1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11#ifndef EIGEN_DIAGONALMATRIX_H
12#define EIGEN_DIAGONALMATRIX_H
13
14namespace Eigen {
15
16#ifndef EIGEN_PARSED_BY_DOXYGEN
17template<typename Derived>
18class DiagonalBase : public EigenBase<Derived>
19{
20 public:
21 typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
22 typedef typename DiagonalVectorType::Scalar Scalar;
23 typedef typename DiagonalVectorType::RealScalar RealScalar;
24 typedef typename internal::traits<Derived>::StorageKind StorageKind;
25 typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
26
27 enum {
28 RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
29 ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
30 MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
31 MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
32 IsVectorAtCompileTime = 0,
33 Flags = NoPreferredStorageOrderBit
34 };
35
36 typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> DenseMatrixType;
37 typedef DenseMatrixType DenseType;
38 typedef DiagonalMatrix<Scalar,DiagonalVectorType::SizeAtCompileTime,DiagonalVectorType::MaxSizeAtCompileTime> PlainObject;
39
40 EIGEN_DEVICE_FUNC
41 inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
42 EIGEN_DEVICE_FUNC
43 inline Derived& derived() { return *static_cast<Derived*>(this); }
44
45 EIGEN_DEVICE_FUNC
46 DenseMatrixType toDenseMatrix() const { return derived(); }
47
48 EIGEN_DEVICE_FUNC
49 inline const DiagonalVectorType& diagonal() const { return derived().diagonal(); }
50 EIGEN_DEVICE_FUNC
51 inline DiagonalVectorType& diagonal() { return derived().diagonal(); }
52
53 EIGEN_DEVICE_FUNC
54 inline Index rows() const { return diagonal().size(); }
55 EIGEN_DEVICE_FUNC
56 inline Index cols() const { return diagonal().size(); }
57
58 template<typename MatrixDerived>
59 EIGEN_DEVICE_FUNC
60 const Product<Derived,MatrixDerived,LazyProduct>
61 operator*(const MatrixBase<MatrixDerived> &matrix) const
62 {
63 return Product<Derived, MatrixDerived, LazyProduct>(derived(),matrix.derived());
64 }
65
66 typedef DiagonalWrapper<const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const DiagonalVectorType> > InverseReturnType;
67 EIGEN_DEVICE_FUNC
68 inline const InverseReturnType
69 inverse() const
70 {
71 return InverseReturnType(diagonal().cwiseInverse());
72 }
73
74 EIGEN_DEVICE_FUNC
75 inline const DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >
76 operator*(const Scalar& scalar) const
77 {
78 return DiagonalWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DiagonalVectorType,Scalar,product) >(diagonal() * scalar);
79 }
80 EIGEN_DEVICE_FUNC
81 friend inline const DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >
82 operator*(const Scalar& scalar, const DiagonalBase& other)
83 {
84 return DiagonalWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar,DiagonalVectorType,product) >(scalar * other.diagonal());
85 }
86};
87
88#endif
89
90/** \class DiagonalMatrix
91 * \ingroup Core_Module
92 *
93 * \brief Represents a diagonal matrix with its storage
94 *
95 * \param _Scalar the type of coefficients
96 * \param SizeAtCompileTime the dimension of the matrix, or Dynamic
97 * \param MaxSizeAtCompileTime the dimension of the matrix, or Dynamic. This parameter is optional and defaults
98 * to SizeAtCompileTime. Most of the time, you do not need to specify it.
99 *
100 * \sa class DiagonalWrapper
101 */
102
103namespace internal {
104template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
105struct traits<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
106 : traits<Matrix<_Scalar,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
107{
108 typedef Matrix<_Scalar,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1> DiagonalVectorType;
109 typedef DiagonalShape StorageKind;
110 enum {
111 Flags = LvalueBit | NoPreferredStorageOrderBit
112 };
113};
114}
115template<typename _Scalar, int SizeAtCompileTime, int MaxSizeAtCompileTime>
116class DiagonalMatrix
117 : public DiagonalBase<DiagonalMatrix<_Scalar,SizeAtCompileTime,MaxSizeAtCompileTime> >
118{
119 public:
120 #ifndef EIGEN_PARSED_BY_DOXYGEN
121 typedef typename internal::traits<DiagonalMatrix>::DiagonalVectorType DiagonalVectorType;
122 typedef const DiagonalMatrix& Nested;
123 typedef _Scalar Scalar;
124 typedef typename internal::traits<DiagonalMatrix>::StorageKind StorageKind;
125 typedef typename internal::traits<DiagonalMatrix>::StorageIndex StorageIndex;
126 #endif
127
128 protected:
129
130 DiagonalVectorType m_diagonal;
131
132 public:
133
134 /** const version of diagonal(). */
135 EIGEN_DEVICE_FUNC
136 inline const DiagonalVectorType& diagonal() const { return m_diagonal; }
137 /** \returns a reference to the stored vector of diagonal coefficients. */
138 EIGEN_DEVICE_FUNC
139 inline DiagonalVectorType& diagonal() { return m_diagonal; }
140
141 /** Default constructor without initialization */
142 EIGEN_DEVICE_FUNC
143 inline DiagonalMatrix() {}
144
145 /** Constructs a diagonal matrix with given dimension */
146 EIGEN_DEVICE_FUNC
147 explicit inline DiagonalMatrix(Index dim) : m_diagonal(dim) {}
148
149 /** 2D constructor. */
150 EIGEN_DEVICE_FUNC
151 inline DiagonalMatrix(const Scalar& x, const Scalar& y) : m_diagonal(x,y) {}
152
153 /** 3D constructor. */
154 EIGEN_DEVICE_FUNC
155 inline DiagonalMatrix(const Scalar& x, const Scalar& y, const Scalar& z) : m_diagonal(x,y,z) {}
156
157 /** Copy constructor. */
158 template<typename OtherDerived>
159 EIGEN_DEVICE_FUNC
160 inline DiagonalMatrix(const DiagonalBase<OtherDerived>& other) : m_diagonal(other.diagonal()) {}
161
162 #ifndef EIGEN_PARSED_BY_DOXYGEN
163 /** copy constructor. prevent a default copy constructor from hiding the other templated constructor */
164 inline DiagonalMatrix(const DiagonalMatrix& other) : m_diagonal(other.diagonal()) {}
165 #endif
166
167 /** generic constructor from expression of the diagonal coefficients */
168 template<typename OtherDerived>
169 EIGEN_DEVICE_FUNC
170 explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : m_diagonal(other)
171 {}
172
173 /** Copy operator. */
174 template<typename OtherDerived>
175 EIGEN_DEVICE_FUNC
176 DiagonalMatrix& operator=(const DiagonalBase<OtherDerived>& other)
177 {
178 m_diagonal = other.diagonal();
179 return *this;
180 }
181
182 #ifndef EIGEN_PARSED_BY_DOXYGEN
183 /** This is a special case of the templated operator=. Its purpose is to
184 * prevent a default operator= from hiding the templated operator=.
185 */
186 EIGEN_DEVICE_FUNC
187 DiagonalMatrix& operator=(const DiagonalMatrix& other)
188 {
189 m_diagonal = other.diagonal();
190 return *this;
191 }
192 #endif
193
194 /** Resizes to given size. */
195 EIGEN_DEVICE_FUNC
196 inline void resize(Index size) { m_diagonal.resize(size); }
197 /** Sets all coefficients to zero. */
198 EIGEN_DEVICE_FUNC
199 inline void setZero() { m_diagonal.setZero(); }
200 /** Resizes and sets all coefficients to zero. */
201 EIGEN_DEVICE_FUNC
202 inline void setZero(Index size) { m_diagonal.setZero(size); }
203 /** Sets this matrix to be the identity matrix of the current size. */
204 EIGEN_DEVICE_FUNC
205 inline void setIdentity() { m_diagonal.setOnes(); }
206 /** Sets this matrix to be the identity matrix of the given size. */
207 EIGEN_DEVICE_FUNC
208 inline void setIdentity(Index size) { m_diagonal.setOnes(size); }
209};
210
211/** \class DiagonalWrapper
212 * \ingroup Core_Module
213 *
214 * \brief Expression of a diagonal matrix
215 *
216 * \param _DiagonalVectorType the type of the vector of diagonal coefficients
217 *
218 * This class is an expression of a diagonal matrix, but not storing its own vector of diagonal coefficients,
219 * instead wrapping an existing vector expression. It is the return type of MatrixBase::asDiagonal()
220 * and most of the time this is the only way that it is used.
221 *
222 * \sa class DiagonalMatrix, class DiagonalBase, MatrixBase::asDiagonal()
223 */
224
225namespace internal {
226template<typename _DiagonalVectorType>
227struct traits<DiagonalWrapper<_DiagonalVectorType> >
228{
229 typedef _DiagonalVectorType DiagonalVectorType;
230 typedef typename DiagonalVectorType::Scalar Scalar;
231 typedef typename DiagonalVectorType::StorageIndex StorageIndex;
232 typedef DiagonalShape StorageKind;
233 typedef typename traits<DiagonalVectorType>::XprKind XprKind;
234 enum {
235 RowsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
236 ColsAtCompileTime = DiagonalVectorType::SizeAtCompileTime,
237 MaxRowsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
238 MaxColsAtCompileTime = DiagonalVectorType::MaxSizeAtCompileTime,
239 Flags = (traits<DiagonalVectorType>::Flags & LvalueBit) | NoPreferredStorageOrderBit
240 };
241};
242}
243
244template<typename _DiagonalVectorType>
245class DiagonalWrapper
246 : public DiagonalBase<DiagonalWrapper<_DiagonalVectorType> >, internal::no_assignment_operator
247{
248 public:
249 #ifndef EIGEN_PARSED_BY_DOXYGEN
250 typedef _DiagonalVectorType DiagonalVectorType;
251 typedef DiagonalWrapper Nested;
252 #endif
253
254 /** Constructor from expression of diagonal coefficients to wrap. */
255 EIGEN_DEVICE_FUNC
256 explicit inline DiagonalWrapper(DiagonalVectorType& a_diagonal) : m_diagonal(a_diagonal) {}
257
258 /** \returns a const reference to the wrapped expression of diagonal coefficients. */
259 EIGEN_DEVICE_FUNC
260 const DiagonalVectorType& diagonal() const { return m_diagonal; }
261
262 protected:
263 typename DiagonalVectorType::Nested m_diagonal;
264};
265
266/** \returns a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
267 *
268 * \only_for_vectors
269 *
270 * Example: \include MatrixBase_asDiagonal.cpp
271 * Output: \verbinclude MatrixBase_asDiagonal.out
272 *
273 * \sa class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
274 **/
275template<typename Derived>
276inline const DiagonalWrapper<const Derived>
277MatrixBase<Derived>::asDiagonal() const
278{
279 return DiagonalWrapper<const Derived>(derived());
280}
281
282/** \returns true if *this is approximately equal to a diagonal matrix,
283 * within the precision given by \a prec.
284 *
285 * Example: \include MatrixBase_isDiagonal.cpp
286 * Output: \verbinclude MatrixBase_isDiagonal.out
287 *
288 * \sa asDiagonal()
289 */
290template<typename Derived>
291bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const
292{
293 if(cols() != rows()) return false;
294 RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
295 for(Index j = 0; j < cols(); ++j)
296 {
297 RealScalar absOnDiagonal = numext::abs(coeff(j,j));
298 if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
299 }
300 for(Index j = 0; j < cols(); ++j)
301 for(Index i = 0; i < j; ++i)
302 {
303 if(!internal::isMuchSmallerThan(coeff(i, j), maxAbsOnDiagonal, prec)) return false;
304 if(!internal::isMuchSmallerThan(coeff(j, i), maxAbsOnDiagonal, prec)) return false;
305 }
306 return true;
307}
308
309namespace internal {
310
311template<> struct storage_kind_to_shape<DiagonalShape> { typedef DiagonalShape Shape; };
312
313struct Diagonal2Dense {};
314
315template<> struct AssignmentKind<DenseShape,DiagonalShape> { typedef Diagonal2Dense Kind; };
316
317// Diagonal matrix to Dense assignment
318template< typename DstXprType, typename SrcXprType, typename Functor>
319struct Assignment<DstXprType, SrcXprType, Functor, Diagonal2Dense>
320{
321 static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
322 {
323 Index dstRows = src.rows();
324 Index dstCols = src.cols();
325 if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
326 dst.resize(dstRows, dstCols);
327
328 dst.setZero();
329 dst.diagonal() = src.diagonal();
330 }
331
332 static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
333 { dst.diagonal() += src.diagonal(); }
334
335 static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar> &/*func*/)
336 { dst.diagonal() -= src.diagonal(); }
337};
338
339} // namespace internal
340
341} // end namespace Eigen
342
343#endif // EIGEN_DIAGONALMATRIX_H
344