KroneckerTensorProduct.h
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
5 // Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
6 // Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
7 //
8 // This Source Code Form is subject to the terms of the Mozilla
9 // Public License v. 2.0. If a copy of the MPL was not distributed
10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
11 
12 #ifndef KRONECKER_TENSOR_PRODUCT_H
13 #define KRONECKER_TENSOR_PRODUCT_H
14 
15 namespace Eigen {
16 
24 template<typename Derived>
25 class KroneckerProductBase : public ReturnByValue<Derived>
26 {
27  private:
29  typedef typename Traits::Scalar Scalar;
30 
31  protected:
32  typedef typename Traits::Lhs Lhs;
33  typedef typename Traits::Rhs Rhs;
34 
35  public:
37  KroneckerProductBase(const Lhs& A, const Rhs& B)
38  : m_A(A), m_B(B)
39  {}
40 
41  inline Index rows() const { return m_A.rows() * m_B.rows(); }
42  inline Index cols() const { return m_A.cols() * m_B.cols(); }
43 
48  Scalar coeff(Index row, Index col) const
49  {
50  return m_A.coeff(row / m_B.rows(), col / m_B.cols()) *
51  m_B.coeff(row % m_B.rows(), col % m_B.cols());
52  }
53 
58  Scalar coeff(Index i) const
59  {
61  return m_A.coeff(i / m_A.size()) * m_B.coeff(i % m_A.size());
62  }
63 
64  protected:
65  typename Lhs::Nested m_A;
66  typename Rhs::Nested m_B;
67 };
68 
81 template<typename Lhs, typename Rhs>
82 class KroneckerProduct : public KroneckerProductBase<KroneckerProduct<Lhs,Rhs> >
83 {
84  private:
86  using Base::m_A;
87  using Base::m_B;
88 
89  public:
91  KroneckerProduct(const Lhs& A, const Rhs& B)
92  : Base(A, B)
93  {}
94 
96  template<typename Dest> void evalTo(Dest& dst) const;
97 };
98 
114 template<typename Lhs, typename Rhs>
115 class KroneckerProductSparse : public KroneckerProductBase<KroneckerProductSparse<Lhs,Rhs> >
116 {
117  private:
119  using Base::m_A;
120  using Base::m_B;
121 
122  public:
124  KroneckerProductSparse(const Lhs& A, const Rhs& B)
125  : Base(A, B)
126  {}
127 
129  template<typename Dest> void evalTo(Dest& dst) const;
130 };
131 
132 template<typename Lhs, typename Rhs>
133 template<typename Dest>
135 {
136  const int BlockRows = Rhs::RowsAtCompileTime,
137  BlockCols = Rhs::ColsAtCompileTime;
138  const Index Br = m_B.rows(),
139  Bc = m_B.cols();
140  for (Index i=0; i < m_A.rows(); ++i)
141  for (Index j=0; j < m_A.cols(); ++j)
142  Block<Dest,BlockRows,BlockCols>(dst,i*Br,j*Bc,Br,Bc) = m_A.coeff(i,j) * m_B;
143 }
144 
145 template<typename Lhs, typename Rhs>
146 template<typename Dest>
148 {
149  Index Br = m_B.rows(), Bc = m_B.cols();
150  dst.resize(this->rows(), this->cols());
151  dst.resizeNonZeros(0);
152 
153  // 1 - evaluate the operands if needed:
154  typedef typename internal::nested_eval<Lhs,Dynamic>::type Lhs1;
155  typedef typename internal::remove_all<Lhs1>::type Lhs1Cleaned;
156  const Lhs1 lhs1(m_A);
157  typedef typename internal::nested_eval<Rhs,Dynamic>::type Rhs1;
158  typedef typename internal::remove_all<Rhs1>::type Rhs1Cleaned;
159  const Rhs1 rhs1(m_B);
160 
161  // 2 - construct respective iterators
162  typedef Eigen::InnerIterator<Lhs1Cleaned> LhsInnerIterator;
163  typedef Eigen::InnerIterator<Rhs1Cleaned> RhsInnerIterator;
164 
165  // compute number of non-zeros per innervectors of dst
166  {
167  // TODO VectorXi is not necessarily big enough!
168  VectorXi nnzA = VectorXi::Zero(Dest::IsRowMajor ? m_A.rows() : m_A.cols());
169  for (Index kA=0; kA < m_A.outerSize(); ++kA)
170  for (LhsInnerIterator itA(lhs1,kA); itA; ++itA)
171  nnzA(Dest::IsRowMajor ? itA.row() : itA.col())++;
172 
173  VectorXi nnzB = VectorXi::Zero(Dest::IsRowMajor ? m_B.rows() : m_B.cols());
174  for (Index kB=0; kB < m_B.outerSize(); ++kB)
175  for (RhsInnerIterator itB(rhs1,kB); itB; ++itB)
176  nnzB(Dest::IsRowMajor ? itB.row() : itB.col())++;
177 
178  Matrix<int,Dynamic,Dynamic,ColMajor> nnzAB = nnzB * nnzA.transpose();
179  dst.reserve(VectorXi::Map(nnzAB.data(), nnzAB.size()));
180  }
181 
182  for (Index kA=0; kA < m_A.outerSize(); ++kA)
183  {
184  for (Index kB=0; kB < m_B.outerSize(); ++kB)
185  {
186  for (LhsInnerIterator itA(lhs1,kA); itA; ++itA)
187  {
188  for (RhsInnerIterator itB(rhs1,kB); itB; ++itB)
189  {
190  Index i = itA.row() * Br + itB.row(),
191  j = itA.col() * Bc + itB.col();
192  dst.insert(i,j) = itA.value() * itB.value();
193  }
194  }
195  }
196  }
197 }
198 
199 namespace internal {
200 
201 template<typename _Lhs, typename _Rhs>
202 struct traits<KroneckerProduct<_Lhs,_Rhs> >
203 {
204  typedef typename remove_all<_Lhs>::type Lhs;
205  typedef typename remove_all<_Rhs>::type Rhs;
208 
209  enum {
214  };
215 
217 };
218 
219 template<typename _Lhs, typename _Rhs>
220 struct traits<KroneckerProductSparse<_Lhs,_Rhs> >
221 {
223  typedef typename remove_all<_Lhs>::type Lhs;
224  typedef typename remove_all<_Rhs>::type Rhs;
228 
229  enum {
230  LhsFlags = Lhs::Flags,
231  RhsFlags = Rhs::Flags,
232 
237 
238  EvalToRowMajor = (int(LhsFlags) & int(RhsFlags) & RowMajorBit),
239  RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),
240 
241  Flags = ((int(LhsFlags) | int(RhsFlags)) & HereditaryBits & RemovedBits)
243  CoeffReadCost = HugeCost
244  };
245 
247 };
248 
249 } // end namespace internal
250 
270 template<typename A, typename B>
272 {
273  return KroneckerProduct<A, B>(a.derived(), b.derived());
274 }
275 
297 template<typename A, typename B>
299 {
301 }
302 
303 } // end namespace Eigen
304 
305 #endif // KRONECKER_TENSOR_PRODUCT_H
SCALAR Scalar
Definition: bench_gemm.cpp:46
promote_index_type< typename Lhs::StorageIndex, typename Rhs::StorageIndex >::type StorageIndex
ScalarBinaryOpTraits< typename Lhs::Scalar, typename Rhs::Scalar >::ReturnType Scalar
const int HugeCost
Definition: Constants.h:44
KroneckerProductBase< KroneckerProductSparse > Base
Scalar * b
Definition: benchVecAdd.cpp:17
A versatible sparse matrix representation.
Definition: SparseMatrix.h:96
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar * data() const
Scalar coeff(Index row, Index col) const
internal::traits< Derived > Traits
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
void evalTo(Dest &dst) const
Evaluate the Kronecker tensor product.
const unsigned int RowMajorBit
Definition: Constants.h:66
KroneckerProductBase< KroneckerProduct > Base
ScalarBinaryOpTraits< typename Lhs::Scalar, typename Rhs::Scalar >::ReturnType Scalar
const unsigned int HereditaryBits
Definition: Constants.h:195
KroneckerProductSparse(const Lhs &A, const Rhs &B)
Constructor.
m row(1)
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
EIGEN_DEVICE_FUNC void evalTo(Dest &dst) const
Definition: ReturnByValue.h:61
promote_index_type< typename Lhs::StorageIndex, typename Rhs::StorageIndex >::type StorageIndex
KroneckerProductBase(const Lhs &A, const Rhs &B)
Constructor.
DenseIndex ret
static const int Cols
cwise_promote_storage_type< typename traits< Lhs >::StorageKind, typename traits< Rhs >::StorageKind, scalar_product_op< typename Lhs::Scalar, typename Rhs::Scalar > >::ret StorageKind
Expression of a fixed-size or dynamic-size block.
Definition: Block.h:103
m col(1)
Determines whether the given binary operation of two numeric types is allowed and what the scalar ret...
Definition: XprHelper.h:801
KroneckerProduct(const Lhs &A, const Rhs &B)
Constructor.
KroneckerProduct< A, B > kroneckerProduct(const MatrixBase< A > &a, const MatrixBase< B > &b)
const unsigned int EvalBeforeNestingBit
Definition: Constants.h:70
Generic expression where a coefficient-wise unary operator is applied to an expression.
Definition: CwiseUnaryOp.h:55
The matrix class, also used for vectors and row-vectors.
void evalTo(Dest &dst) const
Evaluate the Kronecker tensor product.
#define EIGEN_STATIC_ASSERT_VECTOR_ONLY(TYPE)
Definition: StaticAssert.h:142
EIGEN_DEVICE_FUNC Derived & derived()
Definition: EigenBase.h:46
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
Kronecker tensor product helper class for dense matrices.
The base class of dense and sparse Kronecker product.
std::ptrdiff_t j
Kronecker tensor product helper class for sparse matrices.
An InnerIterator allows to loop over the element of any matrix expression.
Definition: CoreIterators.h:33


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autogenerated on Tue Jul 4 2023 02:34:30