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KroneckerTensorProduct.h
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
15namespace Eigen {
16
24template<typename Derived>
25class KroneckerProductBase : public ReturnByValue<Derived>
26{
27 private:
28 typedef typename internal::traits<Derived> Traits;
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 {
60 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
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
81template<typename Lhs, typename Rhs>
82class 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
114template<typename Lhs, typename Rhs>
115class 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
132template<typename Lhs, typename Rhs>
133template<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
145template<typename Lhs, typename Rhs>
146template<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
199namespace internal {
200
201template<typename _Lhs, typename _Rhs>
202struct traits<KroneckerProduct<_Lhs,_Rhs> >
203{
204 typedef typename remove_all<_Lhs>::type Lhs;
205 typedef typename remove_all<_Rhs>::type Rhs;
207 typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;
208
209 enum {
210 Rows = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,
211 Cols = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,
212 MaxRows = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,
213 MaxCols = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret
214 };
215
216 typedef Matrix<Scalar,Rows,Cols> ReturnType;
217};
218
219template<typename _Lhs, typename _Rhs>
220struct traits<KroneckerProductSparse<_Lhs,_Rhs> >
221{
222 typedef MatrixXpr XprKind;
223 typedef typename remove_all<_Lhs>::type Lhs;
224 typedef typename remove_all<_Rhs>::type Rhs;
225 typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
226 typedef typename cwise_promote_storage_type<typename traits<Lhs>::StorageKind, typename traits<Rhs>::StorageKind, scalar_product_op<typename Lhs::Scalar, typename Rhs::Scalar> >::ret StorageKind;
227 typedef typename promote_index_type<typename Lhs::StorageIndex, typename Rhs::StorageIndex>::type StorageIndex;
228
229 enum {
230 LhsFlags = Lhs::Flags,
231 RhsFlags = Rhs::Flags,
232
233 RowsAtCompileTime = size_at_compile_time<traits<Lhs>::RowsAtCompileTime, traits<Rhs>::RowsAtCompileTime>::ret,
234 ColsAtCompileTime = size_at_compile_time<traits<Lhs>::ColsAtCompileTime, traits<Rhs>::ColsAtCompileTime>::ret,
235 MaxRowsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxRowsAtCompileTime, traits<Rhs>::MaxRowsAtCompileTime>::ret,
236 MaxColsAtCompileTime = size_at_compile_time<traits<Lhs>::MaxColsAtCompileTime, traits<Rhs>::MaxColsAtCompileTime>::ret,
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
246 typedef SparseMatrix<Scalar, 0, StorageIndex> ReturnType;
247};
248
249} // end namespace internal
250
270template<typename A, typename B>
272{
273 return KroneckerProduct<A, B>(a.derived(), b.derived());
274}
275
297template<typename A, typename B>
299{
300 return KroneckerProductSparse<A,B>(a.derived(), b.derived());
301}
302
303} // end namespace Eigen
304
305#endif // KRONECKER_TENSOR_PRODUCT_H
The base class of dense and sparse Kronecker product.
Definition: KroneckerTensorProduct.h:26
Scalar coeff(Index row, Index col) const
Definition: KroneckerTensorProduct.h:48
KroneckerProductBase(const Lhs &A, const Rhs &B)
Constructor.
Definition: KroneckerTensorProduct.h:37
Scalar coeff(Index i) const
Definition: KroneckerTensorProduct.h:58
Kronecker tensor product helper class for sparse matrices.
Definition: KroneckerTensorProduct.h:116
void evalTo(Dest &dst) const
Evaluate the Kronecker tensor product.
Definition: KroneckerTensorProduct.h:147
KroneckerProductSparse(const Lhs &A, const Rhs &B)
Constructor.
Definition: KroneckerTensorProduct.h:124
Kronecker tensor product helper class for dense matrices.
Definition: KroneckerTensorProduct.h:83
KroneckerProduct(const Lhs &A, const Rhs &B)
Constructor.
Definition: KroneckerTensorProduct.h:91
void evalTo(Dest &dst) const
Evaluate the Kronecker tensor product.
Definition: KroneckerTensorProduct.h:134
KroneckerProduct< A, B > kroneckerProduct(const MatrixBase< A > &a, const MatrixBase< B > &b)
Definition: KroneckerTensorProduct.h:271
const unsigned int EvalBeforeNestingBit
const unsigned int RowMajorBit
Namespace containing all symbols from the Eigen library.
const int HugeCost
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
Derived & derived()