This file is indexed.

/usr/include/dune/common/fmatrix.hh is in libdune-common-dev 2.2.1-2.

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
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
// -*- tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=8 sw=2 sts=2:
// $Id: fmatrix.hh 6785 2012-05-31 22:07:47Z sander $
#ifndef DUNE_FMATRIX_HH
#define DUNE_FMATRIX_HH

#include <cmath>
#include <cstddef>
#include <iostream>

#include <dune/common/misc.hh>
#include <dune/common/exceptions.hh>
#include <dune/common/fvector.hh>
#include <dune/common/densematrix.hh>
#include <dune/common/precision.hh>
#include <dune/common/static_assert.hh>

namespace Dune
{
   
/** 
    @addtogroup DenseMatVec
    @{
*/

/*! \file

\brief  Implements a matrix constructed from a given type
  representing a field and compile-time given number of rows and columns.
*/

  template< class K, int ROWS, int COLS > class FieldMatrix;

  template< class K, int ROWS, int COLS >
  struct DenseMatVecTraits< FieldMatrix<K,ROWS,COLS> >
  {
    typedef FieldMatrix<K,ROWS,COLS> derived_type;

    // each row is implemented by a field vector
    typedef FieldVector<K,COLS> row_type;

    typedef row_type &row_reference;
    typedef const row_type &const_row_reference;

    typedef Dune::array<row_type,ROWS> container_type;
    typedef K value_type;
    typedef typename container_type::size_type size_type;
  };
  
  template< class K, int ROWS, int COLS >
  struct FieldTraits< FieldMatrix<K,ROWS,COLS> >
  {
    typedef typename FieldTraits<K>::field_type field_type;
    typedef typename FieldTraits<K>::real_type real_type;
  };

  /** 
      @brief A dense n x m matrix.

  Matrices represent linear maps from a vector space V to a vector space W.
       This class represents such a linear map by storing a two-dimensional
       %array of numbers of a given field type K. The number of rows and
       columns is given at compile time.
  */
  template<class K, int ROWS, int COLS>
  class FieldMatrix : public DenseMatrix< FieldMatrix<K,ROWS,COLS> >
  {
    Dune::array< FieldVector<K,COLS>, ROWS > _data;
    typedef DenseMatrix< FieldMatrix<K,ROWS,COLS> > Base;
  public:

    //! export size
    enum {
      //! The number of rows.
      rows = ROWS, 
      //! The number of columns.
      cols = COLS
    };

    typedef typename Base::size_type size_type;
    typedef typename Base::row_type row_type;
   
    typedef typename Base::row_reference row_reference;
    typedef typename Base::const_row_reference const_row_reference;

    //===== constructors
    /** \brief Default constructor
     */
    FieldMatrix () {}

    /** \brief Constructor initializing the whole matrix with a scalar
     */
    explicit FieldMatrix (const K& k)
    {
      for (size_type i=0; i<rows; i++) _data[i] = k;
    }

    template<typename T>
    explicit FieldMatrix (const T& t)
    {
      DenseMatrixAssigner<Conversion<T,K>::exists>::assign(*this, t);
    }
    
    //===== assignment
    using Base::operator=;

    // To be removed!
#if 0
    //! Multiplies M from the left to this matrix
    FieldMatrix& leftmultiply (const FieldMatrix<K,rows,rows>& M)
    {
      FieldMatrix<K,rows,cols> C(*this);
      
      for (size_type i=0; i<rows; i++)
        for (size_type j=0; j<cols; j++) {
          (*this)[i][j] = 0;
          for (size_type k=0; k<rows; k++)
            (*this)[i][j] += M[i][k]*C[k][j];
        }
      
      return *this;
    }
#endif
 
    //! Multiplies M from the left to this matrix, this matrix is not modified
    template<int l>
    FieldMatrix<K,l,cols> leftmultiplyany (const FieldMatrix<K,l,rows>& M) const
    {
      FieldMatrix<K,l,cols> C;
      
      for (size_type i=0; i<l; i++) {
        for (size_type j=0; j<cols; j++) {
          C[i][j] = 0;
          for (size_type k=0; k<rows; k++)
            C[i][j] += M[i][k]*(*this)[k][j];
        }
      }
      return C;
    }

    //! Multiplies M from the right to this matrix
    FieldMatrix& rightmultiply (const FieldMatrix<K,cols,cols>& M)
    {
      FieldMatrix<K,rows,cols> C(*this);
      
      for (size_type i=0; i<rows; i++)
        for (size_type j=0; j<cols; j++) {
          (*this)[i][j] = 0;
          for (size_type k=0; k<cols; k++)
            (*this)[i][j] += C[i][k]*M[k][j];
        }
      return *this;
    }

    //! Multiplies M from the right to this matrix, this matrix is not modified
    template<int l>
    FieldMatrix<K,rows,l> rightmultiplyany (const FieldMatrix<K,cols,l>& M) const
    {
      FieldMatrix<K,rows,l> C;
      
      for (size_type i=0; i<rows; i++) {
        for (size_type j=0; j<l; j++) {
          C[i][j] = 0;
          for (size_type k=0; k<cols; k++)
            C[i][j] += (*this)[i][k]*M[k][j];
        }
      }
      return C;
    }
    
    // make this thing a matrix
    size_type mat_rows() const { return ROWS; }
    size_type mat_cols() const { return COLS; }

    row_reference mat_access ( size_type i )
    {
      assert(i < ROWS);
      return _data[i];
    }

    const_row_reference mat_access ( size_type i ) const
    {
      assert(i < ROWS);
      return _data[i];
    }
  };

#ifndef DOXYGEN // hide specialization
  /** \brief Special type for 1x1 matrices
   */
  template<class K>
  class FieldMatrix<K,1,1> : public DenseMatrix< FieldMatrix<K,1,1> >
  {
    FieldVector<K,1> _data;
    typedef DenseMatrix< FieldMatrix<K,1,1> > Base;
  public:
    // standard constructor and everything is sufficient ...
    
    //===== type definitions and constants
    
    //! The type used for index access and size operations
    typedef typename Base::size_type size_type;
    
    //! We are at the leaf of the block recursion
    enum {
      //! The number of block levels we contain.
      //! This is always one for this type.
      blocklevel = 1
    };

    typedef typename Base::row_type row_type;
   
    typedef typename Base::row_reference row_reference;
    typedef typename Base::const_row_reference const_row_reference;

    //! export size
    enum {
      //! \brief The number of rows.
      //! This is always one for this type.
      rows = 1,
      //! \brief The number of columns.
      //! This is always one for this type.
      cols = 1
    };

    //===== constructors
    /** \brief Default constructor
     */
    FieldMatrix () {}
    
    /** \brief Constructor initializing the whole matrix with a scalar
     */
    FieldMatrix (const K& k)
    {
      _data[0] = k;
    }
    template<typename T>
    FieldMatrix(const T& t)
    {
      DenseMatrixAssigner<Conversion<T,K>::exists>::assign(*this, t);
    }
    
    //===== solve

    //! Multiplies M from the left to this matrix, this matrix is not modified
    template<int l>
    FieldMatrix<K,l,1> leftmultiplyany (const FieldMatrix<K,l,1>& M) const
    {
      FieldMatrix<K,l,1> C;
      for (size_type j=0; j<l; j++)
        C[j][0] = M[j][0]*(*this)[0][0];
      return C;
    }

    //! left multiplication
    FieldMatrix& rightmultiply (const FieldMatrix& M)
    {
      _data[0] *= M[0][0];
      return *this;
    }

    //! Multiplies M from the right to this matrix, this matrix is not modified
    template<int l>
    FieldMatrix<K,1,l> rightmultiplyany (const FieldMatrix<K,1,l>& M) const
    {
      FieldMatrix<K,1,l> C;
      
      for (size_type j=0; j<l; j++)
        C[0][j] = M[0][j]*_data[0];
      return C;
    }

    // make this thing a matrix
    size_type mat_rows() const { return 1; }
    size_type mat_cols() const { return 1; }

    row_reference mat_access ( size_type i )
    {
      assert(i == 0);
      return _data;
    }

    const_row_reference mat_access ( size_type i ) const
    {
      assert(i == 0);
      return _data;
    }

    //! add scalar
    FieldMatrix& operator+= (const K& k)
    {
      _data[0] += k;
      return (*this);
    }

    //! subtract scalar
    FieldMatrix& operator-= (const K& k)
    {
      _data[0] -= k;
      return (*this);
    }
    
    //! multiplication with scalar
    FieldMatrix& operator*= (const K& k)
    {
      _data[0] *= k;
      return (*this);
    }

    //! division by scalar
    FieldMatrix& operator/= (const K& k)
    {
      _data[0] /= k;
      return (*this);
    }

    //===== conversion operator

    operator K () const { return _data[0]; }

  };

  /** \brief Sends the matrix to an output stream */
  template<typename K>
  std::ostream& operator<< (std::ostream& s, const FieldMatrix<K,1,1>& a)
  {
    s << a[0][0];
    return s;
  }

#endif // DOXYGEN

namespace FMatrixHelp {

//! invert scalar without changing the original matrix 
template <typename K>
static inline K invertMatrix (const FieldMatrix<K,1,1> &matrix, FieldMatrix<K,1,1> &inverse)
{
  inverse[0][0] = 1.0/matrix[0][0];
  return matrix[0][0];
}

//! invert scalar without changing the original matrix 
template <typename K>
static inline K invertMatrix_retTransposed (const FieldMatrix<K,1,1> &matrix, FieldMatrix<K,1,1> &inverse)
{
  return invertMatrix(matrix,inverse); 
}


//! invert 2x2 Matrix without changing the original matrix
template <typename K>
static inline K invertMatrix (const FieldMatrix<K,2,2> &matrix, FieldMatrix<K,2,2> &inverse)
{
  // code generated by maple 
  K det = (matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]);
  K det_1 = 1.0/det;
  inverse[0][0] =   matrix[1][1] * det_1;
  inverse[0][1] = - matrix[0][1] * det_1;
  inverse[1][0] = - matrix[1][0] * det_1;
  inverse[1][1] =   matrix[0][0] * det_1;
  return det;
}

//! invert 2x2 Matrix without changing the original matrix
//! return transposed matrix 
template <typename K>
static inline K invertMatrix_retTransposed (const FieldMatrix<K,2,2> &matrix, FieldMatrix<K,2,2> &inverse)
{
  // code generated by maple 
  K det = (matrix[0][0]*matrix[1][1] - matrix[0][1]*matrix[1][0]);
  K det_1 = 1.0/det;
  inverse[0][0] =   matrix[1][1] * det_1;
  inverse[1][0] = - matrix[0][1] * det_1;
  inverse[0][1] = - matrix[1][0] * det_1;
  inverse[1][1] =   matrix[0][0] * det_1;
  return det;
}

//! invert 3x3 Matrix without changing the original matrix
template <typename K>
static inline K invertMatrix (const FieldMatrix<K,3,3> &matrix, FieldMatrix<K,3,3> &inverse)
{
  // code generated by maple 
  K t4  = matrix[0][0] * matrix[1][1];
  K t6  = matrix[0][0] * matrix[1][2];
  K t8  = matrix[0][1] * matrix[1][0];
  K t10 = matrix[0][2] * matrix[1][0];
  K t12 = matrix[0][1] * matrix[2][0];
  K t14 = matrix[0][2] * matrix[2][0];

  K det = (t4*matrix[2][2]-t6*matrix[2][1]-t8*matrix[2][2]+
           t10*matrix[2][1]+t12*matrix[1][2]-t14*matrix[1][1]);
  K t17 = 1.0/det;

  inverse[0][0] =  (matrix[1][1] * matrix[2][2] - matrix[1][2] * matrix[2][1])*t17;
  inverse[0][1] = -(matrix[0][1] * matrix[2][2] - matrix[0][2] * matrix[2][1])*t17;
  inverse[0][2] =  (matrix[0][1] * matrix[1][2] - matrix[0][2] * matrix[1][1])*t17;
  inverse[1][0] = -(matrix[1][0] * matrix[2][2] - matrix[1][2] * matrix[2][0])*t17;
  inverse[1][1] =  (matrix[0][0] * matrix[2][2] - t14) * t17;
  inverse[1][2] = -(t6-t10) * t17;
  inverse[2][0] =  (matrix[1][0] * matrix[2][1] - matrix[1][1] * matrix[2][0]) * t17;
  inverse[2][1] = -(matrix[0][0] * matrix[2][1] - t12) * t17;
  inverse[2][2] =  (t4-t8) * t17;

  return det;
}

//! invert 3x3 Matrix without changing the original matrix
template <typename K>
static inline K invertMatrix_retTransposed (const FieldMatrix<K,3,3> &matrix, FieldMatrix<K,3,3> &inverse)
{
  // code generated by maple 
  K t4  = matrix[0][0] * matrix[1][1];
  K t6  = matrix[0][0] * matrix[1][2];
  K t8  = matrix[0][1] * matrix[1][0];
  K t10 = matrix[0][2] * matrix[1][0];
  K t12 = matrix[0][1] * matrix[2][0];
  K t14 = matrix[0][2] * matrix[2][0];

  K det = (t4*matrix[2][2]-t6*matrix[2][1]-t8*matrix[2][2]+
           t10*matrix[2][1]+t12*matrix[1][2]-t14*matrix[1][1]);
  K t17 = 1.0/det;

  inverse[0][0] =  (matrix[1][1] * matrix[2][2] - matrix[1][2] * matrix[2][1])*t17;
  inverse[1][0] = -(matrix[0][1] * matrix[2][2] - matrix[0][2] * matrix[2][1])*t17;
  inverse[2][0] =  (matrix[0][1] * matrix[1][2] - matrix[0][2] * matrix[1][1])*t17;
  inverse[0][1] = -(matrix[1][0] * matrix[2][2] - matrix[1][2] * matrix[2][0])*t17;
  inverse[1][1] =  (matrix[0][0] * matrix[2][2] - t14) * t17;
  inverse[2][1] = -(t6-t10) * t17;
  inverse[0][2] =  (matrix[1][0] * matrix[2][1] - matrix[1][1] * matrix[2][0]) * t17;
  inverse[1][2] = -(matrix[0][0] * matrix[2][1] - t12) * t17;
  inverse[2][2] =  (t4-t8) * t17;

  return det;
}

//! calculates ret = A * B
template< class K, int m, int n, int p >
static inline void multMatrix ( const FieldMatrix< K, m, n > &A,
                                const FieldMatrix< K, n, p > &B,
                                FieldMatrix< K, m, p > &ret )
{
  typedef typename FieldMatrix< K, m, p > :: size_type size_type;

  for( size_type i = 0; i < m; ++i )
  {
    for( size_type j = 0; j < p; ++j )
    {
      ret[ i ][ j ] = K( 0 );
      for( size_type k = 0; k < n; ++k )
        ret[ i ][ j ] += A[ i ][ k ] * B[ k ][ j ];
    }
  }
}

//! calculates ret= A_t*A
template <typename K, int rows, int cols>
static inline void multTransposedMatrix(const FieldMatrix<K,rows,cols> &matrix, FieldMatrix<K,cols,cols>& ret)
{
  typedef typename FieldMatrix<K,rows,cols>::size_type size_type;
  
  for(size_type i=0; i<cols; i++)
    for(size_type j=0; j<cols; j++)
    {
      ret[i][j]=0.0;
      for(size_type k=0; k<rows; k++)
        ret[i][j]+=matrix[k][i]*matrix[k][j];
    }
}

#if 0
//! calculates ret = matrix * x 
template <typename K, int rows, int cols>
static inline void multAssign(const FieldMatrix<K,rows,cols> &matrix, const FieldVector<K,cols> & x, FieldVector<K,rows> & ret) 
{
  typedef typename FieldMatrix<K,rows,cols>::size_type size_type;
  
  for(size_type i=0; i<rows; ++i)
  {
    ret[i] = 0.0;
    for(size_type j=0; j<cols; ++j)
    {
      ret[i] += matrix[i][j]*x[j];
    }
  }
}
#else
using Dune::DenseMatrixHelp::multAssign;
#endif

//! calculates ret = matrix^T * x 
template <typename K, int rows, int cols>
static inline void multAssignTransposed( const FieldMatrix<K,rows,cols> &matrix, const FieldVector<K,rows> & x, FieldVector<K,cols> & ret) 
{
  typedef typename FieldMatrix<K,rows,cols>::size_type size_type;
  
  for(size_type i=0; i<cols; ++i)
  {
    ret[i] = 0.0;
    for(size_type j=0; j<rows; ++j)
      ret[i] += matrix[j][i]*x[j];
  }
}

//! calculates ret = matrix * x 
template <typename K, int rows, int cols>
static inline FieldVector<K,rows> mult(const FieldMatrix<K,rows,cols> &matrix, const FieldVector<K,cols> & x) 
{
  FieldVector<K,rows> ret;
  multAssign(matrix,x,ret);
  return ret;
}

//! calculates ret = matrix^T * x 
template <typename K, int rows, int cols>
static inline FieldVector<K,cols> multTransposed(const FieldMatrix<K,rows,cols> &matrix, const FieldVector<K,rows> & x) 
{
  FieldVector<K,cols> ret;
  multAssignTransposed( matrix, x, ret );
  return ret; 
}

} // end namespace FMatrixHelp 

/** @} end documentation */

} // end namespace

#include "fmatrixev.hh"
#endif