This file is indexed.

/usr/include/CLHEP/Matrix/Matrix.h is in libclhep-dev 2.1.4.1+dfsg-1.

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
// -*- C++ -*-
// CLASSDOC OFF
// ---------------------------------------------------------------------------
// CLASSDOC ON
//
// This file is a part of the CLHEP - a Class Library for High Energy Physics.
// 
// This is the definition of the HepMatrix class.
// 
// This software written by Nobu Katayama and Mike Smyth, Cornell University.
//
//
// .SS Usage
// The Matrix class does all the obvious things, in all the obvious ways.
// You declare a Matrix by saying
//
// .ft B
//       HepMatrix hm1(n, m);
//
//  To declare a Matrix as a copy of a Matrix hm2, say
//
// .ft B
//       HepMatrix hm1(hm2);
// or
// .ft B
//       HepMatrix hm1 = hm2;
// 
// You can declare initilizations of a Matrix, by giving it a third
// integer argument, either 0 or 1. 0 means initialize to 0, one means
// the identity matrix. If you do not give a third argument the memory
// is not initialized.
//
// .ft B
//       HepMatrix hm1(n, m, 1);
//
// ./"This code has been written by Mike Smyth, and the algorithms used are
// ./"described in the thesis "A Tracking Library for a Silicon Vertex Detector"
// ./"(Mike Smyth, Cornell University, June 1993).
// ./"This is file contains C++ stuff for doing things with Matrices.
// ./"To turn on bound checking, define MATRIX_BOUND_CHECK before including
// ./"this file.
// 
//  To find the number of rows or number of columns, say 
//
// .ft B
// nr = hm1.num_row();
//
// or
//
// .ft B
// nc = hm1.num_col();
//
// You can print a Matrix by
//
// .ft B
// cout << hm1;
//
//  You can add,
//  subtract, and multiply two Matrices.  You can multiply a Matrix by a
//  scalar, on the left or the right.  +=, *=, -= act in the obvious way.
//  hm1 *= hm2 is as hm1 = hm1*hm2. You can also divide by a scalar on the
//  right, or use /= to do the same thing.  
// 
//  You can read or write a Matrix element by saying
//
// .ft B
//  m(row, col) = blah. (1 <= row <= num_row(), 1 <= col <= num_col())
//
// .ft B
//  blah = m(row, col) ...
//
//  m(row, col) is inline, and by default does not do bound checking. 
//  If bound checking is desired, say #define MATRIX_BOUND_CHECK before
//  including matrix.h.
// 
//  You can also access the element using C subscripting operator []
//
// .ft B
//  m[row][col] = blah. (0 <= row < num_row(), 0 <= col < num_col())
//
// .ft B
//  blah = m[row][col] ...
//
//  m[row][col] is inline, and by default does not do bound checking. 
//  If bound checking is desired, say #define MATRIX_BOUND_CHECK before
//  including matrix.h. (Notice the difference in bases in two access
//  methods.) 
//
// .SS Comments on precision
//
//  The user would normally use "Matrix" class whose precision is the same
//  as the other classes of CLHEP (ThreeVec, for example). However, he/she
//  can explicitly choose Matrix (double) or MatrixF (float) if he/she wishes.
//  In the former case, include "Matrix.h." In the latter case, include either
//  "Matrix.h," or "MatrixF.h," or both. The only operators that can talk
//  to each other are the copy constructor and assignment operator.
//
// .ft B
//  Matrix d(3,4,HEP_MATRIX_IDENTITY);
//
// .ft B
//  MatrixF f;
//
// .ft B
//  f = d;
//
// .ft B
//  MatrixF g(d);
//
//  will convert from one to the other.
//
// .SS Other functions
//
// .ft B
//  mt = m.T();
//
//  returns the transpose of m. 
//
// .ft B
//  ms = hm2.sub(row_min, row_max, col_min, col_max);
//
//  returns the subMatrix.
//  hm2(row_min:row_max, col_min:col_max) in matlab terminology.
//  If instead you say
//
// .ft B
//  hm2.sub(row, col, hm1);
//
//  then the subMatrix
//  hm2(row:row+hm1.num_row()-1, col:col+hm1.num_col()-1) is replaced with hm1.
//
// .ft B
// md = dsum(hm1,hm2);
//
// returns the direct sum of the two matrices.
//
// Operations that do not have to be member functions or friends are listed
// towards the end of this man page.
//
//
// To invert a matrix, say
//
// .ft B
// minv = m.inverse(ierr);
//
// ierr will be non-zero if the matrix is singular.
//
// If you can overwrite the matrix, you can use the invert function to avoid
// two extra copies. Use
//
// .ft B
// m.invert(ierr);
//
// Many basic linear algebra functions such as QR decomposition are defined.
// In order to keep the header file a reasonable size, the functions are
// defined in MatrixLinear.h.
//
// 
// .ft B 
//  Note that Matrices run from (1,1) to (n, m), and [0][0] to
//  [n-1][m-1]. The users of the latter form should be careful about sub
//  functions.
//
// ./" The program that this class was orginally used with lots of small
// ./" Matrices.  It was very costly to malloc and free array space every
// ./" time a Matrix is needed.  So, a number of previously freed arrays are
// ./" kept around, and when needed again one of these array is used.  Right
// ./" now, a set of piles of arrays with row <= row_max and col <= col_max
// ./" are kept around.  The piles of kept Matrices can be easily changed.
// ./" Array mallocing and freeing are done only in new_m() and delete_m(),
// ./" so these are the only routines that need to be rewritten.
// 
//  You can do things thinking of a Matrix as a list of numbers.  
//
// .ft B
//  m = hm1.apply(HEP_MATRIX_ELEMENT (*f)(HEP_MATRIX_ELEMENT, int r, int c));
// 
//  applies f to every element of hm1 and places it in m.
//
// .SS See Also:
// SymMatrix[DF].h, GenMatrix[DF].h, DiagMatrix[DF].h Vector[DF].h
// MatrixLinear[DF].h 

#ifndef _Matrix_H_
#define _Matrix_H_

#ifdef GNUPRAGMA
#pragma interface
#endif

#include <vector>

#include "CLHEP/Matrix/defs.h"
#include "CLHEP/Matrix/GenMatrix.h"

namespace CLHEP {

class HepRandom;

class HepSymMatrix;
class HepDiagMatrix;
class HepVector;
class HepRotation;

/**
 * @author
 * @ingroup matrix
 */
class HepMatrix : public HepGenMatrix {
public:
   inline HepMatrix();
   // Default constructor. Gives 0 x 0 matrix. Another Matrix can be
   // assigned to it.

   HepMatrix(int p, int q);
   // Constructor. Gives an unitialized p x q matrix.
   HepMatrix(int p, int q, int i);
   // Constructor. Gives an initialized p x q matrix. 
   // If i=0, it is initialized to all 0. If i=1, the diagonal elements
   // are set to 1.0.

   HepMatrix(int p, int q, HepRandom &r);
   // Constructor with a Random object.

   HepMatrix(const HepMatrix &hm1);
   // Copy constructor.

   HepMatrix(const HepSymMatrix &);
   HepMatrix(const HepDiagMatrix &);
   HepMatrix(const HepVector &);
   // Constructors from SymMatrix, DiagMatrix and Vector.

   virtual ~HepMatrix();
   // Destructor.

   virtual int num_row() const;
   // Returns the number of rows.

   virtual int num_col() const;
   // Returns the number of columns.

   virtual const double & operator()(int row, int col) const;
   virtual double & operator()(int row, int col);
   // Read or write a matrix element. 
   // ** Note that the indexing starts from (1,1). **

   HepMatrix & operator *= (double t);
   // Multiply a Matrix by a floating number.

   HepMatrix & operator /= (double t); 
   // Divide a Matrix by a floating number.

   HepMatrix & operator += ( const HepMatrix &);
   HepMatrix & operator += ( const HepSymMatrix &);
   HepMatrix & operator += ( const HepDiagMatrix &);
   HepMatrix & operator += ( const HepVector &);
   HepMatrix & operator -= ( const HepMatrix &);
   HepMatrix & operator -= ( const HepSymMatrix &);
   HepMatrix & operator -= ( const HepDiagMatrix &);
   HepMatrix & operator -= ( const HepVector &);
   // Add or subtract a Matrix. 
   // When adding/subtracting Vector, Matrix must have num_col of one.

   HepMatrix & operator = ( const HepMatrix &);
   HepMatrix & operator = ( const HepSymMatrix &);
   HepMatrix & operator = ( const HepDiagMatrix &);
   HepMatrix & operator = ( const HepVector &);
   HepMatrix & operator = ( const HepRotation &);
   // Assignment operators.

   HepMatrix operator- () const;
   // unary minus, ie. flip the sign of each element.

   HepMatrix apply(double (*f)(double, int, int)) const;
   // Apply a function to all elements of the matrix.

   HepMatrix T() const;
   // Returns the transpose of a Matrix.

   HepMatrix sub(int min_row, int max_row, int min_col, int max_col) const;
   // Returns a sub matrix of a Matrix.
   // WARNING: rows and columns are numbered from 1
   void sub(int row, int col, const HepMatrix &hm1);
   // Sub matrix of this Matrix is replaced with hm1.
   // WARNING: rows and columns are numbered from 1

   friend inline void swap(HepMatrix &hm1, HepMatrix &hm2);
   // Swap hm1 with hm2.

   inline HepMatrix inverse(int& ierr) const;
   // Invert a Matrix. Matrix must be square and is not changed.
   // Returns ierr = 0 (zero) when successful, otherwise non-zero.

   virtual void invert(int& ierr);
   // Invert a Matrix. Matrix must be square.
   // N.B. the contents of the matrix are replaced by the inverse.
   // Returns ierr = 0 (zero) when successful, otherwise non-zero. 
   // This method has less overhead then inverse().

   inline void invert();
   // Invert a matrix. Throw std::runtime_error on failure.

   inline HepMatrix inverse() const;
   // Invert a matrix. Throw std::runtime_error on failure. 


   double determinant() const;
   // calculate the determinant of the matrix.

   double trace() const;
   // calculate the trace of the matrix (sum of diagonal elements).

   class HepMatrix_row {
   public:
      inline HepMatrix_row(HepMatrix&,int);
      double & operator[](int);
   private:
      HepMatrix& _a;
      int _r;
   };
   class HepMatrix_row_const {
   public:
      inline HepMatrix_row_const (const HepMatrix&,int);
      const double & operator[](int) const;
   private:
      const HepMatrix& _a;
      int _r;
   };
   // helper classes for implementing m[i][j]

   inline HepMatrix_row operator[] (int);
   inline const HepMatrix_row_const operator[] (int) const;
   // Read or write a matrix element.
   // While it may not look like it, you simply do m[i][j] to get an
   // element. 
   // ** Note that the indexing starts from [0][0]. **

protected:
   virtual  int num_size() const;
   virtual void invertHaywood4(int& ierr);
   virtual void invertHaywood5(int& ierr);
   virtual void invertHaywood6(int& ierr);

private:
   friend class HepMatrix_row;
   friend class HepMatrix_row_const;
   friend class HepVector;
   friend class HepSymMatrix;
   friend class HepDiagMatrix;
   // Friend classes.

   friend HepMatrix operator+(const HepMatrix &hm1, const HepMatrix &hm2);
   friend HepMatrix operator-(const HepMatrix &hm1, const HepMatrix &hm2);
   friend HepMatrix operator*(const HepMatrix &hm1, const HepMatrix &hm2);
   friend HepMatrix operator*(const HepMatrix &hm1, const HepSymMatrix &hm2);
   friend HepMatrix operator*(const HepMatrix &hm1, const HepDiagMatrix &hm2);
   friend HepMatrix operator*(const HepSymMatrix &hm1, const HepMatrix &hm2);
   friend HepMatrix operator*(const HepDiagMatrix &hm1, const HepMatrix &hm2);
   friend HepMatrix operator*(const HepVector &hm1, const HepMatrix &hm2);
   friend HepVector operator*(const HepMatrix &hm1, const HepVector &hm2);
   friend HepMatrix operator*(const HepSymMatrix &hm1, const HepSymMatrix &hm2);
   // Multiply a Matrix by a Matrix or Vector.

   friend HepVector solve(const HepMatrix &, const HepVector &);
   // solve the system of linear eq
   friend HepVector qr_solve(HepMatrix *, const HepVector &);
   friend HepMatrix qr_solve(HepMatrix *, const HepMatrix &b);
   friend void tridiagonal(HepSymMatrix *a,HepMatrix *hsm);
   friend void row_house(HepMatrix *,const HepMatrix &, double,
			 int, int, int, int);
   friend void row_house(HepMatrix *,const HepVector &, double,
			 int, int);
   friend void back_solve(const HepMatrix &R, HepVector *b);
   friend void back_solve(const HepMatrix &R, HepMatrix *b);
   friend void col_givens(HepMatrix *A, double c,
			  double s, int k1, int k2, 
			  int rowmin, int rowmax);
   //    Does a column Givens update.
   friend void row_givens(HepMatrix *A, double c,
			  double s, int k1, int k2, 
			  int colmin, int colmax);
   friend void col_house(HepMatrix *,const HepMatrix &, double,
			 int, int, int, int);
   friend HepVector house(const HepMatrix &a,int row,int col);
   friend void house_with_update(HepMatrix *a,int row,int col);
   friend void house_with_update(HepMatrix *a,HepMatrix *v,int row,int col);
   friend void house_with_update2(HepSymMatrix *a,HepMatrix *v,
				  int row,int col); 

   int dfact_matrix(double &det, int *ir);
   // factorize the matrix. If successful, the return code is 0. On
   // return, det is the determinant and ir[] is row-interchange
   // matrix. See CERNLIB's DFACT routine.

   int dfinv_matrix(int *ir);
   // invert the matrix. See CERNLIB DFINV.

#ifdef DISABLE_ALLOC
   std::vector<double > m;
#else
   std::vector<double,Alloc<double,25> > m;
#endif
   int nrow, ncol;
   int size_;
};

// Operations other than member functions for Matrix
// implemented in Matrix.cc and Matrix.icc (inline).

HepMatrix operator*(const HepMatrix &, const HepMatrix &);
HepMatrix operator*(double t, const HepMatrix &);
HepMatrix operator*(const HepMatrix &, double );
// Multiplication operators
// Note that m *= hm1 is always faster than m = m * hm1.

HepMatrix operator/(const HepMatrix &, double );
// m = hm1 / t. (m /= t is faster if you can use it.)

HepMatrix operator+(const HepMatrix &hm1, const HepMatrix &hm2);
// m = hm1 + hm2;
// Note that m += hm1 is always faster than m = m + hm1.

HepMatrix operator-(const HepMatrix &hm1, const HepMatrix &hm2);
// m = hm1 - hm2;
// Note that m -= hm1 is always faster than m = m - hm1.

HepMatrix dsum(const HepMatrix&, const HepMatrix&);
// Direct sum of two matrices. The direct sum of A and B is the matrix 
//        A 0
//        0 B

HepVector solve(const HepMatrix &, const HepVector &);
// solve the system of linear equations using LU decomposition.

std::ostream& operator<<(std::ostream &s, const HepMatrix &q);
// Read in, write out Matrix into a stream.
 
//
// Specialized linear algebra functions
//

HepVector qr_solve(const HepMatrix &A, const HepVector &b);
HepVector qr_solve(HepMatrix *A, const HepVector &b);
HepMatrix qr_solve(const HepMatrix &A, const HepMatrix &b);
HepMatrix qr_solve(HepMatrix *A, const HepMatrix &b);
// Works like backsolve, except matrix does not need to be upper
// triangular. For nonsquare matrix, it solves in the least square sense.

HepMatrix qr_inverse(const HepMatrix &A);
HepMatrix qr_inverse(HepMatrix *A);
// Finds the inverse of a matrix using QR decomposition.  Note, often what
// you really want is solve or backsolve, they can be much quicker than
// inverse in many calculations.


void qr_decomp(HepMatrix *A, HepMatrix *hsm);
HepMatrix qr_decomp(HepMatrix *A);
// Does a QR decomposition of a matrix.

void back_solve(const HepMatrix &R, HepVector *b);
void back_solve(const HepMatrix &R, HepMatrix *b);
// Solves R*x = b where R is upper triangular.  Also has a variation that
// solves a number of equations of this form in one step, where b is a matrix
// with each column a different vector. See also solve.

void col_house(HepMatrix *a, const HepMatrix &v, double vnormsq,
	       int row, int col, int row_start, int col_start);
void col_house(HepMatrix *a, const HepMatrix &v, int row, int col,
	       int row_start, int col_start);
// Does a column Householder update.

void col_givens(HepMatrix *A, double c, double s,
		int k1, int k2, int row_min=1, int row_max=0);
// do a column Givens update

void row_givens(HepMatrix *A, double c, double s,
		int k1, int k2, int col_min=1, int col_max=0);
// do a row Givens update

void givens(double a, double b, double *c, double *s);
// algorithm 5.1.5 in Golub and Van Loan

HepVector house(const HepMatrix &a, int row=1, int col=1);
// Returns a Householder vector to zero elements.

void house_with_update(HepMatrix *a, int row=1, int col=1);
void house_with_update(HepMatrix *a, HepMatrix *v, int row=1, int col=1);
// Finds and does Householder reflection on matrix.

void row_house(HepMatrix *a, const HepVector &v, double vnormsq,
	       int row=1, int col=1);
void row_house(HepMatrix *a, const HepMatrix &v, double vnormsq,
	       int row, int col, int row_start, int col_start);
void row_house(HepMatrix *a, const HepMatrix &v, int row, int col,
	       int row_start, int col_start);
// Does a row Householder update.

}  // namespace CLHEP

#ifdef ENABLE_BACKWARDS_COMPATIBILITY
//  backwards compatibility will be enabled ONLY in CLHEP 1.9
using namespace CLHEP;
#endif

#ifndef HEP_DEBUG_INLINE
#include "CLHEP/Matrix/Matrix.icc"
#endif

#endif /*_Matrix_H*/