lily/constrained-breaking.cc

   1 /*
   2   constrained-breaking.cc -- implement a line breaker that
   3   support limits on the number of systems
   4
   5   source file of the GNU LilyPond music typesetter
   6
   7   (c) 2006--2009 Joe Neeman <joeneeman@gmail.com>
   8 */
   9
  10 #include "constrained-breaking.hh"
  11
  12 #include "international.hh"
  13 #include "main.hh"
  14 #include "output-def.hh"
  15 #include "paper-column.hh"
  16 #include "paper-score.hh"
  17 #include "simple-spacer.hh"
  18 #include "system.hh"
  19 #include "warn.hh"
  20
  21 /*
  22   We use the following optimal substructure. Let W (A) be our weight function.
  23
  24   Let A_{k, n} = (a_{k, n, 1}, ... a_{k, n, k}) be the optimal set of line breaks
  25   for k systems and n potential breakpoints. a_{k, n, k} = n (it is the end of
  26   the piece)
  27
  28   Then A_{k+1, m} is contructed from
  29   min_ {k < j < m} ( W (A_{k, j} :: m) )
  30   where by A::m we denote appending m to the list A
  31
  32   Indices in the code:
  33
  34   The above algorithm makes it easy to end at a point before the end of the
  35   score (just find A_{k, m} for some m < breaks_.size () - 1). However, we must
  36   add information for starting at a point after the beginning. One constructor
  37   allows the specification of a list of starting columns, start_. We then have
  38   start_.size () different solution arrays. state_[i] is the array for the
  39   solution starting at column number start_[i].
  40
  41   The indices "start" and "end" refer to the index in the start_ array of the
  42   desired starting and ending columns.
  43
  44   each solution array looks like
  45    a_{1,1,1} a_{2,1,2} a_{3,1,3} . . .
  46        X     a_{2,2,2} a_{3,2,3} . . .
  47        X         X     a_{3,3,3} . . .
  48        .         .         .     .
  49        .         .         .       .
  50   where the X's mark invalid solutions (can't have more systems than
  51   breakpoints). Note that each value is of the form a_{x, n, x}. This is because
  52   a breakpoint of the form a_{x, n, x-1} will also be called a_{x-1, m, x-1} for
  53   some m < n. Each cell in the array stores the value of its m (ie. the
  54   ending breakpoint of the previous line) as "prev_".
  55
  56   For finding A_{sys, brk}, let "me" be the (sys_count, brk) cell in our
  57   solution array (state_[start][sys * rank + brk]).
  58
  59   Then A_{sys, brk} = A_{sys - 1, me.prev_} :: me
  60 */
  61
  62 /*
  63   start and sys here are indexed from 0.
  64   brk is indexed from starting_breakpoints_[start]
  65   (for brk, starting_breakpoints_[start] is the beginning
  66   of the piece; the smallest value we should ever see here is
  67   starting_breakpoints_[start] + 1) */
  68 bool
  69 Constrained_breaking::calc_subproblem (vsize start, vsize sys, vsize brk)
  70 {
  71   assert (sys < systems_);
  72   assert (start < start_.size ());
  73   assert (brk < breaks_.size ());
  74
  75   bool found_something = false;
  76   vsize start_col = starting_breakpoints_[start];
  77   Matrix<Constrained_break_node> &st = state_[start];
  78   vsize max_index = brk - start_col;
  79   for (vsize j=max_index; j-- > sys;)
  80     {
  81       if (0 == sys && j > 0)
  82         continue; /* the first line cannot have its first break after the beginning */
  83
  84       Line_details const &cur = lines_.at (brk, j + start_col);
  85       if (isinf (cur.force_))
  86         break;
  87
  88       Real prev_f = 0;
  89       Real prev_dem = 0;
  90
  91       if (sys > 0)
  92         {
  93           prev_f = st.at (j, sys-1).details_.force_;
  94           prev_dem = st.at (j, sys-1).demerits_;
  95         }
  96       if (isinf (prev_dem))
  97         continue;
  98
  99       Real dem = combine_demerits (cur.force_, prev_f) + prev_dem + cur.break_penalty_;
 100       Constrained_break_node &n = st.at (max_index, sys);
 101       if (dem < n.demerits_)
 102         {
 103           found_something = true;
 104           n.demerits_ = dem;
 105           n.details_ = cur;
 106           n.prev_ = j;
 107         }
 108     }
 109   return found_something;
 110 }
 111
 112
 113 Column_x_positions
 114 Constrained_breaking::space_line (vsize i, vsize j)
 115 {
 116   bool ragged_right = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
 117   bool ragged_last = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
 118   Column_x_positions col;
 119
 120   vector<Grob*> line (all_.begin () + breaks_[i],
 121                       all_.begin () + breaks_[j] + 1);
 122   Interval line_dims = line_dimensions_int (pscore_->layout (), i);
 123   bool last = j == breaks_.size () - 1;
 124   bool ragged = ragged_right || (last && ragged_last);
 125
 126   /* As a special case, if there is only one line in the score and ragged-right
 127      hasn't been specifically forbidden and the line is stretched, use
 128      ragged spacing. */
 129   if (last && i == 0
 130       && lines_.at (i, j).force_ >= 0
 131       && !scm_is_bool (pscore_->layout ()->c_variable ("ragged-right"))
 132       && !scm_is_bool (pscore_->layout ()->c_variable ("ragged-last")))
 133     ragged = true;
 134
 135   return get_line_configuration (line, line_dims[RIGHT] - line_dims[LEFT], line_dims[LEFT], ragged);
 136 }
 137
 138 void
 139 Constrained_breaking::resize (vsize systems)
 140 {
 141   systems_ = systems;
 142
 143   if (pscore_ && systems_ > valid_systems_)
 144     {
 145       for (vsize i = 0; i < state_.size (); i++)
 146         state_[i].resize (breaks_.size () - starting_breakpoints_[i], systems_, Constrained_break_node ());
 147
 148       /* fill out the matrices */
 149       for (vsize i = 0; i < state_.size (); i++)
 150         for (vsize j = valid_systems_; j < systems_; j++)
 151           for (vsize k = starting_breakpoints_[i] + j + 1; k < breaks_.size (); k++)
 152             if (!calc_subproblem (i, j, k))
 153               break; /* if we couldn't break this, it is too cramped already */
 154       valid_systems_ = systems_;
 155     }
 156 }
 157
 158 vector<Column_x_positions>
 159 Constrained_breaking::solve (vsize start, vsize end, vsize sys_count)
 160 {
 161   vsize start_brk = starting_breakpoints_[start];
 162   vsize end_brk = prepare_solution (start, end, sys_count);
 163
 164   Matrix<Constrained_break_node> const &st = state_[start];
 165   vector<Column_x_positions> ret;
 166
 167   /* find the first solution that satisfies constraints */
 168   for (vsize sys = sys_count-1; sys != VPOS; sys--)
 169     {
 170       for (vsize brk = end_brk; brk != VPOS; brk--)
 171         {
 172           if (!isinf (st.at (brk, sys).details_.force_))
 173             {
 174               if (brk != end_brk)
 175                 {
 176                   warning (_ ("cannot find line breaking that satisfies constraints" ));
 177                   ret.push_back (space_line (brk, end_brk));
 178                 }
 179               /* build up the good solution */
 180               for (vsize cur_sys = sys; cur_sys != VPOS; cur_sys--)
 181                 {
 182                   vsize prev_brk = st.at (brk, cur_sys).prev_;
 183                   assert (brk != VPOS);
 184                   ret.push_back (space_line (prev_brk + start_brk, brk + start_brk));
 185                   brk = prev_brk;
 186                 }
 187               reverse (ret);
 188               return ret;
 189             }
 190         }
 191     }
 192   /* if we get to here, just put everything on one line */
 193   warning (_ ("cannot find line breaking that satisfies constraints"));
 194   ret.push_back (space_line (0, end_brk));
 195   return ret;
 196 }
 197
 198 vector<Column_x_positions>
 199 Constrained_breaking::best_solution (vsize start, vsize end)
 200 {
 201   vsize min_systems = min_system_count (start, end);
 202   vsize max_systems = max_system_count (start, end);
 203   Real best_demerits = infinity_f;
 204   vector<Column_x_positions> best_so_far;
 205
 206   for (vsize i = min_systems; i <= max_systems; i++)
 207     {
 208       vsize brk = prepare_solution (start, end, i);
 209       Real dem = state_[start].at (brk, i-1).demerits_;
 210
 211       if (dem < best_demerits)
 212         {
 213           best_demerits = dem;
 214           best_so_far = solve (start, end, i);
 215         }
 216       else
 217         {
 218           vector<Column_x_positions> cur = solve (start, end, i);
 219           bool too_many_lines = true;
 220
 221           for (vsize j = 0; j < cur.size (); j++)
 222             if (cur[j].force_ < 0)
 223               {
 224                 too_many_lines = false;
 225                 break;
 226               }
 227           if (too_many_lines)
 228             return best_so_far;
 229         }
 230     }
 231   if (best_so_far.size ())
 232     return best_so_far;
 233   return solve (start, end, max_systems);
 234 }
 235
 236 std::vector<Line_details>
 237 Constrained_breaking::line_details (vsize start, vsize end, vsize sys_count)
 238 {
 239   vsize brk = prepare_solution (start, end, sys_count);
 240   Matrix<Constrained_break_node> const &st = state_[start];
 241   vector<Line_details> ret;
 242
 243   for (int sys = sys_count-1; sys >= 0 && brk != VPOS; sys--)
 244     {
 245       ret.push_back (st.at (brk, sys).details_);
 246       brk = st.at (brk, sys).prev_;
 247     }
 248   reverse (ret);
 249   return ret;
 250 }
 251
 252 int
 253 Constrained_breaking::min_system_count (vsize start, vsize end)
 254 {
 255   vsize sys_count;
 256   vsize brk = prepare_solution (start, end, 1);
 257   vsize rank = breaks_.size () - starting_breakpoints_[start];
 258   Matrix<Constrained_break_node> const &st = state_[start];
 259
 260   /* sys_count < rank : rank is the # of breakpoints, we can't have more systems */
 261   for (sys_count = 0; sys_count < rank; sys_count++)
 262     {
 263       if (sys_count >= valid_systems_)
 264         {
 265           resize (sys_count + 3);
 266         }
 267       if (!isinf (st.at (brk, sys_count).details_.force_))
 268         return sys_count + 1;
 269     }
 270   /* no possible breaks satisfy constraints */
 271   return 1;
 272 }
 273
 274 int
 275 Constrained_breaking::max_system_count (vsize start, vsize end)
 276 {
 277   vsize brk = (end >= start_.size ()) ? breaks_.size () - 1 : starting_breakpoints_[end];
 278   return brk - starting_breakpoints_[start];
 279 }
 280
 281 vsize
 282 Constrained_breaking::prepare_solution (vsize start, vsize end, vsize sys_count)
 283 {
 284   assert (start < start_.size () && (end == VPOS || end <= start_.size ()));
 285   assert (start < end);
 286
 287   resize (sys_count);
 288   if (end == start_.size ())
 289     end = VPOS;
 290
 291   vsize brk;
 292   brk = end == VPOS ? breaks_.size () - 1 : starting_breakpoints_[end];
 293   brk -= starting_breakpoints_[start];
 294   return brk;
 295 }
 296
 297 Constrained_breaking::Constrained_breaking (Paper_score *ps)
 298 {
 299   valid_systems_ = systems_ = 0;
 300   start_.push_back (0);
 301   pscore_ = ps;
 302   initialize ();
 303 }
 304
 305 Constrained_breaking::Constrained_breaking (Paper_score *ps, vector<vsize> const &start)
 306   : start_ (start)
 307 {
 308   valid_systems_ = systems_ = 0;
 309   pscore_ = ps;
 310   initialize ();
 311 }
 312
 313 static SCM
 314 min_permission (SCM perm1, SCM perm2)
 315 {
 316   if (perm1 == ly_symbol2scm ("force"))
 317     return perm2;
 318   if (perm1 == ly_symbol2scm ("allow")
 319      && perm2 != ly_symbol2scm ("force"))
 320     return perm2;
 321   return SCM_EOL;
 322 }
 323
 324 /* find the forces for all possible lines and cache ragged_ and ragged_right_ */
 325 void
 326 Constrained_breaking::initialize ()
 327 {
 328   if (!pscore_)
 329     return;
 330
 331   ragged_right_ = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
 332   ragged_last_ = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
 333
 334   Output_def *l = pscore_->layout ();
 335   System *sys = pscore_->root_system ();
 336   Real space = robust_scm2double (l->c_variable ("ideal-system-space"), 0);
 337   SCM padding_scm = l->c_variable ("page-breaking-between-system-padding");
 338   if (!scm_is_number (padding_scm))
 339     padding_scm = l->c_variable ("between-system-padding");
 340   Real padding = robust_scm2double (padding_scm, 0.0);
 341
 342   Interval first_line = line_dimensions_int (pscore_->layout (), 0);
 343   Interval other_lines = line_dimensions_int (pscore_->layout (), 1);
 344   /* do all the rod/spring problems */
 345   breaks_ = pscore_->find_break_indices ();
 346   all_ = pscore_->root_system ()->used_columns ();
 347   lines_.resize (breaks_.size (), breaks_.size (), Line_details ());
 348   vector<Real> forces = get_line_forces (all_,
 349                                          other_lines.length (),
 350                                          other_lines.length () - first_line.length (),
 351                                          ragged_right_);
 352   for (vsize i = 0; i + 1 < breaks_.size (); i++)
 353     {
 354       for (vsize j = i + 1; j < breaks_.size (); j++)
 355         {
 356           int start = Paper_column::get_rank (all_[breaks_[i]]);
 357           int end = Paper_column::get_rank (all_[breaks_[j]]);
 358           Interval extent = sys->pure_height (sys, start, end);
 359           bool last = j == breaks_.size () - 1;
 360           bool ragged = ragged_right_ || (last && ragged_last_);
 361           Line_details &line = lines_.at (j, i);
 362
 363           line.force_ = forces[i*breaks_.size () + j];
 364           if (ragged && last && !isinf (line.force_))
 365             line.force_ = (line.force_ < 0 && j > i + 1) ? infinity_f : 0;
 366           if (isinf (line.force_))
 367             break;
 368
 369           Grob *c = all_[breaks_[j]];
 370           line.break_penalty_ = robust_scm2double (c->get_property ("line-break-penalty"), 0);
 371           line.page_penalty_ = robust_scm2double (c->get_property ("page-break-penalty"), 0);
 372           line.turn_penalty_ = robust_scm2double (c->get_property ("page-turn-penalty"), 0);
 373           line.break_permission_ = c->get_property ("line-break-permission");
 374           line.page_permission_ = c->get_property ("page-break-permission");
 375           line.turn_permission_ = c->get_property ("page-turn-permission");
 376
 377           /* turn permission should always be stricter than page permission
 378              and page permission should always be stricter than line permission */
 379           line.page_permission_ = min_permission (line.break_permission_,
 380                                                   line.page_permission_);
 381           line.turn_permission_ = min_permission (line.page_permission_,
 382                                                   line.turn_permission_);
 383
 384           line.extent_ = (extent.is_empty ()
 385                           || isnan (extent[LEFT])
 386                           || isnan (extent[RIGHT]))
 387             ? Interval (0, 0) : extent;
 388           line.padding_ = padding;
 389           line.space_ = space;
 390           line.inverse_hooke_ = extent.length () + space;
 391         }
 392     }
 393
 394   /* work out all the starting indices */
 395   for (vsize i = 0; i < start_.size (); i++)
 396     {
 397       vsize j;
 398       for (j = 0; j + 1 < breaks_.size () && breaks_[j] < start_[i]; j++)
 399         ;
 400       starting_breakpoints_.push_back (j);
 401       start_[i] = breaks_[j];
 402     }
 403   state_.resize (start_.size ());
 404 }
 405
 406 Real
 407 Constrained_breaking::combine_demerits (Real force, Real prev_force)
 408 {
 409   if (ragged_right_)
 410     return force * force;
 411
 412   return force * force + (prev_force - force) * (prev_force - force);
 413 }
 414