1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
5// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
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_DIAGONAL_H
12#define EIGEN_DIAGONAL_H
13
14namespace Eigen {
15
16/** \class Diagonal
17 * \ingroup Core_Module
18 *
19 * \brief Expression of a diagonal/subdiagonal/superdiagonal in a matrix
20 *
21 * \param MatrixType the type of the object in which we are taking a sub/main/super diagonal
22 * \param DiagIndex the index of the sub/super diagonal. The default is 0 and it means the main diagonal.
23 * A positive value means a superdiagonal, a negative value means a subdiagonal.
24 * You can also use DynamicIndex so the index can be set at runtime.
25 *
26 * The matrix is not required to be square.
27 *
28 * This class represents an expression of the main diagonal, or any sub/super diagonal
29 * of a square matrix. It is the return type of MatrixBase::diagonal() and MatrixBase::diagonal(Index) and most of the
30 * time this is the only way it is used.
31 *
32 * \sa MatrixBase::diagonal(), MatrixBase::diagonal(Index)
33 */
34
35namespace internal {
36template<typename MatrixType, int DiagIndex>
37struct traits<Diagonal<MatrixType,DiagIndex> >
38 : traits<MatrixType>
39{
40 typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
41 typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
42 typedef typename MatrixType::StorageKind StorageKind;
43 enum {
44 RowsAtCompileTime = (int(DiagIndex) == DynamicIndex || int(MatrixType::SizeAtCompileTime) == Dynamic) ? Dynamic
45 : (EIGEN_PLAIN_ENUM_MIN(MatrixType::RowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
46 MatrixType::ColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
47 ColsAtCompileTime = 1,
48 MaxRowsAtCompileTime = int(MatrixType::MaxSizeAtCompileTime) == Dynamic ? Dynamic
49 : DiagIndex == DynamicIndex ? EIGEN_SIZE_MIN_PREFER_FIXED(MatrixType::MaxRowsAtCompileTime,
50 MatrixType::MaxColsAtCompileTime)
51 : (EIGEN_PLAIN_ENUM_MIN(MatrixType::MaxRowsAtCompileTime - EIGEN_PLAIN_ENUM_MAX(-DiagIndex, 0),
52 MatrixType::MaxColsAtCompileTime - EIGEN_PLAIN_ENUM_MAX( DiagIndex, 0))),
53 MaxColsAtCompileTime = 1,
54 MaskLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
55 Flags = (unsigned int)_MatrixTypeNested::Flags & (RowMajorBit | MaskLvalueBit | DirectAccessBit) & ~RowMajorBit, // FIXME DirectAccessBit should not be handled by expressions
56 MatrixTypeOuterStride = outer_stride_at_compile_time<MatrixType>::ret,
57 InnerStrideAtCompileTime = MatrixTypeOuterStride == Dynamic ? Dynamic : MatrixTypeOuterStride+1,
58 OuterStrideAtCompileTime = 0
59 };
60};
61}
62
63template<typename MatrixType, int _DiagIndex> class Diagonal
64 : public internal::dense_xpr_base< Diagonal<MatrixType,_DiagIndex> >::type
65{
66 public:
67
68 enum { DiagIndex = _DiagIndex };
69 typedef typename internal::dense_xpr_base<Diagonal>::type Base;
70 EIGEN_DENSE_PUBLIC_INTERFACE(Diagonal)
71
72 EIGEN_DEVICE_FUNC
73 explicit inline Diagonal(MatrixType& matrix, Index a_index = DiagIndex) : m_matrix(matrix), m_index(a_index)
74 {
75 eigen_assert( a_index <= m_matrix.cols() && -a_index <= m_matrix.rows() );
76 }
77
78 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Diagonal)
79
80 EIGEN_DEVICE_FUNC
81 inline Index rows() const
82 {
83 return m_index.value()<0 ? numext::mini<Index>(m_matrix.cols(),m_matrix.rows()+m_index.value())
84 : numext::mini<Index>(m_matrix.rows(),m_matrix.cols()-m_index.value());
85 }
86
87 EIGEN_DEVICE_FUNC
88 inline Index cols() const { return 1; }
89
90 EIGEN_DEVICE_FUNC
91 inline Index innerStride() const
92 {
93 return m_matrix.outerStride() + 1;
94 }
95
96 EIGEN_DEVICE_FUNC
97 inline Index outerStride() const
98 {
99 return 0;
100 }
101
102 typedef typename internal::conditional<
103 internal::is_lvalue<MatrixType>::value,
104 Scalar,
105 const Scalar
106 >::type ScalarWithConstIfNotLvalue;
107
108 EIGEN_DEVICE_FUNC
109 inline ScalarWithConstIfNotLvalue* data() { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
110 EIGEN_DEVICE_FUNC
111 inline const Scalar* data() const { return &(m_matrix.coeffRef(rowOffset(), colOffset())); }
112
113 EIGEN_DEVICE_FUNC
114 inline Scalar& coeffRef(Index row, Index)
115 {
116 EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
117 return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
118 }
119
120 EIGEN_DEVICE_FUNC
121 inline const Scalar& coeffRef(Index row, Index) const
122 {
123 return m_matrix.coeffRef(row+rowOffset(), row+colOffset());
124 }
125
126 EIGEN_DEVICE_FUNC
127 inline CoeffReturnType coeff(Index row, Index) const
128 {
129 return m_matrix.coeff(row+rowOffset(), row+colOffset());
130 }
131
132 EIGEN_DEVICE_FUNC
133 inline Scalar& coeffRef(Index idx)
134 {
135 EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
136 return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
137 }
138
139 EIGEN_DEVICE_FUNC
140 inline const Scalar& coeffRef(Index idx) const
141 {
142 return m_matrix.coeffRef(idx+rowOffset(), idx+colOffset());
143 }
144
145 EIGEN_DEVICE_FUNC
146 inline CoeffReturnType coeff(Index idx) const
147 {
148 return m_matrix.coeff(idx+rowOffset(), idx+colOffset());
149 }
150
151 EIGEN_DEVICE_FUNC
152 inline const typename internal::remove_all<typename MatrixType::Nested>::type&
153 nestedExpression() const
154 {
155 return m_matrix;
156 }
157
158 EIGEN_DEVICE_FUNC
159 inline Index index() const
160 {
161 return m_index.value();
162 }
163
164 protected:
165 typename internal::ref_selector<MatrixType>::non_const_type m_matrix;
166 const internal::variable_if_dynamicindex<Index, DiagIndex> m_index;
167
168 private:
169 // some compilers may fail to optimize std::max etc in case of compile-time constants...
170 EIGEN_DEVICE_FUNC
171 EIGEN_STRONG_INLINE Index absDiagIndex() const { return m_index.value()>0 ? m_index.value() : -m_index.value(); }
172 EIGEN_DEVICE_FUNC
173 EIGEN_STRONG_INLINE Index rowOffset() const { return m_index.value()>0 ? 0 : -m_index.value(); }
174 EIGEN_DEVICE_FUNC
175 EIGEN_STRONG_INLINE Index colOffset() const { return m_index.value()>0 ? m_index.value() : 0; }
176 // trigger a compile-time error if someone try to call packet
177 template<int LoadMode> typename MatrixType::PacketReturnType packet(Index) const;
178 template<int LoadMode> typename MatrixType::PacketReturnType packet(Index,Index) const;
179};
180
181/** \returns an expression of the main diagonal of the matrix \c *this
182 *
183 * \c *this is not required to be square.
184 *
185 * Example: \include MatrixBase_diagonal.cpp
186 * Output: \verbinclude MatrixBase_diagonal.out
187 *
188 * \sa class Diagonal */
189template<typename Derived>
190inline typename MatrixBase<Derived>::DiagonalReturnType
191MatrixBase<Derived>::diagonal()
192{
193 return DiagonalReturnType(derived());
194}
195
196/** This is the const version of diagonal(). */
197template<typename Derived>
198inline typename MatrixBase<Derived>::ConstDiagonalReturnType
199MatrixBase<Derived>::diagonal() const
200{
201 return ConstDiagonalReturnType(derived());
202}
203
204/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
205 *
206 * \c *this is not required to be square.
207 *
208 * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
209 * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
210 *
211 * Example: \include MatrixBase_diagonal_int.cpp
212 * Output: \verbinclude MatrixBase_diagonal_int.out
213 *
214 * \sa MatrixBase::diagonal(), class Diagonal */
215template<typename Derived>
216inline typename MatrixBase<Derived>::DiagonalDynamicIndexReturnType
217MatrixBase<Derived>::diagonal(Index index)
218{
219 return DiagonalDynamicIndexReturnType(derived(), index);
220}
221
222/** This is the const version of diagonal(Index). */
223template<typename Derived>
224inline typename MatrixBase<Derived>::ConstDiagonalDynamicIndexReturnType
225MatrixBase<Derived>::diagonal(Index index) const
226{
227 return ConstDiagonalDynamicIndexReturnType(derived(), index);
228}
229
230/** \returns an expression of the \a DiagIndex-th sub or super diagonal of the matrix \c *this
231 *
232 * \c *this is not required to be square.
233 *
234 * The template parameter \a DiagIndex represent a super diagonal if \a DiagIndex > 0
235 * and a sub diagonal otherwise. \a DiagIndex == 0 is equivalent to the main diagonal.
236 *
237 * Example: \include MatrixBase_diagonal_template_int.cpp
238 * Output: \verbinclude MatrixBase_diagonal_template_int.out
239 *
240 * \sa MatrixBase::diagonal(), class Diagonal */
241template<typename Derived>
242template<int Index_>
243inline typename MatrixBase<Derived>::template DiagonalIndexReturnType<Index_>::Type
244MatrixBase<Derived>::diagonal()
245{
246 return typename DiagonalIndexReturnType<Index_>::Type(derived());
247}
248
249/** This is the const version of diagonal<int>(). */
250template<typename Derived>
251template<int Index_>
252inline typename MatrixBase<Derived>::template ConstDiagonalIndexReturnType<Index_>::Type
253MatrixBase<Derived>::diagonal() const
254{
255 return typename ConstDiagonalIndexReturnType<Index_>::Type(derived());
256}
257
258} // end namespace Eigen
259
260#endif // EIGEN_DIAGONAL_H
261