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
17 /*!
18 * \ingroup KroneckerProduct_Module
19 *
20 * \brief The base class of dense and sparse Kronecker product.
21 *
22 * \tparam Derived is the derived type.
23 */
24 template<typename Derived>
25 class 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:
36 /*! \brief Constructor. */
KroneckerProductBase(const Lhs & A,const Rhs & B)37 KroneckerProductBase(const Lhs& A, const Rhs& B)
38 : m_A(A), m_B(B)
39 {}
40
rows()41 inline Index rows() const { return m_A.rows() * m_B.rows(); }
cols()42 inline Index cols() const { return m_A.cols() * m_B.cols(); }
43
44 /*!
45 * This overrides ReturnByValue::coeff because this function is
46 * efficient enough.
47 */
coeff(Index row,Index col)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
54 /*!
55 * This overrides ReturnByValue::coeff because this function is
56 * efficient enough.
57 */
coeff(Index i)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
69 /*!
70 * \ingroup KroneckerProduct_Module
71 *
72 * \brief Kronecker tensor product helper class for dense matrices
73 *
74 * This class is the return value of kroneckerProduct(MatrixBase,
75 * MatrixBase). Use the function rather than construct this class
76 * directly to avoid specifying template prarameters.
77 *
78 * \tparam Lhs Type of the left-hand side, a matrix expression.
79 * \tparam Rhs Type of the rignt-hand side, a matrix expression.
80 */
81 template<typename Lhs, typename Rhs>
82 class KroneckerProduct : public KroneckerProductBase<KroneckerProduct<Lhs,Rhs> >
83 {
84 private:
85 typedef KroneckerProductBase<KroneckerProduct> Base;
86 using Base::m_A;
87 using Base::m_B;
88
89 public:
90 /*! \brief Constructor. */
KroneckerProduct(const Lhs & A,const Rhs & B)91 KroneckerProduct(const Lhs& A, const Rhs& B)
92 : Base(A, B)
93 {}
94
95 /*! \brief Evaluate the Kronecker tensor product. */
96 template<typename Dest> void evalTo(Dest& dst) const;
97 };
98
99 /*!
100 * \ingroup KroneckerProduct_Module
101 *
102 * \brief Kronecker tensor product helper class for sparse matrices
103 *
104 * If at least one of the operands is a sparse matrix expression,
105 * then this class is returned and evaluates into a sparse matrix.
106 *
107 * This class is the return value of kroneckerProduct(EigenBase,
108 * EigenBase). Use the function rather than construct this class
109 * directly to avoid specifying template prarameters.
110 *
111 * \tparam Lhs Type of the left-hand side, a matrix expression.
112 * \tparam Rhs Type of the rignt-hand side, a matrix expression.
113 */
114 template<typename Lhs, typename Rhs>
115 class KroneckerProductSparse : public KroneckerProductBase<KroneckerProductSparse<Lhs,Rhs> >
116 {
117 private:
118 typedef KroneckerProductBase<KroneckerProductSparse> Base;
119 using Base::m_A;
120 using Base::m_B;
121
122 public:
123 /*! \brief Constructor. */
KroneckerProductSparse(const Lhs & A,const Rhs & B)124 KroneckerProductSparse(const Lhs& A, const Rhs& B)
125 : Base(A, B)
126 {}
127
128 /*! \brief Evaluate the Kronecker tensor product. */
129 template<typename Dest> void evalTo(Dest& dst) const;
130 };
131
132 template<typename Lhs, typename Rhs>
133 template<typename Dest>
evalTo(Dest & dst)134 void KroneckerProduct<Lhs,Rhs>::evalTo(Dest& dst) const
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>
evalTo(Dest & dst)147 void KroneckerProductSparse<Lhs,Rhs>::evalTo(Dest& dst) const
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;
206 typedef typename ScalarBinaryOpTraits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
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
219 template<typename _Lhs, typename _Rhs>
220 struct 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 = (LhsFlags & RhsFlags & RowMajorBit),
239 RemovedBits = ~(EvalToRowMajor ? 0 : RowMajorBit),
240
241 Flags = ((LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)
242 | EvalBeforeNestingBit,
243 CoeffReadCost = HugeCost
244 };
245
246 typedef SparseMatrix<Scalar, 0, StorageIndex> ReturnType;
247 };
248
249 } // end namespace internal
250
251 /*!
252 * \ingroup KroneckerProduct_Module
253 *
254 * Computes Kronecker tensor product of two dense matrices
255 *
256 * \warning If you want to replace a matrix by its Kronecker product
257 * with some matrix, do \b NOT do this:
258 * \code
259 * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
260 * \endcode
261 * instead, use eval() to work around this:
262 * \code
263 * A = kroneckerProduct(A,B).eval();
264 * \endcode
265 *
266 * \param a Dense matrix a
267 * \param b Dense matrix b
268 * \return Kronecker tensor product of a and b
269 */
270 template<typename A, typename B>
271 KroneckerProduct<A,B> kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b)
272 {
273 return KroneckerProduct<A, B>(a.derived(), b.derived());
274 }
275
276 /*!
277 * \ingroup KroneckerProduct_Module
278 *
279 * Computes Kronecker tensor product of two matrices, at least one of
280 * which is sparse
281 *
282 * \warning If you want to replace a matrix by its Kronecker product
283 * with some matrix, do \b NOT do this:
284 * \code
285 * A = kroneckerProduct(A,B); // bug!!! caused by aliasing effect
286 * \endcode
287 * instead, use eval() to work around this:
288 * \code
289 * A = kroneckerProduct(A,B).eval();
290 * \endcode
291 *
292 * \param a Dense/sparse matrix a
293 * \param b Dense/sparse matrix b
294 * \return Kronecker tensor product of a and b, stored in a sparse
295 * matrix
296 */
297 template<typename A, typename B>
298 KroneckerProductSparse<A,B> kroneckerProduct(const EigenBase<A>& a, const EigenBase<B>& b)
299 {
300 return KroneckerProductSparse<A,B>(a.derived(), b.derived());
301 }
302
303 } // end namespace Eigen
304
305 #endif // KRONECKER_TENSOR_PRODUCT_H
306