2 constrained-breaking.cc -- implement a line breaker that
3 support limits on the number of systems
5 source file of the GNU LilyPond music typesetter
7 (c) 2006--2007 Joe Neeman <joeneeman@gmail.com>
10 #include "constrained-breaking.hh"
12 #include "international.hh"
14 #include "output-def.hh"
15 #include "paper-column.hh"
16 #include "paper-score.hh"
17 #include "simple-spacer.hh"
22 We use the following optimal substructure. Let W (A) be our weight function.
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
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
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].
41 The indices "start" and "end" refer to the index in the start_ array of the
42 desired starting and ending columns.
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} . . .
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_".
56 For finding A_{sys, brk}, let "me" be the (sys_count, brk) cell in our
57 solution array (state_[start][sys * rank + brk]).
59 Then A_{sys, brk} = A_{sys - 1, me.prev_} :: me
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) */
69 Constrained_breaking::calc_subproblem (vsize start, vsize sys, vsize brk)
71 assert (sys < systems_);
72 assert (start < start_.size ());
73 assert (brk < breaks_.size ());
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;)
81 if (0 == sys && j > 0)
82 continue; /* the first line cannot have its first break after the beginning */
84 Line_details const &cur = lines_.at (brk, j + start_col);
85 if (isinf (cur.force_))
93 prev_f = st.at (j, sys-1).details_.force_;
94 prev_dem = st.at (j, sys-1).demerits_;
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_)
103 found_something = true;
109 return found_something;
114 Constrained_breaking::space_line (vsize i, vsize j)
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;
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);
126 return get_line_configuration (line, line_dims[RIGHT] - line_dims[LEFT], line_dims[LEFT], ragged);
130 Constrained_breaking::resize (vsize systems)
134 if (pscore_ && systems_ > valid_systems_)
136 for (vsize i = 0; i < state_.size (); i++)
137 state_[i].resize (breaks_.size () - starting_breakpoints_[i], systems_, Constrained_break_node ());
139 /* fill out the matrices */
140 for (vsize i = 0; i < state_.size (); i++)
141 for (vsize j = valid_systems_; j < systems_; j++)
142 for (vsize k = starting_breakpoints_[i] + j + 1; k < breaks_.size (); k++)
143 if (!calc_subproblem (i, j, k))
144 break; /* if we couldn't break this, it is too cramped already */
145 valid_systems_ = systems_;
149 vector<Column_x_positions>
150 Constrained_breaking::solve (vsize start, vsize end, vsize sys_count)
152 vsize start_brk = starting_breakpoints_[start];
153 vsize end_brk = prepare_solution (start, end, sys_count);
155 Matrix<Constrained_break_node> const &st = state_[start];
156 vector<Column_x_positions> ret;
158 /* find the first solution that satisfies constraints */
159 for (vsize sys = sys_count-1; sys != VPOS; sys--)
161 for (vsize brk = end_brk; brk != VPOS; brk--)
163 if (!isinf (st.at (brk, sys).details_.force_))
167 warning (_ ("cannot find line breaking that satisfies constraints" ));
168 ret.push_back (space_line (brk, end_brk));
170 /* build up the good solution */
171 for (vsize cur_sys = sys; cur_sys != VPOS; cur_sys--)
173 vsize prev_brk = st.at (brk, cur_sys).prev_;
174 assert (brk != VPOS);
175 ret.push_back (space_line (prev_brk + start_brk, brk + start_brk));
183 /* if we get to here, just put everything on one line */
184 warning (_ ("cannot find line breaking that satisfies constraints"));
185 ret.push_back (space_line (0, end_brk));
189 vector<Column_x_positions>
190 Constrained_breaking::best_solution (vsize start, vsize end)
192 vsize min_systems = min_system_count (start, end);
193 vsize max_systems = max_system_count (start, end);
194 Real best_demerits = infinity_f;
195 vector<Column_x_positions> best_so_far;
197 for (vsize i = min_systems; i <= max_systems; i++)
199 vsize brk = prepare_solution (start, end, i);
200 Real dem = state_[start].at (brk, i-1).demerits_;
202 if (dem < best_demerits)
205 best_so_far = solve (start, end, i);
209 vector<Column_x_positions> cur = solve (start, end, i);
210 bool too_many_lines = true;
212 for (vsize j = 0; j < cur.size (); j++)
213 if (cur[j].force_ < 0)
215 too_many_lines = false;
222 if (best_so_far.size ())
224 return solve (start, end, max_systems);
227 std::vector<Line_details>
228 Constrained_breaking::line_details (vsize start, vsize end, vsize sys_count)
230 vsize brk = prepare_solution (start, end, sys_count);
231 Matrix<Constrained_break_node> const &st = state_[start];
232 vector<Line_details> ret;
234 for (int sys = sys_count-1; sys >= 0 && brk != VPOS; sys--)
236 ret.push_back (st.at (brk, sys).details_);
237 brk = st.at (brk, sys).prev_;
244 Constrained_breaking::min_system_count (vsize start, vsize end)
247 vsize brk = prepare_solution (start, end, 1);
248 vsize rank = breaks_.size () - starting_breakpoints_[start];
249 Matrix<Constrained_break_node> const &st = state_[start];
251 /* sys_count < rank : rank is the # of breakpoints, we can't have more systems */
252 for (sys_count = 0; sys_count < rank; sys_count++)
254 if (sys_count >= valid_systems_)
256 resize (sys_count + 3);
258 if (!isinf (st.at (brk, sys_count).details_.force_))
259 return sys_count + 1;
261 /* no possible breaks satisfy constraints */
266 Constrained_breaking::max_system_count (vsize start, vsize end)
268 vsize brk = (end >= start_.size ()) ? breaks_.size () : starting_breakpoints_[end];
269 return brk - starting_breakpoints_[start];
273 Constrained_breaking::prepare_solution (vsize start, vsize end, vsize sys_count)
275 assert (start < start_.size () && (end == VPOS || end <= start_.size ()));
276 assert (start < end);
279 if (end == start_.size ())
283 brk = end == VPOS ? breaks_.size () - 1 : starting_breakpoints_[end];
284 brk -= starting_breakpoints_[start];
288 Constrained_breaking::Constrained_breaking (Paper_score *ps)
290 valid_systems_ = systems_ = 0;
291 start_.push_back (0);
296 Constrained_breaking::Constrained_breaking (Paper_score *ps, vector<vsize> const &start)
299 valid_systems_ = systems_ = 0;
305 min_permission (SCM perm1, SCM perm2)
307 if (perm1 == ly_symbol2scm ("force"))
309 if (perm1 == ly_symbol2scm ("allow")
310 && perm2 != ly_symbol2scm ("force"))
315 /* find the forces for all possible lines and cache ragged_ and ragged_right_ */
317 Constrained_breaking::initialize ()
322 ragged_right_ = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
323 ragged_last_ = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
325 Output_def *l = pscore_->layout ();
326 System *sys = pscore_->root_system ();
327 Real space = robust_scm2double (l->c_variable ("ideal-system-space"), 0);
328 SCM padding_scm = l->c_variable ("page-breaking-between-system-padding");
329 if (!scm_is_number (padding_scm))
330 padding_scm = l->c_variable ("between-system-padding");
331 Real padding = robust_scm2double (padding_scm, 0.0);
333 Interval first_line = line_dimensions_int (pscore_->layout (), 0);
334 Interval other_lines = line_dimensions_int (pscore_->layout (), 1);
335 /* do all the rod/spring problems */
336 breaks_ = pscore_->find_break_indices ();
337 all_ = pscore_->root_system ()->used_columns ();
338 lines_.resize (breaks_.size (), breaks_.size (), Line_details ());
339 vector<Real> forces = get_line_forces (all_,
340 other_lines.length (),
341 other_lines.length () - first_line.length (),
343 for (vsize i = 0; i + 1 < breaks_.size (); i++)
345 for (vsize j = i + 1; j < breaks_.size (); j++)
347 int start = Paper_column::get_rank (all_[breaks_[i]]);
348 int end = Paper_column::get_rank (all_[breaks_[j]]);
349 Interval extent = sys->pure_height (sys, start, end);
350 bool last = j == breaks_.size () - 1;
351 bool ragged = ragged_right_ || (last && ragged_last_);
352 Line_details &line = lines_.at (j, i);
354 line.force_ = forces[i*breaks_.size () + j];
355 if (ragged && last && !isinf (line.force_))
356 line.force_ = (line.force_ < 0 && j > i + 1) ? infinity_f : 0;
357 if (isinf (line.force_))
360 Grob *c = all_[breaks_[j]];
361 line.break_penalty_ = robust_scm2double (c->get_property ("line-break-penalty"), 0);
362 line.page_penalty_ = robust_scm2double (c->get_property ("page-break-penalty"), 0);
363 line.turn_penalty_ = robust_scm2double (c->get_property ("page-turn-penalty"), 0);
364 line.break_permission_ = c->get_property ("line-break-permission");
365 line.page_permission_ = c->get_property ("page-break-permission");
366 line.turn_permission_ = c->get_property ("page-turn-permission");
368 /* turn permission should always be stricter than page permission
369 and page permission should always be stricter than line permission */
370 line.page_permission_ = min_permission (line.break_permission_,
371 line.page_permission_);
372 line.turn_permission_ = min_permission (line.page_permission_,
373 line.turn_permission_);
375 line.extent_ = (extent.is_empty ()
376 || isnan (extent[LEFT])
377 || isnan (extent[RIGHT]))
378 ? Interval (0, 0) : extent;
379 line.padding_ = padding;
381 line.inverse_hooke_ = extent.length () + space;
385 /* work out all the starting indices */
386 for (vsize i = 0; i < start_.size (); i++)
389 for (j = 0; j + 1 < breaks_.size () && breaks_[j] < start_[i]; j++)
391 starting_breakpoints_.push_back (j);
392 start_[i] = breaks_[j];
394 state_.resize (start_.size ());
398 Constrained_breaking::combine_demerits (Real force, Real prev_force)
401 return force * force;
403 return force * force + (prev_force - force) * (prev_force - force);