ConstrainedSolver.hh 14.1 KB
Newer Older
Henrik Zimmer's avatar
Henrik Zimmer committed
1
2
/*===========================================================================*\
 *                                                                           *
Henrik Zimmer's avatar
Henrik Zimmer committed
3
 *                               CoMISo                                      *
Henrik Zimmer's avatar
Henrik Zimmer committed
4
 *      Copyright (C) 2008-2009 by Computer Graphics Group, RWTH Aachen      *
Henrik Zimmer's avatar
Henrik Zimmer committed
5
 *                           www.rwth-graphics.de                            *
Henrik Zimmer's avatar
Henrik Zimmer committed
6
 *                                                                           *
Henrik Zimmer's avatar
Henrik Zimmer committed
7
8
 *---------------------------------------------------------------------------* 
 *  This file is part of CoMISo.                                             *
Henrik Zimmer's avatar
Henrik Zimmer committed
9
 *                                                                           *
Henrik Zimmer's avatar
Henrik Zimmer committed
10
11
12
13
 *  CoMISo 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 3 of the License, or        *
 *  (at your option) any later version.                                      *
Henrik Zimmer's avatar
Henrik Zimmer committed
14
 *                                                                           *
Henrik Zimmer's avatar
Henrik Zimmer committed
15
16
17
 *  CoMISo 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            *
Henrik Zimmer's avatar
Henrik Zimmer committed
18
 *  GNU General Public License for more details.                             *
Henrik Zimmer's avatar
Henrik Zimmer committed
19
 *                                                                           *
Henrik Zimmer's avatar
Henrik Zimmer committed
20
21
 *  You should have received a copy of the GNU General Public License        *
 *  along with CoMISo.  If not, see <http://www.gnu.org/licenses/>.          *
Henrik Zimmer's avatar
Henrik Zimmer committed
22
23
 *                                                                           *
\*===========================================================================*/ 
Henrik Zimmer's avatar
Henrik Zimmer committed
24
25


26
27
28
29
30
31
32
//=============================================================================
//
//  CLASS ConstrainedSolver
//
//=============================================================================


33
34
#ifndef COMISO_CONSTRAINEDSOLVER_HH
#define COMISO_CONSTRAINEDSOLVER_HH
35
36
37


//== INCLUDES =================================================================
Henrik Zimmer's avatar
Henrik Zimmer committed
38
#include <CoMISo/Config/CoMISoDefines.hh>
39
40
41
42
43
44
45
46
47
48
49

#include "GMM_Tools.hh"
#include "MISolver.hh"
#include <vector>

//== FORWARDDECLARATIONS ======================================================

//== DEFINES ==================================================================
#define ROUND(x) ((x)<0?int((x)-0.5):int((x)+0.5))
//== NAMESPACES ===============================================================

50
namespace COMISO {
51
52
53
54
55
56
57
58
59
60
61
62
63
64
//== CLASS DEFINITION =========================================================

/** \class ConstrainedSolver ConstrainedSolver.hh <ACG/.../ConstrainedSolver.hh>

  Takes a linear (symmetric) system of equations and a set of linear constraints and solves it.
 */

class COMISODLLEXPORT ConstrainedSolver
{
public:
  typedef gmm::csc_matrix<double>  CSCMatrix;


  /// default Constructor
Henrik Zimmer's avatar
   
Henrik Zimmer committed
65
66
67
  /** _do_gcd specifies if a greatest common devisor correction should be used when no (+-)1-coefficient is found*/
  ConstrainedSolver( bool _do_gcd = true): do_gcd_(_do_gcd)
  { epsilon_ = 1e-8; epsilon_squared_ = 1e-16; noisy_ = 1; }
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

  /// Destructor
  ~ConstrainedSolver() { }

/** @name Contrained solvers
 * Functions to solve constrained linear systems of the form Ax=b (stemming from quadratic energies). 
 * The constraints can be linear constraints of the form \f$ x_1*c_1+ \cdots +x_n*c_n=c \f$ as well as integer constraints \f$x_i\in \mathbf{Z}\f$. 
 * The system is then solved with these constraints in mind. For solving the system the Mixed-Integer Solver \a MISolver is used. 
 */
/*@{*/

/// Quadratic matrix constrained solver
/**  
  *  Takes a system of the form Ax=b, a constraint matrix C and a set of variables _to_round to be rounded to integers. \f$ A\in \mathbf{R}^{n\times n}\f$
  *  @param _constraints row matrix with rows of the form \f$ [c_1, c_2, \cdots, c_n, c_{n+1}] \f$ corresponding to the linear equation \f$ c_1*x_1+\cdots+c_n*x_n + c_{n+1}=0 \f$.
  *  @param _A nxn-dimensional column matrix of the system 
  *  @param _x n-dimensional variable vector
  *  @param _rhs n-dimensional right hand side.
  *  @param _idx_to_round indices i of variables x_i that shall be rounded
  *  @param _reg_factor regularization factor. Helps unstable, low rank system to become solvable. Adds \f$ \_reg\_factor*mean(trace(_A))*Id \f$ to A.
  *  @param _show_miso_settings should the (QT) dialog of the Mixed-Integer solver pop up?
  *  @param _show_timings shall some timings be printed?
  */
  template<class RMatrixT, class CMatrixT, class VectorT, class VectorIT >
  void solve(
      RMatrixT& _constraints,
      CMatrixT& _A, 
      VectorT&  _x,
      VectorT&  _rhs,
      VectorIT& _idx_to_round,
      double    _reg_factor = 0.0,
      bool      _show_miso_settings = true,
      bool      _show_timings = true );

David Bommes's avatar
David Bommes committed
102
103
104
105
106
107
108
109
110
111
112
113
  // const version of above function
  template<class RMatrixT, class CMatrixT, class VectorT, class VectorIT >
  void solve_const(
      const RMatrixT& _constraints,
      const CMatrixT& _A, 
            VectorT&  _x,
      const VectorT&  _rhs,
      const VectorIT& _idx_to_round,
            double    _reg_factor = 0.0,
            bool      _show_miso_settings = true,
            bool      _show_timings = true );

114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135

/// Non-Quadratic matrix constrained solver
/**  
  *  Same as above, but performs the elimination of the constraints directly on the B matrix of \f$ x^\top B^\top Bx \f$, where B has m rows (equations) and (n+1) columns \f$ [x_1, x_2, \dots, \x_n, -rhs] \f$. \note This function might be more efficient in some cases, but generally the solver for the quadratic matrix above is a safer bet. Needs further testing.
  *  \note Internally the \f$ A=B^\top B \f$ matrix is formed.
  *  @param _constraints row matrix with rows of the form \f$ [c_1, c_2, \cdots, c_n, c_{n+1}] \f$ corresponding to the linear equation \f$ c_1*x_1+\cdots+c_n*x_n + c_{n+1}=0 \f$.
  *  @param _B mx(n+1)-dimensional column matrix of the system 
  *  @param _x n-dimensional variable vector
  *  @param _idx_to_round indices i of variables x_i that shall be rounded
  *  @param _reg_factor regularization factor. Helps unstable, low rank system to become solvable.
  *  @param _show_miso_settings should the (QT) dialog of the Mixed-Integer solver pop up?
  *  @param _show_timings shall some timings be printed?
  */
  template<class RMatrixT, class VectorT, class VectorIT >
  void solve(
      RMatrixT& _constraints,
      RMatrixT& _B, 
      VectorT&  _x,
      VectorIT& _idx_to_round,
      double    _reg_factor = 0.0,
      bool      _show_miso_settings = true,
      bool      _show_timings = true );
David Bommes's avatar
David Bommes committed
136
137
138
139
140
141
142
143
144
145
146
147

  // const version of above function
  template<class RMatrixT, class VectorT, class VectorIT >
  void solve_const(
      RMatrixT& _constraints,
      RMatrixT& _B, 
      VectorT&  _x,
      VectorIT& _idx_to_round,
      double    _reg_factor = 0.0,
      bool      _show_miso_settings = true,
      bool      _show_timings = true );

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
/*@}*/

/** @name Eliminate constraints
 * Functions to eliminate (or integrate) linear constraints from an equation system. These functions are used internally by the \a solve functions.
 */
/*@{*/

/// Make constraints independent
/**  
  *  This function performs a Gauss elimination on the constraint matrix making the constraints easier to eliminate. 
  *  \note A certain amount of independence of the constraints is assumed.
  *  \note contradicting constraints will be ignored.
  *  \warning care must be taken when non-trivial constraints occur where some of the variables contain integer-variables (to be rounded) as the optimal result might not always occur.
  *  @param _constraints  row matrix with constraints
  *  @param _idx_to_round indices of variables to be rounded (these must be considered.)
  *  @param _c_elim the "returned" vector of variable indices and the order in which the can be eliminated.
  */
  template<class RMatrixT, class VectorIT >
  void make_constraints_independent(
      RMatrixT&         _constraints,
			VectorIT&         _idx_to_round,
			std::vector<int>& _c_elim );

/// Eliminate constraints on a factored matrix B
/**  
  *  \note Constraints are assumed to have been made independent by \a make_constraints_independent.
  *  @param _constraints row matrix with constraints (n+1 columns) 
  *  @param _B system row matrix mx(n+1)
  *  @param _idx_to_round indices to be rounded
  *  @param _c_elim the indices of the variables to be eliminated.
  *  @param _new_idx the created re-indexing map. new_idx[i] = -1 means x_i eliminated, new_idx[i] = j means x_i is now at index j.
  *  @param _Bcol resulting (smaller) column matrix to be used for future computations. (e.g. convert to CSC and solve)
  */
  template<class SVector1T, class SVector2T, class VectorIT, class SVector3T>
  void eliminate_constraints(
      gmm::row_matrix<SVector1T>& _constraints,
			gmm::row_matrix<SVector2T>& _B, 
			VectorIT&                   _idx_to_round,
			std::vector<int>&           _c_elim,
			std::vector<int>&           _new_idx,
			gmm::col_matrix<SVector3T>& _Bcol);

/// Eliminate constraints on a quadratic matrix A
/**  
  *  \note Constraints are assumed to have been made independent by \a make_constraints_independent.
  *  \note _x must have correct size (same as _rhs)
  *  @param _constraints row matrix with constraints (n+1 columns) 
  *  @param _A system row matrix nxn)
  *  @param _x variable vector
  *  @param _rhs right hand side
  *  @param _idx_to_round indices to be rounded
  *  @param _c_elim the indices of the variables to be eliminated.
  *  @param _new_idx the created re-indexing map. new_idx[i] = -1 means x_i eliminated, new_idx[i] = j means x_i is now at index j.
  *  @param _Acsc resulting (smaller) column (csc) matrix to be used for future computations.
  */
 
  template<class SVector1T, class SVector2T, class VectorIT, class CSCMatrixT>
  void eliminate_constraints(
      gmm::row_matrix<SVector1T>& _constraints,
      gmm::col_matrix<SVector2T>& _A, 
      std::vector<double>&        _x, 
      std::vector<double>&        _rhs, 
      VectorIT&                   _idx_to_round,
      std::vector<int>&           _c_elim,
      std::vector<int>&           _new_idx,
      CSCMatrixT&                 _Acsc);

/// Restore a solution vector to the un-eliminated size
/**  
  *  @param _constraints row matrix with constraints (n+1 columns) 
  *  @param _x solution vector to reduced/eliminated system (result will also be written here)
  *  @param _c_elim vector of eliminated indices 
  *  @param _new_idx re-indexing vector
  */
 
  template<class RMatrixT, class VectorT >
  void restore_eliminated_vars( RMatrixT&         _constraints,
				VectorT&          _x,
				std::vector<int>& _c_elim,
				std::vector<int>& _new_idx);


/*@}*/

232
  /// Set numerical epsilon for valid constraint coefficient
233
  void set_epsilon( double _epsilon) { epsilon_ = _epsilon; epsilon_squared_ = epsilon_*epsilon_;}
234

235
236
237
  /// Set noise-level (how much std output is given) 0 basically none, 1 important stuff (warning/timing, is default), 2+ not so important
  void set_noisy( int _noisy) { noisy_ = _noisy;}

238
239
240
241
242
243
244
245
246
247
248
/** @name Verify the result.
 * Functions to verify the result of the constrained solver. Are the constraints met, are the correct variables correctly rounded ...
 */
/*@{*/


  template<class RMatrixT, class CMatrixT, class VectorT>
  double verify_constrained_system( 
				   const RMatrixT& _conditions,
				   const CMatrixT& _A,
				   const VectorT&  _x,
David Bommes's avatar
David Bommes committed
249
250
				   const VectorT&  _rhs,
				   double          _eps = 1e-9);
251
252
253
254
255
256
257

  template<class RMatrixT, class CMatrixT, class VectorT, class VectorIT>
  double verify_constrained_system_round( 
					 const RMatrixT& _conditions,
					 const CMatrixT& _A,
					 const VectorT&  _x,
					 const VectorT&  _rhs,
David Bommes's avatar
David Bommes committed
258
259
					 const VectorIT& _idx_to_round,
					 double          _eps = 1e-9);
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

  template<class RMatrixT, class VectorT, class VectorIT>
  void verify_mi_factored( const RMatrixT& _conditions,
			   const RMatrixT& _B, 
			   const VectorT&  _x,
			   const VectorIT& _idx_to_round );
/*@}*/

private:

  template<class RowT, class MatrixT>
  void add_row( int       _row_i,
		double    _coeff,
		RowT      _row, 
		MatrixT&  _mat );

  template<class RowT, class RMatrixT, class CMatrixT>
  void add_row_simultaneously( int       _row_i,
			       double    _coeff,
			       RowT      _row, 
			       RMatrixT& _rmat,
			       CMatrixT& _cmat );


  template<class CMatrixT, class VectorT, class VectorIT>
  double setup_and_solve_system( CMatrixT& _B,
			       VectorT&  _x,
			       VectorIT& _idx_to_round,
			       double    _reg_factor,
			       bool      _show_miso_settings);


  // warning: order of replacement not the same as in _columns (internal sort)
  template<class CMatrixT>
  void eliminate_columns( CMatrixT& _M,
			  const std::vector< int >& _columns);

Henrik Zimmer's avatar
   
Henrik Zimmer committed
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
  inline int gcd( int _a, int _b)
  {
    while( _b != 0)
    {
      int t(_b);
      _b = _a%_b;
      _a = t;
    }
    return _a;
  }

  int find_gcd(std::vector<int>& _v_gcd, int& _n_ints);
  // TODO if no gcd correction was possible, at least use a variable divisible by 2 as new elim_j (to avoid in-exactness e.g. 1/3)
  template<class RMatrixT>
  bool update_constraint_gcd( RMatrixT& _constraints, 
                              int _row_i,
                              int& _elim_j,
                              std::vector<int>& _v_gcd,
                              int& _n_ints);

317
318
319
320
321
322
323
private:

  /// Copy constructor (not used)
  ConstrainedSolver(const ConstrainedSolver& _rhs);

  /// Assignment operator (not used)
  ConstrainedSolver& operator=(const ConstrainedSolver& _rhs);
324
325

  double epsilon_;
326
  double epsilon_squared_;
327
  int    noisy_;
Henrik Zimmer's avatar
   
Henrik Zimmer committed
328
  bool   do_gcd_;
329
330
331
332
};


//=============================================================================
333
} // namespace COMISO
334
//=============================================================================
335
336
#if defined(INCLUDE_TEMPLATES) && !defined(COMISO_CONSTRAINEDSOLVER_C)
#define COMISO_CONSTRAINEDSOLVER_TEMPLATES
337
338
339
#include "ConstrainedSolverT.cc"
#endif
//=============================================================================
340
#endif // COMISO_CONSTRAINEDSOLVER_HH defined
341
342
//=============================================================================