1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2006-2010 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
12#ifndef EIGEN_PARSED_BY_DOXYGEN
13
14/** \internal expression type of a column */
15typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, 1, !IsRowMajor> ColXpr;
16typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, 1, !IsRowMajor> ConstColXpr;
17/** \internal expression type of a row */
18typedef Block<Derived, 1, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> RowXpr;
19typedef const Block<const Derived, 1, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> ConstRowXpr;
20/** \internal expression type of a block of whole columns */
21typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, Dynamic, !IsRowMajor> ColsBlockXpr;
22typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, Dynamic, !IsRowMajor> ConstColsBlockXpr;
23/** \internal expression type of a block of whole rows */
24typedef Block<Derived, Dynamic, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> RowsBlockXpr;
25typedef const Block<const Derived, Dynamic, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> ConstRowsBlockXpr;
26/** \internal expression type of a block of whole columns */
27template<int N> struct NColsBlockXpr { typedef Block<Derived, internal::traits<Derived>::RowsAtCompileTime, N, !IsRowMajor> Type; };
28template<int N> struct ConstNColsBlockXpr { typedef const Block<const Derived, internal::traits<Derived>::RowsAtCompileTime, N, !IsRowMajor> Type; };
29/** \internal expression type of a block of whole rows */
30template<int N> struct NRowsBlockXpr { typedef Block<Derived, N, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> Type; };
31template<int N> struct ConstNRowsBlockXpr { typedef const Block<const Derived, N, internal::traits<Derived>::ColsAtCompileTime, IsRowMajor> Type; };
32
33typedef VectorBlock<Derived> SegmentReturnType;
34typedef const VectorBlock<const Derived> ConstSegmentReturnType;
35template<int Size> struct FixedSegmentReturnType { typedef VectorBlock<Derived, Size> Type; };
36template<int Size> struct ConstFixedSegmentReturnType { typedef const VectorBlock<const Derived, Size> Type; };
37
38#endif // not EIGEN_PARSED_BY_DOXYGEN
39
40/** \returns a dynamic-size expression of a block in *this.
41  *
42  * \param startRow the first row in the block
43  * \param startCol the first column in the block
44  * \param blockRows the number of rows in the block
45  * \param blockCols the number of columns in the block
46  *
47  * Example: \include MatrixBase_block_int_int_int_int.cpp
48  * Output: \verbinclude MatrixBase_block_int_int_int_int.out
49  *
50  * \note Even though the returned expression has dynamic size, in the case
51  * when it is applied to a fixed-size matrix, it inherits a fixed maximal size,
52  * which means that evaluating it does not cause a dynamic memory allocation.
53  *
54  * \sa class Block, block(Index,Index)
55  */
56inline Block<Derived> block(Index startRow, Index startCol, Index blockRows, Index blockCols)
57{
58  return Block<Derived>(derived(), startRow, startCol, blockRows, blockCols);
59}
60
61/** This is the const version of block(Index,Index,Index,Index). */
62inline const Block<const Derived> block(Index startRow, Index startCol, Index blockRows, Index blockCols) const
63{
64  return Block<const Derived>(derived(), startRow, startCol, blockRows, blockCols);
65}
66
67
68
69
70/** \returns a dynamic-size expression of a top-right corner of *this.
71  *
72  * \param cRows the number of rows in the corner
73  * \param cCols the number of columns in the corner
74  *
75  * Example: \include MatrixBase_topRightCorner_int_int.cpp
76  * Output: \verbinclude MatrixBase_topRightCorner_int_int.out
77  *
78  * \sa class Block, block(Index,Index,Index,Index)
79  */
80inline Block<Derived> topRightCorner(Index cRows, Index cCols)
81{
82  return Block<Derived>(derived(), 0, cols() - cCols, cRows, cCols);
83}
84
85/** This is the const version of topRightCorner(Index, Index).*/
86inline const Block<const Derived> topRightCorner(Index cRows, Index cCols) const
87{
88  return Block<const Derived>(derived(), 0, cols() - cCols, cRows, cCols);
89}
90
91/** \returns an expression of a fixed-size top-right corner of *this.
92  *
93  * \tparam CRows the number of rows in the corner
94  * \tparam CCols the number of columns in the corner
95  *
96  * Example: \include MatrixBase_template_int_int_topRightCorner.cpp
97  * Output: \verbinclude MatrixBase_template_int_int_topRightCorner.out
98  *
99  * \sa class Block, block<int,int>(Index,Index)
100  */
101template<int CRows, int CCols>
102inline Block<Derived, CRows, CCols> topRightCorner()
103{
104  return Block<Derived, CRows, CCols>(derived(), 0, cols() - CCols);
105}
106
107/** This is the const version of topRightCorner<int, int>().*/
108template<int CRows, int CCols>
109inline const Block<const Derived, CRows, CCols> topRightCorner() const
110{
111  return Block<const Derived, CRows, CCols>(derived(), 0, cols() - CCols);
112}
113
114/** \returns an expression of a top-right corner of *this.
115  *
116  * \tparam CRows number of rows in corner as specified at compile-time
117  * \tparam CCols number of columns in corner as specified at compile-time
118  * \param  cRows number of rows in corner as specified at run-time
119  * \param  cCols number of columns in corner as specified at run-time
120  *
121  * This function is mainly useful for corners where the number of rows is specified at compile-time
122  * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
123  * information should not contradict. In other words, \a cRows should equal \a CRows unless
124  * \a CRows is \a Dynamic, and the same for the number of columns.
125  *
126  * Example: \include MatrixBase_template_int_int_topRightCorner_int_int.cpp
127  * Output: \verbinclude MatrixBase_template_int_int_topRightCorner_int_int.out
128  *
129  * \sa class Block
130  */
131template<int CRows, int CCols>
132inline Block<Derived, CRows, CCols> topRightCorner(Index cRows, Index cCols)
133{
134  return Block<Derived, CRows, CCols>(derived(), 0, cols() - cCols, cRows, cCols);
135}
136
137/** This is the const version of topRightCorner<int, int>(Index, Index).*/
138template<int CRows, int CCols>
139inline const Block<const Derived, CRows, CCols> topRightCorner(Index cRows, Index cCols) const
140{
141  return Block<const Derived, CRows, CCols>(derived(), 0, cols() - cCols, cRows, cCols);
142}
143
144
145
146/** \returns a dynamic-size expression of a top-left corner of *this.
147  *
148  * \param cRows the number of rows in the corner
149  * \param cCols the number of columns in the corner
150  *
151  * Example: \include MatrixBase_topLeftCorner_int_int.cpp
152  * Output: \verbinclude MatrixBase_topLeftCorner_int_int.out
153  *
154  * \sa class Block, block(Index,Index,Index,Index)
155  */
156inline Block<Derived> topLeftCorner(Index cRows, Index cCols)
157{
158  return Block<Derived>(derived(), 0, 0, cRows, cCols);
159}
160
161/** This is the const version of topLeftCorner(Index, Index).*/
162inline const Block<const Derived> topLeftCorner(Index cRows, Index cCols) const
163{
164  return Block<const Derived>(derived(), 0, 0, cRows, cCols);
165}
166
167/** \returns an expression of a fixed-size top-left corner of *this.
168  *
169  * The template parameters CRows and CCols are the number of rows and columns in the corner.
170  *
171  * Example: \include MatrixBase_template_int_int_topLeftCorner.cpp
172  * Output: \verbinclude MatrixBase_template_int_int_topLeftCorner.out
173  *
174  * \sa class Block, block(Index,Index,Index,Index)
175  */
176template<int CRows, int CCols>
177inline Block<Derived, CRows, CCols> topLeftCorner()
178{
179  return Block<Derived, CRows, CCols>(derived(), 0, 0);
180}
181
182/** This is the const version of topLeftCorner<int, int>().*/
183template<int CRows, int CCols>
184inline const Block<const Derived, CRows, CCols> topLeftCorner() const
185{
186  return Block<const Derived, CRows, CCols>(derived(), 0, 0);
187}
188
189/** \returns an expression of a top-left corner of *this.
190  *
191  * \tparam CRows number of rows in corner as specified at compile-time
192  * \tparam CCols number of columns in corner as specified at compile-time
193  * \param  cRows number of rows in corner as specified at run-time
194  * \param  cCols number of columns in corner as specified at run-time
195  *
196  * This function is mainly useful for corners where the number of rows is specified at compile-time
197  * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
198  * information should not contradict. In other words, \a cRows should equal \a CRows unless
199  * \a CRows is \a Dynamic, and the same for the number of columns.
200  *
201  * Example: \include MatrixBase_template_int_int_topLeftCorner_int_int.cpp
202  * Output: \verbinclude MatrixBase_template_int_int_topLeftCorner_int_int.out
203  *
204  * \sa class Block
205  */
206template<int CRows, int CCols>
207inline Block<Derived, CRows, CCols> topLeftCorner(Index cRows, Index cCols)
208{
209  return Block<Derived, CRows, CCols>(derived(), 0, 0, cRows, cCols);
210}
211
212/** This is the const version of topLeftCorner<int, int>(Index, Index).*/
213template<int CRows, int CCols>
214inline const Block<const Derived, CRows, CCols> topLeftCorner(Index cRows, Index cCols) const
215{
216  return Block<const Derived, CRows, CCols>(derived(), 0, 0, cRows, cCols);
217}
218
219
220
221/** \returns a dynamic-size expression of a bottom-right corner of *this.
222  *
223  * \param cRows the number of rows in the corner
224  * \param cCols the number of columns in the corner
225  *
226  * Example: \include MatrixBase_bottomRightCorner_int_int.cpp
227  * Output: \verbinclude MatrixBase_bottomRightCorner_int_int.out
228  *
229  * \sa class Block, block(Index,Index,Index,Index)
230  */
231inline Block<Derived> bottomRightCorner(Index cRows, Index cCols)
232{
233  return Block<Derived>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
234}
235
236/** This is the const version of bottomRightCorner(Index, Index).*/
237inline const Block<const Derived> bottomRightCorner(Index cRows, Index cCols) const
238{
239  return Block<const Derived>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
240}
241
242/** \returns an expression of a fixed-size bottom-right corner of *this.
243  *
244  * The template parameters CRows and CCols are the number of rows and columns in the corner.
245  *
246  * Example: \include MatrixBase_template_int_int_bottomRightCorner.cpp
247  * Output: \verbinclude MatrixBase_template_int_int_bottomRightCorner.out
248  *
249  * \sa class Block, block(Index,Index,Index,Index)
250  */
251template<int CRows, int CCols>
252inline Block<Derived, CRows, CCols> bottomRightCorner()
253{
254  return Block<Derived, CRows, CCols>(derived(), rows() - CRows, cols() - CCols);
255}
256
257/** This is the const version of bottomRightCorner<int, int>().*/
258template<int CRows, int CCols>
259inline const Block<const Derived, CRows, CCols> bottomRightCorner() const
260{
261  return Block<const Derived, CRows, CCols>(derived(), rows() - CRows, cols() - CCols);
262}
263
264/** \returns an expression of a bottom-right corner of *this.
265  *
266  * \tparam CRows number of rows in corner as specified at compile-time
267  * \tparam CCols number of columns in corner as specified at compile-time
268  * \param  cRows number of rows in corner as specified at run-time
269  * \param  cCols number of columns in corner as specified at run-time
270  *
271  * This function is mainly useful for corners where the number of rows is specified at compile-time
272  * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
273  * information should not contradict. In other words, \a cRows should equal \a CRows unless
274  * \a CRows is \a Dynamic, and the same for the number of columns.
275  *
276  * Example: \include MatrixBase_template_int_int_bottomRightCorner_int_int.cpp
277  * Output: \verbinclude MatrixBase_template_int_int_bottomRightCorner_int_int.out
278  *
279  * \sa class Block
280  */
281template<int CRows, int CCols>
282inline Block<Derived, CRows, CCols> bottomRightCorner(Index cRows, Index cCols)
283{
284  return Block<Derived, CRows, CCols>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
285}
286
287/** This is the const version of bottomRightCorner<int, int>(Index, Index).*/
288template<int CRows, int CCols>
289inline const Block<const Derived, CRows, CCols> bottomRightCorner(Index cRows, Index cCols) const
290{
291  return Block<const Derived, CRows, CCols>(derived(), rows() - cRows, cols() - cCols, cRows, cCols);
292}
293
294
295
296/** \returns a dynamic-size expression of a bottom-left corner of *this.
297  *
298  * \param cRows the number of rows in the corner
299  * \param cCols the number of columns in the corner
300  *
301  * Example: \include MatrixBase_bottomLeftCorner_int_int.cpp
302  * Output: \verbinclude MatrixBase_bottomLeftCorner_int_int.out
303  *
304  * \sa class Block, block(Index,Index,Index,Index)
305  */
306inline Block<Derived> bottomLeftCorner(Index cRows, Index cCols)
307{
308  return Block<Derived>(derived(), rows() - cRows, 0, cRows, cCols);
309}
310
311/** This is the const version of bottomLeftCorner(Index, Index).*/
312inline const Block<const Derived> bottomLeftCorner(Index cRows, Index cCols) const
313{
314  return Block<const Derived>(derived(), rows() - cRows, 0, cRows, cCols);
315}
316
317/** \returns an expression of a fixed-size bottom-left corner of *this.
318  *
319  * The template parameters CRows and CCols are the number of rows and columns in the corner.
320  *
321  * Example: \include MatrixBase_template_int_int_bottomLeftCorner.cpp
322  * Output: \verbinclude MatrixBase_template_int_int_bottomLeftCorner.out
323  *
324  * \sa class Block, block(Index,Index,Index,Index)
325  */
326template<int CRows, int CCols>
327inline Block<Derived, CRows, CCols> bottomLeftCorner()
328{
329  return Block<Derived, CRows, CCols>(derived(), rows() - CRows, 0);
330}
331
332/** This is the const version of bottomLeftCorner<int, int>().*/
333template<int CRows, int CCols>
334inline const Block<const Derived, CRows, CCols> bottomLeftCorner() const
335{
336  return Block<const Derived, CRows, CCols>(derived(), rows() - CRows, 0);
337}
338
339/** \returns an expression of a bottom-left corner of *this.
340  *
341  * \tparam CRows number of rows in corner as specified at compile-time
342  * \tparam CCols number of columns in corner as specified at compile-time
343  * \param  cRows number of rows in corner as specified at run-time
344  * \param  cCols number of columns in corner as specified at run-time
345  *
346  * This function is mainly useful for corners where the number of rows is specified at compile-time
347  * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
348  * information should not contradict. In other words, \a cRows should equal \a CRows unless
349  * \a CRows is \a Dynamic, and the same for the number of columns.
350  *
351  * Example: \include MatrixBase_template_int_int_bottomLeftCorner_int_int.cpp
352  * Output: \verbinclude MatrixBase_template_int_int_bottomLeftCorner_int_int.out
353  *
354  * \sa class Block
355  */
356template<int CRows, int CCols>
357inline Block<Derived, CRows, CCols> bottomLeftCorner(Index cRows, Index cCols)
358{
359  return Block<Derived, CRows, CCols>(derived(), rows() - cRows, 0, cRows, cCols);
360}
361
362/** This is the const version of bottomLeftCorner<int, int>(Index, Index).*/
363template<int CRows, int CCols>
364inline const Block<const Derived, CRows, CCols> bottomLeftCorner(Index cRows, Index cCols) const
365{
366  return Block<const Derived, CRows, CCols>(derived(), rows() - cRows, 0, cRows, cCols);
367}
368
369
370
371/** \returns a block consisting of the top rows of *this.
372  *
373  * \param n the number of rows in the block
374  *
375  * Example: \include MatrixBase_topRows_int.cpp
376  * Output: \verbinclude MatrixBase_topRows_int.out
377  *
378  * \sa class Block, block(Index,Index,Index,Index)
379  */
380inline RowsBlockXpr topRows(Index n)
381{
382  return RowsBlockXpr(derived(), 0, 0, n, cols());
383}
384
385/** This is the const version of topRows(Index).*/
386inline ConstRowsBlockXpr topRows(Index n) const
387{
388  return ConstRowsBlockXpr(derived(), 0, 0, n, cols());
389}
390
391/** \returns a block consisting of the top rows of *this.
392  *
393  * \tparam N the number of rows in the block as specified at compile-time
394  * \param n the number of rows in the block as specified at run-time
395  *
396  * The compile-time and run-time information should not contradict. In other words,
397  * \a n should equal \a N unless \a N is \a Dynamic.
398  *
399  * Example: \include MatrixBase_template_int_topRows.cpp
400  * Output: \verbinclude MatrixBase_template_int_topRows.out
401  *
402  * \sa class Block, block(Index,Index,Index,Index)
403  */
404template<int N>
405inline typename NRowsBlockXpr<N>::Type topRows(Index n = N)
406{
407  return typename NRowsBlockXpr<N>::Type(derived(), 0, 0, n, cols());
408}
409
410/** This is the const version of topRows<int>().*/
411template<int N>
412inline typename ConstNRowsBlockXpr<N>::Type topRows(Index n = N) const
413{
414  return typename ConstNRowsBlockXpr<N>::Type(derived(), 0, 0, n, cols());
415}
416
417
418
419/** \returns a block consisting of the bottom rows of *this.
420  *
421  * \param n the number of rows in the block
422  *
423  * Example: \include MatrixBase_bottomRows_int.cpp
424  * Output: \verbinclude MatrixBase_bottomRows_int.out
425  *
426  * \sa class Block, block(Index,Index,Index,Index)
427  */
428inline RowsBlockXpr bottomRows(Index n)
429{
430  return RowsBlockXpr(derived(), rows() - n, 0, n, cols());
431}
432
433/** This is the const version of bottomRows(Index).*/
434inline ConstRowsBlockXpr bottomRows(Index n) const
435{
436  return ConstRowsBlockXpr(derived(), rows() - n, 0, n, cols());
437}
438
439/** \returns a block consisting of the bottom rows of *this.
440  *
441  * \tparam N the number of rows in the block as specified at compile-time
442  * \param n the number of rows in the block as specified at run-time
443  *
444  * The compile-time and run-time information should not contradict. In other words,
445  * \a n should equal \a N unless \a N is \a Dynamic.
446  *
447  * Example: \include MatrixBase_template_int_bottomRows.cpp
448  * Output: \verbinclude MatrixBase_template_int_bottomRows.out
449  *
450  * \sa class Block, block(Index,Index,Index,Index)
451  */
452template<int N>
453inline typename NRowsBlockXpr<N>::Type bottomRows(Index n = N)
454{
455  return typename NRowsBlockXpr<N>::Type(derived(), rows() - n, 0, n, cols());
456}
457
458/** This is the const version of bottomRows<int>().*/
459template<int N>
460inline typename ConstNRowsBlockXpr<N>::Type bottomRows(Index n = N) const
461{
462  return typename ConstNRowsBlockXpr<N>::Type(derived(), rows() - n, 0, n, cols());
463}
464
465
466
467/** \returns a block consisting of a range of rows of *this.
468  *
469  * \param startRow the index of the first row in the block
470  * \param n the number of rows in the block
471  *
472  * Example: \include DenseBase_middleRows_int.cpp
473  * Output: \verbinclude DenseBase_middleRows_int.out
474  *
475  * \sa class Block, block(Index,Index,Index,Index)
476  */
477inline RowsBlockXpr middleRows(Index startRow, Index n)
478{
479  return RowsBlockXpr(derived(), startRow, 0, n, cols());
480}
481
482/** This is the const version of middleRows(Index,Index).*/
483inline ConstRowsBlockXpr middleRows(Index startRow, Index n) const
484{
485  return ConstRowsBlockXpr(derived(), startRow, 0, n, cols());
486}
487
488/** \returns a block consisting of a range of rows of *this.
489  *
490  * \tparam N the number of rows in the block as specified at compile-time
491  * \param startRow the index of the first row in the block
492  * \param n the number of rows in the block as specified at run-time
493  *
494  * The compile-time and run-time information should not contradict. In other words,
495  * \a n should equal \a N unless \a N is \a Dynamic.
496  *
497  * Example: \include DenseBase_template_int_middleRows.cpp
498  * Output: \verbinclude DenseBase_template_int_middleRows.out
499  *
500  * \sa class Block, block(Index,Index,Index,Index)
501  */
502template<int N>
503inline typename NRowsBlockXpr<N>::Type middleRows(Index startRow, Index n = N)
504{
505  return typename NRowsBlockXpr<N>::Type(derived(), startRow, 0, n, cols());
506}
507
508/** This is the const version of middleRows<int>().*/
509template<int N>
510inline typename ConstNRowsBlockXpr<N>::Type middleRows(Index startRow, Index n = N) const
511{
512  return typename ConstNRowsBlockXpr<N>::Type(derived(), startRow, 0, n, cols());
513}
514
515
516
517/** \returns a block consisting of the left columns of *this.
518  *
519  * \param n the number of columns in the block
520  *
521  * Example: \include MatrixBase_leftCols_int.cpp
522  * Output: \verbinclude MatrixBase_leftCols_int.out
523  *
524  * \sa class Block, block(Index,Index,Index,Index)
525  */
526inline ColsBlockXpr leftCols(Index n)
527{
528  return ColsBlockXpr(derived(), 0, 0, rows(), n);
529}
530
531/** This is the const version of leftCols(Index).*/
532inline ConstColsBlockXpr leftCols(Index n) const
533{
534  return ConstColsBlockXpr(derived(), 0, 0, rows(), n);
535}
536
537/** \returns a block consisting of the left columns of *this.
538  *
539  * \tparam N the number of columns in the block as specified at compile-time
540  * \param n the number of columns in the block as specified at run-time
541  *
542  * The compile-time and run-time information should not contradict. In other words,
543  * \a n should equal \a N unless \a N is \a Dynamic.
544  *
545  * Example: \include MatrixBase_template_int_leftCols.cpp
546  * Output: \verbinclude MatrixBase_template_int_leftCols.out
547  *
548  * \sa class Block, block(Index,Index,Index,Index)
549  */
550template<int N>
551inline typename NColsBlockXpr<N>::Type leftCols(Index n = N)
552{
553  return typename NColsBlockXpr<N>::Type(derived(), 0, 0, rows(), n);
554}
555
556/** This is the const version of leftCols<int>().*/
557template<int N>
558inline typename ConstNColsBlockXpr<N>::Type leftCols(Index n = N) const
559{
560  return typename ConstNColsBlockXpr<N>::Type(derived(), 0, 0, rows(), n);
561}
562
563
564
565/** \returns a block consisting of the right columns of *this.
566  *
567  * \param n the number of columns in the block
568  *
569  * Example: \include MatrixBase_rightCols_int.cpp
570  * Output: \verbinclude MatrixBase_rightCols_int.out
571  *
572  * \sa class Block, block(Index,Index,Index,Index)
573  */
574inline ColsBlockXpr rightCols(Index n)
575{
576  return ColsBlockXpr(derived(), 0, cols() - n, rows(), n);
577}
578
579/** This is the const version of rightCols(Index).*/
580inline ConstColsBlockXpr rightCols(Index n) const
581{
582  return ConstColsBlockXpr(derived(), 0, cols() - n, rows(), n);
583}
584
585/** \returns a block consisting of the right columns of *this.
586  *
587  * \tparam N the number of columns in the block as specified at compile-time
588  * \param n the number of columns in the block as specified at run-time
589  *
590  * The compile-time and run-time information should not contradict. In other words,
591  * \a n should equal \a N unless \a N is \a Dynamic.
592  *
593  * Example: \include MatrixBase_template_int_rightCols.cpp
594  * Output: \verbinclude MatrixBase_template_int_rightCols.out
595  *
596  * \sa class Block, block(Index,Index,Index,Index)
597  */
598template<int N>
599inline typename NColsBlockXpr<N>::Type rightCols(Index n = N)
600{
601  return typename NColsBlockXpr<N>::Type(derived(), 0, cols() - n, rows(), n);
602}
603
604/** This is the const version of rightCols<int>().*/
605template<int N>
606inline typename ConstNColsBlockXpr<N>::Type rightCols(Index n = N) const
607{
608  return typename ConstNColsBlockXpr<N>::Type(derived(), 0, cols() - n, rows(), n);
609}
610
611
612
613/** \returns a block consisting of a range of columns of *this.
614  *
615  * \param startCol the index of the first column in the block
616  * \param numCols the number of columns in the block
617  *
618  * Example: \include DenseBase_middleCols_int.cpp
619  * Output: \verbinclude DenseBase_middleCols_int.out
620  *
621  * \sa class Block, block(Index,Index,Index,Index)
622  */
623inline ColsBlockXpr middleCols(Index startCol, Index numCols)
624{
625  return ColsBlockXpr(derived(), 0, startCol, rows(), numCols);
626}
627
628/** This is the const version of middleCols(Index,Index).*/
629inline ConstColsBlockXpr middleCols(Index startCol, Index numCols) const
630{
631  return ConstColsBlockXpr(derived(), 0, startCol, rows(), numCols);
632}
633
634/** \returns a block consisting of a range of columns of *this.
635  *
636  * \tparam N the number of columns in the block as specified at compile-time
637  * \param startCol the index of the first column in the block
638  * \param n the number of columns in the block as specified at run-time
639  *
640  * The compile-time and run-time information should not contradict. In other words,
641  * \a n should equal \a N unless \a N is \a Dynamic.
642  *
643  * Example: \include DenseBase_template_int_middleCols.cpp
644  * Output: \verbinclude DenseBase_template_int_middleCols.out
645  *
646  * \sa class Block, block(Index,Index,Index,Index)
647  */
648template<int N>
649inline typename NColsBlockXpr<N>::Type middleCols(Index startCol, Index n = N)
650{
651  return typename NColsBlockXpr<N>::Type(derived(), 0, startCol, rows(), n);
652}
653
654/** This is the const version of middleCols<int>().*/
655template<int N>
656inline typename ConstNColsBlockXpr<N>::Type middleCols(Index startCol, Index n = N) const
657{
658  return typename ConstNColsBlockXpr<N>::Type(derived(), 0, startCol, rows(), n);
659}
660
661
662
663/** \returns a fixed-size expression of a block in *this.
664  *
665  * The template parameters \a BlockRows and \a BlockCols are the number of
666  * rows and columns in the block.
667  *
668  * \param startRow the first row in the block
669  * \param startCol the first column in the block
670  *
671  * Example: \include MatrixBase_block_int_int.cpp
672  * Output: \verbinclude MatrixBase_block_int_int.out
673  *
674  * \note since block is a templated member, the keyword template has to be used
675  * if the matrix type is also a template parameter: \code m.template block<3,3>(1,1); \endcode
676  *
677  * \sa class Block, block(Index,Index,Index,Index)
678  */
679template<int BlockRows, int BlockCols>
680inline Block<Derived, BlockRows, BlockCols> block(Index startRow, Index startCol)
681{
682  return Block<Derived, BlockRows, BlockCols>(derived(), startRow, startCol);
683}
684
685/** This is the const version of block<>(Index, Index). */
686template<int BlockRows, int BlockCols>
687inline const Block<const Derived, BlockRows, BlockCols> block(Index startRow, Index startCol) const
688{
689  return Block<const Derived, BlockRows, BlockCols>(derived(), startRow, startCol);
690}
691
692/** \returns an expression of a block in *this.
693  *
694  * \tparam BlockRows number of rows in block as specified at compile-time
695  * \tparam BlockCols number of columns in block as specified at compile-time
696  * \param  startRow  the first row in the block
697  * \param  startCol  the first column in the block
698  * \param  blockRows number of rows in block as specified at run-time
699  * \param  blockCols number of columns in block as specified at run-time
700  *
701  * This function is mainly useful for blocks where the number of rows is specified at compile-time
702  * and the number of columns is specified at run-time, or vice versa. The compile-time and run-time
703  * information should not contradict. In other words, \a blockRows should equal \a BlockRows unless
704  * \a BlockRows is \a Dynamic, and the same for the number of columns.
705  *
706  * Example: \include MatrixBase_template_int_int_block_int_int_int_int.cpp
707  * Output: \verbinclude MatrixBase_template_int_int_block_int_int_int_int.cpp
708  *
709  * \sa class Block, block(Index,Index,Index,Index)
710  */
711template<int BlockRows, int BlockCols>
712inline Block<Derived, BlockRows, BlockCols> block(Index startRow, Index startCol,
713                                                  Index blockRows, Index blockCols)
714{
715  return Block<Derived, BlockRows, BlockCols>(derived(), startRow, startCol, blockRows, blockCols);
716}
717
718/** This is the const version of block<>(Index, Index, Index, Index). */
719template<int BlockRows, int BlockCols>
720inline const Block<const Derived, BlockRows, BlockCols> block(Index startRow, Index startCol,
721                                                              Index blockRows, Index blockCols) const
722{
723  return Block<const Derived, BlockRows, BlockCols>(derived(), startRow, startCol, blockRows, blockCols);
724}
725
726/** \returns an expression of the \a i-th column of *this. Note that the numbering starts at 0.
727  *
728  * Example: \include MatrixBase_col.cpp
729  * Output: \verbinclude MatrixBase_col.out
730  *
731  * \sa row(), class Block */
732inline ColXpr col(Index i)
733{
734  return ColXpr(derived(), i);
735}
736
737/** This is the const version of col(). */
738inline ConstColXpr col(Index i) const
739{
740  return ConstColXpr(derived(), i);
741}
742
743/** \returns an expression of the \a i-th row of *this. Note that the numbering starts at 0.
744  *
745  * Example: \include MatrixBase_row.cpp
746  * Output: \verbinclude MatrixBase_row.out
747  *
748  * \sa col(), class Block */
749inline RowXpr row(Index i)
750{
751  return RowXpr(derived(), i);
752}
753
754/** This is the const version of row(). */
755inline ConstRowXpr row(Index i) const
756{
757  return ConstRowXpr(derived(), i);
758}
759
760/** \returns a dynamic-size expression of a segment (i.e. a vector block) in *this.
761  *
762  * \only_for_vectors
763  *
764  * \param start the first coefficient in the segment
765  * \param n the number of coefficients in the segment
766  *
767  * Example: \include MatrixBase_segment_int_int.cpp
768  * Output: \verbinclude MatrixBase_segment_int_int.out
769  *
770  * \note Even though the returned expression has dynamic size, in the case
771  * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
772  * which means that evaluating it does not cause a dynamic memory allocation.
773  *
774  * \sa class Block, segment(Index)
775  */
776inline SegmentReturnType segment(Index start, Index n)
777{
778  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
779  return SegmentReturnType(derived(), start, n);
780}
781
782
783/** This is the const version of segment(Index,Index).*/
784inline ConstSegmentReturnType segment(Index start, Index n) const
785{
786  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
787  return ConstSegmentReturnType(derived(), start, n);
788}
789
790/** \returns a dynamic-size expression of the first coefficients of *this.
791  *
792  * \only_for_vectors
793  *
794  * \param n the number of coefficients in the segment
795  *
796  * Example: \include MatrixBase_start_int.cpp
797  * Output: \verbinclude MatrixBase_start_int.out
798  *
799  * \note Even though the returned expression has dynamic size, in the case
800  * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
801  * which means that evaluating it does not cause a dynamic memory allocation.
802  *
803  * \sa class Block, block(Index,Index)
804  */
805inline SegmentReturnType head(Index n)
806{
807  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
808  return SegmentReturnType(derived(), 0, n);
809}
810
811/** This is the const version of head(Index).*/
812inline ConstSegmentReturnType head(Index n) const
813{
814  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
815  return ConstSegmentReturnType(derived(), 0, n);
816}
817
818/** \returns a dynamic-size expression of the last coefficients of *this.
819  *
820  * \only_for_vectors
821  *
822  * \param n the number of coefficients in the segment
823  *
824  * Example: \include MatrixBase_end_int.cpp
825  * Output: \verbinclude MatrixBase_end_int.out
826  *
827  * \note Even though the returned expression has dynamic size, in the case
828  * when it is applied to a fixed-size vector, it inherits a fixed maximal size,
829  * which means that evaluating it does not cause a dynamic memory allocation.
830  *
831  * \sa class Block, block(Index,Index)
832  */
833inline SegmentReturnType tail(Index n)
834{
835  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
836  return SegmentReturnType(derived(), this->size() - n, n);
837}
838
839/** This is the const version of tail(Index).*/
840inline ConstSegmentReturnType tail(Index n) const
841{
842  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
843  return ConstSegmentReturnType(derived(), this->size() - n, n);
844}
845
846/** \returns a fixed-size expression of a segment (i.e. a vector block) in \c *this
847  *
848  * \only_for_vectors
849  *
850  * \tparam N the number of coefficients in the segment as specified at compile-time
851  * \param start the index of the first element in the segment
852  * \param n the number of coefficients in the segment as specified at compile-time
853  *
854  * The compile-time and run-time information should not contradict. In other words,
855  * \a n should equal \a N unless \a N is \a Dynamic.
856  *
857  * Example: \include MatrixBase_template_int_segment.cpp
858  * Output: \verbinclude MatrixBase_template_int_segment.out
859  *
860  * \sa class Block
861  */
862template<int N>
863inline typename FixedSegmentReturnType<N>::Type segment(Index start, Index n = N)
864{
865  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
866  return typename FixedSegmentReturnType<N>::Type(derived(), start, n);
867}
868
869/** This is the const version of segment<int>(Index).*/
870template<int N>
871inline typename ConstFixedSegmentReturnType<N>::Type segment(Index start, Index n = N) const
872{
873  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
874  return typename ConstFixedSegmentReturnType<N>::Type(derived(), start, n);
875}
876
877/** \returns a fixed-size expression of the first coefficients of *this.
878  *
879  * \only_for_vectors
880  *
881  * \tparam N the number of coefficients in the segment as specified at compile-time
882  * \param  n the number of coefficients in the segment as specified at run-time
883  *
884  * The compile-time and run-time information should not contradict. In other words,
885  * \a n should equal \a N unless \a N is \a Dynamic.
886  *
887  * Example: \include MatrixBase_template_int_start.cpp
888  * Output: \verbinclude MatrixBase_template_int_start.out
889  *
890  * \sa class Block
891  */
892template<int N>
893inline typename FixedSegmentReturnType<N>::Type head(Index n = N)
894{
895  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
896  return typename FixedSegmentReturnType<N>::Type(derived(), 0, n);
897}
898
899/** This is the const version of head<int>().*/
900template<int N>
901inline typename ConstFixedSegmentReturnType<N>::Type head(Index n = N) const
902{
903  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
904  return typename ConstFixedSegmentReturnType<N>::Type(derived(), 0, n);
905}
906
907/** \returns a fixed-size expression of the last coefficients of *this.
908  *
909  * \only_for_vectors
910  *
911  * \tparam N the number of coefficients in the segment as specified at compile-time
912  * \param  n the number of coefficients in the segment as specified at run-time
913  *
914  * The compile-time and run-time information should not contradict. In other words,
915  * \a n should equal \a N unless \a N is \a Dynamic.
916  *
917  * Example: \include MatrixBase_template_int_end.cpp
918  * Output: \verbinclude MatrixBase_template_int_end.out
919  *
920  * \sa class Block
921  */
922template<int N>
923inline typename FixedSegmentReturnType<N>::Type tail(Index n = N)
924{
925  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
926  return typename FixedSegmentReturnType<N>::Type(derived(), size() - n);
927}
928
929/** This is the const version of tail<int>.*/
930template<int N>
931inline typename ConstFixedSegmentReturnType<N>::Type tail(Index n = N) const
932{
933  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
934  return typename ConstFixedSegmentReturnType<N>::Type(derived(), size() - n);
935}
936