1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
|
/*
* Tiny Vector Matrix Library
* Dense Vector Matrix Libary of Tiny size using Expression Templates
*
* Copyright (C) 2001 - 2003 Olaf Petzold <opetzold@users.sourceforge.net>
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* $Id: VectorFunctions.h,v 1.17 2005/03/25 07:11:29 opetzold Exp $
*/
#ifndef TVMET_XPR_VECTOR_FUNCTIONS_H
#define TVMET_XPR_VECTOR_FUNCTIONS_H
namespace tvmet {
/* forwards */
template<class T, int Sz> class Vector;
/*********************************************************
* PART I: DECLARATION
*********************************************************/
/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
* Vector arithmetic functions add, sub, mul and div
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/
/*
* function(XprVector<E1, Sz>, XprVector<E2, Sz>)
*/
#define TVMET_DECLARE_MACRO(NAME) \
template<class E1, class E2, int Sz> \
XprVector< \
XprBinOp< \
Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \
XprVector<E1, Sz>, \
XprVector<E2, Sz> \
>, \
Sz \
> \
NAME (const XprVector<E1, Sz>& lhs, \
const XprVector<E2, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;
TVMET_DECLARE_MACRO(add) // per se element wise
TVMET_DECLARE_MACRO(sub) // per se element wise
TVMET_DECLARE_MACRO(mul) // per se element wise
namespace element_wise {
TVMET_DECLARE_MACRO(div) // not defined for vectors
}
#undef TVMET_DECLARE_MACRO
/*
* function(XprVector<E, Sz>, POD)
* function(POD, XprVector<E, Sz>)
* Note: - operations +,-,*,/ are per se element wise
*/
#define TVMET_DECLARE_MACRO(NAME, POD) \
template<class E, int Sz> \
XprVector< \
XprBinOp< \
Fcnl_##NAME< typename E::value_type, POD >, \
XprVector<E, Sz>, \
XprLiteral< POD > \
>, \
Sz \
> \
NAME (const XprVector<E, Sz>& lhs, \
POD rhs) TVMET_CXX_ALWAYS_INLINE; \
\
template<class E, int Sz> \
XprVector< \
XprBinOp< \
Fcnl_##NAME< POD, typename E::value_type>, \
XprLiteral< POD >, \
XprVector<E, Sz> \
>, \
Sz \
> \
NAME (POD lhs, \
const XprVector<E, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;
TVMET_DECLARE_MACRO(add, int)
TVMET_DECLARE_MACRO(sub, int)
TVMET_DECLARE_MACRO(mul, int)
TVMET_DECLARE_MACRO(div, int)
#if defined(TVMET_HAVE_LONG_LONG)
TVMET_DECLARE_MACRO(add, long long int)
TVMET_DECLARE_MACRO(sub, long long int)
TVMET_DECLARE_MACRO(mul, long long int)
TVMET_DECLARE_MACRO(div, long long int)
#endif
TVMET_DECLARE_MACRO(add, float)
TVMET_DECLARE_MACRO(sub, float)
TVMET_DECLARE_MACRO(mul, float)
TVMET_DECLARE_MACRO(div, float)
TVMET_DECLARE_MACRO(add, double)
TVMET_DECLARE_MACRO(sub, double)
TVMET_DECLARE_MACRO(mul, double)
TVMET_DECLARE_MACRO(div, double)
#if defined(TVMET_HAVE_LONG_DOUBLE)
TVMET_DECLARE_MACRO(add, long double)
TVMET_DECLARE_MACRO(sub, long double)
TVMET_DECLARE_MACRO(mul, long double)
TVMET_DECLARE_MACRO(div, long double)
#endif
#undef TVMET_DECLARE_MACRO
#if defined(TVMET_HAVE_COMPLEX)
/*
* function(XprMatrix<E, Rows, Cols>, complex<T>)
* function(complex<T>, XprMatrix<E, Rows, Cols>)
* Note: - operations +,-,*,/ are per se element wise
* \todo type promotion
*/
#define TVMET_DECLARE_MACRO(NAME) \
template<class E, int Sz, class T> \
XprVector< \
XprBinOp< \
Fcnl_##NAME< typename E::value_type, std::complex<T> >, \
XprVector<E, Sz>, \
XprLiteral< std::complex<T> > \
>, \
Sz \
> \
NAME (const XprVector<E, Sz>& lhs, \
const std::complex<T>& rhs) TVMET_CXX_ALWAYS_INLINE; \
\
template<class E, int Sz, class T> \
XprVector< \
XprBinOp< \
Fcnl_##NAME< std::complex<T>, typename E::value_type>, \
XprLiteral< std::complex<T> >, \
XprVector<E, Sz> \
>, \
Sz \
> \
NAME (const std::complex<T>& lhs, \
const XprVector<E, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;
TVMET_DECLARE_MACRO(add)
TVMET_DECLARE_MACRO(sub)
TVMET_DECLARE_MACRO(mul)
TVMET_DECLARE_MACRO(div)
#undef TVMET_DECLARE_MACRO
#endif // defined(TVMET_HAVE_COMPLEX)
/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
* vector specific functions
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/
template<class E, int Sz>
typename NumericTraits<typename E::value_type>::sum_type
sum(const XprVector<E, Sz>& v) TVMET_CXX_ALWAYS_INLINE;
template<class E, int Sz>
typename NumericTraits<typename E::value_type>::sum_type
product(const XprVector<E, Sz>& v) TVMET_CXX_ALWAYS_INLINE;
template<class E1, class E2, int Sz>
typename PromoteTraits<
typename E1::value_type,
typename E2::value_type
>::value_type
dot(const XprVector<E1, Sz>& lhs,
const XprVector<E2, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;
template<class T, class E, int Sz>
typename PromoteTraits<T, typename E::value_type>::value_type
dot(const Vector<T, Sz>& lhs,
const XprVector<E, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;
template<class E, class T, int Sz>
typename PromoteTraits<T, typename E::value_type>::value_type
dot(const XprVector<E, Sz>& lhs,
const Vector<T, Sz>& rhs) TVMET_CXX_ALWAYS_INLINE;
template<class E1, class E2>
Vector<
typename PromoteTraits<
typename E1::value_type,
typename E2::value_type
>::value_type,
3
>
cross(const XprVector<E1, 3>& lhs,
const XprVector<E2, 3>& rhs) TVMET_CXX_ALWAYS_INLINE;
template<class T, class E>
Vector<
typename PromoteTraits<T, typename E::value_type>::value_type, 3>
cross(const Vector<T, 3>& lhs,
const XprVector<E, 3>& rhs) TVMET_CXX_ALWAYS_INLINE;
template<class E, class T>
Vector<
typename PromoteTraits<T, typename E::value_type>::value_type, 3>
cross(const XprVector<E, 3>& lhs,
const Vector<T, 3>& rhs) TVMET_CXX_ALWAYS_INLINE;
template<class E, int Sz>
typename NumericTraits<typename E::value_type>::sum_type
norm1(const XprVector<E, Sz>& v) TVMET_CXX_ALWAYS_INLINE;
template<class E, int Sz>
typename NumericTraits<typename E::value_type>::sum_type
norm2(const XprVector<E, Sz>& v) TVMET_CXX_ALWAYS_INLINE;
template<class E, int Sz>
XprVector<
XprBinOp<
Fcnl_div<typename E::value_type, typename E::value_type>,
XprVector<E, Sz>,
XprLiteral<typename E::value_type>
>,
Sz
>
normalize(const XprVector<E, Sz>& v) TVMET_CXX_ALWAYS_INLINE;
/*********************************************************
* PART II: IMPLEMENTATION
*********************************************************/
/*
* function(XprVector<E1, Sz>, XprVector<E2, Sz>)
*/
#define TVMET_IMPLEMENT_MACRO(NAME) \
template<class E1, class E2, int Sz> \
inline \
XprVector< \
XprBinOp< \
Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \
XprVector<E1, Sz>, \
XprVector<E2, Sz> \
>, \
Sz \
> \
NAME (const XprVector<E1, Sz>& lhs, const XprVector<E2, Sz>& rhs) { \
typedef XprBinOp< \
Fcnl_##NAME<typename E1::value_type, typename E2::value_type>, \
XprVector<E1, Sz>, \
XprVector<E2, Sz> \
> expr_type; \
return XprVector<expr_type, Sz>(expr_type(lhs, rhs)); \
}
TVMET_IMPLEMENT_MACRO(add) // per se element wise
TVMET_IMPLEMENT_MACRO(sub) // per se element wise
TVMET_IMPLEMENT_MACRO(mul) // per se element wise
namespace element_wise {
TVMET_IMPLEMENT_MACRO(div) // not defined for vectors
}
#undef TVMET_IMPLEMENT_MACRO
/*
* function(XprVector<E, Sz>, POD)
* function(POD, XprVector<E, Sz>)
* Note: - operations +,-,*,/ are per se element wise
*/
#define TVMET_IMPLEMENT_MACRO(NAME, POD) \
template<class E, int Sz> \
inline \
XprVector< \
XprBinOp< \
Fcnl_##NAME< typename E::value_type, POD >, \
XprVector<E, Sz>, \
XprLiteral< POD > \
>, \
Sz \
> \
NAME (const XprVector<E, Sz>& lhs, POD rhs) { \
typedef XprBinOp< \
Fcnl_##NAME< typename E::value_type, POD >, \
XprVector<E, Sz>, \
XprLiteral< POD > \
> expr_type; \
return XprVector<expr_type, Sz>( \
expr_type(lhs, XprLiteral< POD >(rhs))); \
} \
\
template<class E, int Sz> \
inline \
XprVector< \
XprBinOp< \
Fcnl_##NAME< POD, typename E::value_type>, \
XprLiteral< POD >, \
XprVector<E, Sz> \
>, \
Sz \
> \
NAME (POD lhs, const XprVector<E, Sz>& rhs) { \
typedef XprBinOp< \
Fcnl_##NAME< POD, typename E::value_type>, \
XprLiteral< POD >, \
XprVector<E, Sz> \
> expr_type; \
return XprVector<expr_type, Sz>( \
expr_type(XprLiteral< POD >(lhs), rhs)); \
}
TVMET_IMPLEMENT_MACRO(add, int)
TVMET_IMPLEMENT_MACRO(sub, int)
TVMET_IMPLEMENT_MACRO(mul, int)
TVMET_IMPLEMENT_MACRO(div, int)
#if defined(TVMET_HAVE_LONG_LONG)
TVMET_IMPLEMENT_MACRO(add, long long int)
TVMET_IMPLEMENT_MACRO(sub, long long int)
TVMET_IMPLEMENT_MACRO(mul, long long int)
TVMET_IMPLEMENT_MACRO(div, long long int)
#endif
TVMET_IMPLEMENT_MACRO(add, float)
TVMET_IMPLEMENT_MACRO(sub, float)
TVMET_IMPLEMENT_MACRO(mul, float)
TVMET_IMPLEMENT_MACRO(div, float)
TVMET_IMPLEMENT_MACRO(add, double)
TVMET_IMPLEMENT_MACRO(sub, double)
TVMET_IMPLEMENT_MACRO(mul, double)
TVMET_IMPLEMENT_MACRO(div, double)
#if defined(TVMET_HAVE_LONG_DOUBLE)
TVMET_IMPLEMENT_MACRO(add, long double)
TVMET_IMPLEMENT_MACRO(sub, long double)
TVMET_IMPLEMENT_MACRO(mul, long double)
TVMET_IMPLEMENT_MACRO(div, long double)
#endif
#undef TVMET_IMPLEMENT_MACRO
#if defined(TVMET_HAVE_COMPLEX)
/*
* function(XprMatrix<E, Rows, Cols>, complex<T>)
* function(complex<T>, XprMatrix<E, Rows, Cols>)
* Note: - operations +,-,*,/ are per se element wise
* \todo type promotion
*/
#define TVMET_IMPLEMENT_MACRO(NAME) \
template<class E, int Sz, class T> \
inline \
XprVector< \
XprBinOp< \
Fcnl_##NAME< typename E::value_type, std::complex<T> >, \
XprVector<E, Sz>, \
XprLiteral< std::complex<T> > \
>, \
Sz \
> \
NAME (const XprVector<E, Sz>& lhs, const std::complex<T>& rhs) { \
typedef XprBinOp< \
Fcnl_##NAME< typename E::value_type, std::complex<T> >, \
XprVector<E, Sz>, \
XprLiteral< std::complex<T> > \
> expr_type; \
return XprVector<expr_type, Sz>( \
expr_type(lhs, XprLiteral< std::complex<T> >(rhs))); \
} \
\
template<class E, int Sz, class T> \
inline \
XprVector< \
XprBinOp< \
Fcnl_##NAME< std::complex<T>, typename E::value_type>, \
XprLiteral< std::complex<T> >, \
XprVector<E, Sz> \
>, \
Sz \
> \
NAME (const std::complex<T>& lhs, const XprVector<E, Sz>& rhs) { \
typedef XprBinOp< \
Fcnl_##NAME< std::complex<T>, typename E::value_type>, \
XprLiteral< std::complex<T> >, \
XprVector<E, Sz> \
> expr_type; \
return XprVector<expr_type, Sz>( \
expr_type(XprLiteral< std::complex<T> >(lhs), rhs)); \
}
TVMET_IMPLEMENT_MACRO(add)
TVMET_IMPLEMENT_MACRO(sub)
TVMET_IMPLEMENT_MACRO(mul)
TVMET_IMPLEMENT_MACRO(div)
#undef TVMET_IMPLEMENT_MACRO
#endif // defined(TVMET_HAVE_COMPLEX)
/*++++++++++++++++++++++++++++++++++++++++++++++++++++++++
* vector specific functions
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++*/
/**
* \fn sum(const XprVector<E, Sz>& v)
* \brief Compute the sum of the vector expression.
* \ingroup _unary_function
*
* Simply compute the sum of the given vector as:
* \f[
* \sum_{i = 0}^{Sz-1} v[i]
* \f]
*/
template<class E, int Sz>
inline
typename NumericTraits<typename E::value_type>::sum_type
sum(const XprVector<E, Sz>& v) {
return meta::Vector<Sz>::sum(v);
}
/**
* \fn product(const XprVector<E, Sz>& v)
* \brief Compute the product of the vector elements.
* \ingroup _unary_function
*
* Simply computer the product of the given vector expression as:
* \f[
* \prod_{i = 0}^{Sz - 1} v[i]
* \f]
*/
template<class E, int Sz>
inline
typename NumericTraits<typename E::value_type>::sum_type
product(const XprVector<E, Sz>& v) {
return meta::Vector<Sz>::product(v);
}
/**
* \fn dot(const XprVector<E1, Sz>& lhs, const XprVector<E2, Sz>& rhs)
* \brief Compute the dot/inner product
* \ingroup _binary_function
*
* Compute the dot product as:
* \f[
* \sum_{i = 0}^{Sz - 1} ( lhs[i] * rhs[i] )
* \f]
* where lhs is a column vector and rhs is a row vector, both vectors
* have the same dimension.
*/
template<class E1, class E2, int Sz>
inline
typename PromoteTraits<
typename E1::value_type,
typename E2::value_type
>::value_type
dot(const XprVector<E1, Sz>& lhs, const XprVector<E2, Sz>& rhs) {
return meta::Vector<Sz>::dot(lhs, rhs);
}
/**
* \fn dot(const Vector<T, Sz>& lhs, const XprVector<E, Sz>& rhs)
* \brief Compute the dot/inner product
* \ingroup _binary_function
*
* Compute the dot product as:
* \f[
* \sum_{i = 0}^{Sz - 1} ( lhs[i] * rhs[i] )
* \f]
* where lhs is a column vector and rhs is a row vector, both vectors
* have the same dimension.
*/
template<class T, class E, int Sz>
inline
typename PromoteTraits<T, typename E::value_type>::value_type
dot(const Vector<T, Sz>& lhs, const XprVector<E, Sz>& rhs) {
return meta::Vector<Sz>::dot(lhs, rhs);
}
/**
* \fn dot(const XprVector<E, Sz>& lhs, const Vector<T, Sz>& rhs)
* \brief Compute the dot/inner product
* \ingroup _binary_function
*
* Compute the dot product as:
* \f[
* \sum_{i = 0}^{Sz - 1} ( lhs[i] * rhs[i] )
* \f]
* where lhs is a column vector and rhs is a row vector, both vectors
* have the same dimension.
*/
template<class E, class T, int Sz>
inline
typename PromoteTraits<T, typename E::value_type>::value_type
dot(const XprVector<E, Sz>& lhs, const Vector<T, Sz>& rhs) {
return meta::Vector<Sz>::dot(lhs, rhs);
}
/**
* \fn cross(const XprVector<E1, 3>& lhs, const XprVector<E2, 3>& rhs)
* \brief Compute the cross/outer product
* \ingroup _binary_function
* \note working only for vectors of size = 3
* \todo Implement vector outer product as ET and MT, returning a XprVector
*/
template<class E1, class E2>
inline
Vector<
typename PromoteTraits<
typename E1::value_type,
typename E2::value_type
>::value_type,
3
>
cross(const XprVector<E1, 3>& lhs, const XprVector<E2, 3>& rhs) {
typedef typename PromoteTraits<
typename E1::value_type,
typename E2::value_type
>::value_type value_type;
return Vector<value_type, 3>(lhs(1)*rhs(2) - rhs(1)*lhs(2),
rhs(0)*lhs(2) - lhs(0)*rhs(2),
lhs(0)*rhs(1) - rhs(0)*lhs(1));
}
/**
* \fn cross(const XprVector<E, 3>& lhs, const Vector<T, 3>& rhs)
* \brief Compute the cross/outer product
* \ingroup _binary_function
* \note working only for vectors of size = 3
* \todo Implement vector outer product as ET and MT, returning a XprVector
*/
template<class E, class T>
inline
Vector<
typename PromoteTraits<T, typename E::value_type>::value_type, 3>
cross(const XprVector<E, 3>& lhs, const Vector<T, 3>& rhs) {
typedef typename PromoteTraits<
typename E::value_type, T>::value_type value_type;
return Vector<value_type, 3>(lhs(1)*rhs(2) - rhs(1)*lhs(2),
rhs(0)*lhs(2) - lhs(0)*rhs(2),
lhs(0)*rhs(1) - rhs(0)*lhs(1));
}
/**
* \fn cross(const Vector<T, 3>& lhs, const XprVector<E, 3>& rhs)
* \brief Compute the cross/outer product
* \ingroup _binary_function
* \note working only for vectors of size = 3
* \todo Implement vector outer product as ET and MT, returning a XprVector
*/
template<class T1, class E2>
inline
Vector<
typename PromoteTraits<T1, typename E2::value_type>::value_type, 3>
cross(const Vector<T1, 3>& lhs, const XprVector<E2, 3>& rhs) {
typedef typename PromoteTraits<
typename E2::value_type, T1>::value_type value_type;
return Vector<value_type, 3>(lhs(1)*rhs(2) - rhs(1)*lhs(2),
rhs(0)*lhs(2) - lhs(0)*rhs(2),
lhs(0)*rhs(1) - rhs(0)*lhs(1));
}
/**
* \fn norm1(const XprVector<E, Sz>& v)
* \brief The \f$l_1\f$ norm of a vector expression.
* \ingroup _unary_function
* The norm of any vector is just the square root of the dot product of
* a vector with itself, or
*
* \f[
* |Vector<T, Sz> v| = |v| = \sum_{i=0}^{Sz-1}\,|v[i]|
* \f]
*/
template<class E, int Sz>
inline
typename NumericTraits<typename E::value_type>::sum_type
norm1(const XprVector<E, Sz>& v) {
return sum(abs(v));
}
/**
* \fn norm2(const XprVector<E, Sz>& v)
* \brief The euklidian norm (or \f$l_2\f$ norm) of a vector expression.
* \ingroup _unary_function
* The norm of any vector is just the square root of the dot product of
* a vector with itself, or
*
* \f[
* |Vector<T, Sz> v| = |v| = \sqrt{ \sum_{i=0}^{Sz-1}\,v[i]^2 }
* \f]
*
* \note The internal cast for Vector<int> avoids warnings on sqrt.
*/
template<class E, int Sz>
inline
typename NumericTraits<typename E::value_type>::sum_type
norm2(const XprVector<E, Sz>& v) {
typedef typename E::value_type value_type;
return static_cast<value_type>( std::sqrt(static_cast<value_type>(dot(v, v))) );
}
/**
* \fn normalize(const XprVector<E, Sz>& v)
* \brief Normalize the given vector expression.
* \ingroup _unary_function
* \sa norm2
*
* using the equation:
* \f[
* \frac{Vector<T, Sz> v}{\sqrt{ \sum_{i=0}^{Sz-1}\,v[i]^2 }}
* \f]
*/
template<class E, int Sz>
inline
XprVector<
XprBinOp<
Fcnl_div<typename E::value_type, typename E::value_type>,
XprVector<E, Sz>,
XprLiteral<typename E::value_type>
>,
Sz
>
normalize(const XprVector<E, Sz>& v) {
typedef typename E::value_type value_type;
typedef XprBinOp<
Fcnl_div<value_type, value_type>,
XprVector<E, Sz>,
XprLiteral<value_type>
> expr_type;
return XprVector<expr_type, Sz>(
expr_type(v, XprLiteral< value_type >(norm2(v))));
}
} // namespace tvmet
#endif // TVMET_XPR_VECTOR_FUNCTIONS_H
// Local Variables:
// mode:C++
// End:
|
