1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2006-2010 Benoit Jacob <[email protected]>
5// Copyright (C) 2008-2009 Gael Guennebaud <[email protected]>
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_MATRIX_H
12#define EIGEN_MATRIX_H
13
14namespace Eigen {
15
16namespace internal {
17template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
18struct traits<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
19{
20private:
21 enum { size = internal::size_at_compile_time<_Rows,_Cols>::ret };
22 typedef typename find_best_packet<_Scalar,size>::type PacketScalar;
23 enum {
24 row_major_bit = _Options&RowMajor ? RowMajorBit : 0,
25 is_dynamic_size_storage = _MaxRows==Dynamic || _MaxCols==Dynamic,
26 max_size = is_dynamic_size_storage ? Dynamic : _MaxRows*_MaxCols,
27 default_alignment = compute_default_alignment<_Scalar,max_size>::value,
28 actual_alignment = ((_Options&DontAlign)==0) ? default_alignment : 0,
29 required_alignment = unpacket_traits<PacketScalar>::alignment,
30 packet_access_bit = (packet_traits<_Scalar>::Vectorizable && (EIGEN_UNALIGNED_VECTORIZE || (actual_alignment>=required_alignment))) ? PacketAccessBit : 0
31 };
32
33public:
34 typedef _Scalar Scalar;
35 typedef Dense StorageKind;
36 typedef Eigen::Index StorageIndex;
37 typedef MatrixXpr XprKind;
38 enum {
39 RowsAtCompileTime = _Rows,
40 ColsAtCompileTime = _Cols,
41 MaxRowsAtCompileTime = _MaxRows,
42 MaxColsAtCompileTime = _MaxCols,
43 Flags = compute_matrix_flags<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>::ret,
44 Options = _Options,
45 InnerStrideAtCompileTime = 1,
46 OuterStrideAtCompileTime = (Options&RowMajor) ? ColsAtCompileTime : RowsAtCompileTime,
47
48 // FIXME, the following flag in only used to define NeedsToAlign in PlainObjectBase
49 EvaluatorFlags = LinearAccessBit | DirectAccessBit | packet_access_bit | row_major_bit,
50 Alignment = actual_alignment
51 };
52};
53}
54
55/** \class Matrix
56 * \ingroup Core_Module
57 *
58 * \brief The matrix class, also used for vectors and row-vectors
59 *
60 * The %Matrix class is the work-horse for all \em dense (\ref dense "note") matrices and vectors within Eigen.
61 * Vectors are matrices with one column, and row-vectors are matrices with one row.
62 *
63 * The %Matrix class encompasses \em both fixed-size and dynamic-size objects (\ref fixedsize "note").
64 *
65 * The first three template parameters are required:
66 * \tparam _Scalar Numeric type, e.g. float, double, int or std::complex<float>.
67 * User defined scalar types are supported as well (see \ref user_defined_scalars "here").
68 * \tparam _Rows Number of rows, or \b Dynamic
69 * \tparam _Cols Number of columns, or \b Dynamic
70 *
71 * The remaining template parameters are optional -- in most cases you don't have to worry about them.
72 * \tparam _Options A combination of either \b #RowMajor or \b #ColMajor, and of either
73 * \b #AutoAlign or \b #DontAlign.
74 * The former controls \ref TopicStorageOrders "storage order", and defaults to column-major. The latter controls alignment, which is required
75 * for vectorization. It defaults to aligning matrices except for fixed sizes that aren't a multiple of the packet size.
76 * \tparam _MaxRows Maximum number of rows. Defaults to \a _Rows (\ref maxrows "note").
77 * \tparam _MaxCols Maximum number of columns. Defaults to \a _Cols (\ref maxrows "note").
78 *
79 * Eigen provides a number of typedefs covering the usual cases. Here are some examples:
80 *
81 * \li \c Matrix2d is a 2x2 square matrix of doubles (\c Matrix<double, 2, 2>)
82 * \li \c Vector4f is a vector of 4 floats (\c Matrix<float, 4, 1>)
83 * \li \c RowVector3i is a row-vector of 3 ints (\c Matrix<int, 1, 3>)
84 *
85 * \li \c MatrixXf is a dynamic-size matrix of floats (\c Matrix<float, Dynamic, Dynamic>)
86 * \li \c VectorXf is a dynamic-size vector of floats (\c Matrix<float, Dynamic, 1>)
87 *
88 * \li \c Matrix2Xf is a partially fixed-size (dynamic-size) matrix of floats (\c Matrix<float, 2, Dynamic>)
89 * \li \c MatrixX3d is a partially dynamic-size (fixed-size) matrix of double (\c Matrix<double, Dynamic, 3>)
90 *
91 * See \link matrixtypedefs this page \endlink for a complete list of predefined \em %Matrix and \em Vector typedefs.
92 *
93 * You can access elements of vectors and matrices using normal subscripting:
94 *
95 * \code
96 * Eigen::VectorXd v(10);
97 * v[0] = 0.1;
98 * v[1] = 0.2;
99 * v(0) = 0.3;
100 * v(1) = 0.4;
101 *
102 * Eigen::MatrixXi m(10, 10);
103 * m(0, 1) = 1;
104 * m(0, 2) = 2;
105 * m(0, 3) = 3;
106 * \endcode
107 *
108 * This class can be extended with the help of the plugin mechanism described on the page
109 * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_MATRIX_PLUGIN.
110 *
111 * <i><b>Some notes:</b></i>
112 *
113 * <dl>
114 * <dt><b>\anchor dense Dense versus sparse:</b></dt>
115 * <dd>This %Matrix class handles dense, not sparse matrices and vectors. For sparse matrices and vectors, see the Sparse module.
116 *
117 * Dense matrices and vectors are plain usual arrays of coefficients. All the coefficients are stored, in an ordinary contiguous array.
118 * This is unlike Sparse matrices and vectors where the coefficients are stored as a list of nonzero coefficients.</dd>
119 *
120 * <dt><b>\anchor fixedsize Fixed-size versus dynamic-size:</b></dt>
121 * <dd>Fixed-size means that the numbers of rows and columns are known are compile-time. In this case, Eigen allocates the array
122 * of coefficients as a fixed-size array, as a class member. This makes sense for very small matrices, typically up to 4x4, sometimes up
123 * to 16x16. Larger matrices should be declared as dynamic-size even if one happens to know their size at compile-time.
124 *
125 * Dynamic-size means that the numbers of rows or columns are not necessarily known at compile-time. In this case they are runtime
126 * variables, and the array of coefficients is allocated dynamically on the heap.
127 *
128 * Note that \em dense matrices, be they Fixed-size or Dynamic-size, <em>do not</em> expand dynamically in the sense of a std::map.
129 * If you want this behavior, see the Sparse module.</dd>
130 *
131 * <dt><b>\anchor maxrows _MaxRows and _MaxCols:</b></dt>
132 * <dd>In most cases, one just leaves these parameters to the default values.
133 * These parameters mean the maximum size of rows and columns that the matrix may have. They are useful in cases
134 * when the exact numbers of rows and columns are not known are compile-time, but it is known at compile-time that they cannot
135 * exceed a certain value. This happens when taking dynamic-size blocks inside fixed-size matrices: in this case _MaxRows and _MaxCols
136 * are the dimensions of the original matrix, while _Rows and _Cols are Dynamic.</dd>
137 * </dl>
138 *
139 * <i><b>ABI and storage layout</b></i>
140 *
141 * The table below summarizes the ABI of some possible Matrix instances which is fixed thorough the lifetime of Eigen 3.
142 * <table class="manual">
143 * <tr><th>Matrix type</th><th>Equivalent C structure</th></tr>
144 * <tr><td>\code Matrix<T,Dynamic,Dynamic> \endcode</td><td>\code
145 * struct {
146 * T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
147 * Eigen::Index rows, cols;
148 * };
149 * \endcode</td></tr>
150 * <tr class="alt"><td>\code
151 * Matrix<T,Dynamic,1>
152 * Matrix<T,1,Dynamic> \endcode</td><td>\code
153 * struct {
154 * T *data; // with (size_t(data)%EIGEN_MAX_ALIGN_BYTES)==0
155 * Eigen::Index size;
156 * };
157 * \endcode</td></tr>
158 * <tr><td>\code Matrix<T,Rows,Cols> \endcode</td><td>\code
159 * struct {
160 * T data[Rows*Cols]; // with (size_t(data)%A(Rows*Cols*sizeof(T)))==0
161 * };
162 * \endcode</td></tr>
163 * <tr class="alt"><td>\code Matrix<T,Dynamic,Dynamic,0,MaxRows,MaxCols> \endcode</td><td>\code
164 * struct {
165 * T data[MaxRows*MaxCols]; // with (size_t(data)%A(MaxRows*MaxCols*sizeof(T)))==0
166 * Eigen::Index rows, cols;
167 * };
168 * \endcode</td></tr>
169 * </table>
170 * Note that in this table Rows, Cols, MaxRows and MaxCols are all positive integers. A(S) is defined to the largest possible power-of-two
171 * smaller to EIGEN_MAX_STATIC_ALIGN_BYTES.
172 *
173 * \see MatrixBase for the majority of the API methods for matrices, \ref TopicClassHierarchy,
174 * \ref TopicStorageOrders
175 */
176
177template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
178class Matrix
179 : public PlainObjectBase<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols> >
180{
181 public:
182
183 /** \brief Base class typedef.
184 * \sa PlainObjectBase
185 */
186 typedef PlainObjectBase<Matrix> Base;
187
188 enum { Options = _Options };
189
190 EIGEN_DENSE_PUBLIC_INTERFACE(Matrix)
191
192 typedef typename Base::PlainObject PlainObject;
193
194 using Base::base;
195 using Base::coeffRef;
196
197 /**
198 * \brief Assigns matrices to each other.
199 *
200 * \note This is a special case of the templated operator=. Its purpose is
201 * to prevent a default operator= from hiding the templated operator=.
202 *
203 * \callgraph
204 */
205 EIGEN_DEVICE_FUNC
206 EIGEN_STRONG_INLINE Matrix& operator=(const Matrix& other)
207 {
208 return Base::_set(other);
209 }
210
211 /** \internal
212 * \brief Copies the value of the expression \a other into \c *this with automatic resizing.
213 *
214 * *this might be resized to match the dimensions of \a other. If *this was a null matrix (not already initialized),
215 * it will be initialized.
216 *
217 * Note that copying a row-vector into a vector (and conversely) is allowed.
218 * The resizing, if any, is then done in the appropriate way so that row-vectors
219 * remain row-vectors and vectors remain vectors.
220 */
221 template<typename OtherDerived>
222 EIGEN_DEVICE_FUNC
223 EIGEN_STRONG_INLINE Matrix& operator=(const DenseBase<OtherDerived>& other)
224 {
225 return Base::_set(other);
226 }
227
228 /* Here, doxygen failed to copy the brief information when using \copydoc */
229
230 /**
231 * \brief Copies the generic expression \a other into *this.
232 * \copydetails DenseBase::operator=(const EigenBase<OtherDerived> &other)
233 */
234 template<typename OtherDerived>
235 EIGEN_DEVICE_FUNC
236 EIGEN_STRONG_INLINE Matrix& operator=(const EigenBase<OtherDerived> &other)
237 {
238 return Base::operator=(other);
239 }
240
241 template<typename OtherDerived>
242 EIGEN_DEVICE_FUNC
243 EIGEN_STRONG_INLINE Matrix& operator=(const ReturnByValue<OtherDerived>& func)
244 {
245 return Base::operator=(func);
246 }
247
248 /** \brief Default constructor.
249 *
250 * For fixed-size matrices, does nothing.
251 *
252 * For dynamic-size matrices, creates an empty matrix of size 0. Does not allocate any array. Such a matrix
253 * is called a null matrix. This constructor is the unique way to create null matrices: resizing
254 * a matrix to 0 is not supported.
255 *
256 * \sa resize(Index,Index)
257 */
258 EIGEN_DEVICE_FUNC
259 EIGEN_STRONG_INLINE Matrix() : Base()
260 {
261 Base::_check_template_params();
262 EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED
263 }
264
265 // FIXME is it still needed
266 EIGEN_DEVICE_FUNC
267 explicit Matrix(internal::constructor_without_unaligned_array_assert)
268 : Base(internal::constructor_without_unaligned_array_assert())
269 { Base::_check_template_params(); EIGEN_INITIALIZE_COEFFS_IF_THAT_OPTION_IS_ENABLED }
270
271#if EIGEN_HAS_RVALUE_REFERENCES
272 EIGEN_DEVICE_FUNC
273 Matrix(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
274 : Base(std::move(other))
275 {
276 Base::_check_template_params();
277 }
278 EIGEN_DEVICE_FUNC
279 Matrix& operator=(Matrix&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
280 {
281 other.swap(*this);
282 return *this;
283 }
284#endif
285
286 #ifndef EIGEN_PARSED_BY_DOXYGEN
287
288 // This constructor is for both 1x1 matrices and dynamic vectors
289 template<typename T>
290 EIGEN_DEVICE_FUNC
291 EIGEN_STRONG_INLINE explicit Matrix(const T& x)
292 {
293 Base::_check_template_params();
294 Base::template _init1<T>(x);
295 }
296
297 template<typename T0, typename T1>
298 EIGEN_DEVICE_FUNC
299 EIGEN_STRONG_INLINE Matrix(const T0& x, const T1& y)
300 {
301 Base::_check_template_params();
302 Base::template _init2<T0,T1>(x, y);
303 }
304 #else
305 /** \brief Constructs a fixed-sized matrix initialized with coefficients starting at \a data */
306 EIGEN_DEVICE_FUNC
307 explicit Matrix(const Scalar *data);
308
309 /** \brief Constructs a vector or row-vector with given dimension. \only_for_vectors
310 *
311 * This is useful for dynamic-size vectors. For fixed-size vectors,
312 * it is redundant to pass these parameters, so one should use the default constructor
313 * Matrix() instead.
314 *
315 * \warning This constructor is disabled for fixed-size \c 1x1 matrices. For instance,
316 * calling Matrix<double,1,1>(1) will call the initialization constructor: Matrix(const Scalar&).
317 * For fixed-size \c 1x1 matrices it is therefore recommended to use the default
318 * constructor Matrix() instead, especially when using one of the non standard
319 * \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives).
320 */
321 EIGEN_STRONG_INLINE explicit Matrix(Index dim);
322 /** \brief Constructs an initialized 1x1 matrix with the given coefficient */
323 Matrix(const Scalar& x);
324 /** \brief Constructs an uninitialized matrix with \a rows rows and \a cols columns.
325 *
326 * This is useful for dynamic-size matrices. For fixed-size matrices,
327 * it is redundant to pass these parameters, so one should use the default constructor
328 * Matrix() instead.
329 *
330 * \warning This constructor is disabled for fixed-size \c 1x2 and \c 2x1 vectors. For instance,
331 * calling Matrix2f(2,1) will call the initialization constructor: Matrix(const Scalar& x, const Scalar& y).
332 * For fixed-size \c 1x2 or \c 2x1 vectors it is therefore recommended to use the default
333 * constructor Matrix() instead, especially when using one of the non standard
334 * \c EIGEN_INITIALIZE_MATRICES_BY_{ZERO,\c NAN} macros (see \ref TopicPreprocessorDirectives).
335 */
336 EIGEN_DEVICE_FUNC
337 Matrix(Index rows, Index cols);
338
339 /** \brief Constructs an initialized 2D vector with given coefficients */
340 Matrix(const Scalar& x, const Scalar& y);
341 #endif
342
343 /** \brief Constructs an initialized 3D vector with given coefficients */
344 EIGEN_DEVICE_FUNC
345 EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z)
346 {
347 Base::_check_template_params();
348 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 3)
349 m_storage.data()[0] = x;
350 m_storage.data()[1] = y;
351 m_storage.data()[2] = z;
352 }
353 /** \brief Constructs an initialized 4D vector with given coefficients */
354 EIGEN_DEVICE_FUNC
355 EIGEN_STRONG_INLINE Matrix(const Scalar& x, const Scalar& y, const Scalar& z, const Scalar& w)
356 {
357 Base::_check_template_params();
358 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Matrix, 4)
359 m_storage.data()[0] = x;
360 m_storage.data()[1] = y;
361 m_storage.data()[2] = z;
362 m_storage.data()[3] = w;
363 }
364
365
366 /** \brief Copy constructor */
367 EIGEN_DEVICE_FUNC
368 EIGEN_STRONG_INLINE Matrix(const Matrix& other) : Base(other)
369 { }
370
371 /** \brief Copy constructor for generic expressions.
372 * \sa MatrixBase::operator=(const EigenBase<OtherDerived>&)
373 */
374 template<typename OtherDerived>
375 EIGEN_DEVICE_FUNC
376 EIGEN_STRONG_INLINE Matrix(const EigenBase<OtherDerived> &other)
377 : Base(other.derived())
378 { }
379
380 EIGEN_DEVICE_FUNC inline Index innerStride() const { return 1; }
381 EIGEN_DEVICE_FUNC inline Index outerStride() const { return this->innerSize(); }
382
383 /////////// Geometry module ///////////
384
385 template<typename OtherDerived>
386 EIGEN_DEVICE_FUNC
387 explicit Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
388 template<typename OtherDerived>
389 EIGEN_DEVICE_FUNC
390 Matrix& operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r);
391
392 // allow to extend Matrix outside Eigen
393 #ifdef EIGEN_MATRIX_PLUGIN
394 #include EIGEN_MATRIX_PLUGIN
395 #endif
396
397 protected:
398 template <typename Derived, typename OtherDerived, bool IsVector>
399 friend struct internal::conservative_resize_like_impl;
400
401 using Base::m_storage;
402};
403
404/** \defgroup matrixtypedefs Global matrix typedefs
405 *
406 * \ingroup Core_Module
407 *
408 * Eigen defines several typedef shortcuts for most common matrix and vector types.
409 *
410 * The general patterns are the following:
411 *
412 * \c MatrixSizeType where \c Size can be \c 2,\c 3,\c 4 for fixed size square matrices or \c X for dynamic size,
413 * and where \c Type can be \c i for integer, \c f for float, \c d for double, \c cf for complex float, \c cd
414 * for complex double.
415 *
416 * For example, \c Matrix3d is a fixed-size 3x3 matrix type of doubles, and \c MatrixXf is a dynamic-size matrix of floats.
417 *
418 * There are also \c VectorSizeType and \c RowVectorSizeType which are self-explanatory. For example, \c Vector4cf is
419 * a fixed-size vector of 4 complex floats.
420 *
421 * \sa class Matrix
422 */
423
424#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \
425/** \ingroup matrixtypedefs */ \
426typedef Matrix<Type, Size, Size> Matrix##SizeSuffix##TypeSuffix; \
427/** \ingroup matrixtypedefs */ \
428typedef Matrix<Type, Size, 1> Vector##SizeSuffix##TypeSuffix; \
429/** \ingroup matrixtypedefs */ \
430typedef Matrix<Type, 1, Size> RowVector##SizeSuffix##TypeSuffix;
431
432#define EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, Size) \
433/** \ingroup matrixtypedefs */ \
434typedef Matrix<Type, Size, Dynamic> Matrix##Size##X##TypeSuffix; \
435/** \ingroup matrixtypedefs */ \
436typedef Matrix<Type, Dynamic, Size> Matrix##X##Size##TypeSuffix;
437
438#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
439EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
440EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
441EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
442EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) \
443EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 2) \
444EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 3) \
445EIGEN_MAKE_FIXED_TYPEDEFS(Type, TypeSuffix, 4)
446
447EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
448EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
449EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)
450EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<float>, cf)
451EIGEN_MAKE_TYPEDEFS_ALL_SIZES(std::complex<double>, cd)
452
453#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
454#undef EIGEN_MAKE_TYPEDEFS
455#undef EIGEN_MAKE_FIXED_TYPEDEFS
456
457} // end namespace Eigen
458
459#endif // EIGEN_MATRIX_H
460