This file is indexed.

/usr/include/rheolef/tensor.h is in librheolef-dev 6.7-6.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  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
# ifndef _RHEOLEF_TENSOR_H
# define _RHEOLEF_TENSOR_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef 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 General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
/// 
/// =========================================================================

/*Class:tensor
NAME: @code{tensor} - a N*N tensor, N=1,2,3
@cindex tensor
@clindex tensor
@clindex point
@clindex field
SYNOPSYS:
@noindent
The @code{tensor} class defines a 3*3 tensor, as the value of
a tensorial valued field. Basic algebra with scalars, vectors
of R^3 (i.e. the @code{point} class) and @code{tensor} objects
are supported.
AUTHOR: Pierre.Saramito@imag.fr
DATE:   9 october 2003
End:
*/

#include "rheolef/point.h"
namespace rheolef {

//<tensor:
template<class T>
class tensor_basic {
    public:

	typedef size_t size_type;
	typedef T      element_type;
	typedef T      float_type;

// allocators:

	tensor_basic (const T& init_val = 0);
	tensor_basic (T x[3][3]);
	tensor_basic (const tensor_basic<T>& a);
	static tensor_basic<T> eye (size_type d = 3);

#ifdef _RHEOLEF_HAVE_STD_INITIALIZER_LIST
        tensor_basic (const std::initializer_list<std::initializer_list<T> >& il);
#endif // _RHEOLEF_HAVE_STD_INITIALIZER_LIST

// affectation:

	tensor_basic<T>& operator= (const tensor_basic<T>& a);
	tensor_basic<T>& operator= (const T& val);

// modifiers:

	void fill (const T& init_val);
	void reset ();
	void set_row    (const point_basic<T>& r, size_t i, size_t d = 3);
	void set_column (const point_basic<T>& c, size_t j, size_t d = 3);

// accessors:

	T& operator()(size_type i, size_type j);
	const T& operator()(size_type i, size_type j) const;
	point_basic<T>  row(size_type i) const;
	point_basic<T>  col(size_type i) const;
	size_t nrow() const; // = 3, for template matrix compatibility
	size_t ncol() const;

// inputs/outputs:

	std::ostream& put (std::ostream& s, size_type d = 3) const;
	std::istream& get (std::istream&);

// algebra:

	bool operator== (const tensor_basic<T>&) const;
	bool operator!= (const tensor_basic<T>& b) const { return ! operator== (b); }
	const tensor_basic<T>& operator+ () const { return *this; }
	tensor_basic<T> operator- () const;
        tensor_basic<T> operator+ (const tensor_basic<T>& b) const;
        tensor_basic<T> operator- (const tensor_basic<T>& b) const;
        tensor_basic<T> operator* (const tensor_basic<T>& b) const;
	tensor_basic<T> operator* (const T& k) const;
	tensor_basic<T> operator/ (const T& k) const; 
	point_basic<T>  operator* (const point_basic<T>&) const;
        point_basic<T>  trans_mult (const point_basic<T>& x) const;

// metric and geometric transformations:

	T determinant (size_type d = 3) const;

// spectral:
	// eigenvalues & eigenvectors:
	// a = q*d*q^T
	// a may be symmetric
	// where q=(q1,q2,q3) are eigenvectors in rows (othonormal matrix)
	// and   d=(d1,d2,d3) are eigenvalues, sorted in decreasing order d1 >= d2 >= d3
	// return d
	point_basic<T> eig (tensor_basic<T>& q, size_t dim = 3) const;
	point_basic<T> eig (size_t dim = 3) const;

	// singular value decomposition:
	// a = u*s*v^T
	// a can be unsymmetric
	// where u=(u1,u2,u3) are left pseudo-eigenvectors in rows (othonormal matrix)
	//       v=(v1,v2,v3) are right pseudo-eigenvectors in rows (othonormal matrix)
	// and   s=(s1,s2,s3) are eigenvalues, sorted in decreasing order s1 >= s2 >= s3
	// return s
	point_basic<T> svd (tensor_basic<T>& u, tensor_basic<T>& v, size_t dim = 3) const;

// data:
	T _x[3][3];
};
typedef tensor_basic<Float> tensor;

// algebra (cont.)

template <class U>
point_basic<U>  operator* (const point_basic<U>& yt, const tensor_basic<U>& a);
template <class U>
tensor_basic<U> trans (const tensor_basic<U>& a, size_t d = 3);
template <class U>
void prod (const tensor_basic<U>& a, const tensor_basic<U>& b, tensor_basic<U>& result,
	size_t di=3, size_t dj=3, size_t dk=3);
// tr(a) = a00 + a11 + a22
template <class U>
U tr (const tensor_basic<U>& a, size_t d=3); 
template <class U>
U ddot (const tensor_basic<U>&, const tensor_basic<U>&);
// a = u otimes v <==> aij = ui*vj
template <class U>
tensor_basic<U> otimes (const point_basic<U>& u, const point_basic<U>& v, size_t d=3);
template <class U>
tensor_basic<U> inv  (const tensor_basic<U>& a, size_t d = 3);
template <class U>
tensor_basic<U> diag (const point_basic<U>& d);
template <class U>
point_basic<U> diag (const tensor_basic<U>& a);
template <class U>
U determinant (const tensor_basic<U>& A, size_t d = 3);
template <class U>
bool invert_3x3 (const tensor_basic<U>& A, tensor_basic<U>& result);

// nonlinear algebra:
template<class T>
tensor_basic<T> exp (const tensor_basic<T>& a, size_t d = 3);

// inputs/outputs:
template<class T>
inline
std::istream& operator>> (std::istream& in, tensor_basic<T>& a)
{
    return a.get (in);
}
template<class T>
inline
std::ostream& operator<< (std::ostream& out, const tensor_basic<T>& a)
{
    return a.put (out); 
}
// t += a otimes b
template<class T>
void cumul_otimes (tensor_basic<T>& t, const point_basic<T>& a, const point_basic<T>& b, size_t na = 3);
template<class T>
void cumul_otimes (tensor_basic<T>& t, const point_basic<T>& a, const point_basic<T>& b, size_t na, size_t nb);
//>tensor:

// -----------------------------------------------------------------------
// inlined
// -----------------------------------------------------------------------
template<class T> struct  float_traits<tensor_basic<T> > { typedef typename float_traits<T>::type type; };
template<class T> struct scalar_traits<tensor_basic<T> > { typedef T type; };

template<class T>
inline
void
tensor_basic<T>::fill (const T& init_val)
{ 
    for (size_type i = 0; i < 3; i++) for (size_type j = 0; j < 3; j++)
      _x[i][j] = init_val;
}
template<class T>
inline
void
tensor_basic<T>::reset ()
{
    fill (0);
}
template<class T>
inline
tensor_basic<T>::tensor_basic (const T& init_val)
{ 
    fill (init_val);
}
template<class T>
inline
tensor_basic<T>::tensor_basic (T x[3][3])
{
    for (size_type i = 0; i < 3; i++) for (size_type j = 0; j < 3; j++)
      _x[i][j] = x[i][j];
}
template<class T>
inline
tensor_basic<T>::tensor_basic (const tensor_basic<T>& a)
{
    for (size_type i = 0; i < 3; i++) for (size_type j = 0; j < 3; j++)
      _x[i][j] = a._x[i][j];
}
#ifdef _RHEOLEF_HAVE_STD_INITIALIZER_LIST
template<class T>
tensor_basic<T>::tensor_basic (const std::initializer_list<std::initializer_list<T> >& il) : _x() {
#ifdef _RHEOLEF_HAVE_STD_INITIALIZER_ITERATOR
    typedef typename std::initializer_list<std::initializer_list<T> >::const_iterator const_iterator;
    typedef typename std::initializer_list<T>::const_iterator                         const_iterator_row;
#else // _RHEOLEF_HAVE_STD_INITIALIZER_ITERATOR
    typedef const std::initializer_list<T>* const_iterator;
    typedef const T*                        const_iterator_row;
#endif // _RHEOLEF_HAVE_STD_INITIALIZER_ITERATOR
    fill (T());
    check_macro (il.size() <= 3, "unexpected initializer list size=" << il.size() << " > 3");
    size_type i = 0;
    for (const_iterator iter = il.begin(); iter != il.end(); ++iter, ++i) {
      const std::initializer_list<T>& row = *iter;
      check_macro (row.size() <= 3, "unexpected initializer list size=" << row.size() << " > 3");
      size_type j = 0;
      for (const_iterator_row jter = row.begin(); jter != row.end(); ++jter, ++j) {
        _x[i][j] = *jter;
      }
    }
}
#endif // _RHEOLEF_HAVE_STD_INITIALIZER_LIST
template<class T>
inline
tensor_basic<T>&
tensor_basic<T>::operator= (const tensor_basic<T>& a)
{
    for (size_type i = 0; i < 3; i++) for (size_type j = 0; j < 3; j++)
      _x[i][j] = a._x[i][j];
    return *this;
}
template<class T>
inline
tensor_basic<T>&
tensor_basic<T>::operator= (const T& val)
{
    for (size_type i = 0; i < 3; i++) for (size_type j = 0; j < 3; j++)
      _x[i][j] = val;
    return *this;
}
template<class T>
inline
size_t
tensor_basic<T>::nrow() const
{
  return 3;
}
template<class T>
inline
size_t
tensor_basic<T>::ncol() const
{
  return 3;
}
template<class T>
inline
T&
tensor_basic<T>::operator()(size_type i, size_type j)  
{
    return _x[i%3][j%3];
}
template<class T>
inline
const T&
tensor_basic<T>::operator()(size_type i, size_type j) const
{
    return _x[i%3][j%3];
}
template <class T, class U>
inline
typename
std::enable_if<
  details::is_rheolef_arithmetic<U>::value
 ,tensor_basic<T>
>::type
operator* (const U& k, const tensor_basic<T>& a) 
{
    return a*k;
}
template<class T>
inline
tensor_basic<T>
tensor_basic<T>::operator/ (const T& k) const
{
    return operator* (1./k);
}
template<class T>
inline
point_basic<T>
tensor_basic<T>::trans_mult (const point_basic<T>& x) const
{
    return x*(*this);
}
template<class T>
inline
void
cumul_otimes (tensor_basic<T>& t, const point_basic<T>& a, const point_basic<T>& b, size_t n)
{
    cumul_otimes (t, a, b, n, n);
}
template<class T>
inline
tensor_basic<T>
otimes (const point_basic<T>& u, const point_basic<T>& v, size_t d)
{
    tensor_basic<T> a;
    cumul_otimes (a, u, v, d, d);
    return a;
}
template<class T>
inline
T
determinant (const tensor_basic<T>& A, size_t d)
{ 
    return A.determinant (d);
}
template<class T>
inline
tensor_basic<T>
diag (const point_basic<T>& d)
{
  tensor_basic<T> a;
  a(0,0) = d[0];
  a(1,1) = d[1];
  a(2,2) = d[2];
  return a;
}
template<class T>
inline
point_basic<T>
diag (const tensor_basic<T>& a)
{
  point_basic<T> d;
  d[0] = a(0,0);
  d[1] = a(1,1);
  d[2] = a(2,2);
  return d;
}
template <class T>
inline
T
tr (const tensor_basic<T>& a, size_t d) {
  T sum = 0;
  for (size_t i = 0; i < d; i++) sum += a(i,i);
  return sum;
} 
template<class T>
inline
void
tensor_basic<T>::set_column (const point_basic<T>& c, size_t j, size_t d)
{
  for (size_t i = 0; i < d; i++)
    operator()(i,j) = c[i];
}
template<class T>
inline
void
tensor_basic<T>::set_row (const point_basic<T>& r, size_t i, size_t d)
{
  for (size_t j = 0; j < d; j++)
    operator()(i,j) = r[j];
}
template<class T>
inline
tensor_basic<T>
tensor_basic<T>::eye (size_type d)
{
  tensor_basic<T> I;
  for (size_t i = 0; i < d; i++)
    I(i,i) = 1;
  return I;
}
template <class T>
inline
T
norm2 (const tensor_basic<T>& a)
{
  return ddot(a,a);
}
template <class T>
inline
T
dist2 (const tensor_basic<T>& a, const tensor_basic<T>& b)
{
  return norm2(a-b);
}
template <class U>
inline
U
norm  (const tensor_basic<U>& a)
{
  return sqrt(norm2(a));
}
template <class U>
inline
U
dist (const tensor_basic<U>& a, const tensor_basic<U>& b)
{
  return norm(a-b);
}

}// namespace rheolef
# endif /* _RHEOLEF_TENSOR_H */