const Index n = this->m_j_size;
811 
812     // define data mappers for Lhs and Rhs
813     typedef typename internal::remove_const<typename EvalLeftArgType::Scalar>::type LhsScalar;
814     typedef typename internal::remove_const<typename EvalRightArgType::Scalar>::type RhsScalar;
815 
816     typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;
817     typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;
818 
819     const Index lhs_packet_size = internal::unpacket_traits<typename LeftEvaluator::PacketReturnType>::size;
820     const Index rhs_packet_size = internal::unpacket_traits<typename RightEvaluator::PacketReturnType>::size;
821 
822     typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs,
823                                                    LeftEvaluator, left_nocontract_t,
824                                                    contract_t, lhs_packet_size,
825                                                    lhs_inner_dim_contiguous,
826                                                    false, Unaligned> LhsMapper;
827 
828     typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs,
829                                                    RightEvaluator, right_nocontract_t,
830                                                    contract_t, rhs_packet_size,
831                                                    rhs_inner_dim_contiguous,
832                                                    rhs_inner_dim_reordered, Unaligned> RhsMapper;
833 
834     typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;
835 
836     typedef internal::TensorContractionKernel<
837         Scalar, LhsScalar, RhsScalar, Index, OutputMapper, LhsMapper, RhsMapper>
838         TensorContractionKernel;
839 
840     // initialize data mappers
841     LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides,
842                   this->m_left_contracting_strides, this->m_k_strides);
843 
844     RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides,
845                   this->m_right_contracting_strides, this->m_k_strides);
846 
847     OutputMapper output(buffer, m);
848 
849     // Sizes of the blocks to load in cache. See the Goto paper for details.
850     internal::TensorContractionBlocking<Scalar, LhsScalar, RhsScalar,
851                                         Index, internal::ShardByCol>
852         blocking(k_slice, m, n, num_threads);
853     const Index kc = blocking.kc();
854     const Index mc = numext::mini(m, blocking.mc());
855     const Index nc = numext::mini(n, blocking.nc());
856 
857     typedef typename TensorContractionKernel::LhsBlock LhsBlock;
858     typedef typename TensorContractionKernel::RhsBlock RhsBlock;
859 
860     LhsBlock blockA;
861     RhsBlock blockB;
862 
863     TensorContractionKernel kernel(m, k_slice, n, mc, kc, nc);
864 
865     typedef typename TensorContractionKernel::BlockMemHandle BlockMemHandle;
866     const BlockMemHandle packed_mem =
867         kernel.allocate(this->m_device, &blockA, &blockB);
868 
869     // If a contraction kernel does not support beta, explicitly initialize
870     // output buffer with zeroes.
871     if (!TensorContractionKernel::HasBeta) {
872       this->m_device.memset(buffer, 0, m * n * sizeof(Scalar));
873     }
874 
875     for(Index i2=0; i2<m; i2+=mc)
876     {
877       const Index actual_mc = numext::mini(i2+mc,m)-i2;
878       for (Index k2 = k_start; k2 < k_end; k2 += kc) {
879         // make sure we don't overshoot right edge of left matrix, then pack vertical panel
880         const Index actual_kc = numext::mini(k2 + kc, k_end) - k2;
881         kernel.packLhs(&blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
882 
883         // If kernel supports beta, there is no need to initialize output
884         // buffer with zeroes.
885         const Scalar alpha = Scalar(1);
886         const Scalar beta = (TensorContractionKernel::HasBeta && k2 == k_start)
887                                 ? Scalar(0)
888                                 : Scalar(1);
889 
890         // series of horizontal blocks
891         for (Index j2 = 0; j2 < n; j2 += nc) {
892           // make sure we don't overshoot right edge of right matrix, then pack block
893           const Index actual_nc = numext::mini(j2 + nc, n) - j2;
894           kernel.packRhs(&blockB, rhs.getSubMapper(k2, j2), actual_kc,
895                          actual_nc);
896 
897           // call gebp (matrix kernel)
898           // The parameters here are copied from Eigen's GEMM implementation
899           const OutputMapper output_mapper = output.getSubMapper(i2, j2);
900           kernel.invoke(output_mapper, blockA, blockB, actual_mc, actual_kc,
901                         actual_nc, alpha, beta);
902 
903           // We are done with this [i2, j2] output block.
904           if (use_output_kernel && k2 + kc >= k_end) {
905             m_output_kernel(output_mapper, m_tensor_contraction_params, i2, j2,
906                             actual_mc, actual_nc);
907           }
908         }
909       }
910     }
911 
912     kernel.deallocate(this->m_device, packed_mem);
913   }
914 
915   EIGEN_STRONG_INLINE void cleanup() {
916     m_leftImpl.cleanup();
917     m_rightImpl.cleanup();
918 
919     if (m_result != NULL) {
920       m_device.deallocate(m_result);
921       m_result = NULL;
922     }
923   }
924 
925   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
926     return m_result[index];
927   }
928 
929   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool) const {
930     return TensorOpCost(sizeof(CoeffReturnType), 0, 0);
931   }
932 
933   template<int LoadMode>
934   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const {
935     return internal::ploadt<PacketReturnType, LoadMode>(m_result + index);
936   }
937 
938   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EvaluatorPointerType data() const { return m_result; }
939 
940 protected:
941   Dimensions m_dimensions;
942 
943   contract_t m_k_strides;
944   contract_t m_left_contracting_strides;
945   contract_t m_right_contracting_strides;
946 
947   bool m_lhs_inner_dim_contiguous;
948   bool m_rhs_inner_dim_contiguous;
949   bool m_rhs_inner_dim_reordered;
950 
951   left_nocontract_t m_i_strides;
952   right_nocontract_t m_j_strides;
953   left_nocontract_t m_left_nocontract_strides;
954   right_nocontract_t m_right_nocontract_strides;
955 
956   Index m_i_size;
957   Index m_j_size;
958   Index m_k_size;
959 
960   TensorContractionParams m_tensor_contraction_params;
961 
962   TensorEvaluator<EvalLeftArgType, Device> m_leftImpl;
963   TensorEvaluator<EvalRightArgType, Device> m_rightImpl;
964   const Device EIGEN_DEVICE_REF m_device;
965   OutputKernelType m_output_kernel;
966   EvaluatorPointerType m_result;
967 };
968 
969 
970 // evaluator for default device
971 template<typename Indices, typename LeftArgType, typename RightArgType, typename OutputKernelType, typename Device>
972 struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> :
973     public TensorContractionEvaluatorBase<
974       TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> > {
975   typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> Self;
976   typedef TensorContractionEvaluatorBase<Self> Base;
977 
978   typedef TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType> XprType;
979   typedef typename internal::remove_const<typename XprType::Scalar>::type Scalar;
980   typedef typename XprType::Index Index;
981   typedef typename XprType::CoeffReturnType CoeffReturnType;
982   typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
983 
984   enum {
985     Layout = TensorEvaluator<LeftArgType, Device>::Layout
986   };
987 
988   // Most of the code is assuming that both input tensors are ColMajor. If the
989   // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS:
990   // If we want to compute A * B = C, where A is LHS and B is RHS, the code
991   // will pretend B is LHS and A is RHS.
992   typedef typename internal::conditional<
993     static_cast<int>(Layout) == static_cast<int>(ColMajor), LeftArgType, RightArgType>::type EvalLeftArgType;
994   typedef typename internal::conditional<
995     static_cast<int>(Layout) == static_cast<int>(ColMajor), RightArgType, LeftArgType>::type EvalRightArgType;
996 
997   static const int LDims =
998       internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;
999   static const int RDims =
1000       internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;
1001   static const int ContractDims = internal::array_size<Indices>::value;
1002 
1003   typedef array<Index, ContractDims> contract_t;
1004   typedef array<Index, LDims - ContractDims> left_nocontract_t;
1005   typedef array<Index, RDims - ContractDims> right_nocontract_t;
1006 
1007   static const int NumDims = LDims + RDims - 2 * ContractDims;
1008 
1009   // Could we use NumDimensions here?
1010   typedef DSizes<Index, NumDims> Dimensions;
1011 
1012   TensorEvaluator(const XprType& op, const Device& device) :
1013       Base(op, device) { }
1014 
1015   template <int Alignment>
1016   void evalProduct(Scalar* buffer) const {
1017     TENSOR_CONTRACTION_DISPATCH(this->template evalProductSequential, Alignment, (buffer));
1018   }
1019 };
1020 
1021 } // end namespace Eigen
1022 
1023 #endif // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_H
1024