lily/ineq-constrained-qp.cc

   1 /*
   2   ineq-constrained-qp.cc -- implement Ineq_constrained_qp
   3
   4   source file of the GNU LilyPond music typesetter
   5
   6   (c) 1996, 1997--1998 Han-Wen Nienhuys <hanwen@cs.uu.nl>
   7 */
   8 #include "ineq-constrained-qp.hh"
   9 #include "qlpsolve.hh"
  10 #include "debug.hh"
  11 #include "choleski.hh"
  12 #include "main.hh"
  13
  14 /*
  15   May be this also should go into a library
  16  */
  17
  18 const int MAXITER=100;          // qlpsolve.hh
  19
  20 const int MAXDEGEN=5;
  21
  22 /*
  23   assume x (idx) == value, and adjust constraints, lin and quad accordingly
  24
  25   TODO: add const_term
  26   */
  27 void
  28 Ineq_constrained_qp::eliminate_var (int idx, Real value)
  29 {
  30   Vector row (quad_.row (idx));
  31   row*= value;
  32
  33   quad_.delete_row (idx);
  34
  35   quad_.delete_column (idx);
  36
  37   lin_.del (idx);
  38   row.del (idx);
  39   lin_ +=row ;
  40
  41   for (int i=0; i < cons_.size(); i++)
  42     {
  43       consrhs_[i] -= cons_[i](idx) *value;
  44       cons_[i].del (idx);
  45     }
  46 }
  47
  48 void
  49 Ineq_constrained_qp::add_inequality_cons (Vector c, double r)
  50 {
  51   cons_.push (c);
  52   consrhs_.push (r);
  53 }
  54
  55 Ineq_constrained_qp::Ineq_constrained_qp (int novars):
  56   quad_ (novars),
  57   lin_ (novars),
  58   const_term_ (0.0)
  59 {
  60 }
  61
  62 void
  63 Ineq_constrained_qp::OK() const
  64 {
  65 #if !defined (NDEBUG) && defined (PARANOID)
  66   assert (cons_.size() == consrhs_.size ());
  67   Matrix Qdif= quad_ - quad_.transposed();
  68   assert (Qdif.norm()/quad_.norm () < EPS);
  69 #endif
  70 }
  71
  72
  73 Real
  74 Ineq_constrained_qp::eval (Vector v)
  75 {
  76   return v * quad_ * v + lin_ * v + const_term_;
  77 }
  78
  79
  80 int
  81 min_elt_index (Vector v)
  82 {
  83   Real m=infinity_f;
  84   int idx=-1;
  85   for (int i = 0; i < v.dim(); i++)
  86     {
  87       if (v (i) < m)
  88         {
  89           idx = i;
  90           m = v (i);
  91         }
  92       assert (v (i) <= infinity_f);
  93     }
  94   return idx;
  95 }
  96
  97
  98 /**the numerical solving. Mordecai Avriel, Nonlinear Programming: analysis and methods (1976)
  99   Prentice Hall.
 100
 101   Section 13.3
 102
 103   This is a "projected gradient" algorithm. Starting from a point x
 104   the next point is found in a direction determined by projecting
 105   the gradient onto the active constraints.  (well, not really the
 106   gradient. The optimal solution obeying the active constraints is
 107   tried. This is why H = Q^-1 in initialisation))
 108
 109
 110   */
 111 Vector
 112 Ineq_constrained_qp::constraint_solve (Vector start) const
 113 {
 114   if (!dim())
 115     return Vector (0);
 116
 117   Active_constraints act (this);
 118   act.OK();
 119
 120
 121   Vector x (start);
 122   Vector gradient=quad_*x+lin_;
 123
 124
 125   //    Real fvalue = x*quad_*x/2 + lin*x + const_term;// it's no use.
 126   Vector last_gradient (gradient);
 127   int iterations=0;
 128
 129   while (iterations++ < MAXITER && act.degenerate_count_i_ < MAXDEGEN)
 130     {
 131       //#ifdef PARANOID
 132       if (experimental_features_global_b)
 133         assert_solution (x);
 134       //#endif
 135
 136       Vector direction= - act.find_active_optimum (gradient);
 137
 138       DOUT << "gradient "<< gradient<< "\ndirection " << direction<< '\n';
 139
 140       if (direction.norm() > EPS)
 141         {
 142           DOUT << act.status() << '\n';
 143
 144           Real unbounded_alfa = 1.0;
 145           Real minalf = unbounded_alfa;
 146
 147           Inactive_iter minidx (act);
 148
 149
 150           /*
 151             we know the optimum on this "hyperplane". Check if we
 152             bump into the edges of the simplex
 153             */
 154
 155           for (Inactive_iter ia (act); ia.ok(); ia++)
 156             {
 157               Real dot = ia.vec() * direction;
 158               if (dot >= 0)
 159                 continue;
 160
 161
 162               Real numerator = ia.rhs () - ia.vec()*x;
 163               if (numerator >= 0)
 164                 {
 165                   if (numerator > EPS)
 166                     {
 167                       warning (_f ("Ineq_constrained_qp::solve (): Constraint off by %f", numerator));
 168                       act.degenerate_count_i_ ++;
 169                     }
 170                   minalf = -numerator;
 171                   minidx = ia;
 172                   break;
 173                 }
 174
 175               Real alfa = numerator / dot;
 176
 177
 178               if (minalf > alfa)
 179                 {
 180                   minidx = ia;
 181                   minalf = alfa;
 182                 }
 183             }
 184
 185           Real optimal_step = minalf;
 186
 187           Vector deltax = direction * optimal_step;
 188           x += deltax;
 189           gradient += optimal_step * (quad_ * deltax);
 190
 191           DOUT << "step = " << optimal_step << " (|dx| = " <<
 192             to_str (deltax.norm()) << ")\n";
 193
 194           if (minalf < unbounded_alfa)
 195             {
 196               /* bumped into an edge. try again, in smaller space. */
 197               act.add_constraint (minidx.idx());
 198               DOUT << "adding cons "<< minidx.idx () << '\n';
 199               continue;
 200             }
 201           /*ASSERT: we are at the optimal solution for this "plane"*/
 202         }
 203
 204       Vector lagrange_mult=act.get_lagrange (gradient);
 205       int m= min_elt_index (lagrange_mult);
 206
 207       if (m>=0 && lagrange_mult (m) > 0)
 208         {
 209           break;                // optimal sol.
 210         }
 211       else if (m<0)
 212         {
 213           assert (gradient.norm() < EPS) ;
 214
 215           break;
 216         }
 217
 218       DOUT << "dropping cons " << m << '\n';
 219       act.drop_constraint (m);
 220     }
 221   if (iterations >= MAXITER)
 222     WARN << _ ("didn't converge!") << '\n';
 223   if (act.degenerate_count_i_ >= MAXDEGEN)
 224     WARN << _ ("Too much degeneracy. ") << '\n';
 225   DOUT <<  ": found " << x << " in " << iterations <<" iterations\n";
 226   assert_solution (x);
 227   return x;
 228 }
 229
 230
 231 Vector
 232 Ineq_constrained_qp::solve (Vector start) const
 233 {
 234   /* no hassle if no constraints*/
 235   if (! cons_.size())
 236     {
 237       Choleski_decomposition chol (quad_);
 238       return - chol.solve (lin_);
 239     }
 240   else
 241     {
 242       return constraint_solve (start);
 243     }
 244 }
 245
 246 int
 247 Ineq_constrained_qp::dim () const
 248 {
 249   return lin_.dim();
 250 }
 251
 252
 253
 254
 255 void
 256 Ineq_constrained_qp::assert_solution (Vector sol) const
 257 {
 258   bool sol_b=true;
 259
 260   for (int i=0; sol_b && i < cons_.size(); i++)
 261     {
 262       Real R=cons_[i] * sol- consrhs_[i];
 263       if (R> -EPS)
 264         sol_b = false;
 265     }
 266 }
 267
 268 void
 269 Ineq_constrained_qp::print() const
 270 {
 271 #ifndef NPRINT
 272   DOUT << "Quad " << quad_;
 273   DOUT << "lin " << lin_ << '\n'
 274        << "const " << const_term_<< '\n';
 275   for (int i=0; i < cons_.size(); i++)
 276     {
 277       DOUT << "constraint["<<i<<"]: " << cons_[i] << " >= " << consrhs_[i];
 278       DOUT << '\n';
 279     }
 280 #endif
 281 }